The ¹⁶O + ¹⁶O reaction Citation Spinka, Harold (1971) The ¹⁶O + ¹⁶O reaction. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/XPJ4-A792. https://resolver.caltech.edu/CaltechTHESIS:11192010-105408465 Abstract The ¹⁶O + ¹⁶O total reaction cross section was measured at six energies between E cm = 6.80 to 11.85 MeV near the astrophysical region of interest. Angular distributions and cross sections for the production of protons, alphas and deuterons were obtained with counter telescopes in a differentially pumped gas target. No ³He or ³H were observed. Cross sections for the formation of ³¹S and ³⁰p were measured by detecting the betas from their radioactive decays. The angular distribution and cross section for production of neutrons was obtained with a "long counter" at E cm = 12 MeV, demonstrating that the ¹⁶O (¹⁶O,pn) process accounts for over 90 % of the ³⁰P formed at this energy. The presence of such three body breakup reactions made the experimental determination of the total cross section difficult. Finally, the ¹⁶O + ¹⁶O → ¹²O (g.s.) + ²⁰Ne (g.s.) reaction was studied with a coincidence technique at E cm = 12 MeV. Gamma spectra were taken at several energies for a number of targets using Ge (Li) counters. Gamma lines from nuclei produced in both two and three body exit channels from ¹⁶O + ¹⁶O reactions were observed. In addition, the gamma yield as a function of bombarding energy was measured in 50 keV (c .M.) steps for both ¹⁶O + ¹⁶O and ¹²C + ¹²C. The ¹⁶O + ¹⁶O gamma yield is smoothly varying, indicating that the ¹⁶O + ¹⁶O reaction cross section does not have large fluctuations with energy similar to the structure seen in ¹²C + ¹²C reactions. Nearly all cross sections were measured relative to the ¹⁶O + ¹⁶O elastic scattering at θ_(lab)= 45° to avoid the problems with direct current integration of heavy ion beams in gas targets. A new, more precise determination of the elastic scattering cross section at θ cm = 90° was made for E cm = 7.3 to 14.4 MeV in steps of 100 keV (C .M.). A previously unknown anomaly was observed near E cm = 10.5 MeV. Elastic scattering cross sections were also obtained for ¹²C + ¹²C in steps of 60 keV C.M. energy from E cm = 3.9 to 8.0 MeV at θ cm = 90° In both cases, gas mixtures were used in the differentially pumped system as the target. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Physics and Astronomy) Degree Grantor: California Institute of Technology Division: Physics, Mathematics and Astronomy Major Option: Physics Minor Option: Astronomy Thesis Availability: Public (worldwide access) Research Advisor(s): Tombrello, Thomas A. Thesis Committee: Unknown, Unknown Defense Date: 23 November 1970 Record Number: CaltechTHESIS:11192010-105408465 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:11192010-105408465 DOI: 10.7907/XPJ4-A792 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 6186 Collection: CaltechTHESIS Deposited By: INVALID USER Deposited On: 22 Nov 2010 19:34 Last Modified: 27 Jun 2024 00:02 Thesis Files Preview PDF - Final Version See Usage Policy. 70MB Repository Staff Only: item control page

THE 160 + 160 REACTION Thesis by Harold Spinka In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasa.dena, California 1911 (Submi tted November 23, 1910) - ii ACKNOWLEDGMENTS I would like to thank the Kellogg Radiation Laboratory faoulty, staff and graduate students for assistance and encouragement during this research. I am thankful to Professor W.A. Fowler and Drs. J.W. Truran and W.D. Arnett for their interest and insight into the a.strophysical a.spects of the problem. I would also like to express my gratitude to Professor T .A. Tombrello for his supervision and suggestions and to Dr. J .R. Patterson for his help in the early stages of the experiments. I am especially indebted to Dr. Hubert Winkler for his active and enthusiastic participation in all pha.ses of this work. Finally, I wish to gratefully aclrnowledge the financial assistance from the National Science Foundation during my graduate studies. This research was supported in part by the National Science Foundation (op - 9114, GP - 19887) (Nonr - 220(47)). and the Office of Naval Research - iii ABSTRACT The 16 0 + 16 0 energies between total reaction cross section was measured at six E = 6.80 to 11.85 MeV near the astrophysical cm region of interest. Angular distributions and cross sections for the production of protons, alphas and deuterons were obtained with counter telescopes in a differentially pumped gas target. No 3He or 3H were observed. Cross sections for the formation of 31 S and 30p were measured by detecting the betas from their radioactive decays. The angular distribution and cross section for production of neutrons was obtained with a "long counter" at demonstrating that the of the 30 160 (16 0 ,pn) formed at this energy. P E em = 12 MeV, process accounts for over 90 % The presence of such three body breakup reactions made the experimental determination of the total cross section difficult. 20Ne (g.s.) Finally, the 160 + 160 -+ 120 (g.s.) + reaction was studied with a coincidence technique at E = 12 MeV. cm Gamma spectra were taken at several energies for a number of targets using Ge (Li) counters. Gamma lines from nuclei produced in both two and three body exit channels from observed. 0 + 12 0• 0 + 16 0 . react~ons were In addition, the gamma yield as a function of bombarding energy was measured in 12 16 The 50 keV (c .M.) steps for both 16 0 + 16 0 indicating that the 16 160 + 160 and gamma. yield is smoothly varying, o + 160 reaction cross section does not have large fluctuations with energy similar to the structure seen in - iv - 12 C + 12 C reactions • Nearly all cross sections were measured relative to the 160 + 160 elastic scattering at ~ab = 450 to avoid the problems with direct current integration o£ heavy ion beams in gas targets. A new, more precise determination of the elastic scattering cross section at 8 em = 900 was made for E cm = 7.3 to Ih.h MeV in steps of 100 keV (C .M.). E == 10.5 MeV. Elastic scattering cross sections were also obtained for l2C + l2c in steps of em 8.0 MeV at 8 cm ::0 90 A previously unknown anomaly was observed near 0 • 60 keV C.M. energy from Ecm = 3.9 to In both cases, gas mixtures were used in the differentially pumped system as the target. - v - TABLE OF CONTENTS INTRODUCTION page The Problem 1 The Expected Results 5 The Experimental Methods 15 ELASTIC SCATTERING Introduction 18 The Differentially Pumped Gas Target 21 Experimental 21 Results 33 GAMMA RAYS 42 Introduction Ge (Li) y Yield Detector Spectra 43 Energy 56 VS. CHARGED PARTICLES Introduction 62 Experimental 65 Data Analysis 90 ACTIVATION METHOD Introduction 109 Experimental 109 Data Analysis 127 Results 132 NEUTRONS Introduction -vi- Experimental 142 Data Analysis 146 12C + 20Ne PRODUCTION Introduction 152 Experimental 153 Data Analysis 157 Results 164 167 CONCLUSIONS APPENDIX I: APPENDIX II ~ C + C and C + 0 Elastic Scattering 12 12 The C + C Y Yield VB. Ecm 177 181 BIBLIOGRAPHY 182 TABLES 185 - 1 - INTRODUCTION The Problem 16 A study of the 0 + 16 0 reaction was made at energies near and below the Coulomb barrier (E cm = 7 - 12 MeV) because of its pos sible importance in astrophysics. Cross sections to all exit channels as a function of energy are the quantities of interest for astrophysics, and numerous experimental techniques were employed to measure these cross sections. The astrophysical interest in this reaction is related to the quest to explain the observed elemental abundances. Nuc1eosyn- thesis is presently believed to occur in large bodies of gas (stars t the primeval fireball, etc.). In high temperature regions of these bodies Hydrogen is converted to Helium, Helium to Carbon and Oxygen, and these to heavier elements up to the iron region. Specifically, conditions are currently envisioned (T O! 2 - 4 X 10 p - 10 5 - 10 8 gm/cm 3 90 K, and time scales of seconds to days) at a cer- tain evolutionary stage in some stars where Oxygen is present in large quantities and burns by 16 + 16 0 0 nuclear reactions. Quiescent Oxygen burning in evolved stars was studied by Cameron (1959) and Tsuda (1963). The important exit channels for these calculations and the respective estimated branching ratios were 31 S + n 30% a t E l : 5 Me V. cm 10%, 31p + p 50%, 100/0, (The interaction radius used to compute - 2 the 16 + 0 16 0 total reaction cross section varied from 7 to 9 fm.) The physical conditions in the star were a central temperature of T - 1.3 X 10 9 0 K, a density of p - 10 5 gm / cm 3 and a time scale of 10 5 - 10 7 a-nuclei years. The main products of Oxygen burning were the 24 Mg , 28 Si and 32S. The inclusion of a number of neutrino formation processes by Fowler and Hoyle (1964a) for temperatures above about 1 X 10 9 oK altered the previous conclusions. Higher burning temperatures are required for quiescent Oxygen burning in order to counterbalance the neutrino energy losses from the star. The particular physical conditions considered were a star of total mass temperatures of T ~ 2.1 - 3.0 X 10 order of days. Oxygen via 16 Above T - 3 X 10 O(y ,a) M ~ 10 solar masses, 9 0 K and time scales on the 9 0 K photodisintegration of the reactions was expected to become important. limiting the temperature range for Oxygen burning. Chiu (1968, 1966) also considered this case for a more massive star (M - 30 solar masses) and a similar temperature 90 T - 2.5 X 1 0 K . In addition, a number of Oxygen burning stellar models were constructed by Rakavy, Shaviv and Zinamon (see Rakavy (1967a,b,c». Truran and Arnett (1970) discussed nucleosynthesis in explosive Oxygen burning as a means of producing elements with 14 :s Z :S 20 from supernovae. They were able to reproduce both the elemental and isotopic abundance features observed in the solar system for these nuclei by assuming densities of 10 gm/cm 3 5 ;$ P ;$ 10 6 and a restricted temperature range about T = 3.6 X 10 9 0 K. - 3 The time scales were on the order of seconds to minutes. Truran and Arnett speculated that the Oxygen burning might occur in a shell of matter not necessarily at the center of the supernova (see also Arnett (1969a,b)). Most of these reactions do not occur at E cm ;: kT Oo! 250 keV because the cross section at this energy is extremely small. Instead, the majority take place near E , which is the energy at the maximum o of the product distributiOn) ( Maxwell-B1~ltzmann • ( of 0 energies The full energy width at Coulomb barrier penetratiOn) factor for 16 0 + 16 0 1/e maximum of the distribution of the number of reactions occurring is .6 (see Fowler and Vogl (1964b) or Fowler, Caughlan and Zimmerman (1967). For 16 0 + 16 0 reactions at T = 3 X 10 9 oK E o = 8.1 MeV .6 = 3 4 MeV 0 Most astrophysical nuclear reactions have a cross section too small to be measured at or near the corresponding E o 0 Conse- quently, cross sections must be extrapolated down many orders of magnitude to the vicinity of E • o A very unusual feature of 16 0 + 16 0 reactions is that they can be measured over part of the energy range where they are important astrophysica1ly. This means that it is not mandatory to have the high precision normally needed for extrapolation of the cross sections to lower energies. It is also quite fortunate - 4since the large number of open exit channels and the presence of three body breakup reactions make the experimental determination of the total cross section difficult. The 16 0 + 16 0 reactions are also interesting from the point of view of nuclear physics. Heavy ion reactions are quite complicated because of the large number of nucleons in both target and projectile. Yet considerable information on nuclear structure of the heavier elements has been derived from heavy ion reaction data. Elastic and inelastic scattering, Ericson fluctuations t transfer reactions and excited state lifetinles are commonly measured. However t few heavy ion reactions have been studied to derive cross sections and angular distributions for all exit channels present. Such a task is monumental at energies far above the Coulomb barrier where there are a large number of open channels, and normally reaction cross section measurements are confined to cases where at least one reaction product is radioactive. A thorough study has been made at sub-Coulomb barrier energies of the 12 C + 12 C system and strong cross section fluctuations were observed (see Almqvist (1960, 1963), Bromley (1960, 1961) and Patterson, Winkler and Zaidins (1969». Weaker structure has been seen in none was apparent in the Coulomb barrier. 16 0 + 16 0 12 C + 16 0, but case in the vicinity of the These facts have caused considerable theoretical research to understand the origin of these fluctuations (see Davis (1960), Vogt (1960), Kompaneets (1961), Wildermuth (1961). lmanashi (1969), and Ml.chaud (1969», and a thorough study of 16 0 + 16 0 - 5reactions near the Coulomb barrier would be us eful to compare with 12C + 12C. The Expected Results Before discussing the experimental methods, the results will be anticipated using ideas from elernentary quantum mechanics and simple compound nucleus theo rYe This will provide a basis for understanding the experimental methods used and the choice of the various quantities measured. In astrophysical calculations a cro ss section variation of the form cr-(E) :::: S~E) exp (- 21fT) - gE) f where T)= is often assumed. particles, and E R and v re 1 is the relative velocity of the incoming is the interaction radius, is the center-of-mass energy. M is the reduced mass, The relation follows from the WKB approximation for a charged particle with orbital angular 2 momentum L = 0 penetrating a Coulomb barrier (V = Z 1 ZZe /r forr > Rand = 0 for r < R). The factor S(E} contains the energy dependence from purely nuclear effects, as well as from nonnuclear effects not properly taken into account by the exponential. - 6 "'"' S(E) is usually assumed to be nearly constant if there are no resonances in the nuclear system. The final measured cross sec- tions are used to obtain S (see the Conclusions Section). However, most of the measurements were made at energies not very far below the Coulomb barrier (E cm ,... 10.5 MeV, R"" 8.8 fm), where the exponential factor does not give a good approximation to the barrier penetration energy dependence. Furthermore, for 16 0 + 16 0 reactions there is a considerable angular momentum involved (classically, L ~ 6 at E cm = 12 MeV), so some variation of S with E is not unexpected. Using the equation above, the drop in cross section from E = 10.5 MeV to the lowest energy measured. E cm cm = 7 MeV, is about a factor of 5000. 16 The exit channels available to E cm = 12 MeV are shown in Figure 1. 0 + 16 0 reactions up to Note that there may be competition between compound nucleus formation and dhect reactions. In the former case the 32 nucleons momentarily form pound nucleus. 32 S, the com- The energy becomes spread among the constituent nucleons so that there is no Ilmemory" of the incoming channel. Then one or more particles "evaporate" from the compound nucleus. In the case of direct reactions the 32S intermediate state is not formed. Examples of the latter are perhaps and 24 Mg + 8 Be channels 15 0 (2a-transfer). + 17 0 and bombarding energy used. 20 <Y/c· of the total 16 0 + 16 0 12 C + 20 Ne (a-transfer) The neutron and proton transfer 15 N + 17 F are open only at the highest Buchler (1969) calculated that less than reaction cross section could be accounted - 7- Figure 1 160 + 160 Exit Channels. All 160 + 160 en t charmels with Q> -10 MeV and y transitions from low lying levels in some residual nuclei are shown. Addi tional en t channels not illustrated are 28 3i + p + t Q = -10.222 MeV 29 3i + 2p + n -10.229 28 3i + 3He + n -10.985 23 Na + p + 2a -12.084 All Q values were computed from the mass table of Mattauch (1965) and the range of energies studied was E = 7 to 12 MeV. Levels 12 20 cm for the C + Ne exit channel correspond to excited states in both nuclei. !60+12c +0 ..:L!:!L ~ 29p+t 29Si+3He ~+'2C 27A1 +p +0 2°Ne+ 30 g ~ ~ -=!l2!.. 29AI+3p ..:W&L ~ :3OSi+2p 3Ip+p ...:!UU... .::l.!...lH... 17F+I~ 170+ 15 0 32S 160+!6~0 2.0 4.0 1.0 8.0 28Si+o bd +2p 31S+ n ~ 24~+20 _ :3O P+d 24~:'aBe ~+p+n . - ~ g~ U27~+a+n~~d .,10.0 ~ ~+6Li ~ ~ :3OS+2n MEV ECM (XI - 9 fo r by the Q' -transfe r channel, so compound nucleus fo rmation is expected to be important. The energy spectrum of light particles b "evaporating" from the compound nucleus can be estimated from Blatt and Weisskopf (1952) #(E) • dE = const • E • fT (E) • wy{E ) . dE c exc Here E exc is the excitation energy of the resulting nucleus Y corresponding to E. the total C. M. kinetic energy of the outgoing particles b + Y. The value of fTc is the cross section for forma- tion of the compound system by particles b nucleus Y incident on the target and can be expressed in terms of charged particle or neutron penetrabllities. The level density in the nucleus Y was taken to be that of a Fermi gas with angular momentum I = 0: = const2 • exp (2..faE exc ). E with a = 4 MeV -1 exc (see Bohr and Mottelson (1969). especially page 187 and Fig. 2-12). The computed neutron. proton and alpha spectra with thresholds for secondary reactions are shown in Figs. 2 - 4. It is evident that three body breakup reactions may have large cross sections. especially at the higher bombarding energies. The Coulomb barrier E co ul for the mass region A'" 30, Z ,.. 15 for protons is about 2.5 MeV and for alphas is about 4.5 MeV. - 10 - Figures 2 - 4 Neutron, Proton and Alpha Evaporation Spectra From 160 + 160 • The C.M. spectra of light particles emitted from 160 + 160 reactions was calculated on the basis of a compound nucleus model at ~ab = 16, 20 and 24 MeV (see the text page 9 )• All particles 'With energies less than the indicated three body thresholds leave the residual nucleus with sufficient energy to permit a second evaporation. :u 1"1 m ~ 0 0 ZN C 01 2.5 5.0 -Ecm (MeV) 7.5 110 + 1&0 -.. n +3I S • 10.0 CALCULATED NEUTRON SPECTRA FROM 12.5 ~ I ~ ~ E 0 0 ZN C (.ell 5 Ecm 10 15 20 + 180 -.. P + 31p. (MeV) 180 CALCULATED PROTON SPECTRA FROM 25 N I-' '":::u CD o o· ~ 10 Ecm (M.V) I~ 20 , 25 I: \.0) I C ~ "0 + "0 .... a +Z·Si· FROM CALCULATED ALPHA SPECTRA ZN ~ - 14 0cff = A useful quantity to compare the different exit channels is Q - E coul • With these values and the computed particle spectra, the branching ratios can b<'l estimated. 32 The S compound nucleus will probably emit roughly equal numbers of protons and alphas (the alphas will compete because the positive Q value is higher for 28 Si + Cl than 31 alphas -- i. e., neutrons + p, counterbalancing the larger P Q eff E co ul for - 5 MeV for both), with somewhat fewer (Oeff - 1.5 MeV), still fewer deuterons, etc. Thus the main nuclei Y left after the first evaporation should be 31 p , and 31 S. 28 Si , Some of these will have an excitation energy above a particle breakup threshold and will generally have a second evaporation. For example, those 31 S will go to entially to 27 Al + P and somewhat less to same way as before. 30 P + p, and 28 . Sl prefer- 24 Mg + a, etc. in the These arguments based on Qe£f suggest the following "branching ratios" for a bombarding energy corresponding to E cm - 12 MeV: Exit Channel Q 28 Si + a 9.592 MeV 31p + P 7.676 31 S + n 30 Si + 2p Q eff liB. R. II lots 1.448 + 5 MeV +5 + 1. 5 0.388 - 4.5 lots +d - 2.412 - 5 some 29 S1 + 3 He - 2.510 - 7 little 30 p + P + n - 4.636 - 7 lots 27 Al + P + a - 1.991 - 9 some 24 Mg + 2a - 0.390 - 9.5 some +t - 7.478 - 11 very little 12C + 20 Ne - 2.431 30 p 29 p Eve rything el s e lots some some (1) <- 11.5 - none - 15 The E!perimental Methods A large proportion of these exit channels involve one or more light charged particles. Angular distributions and cross sections for the production of protons, deuterons and alphas were measured using counter telescopes. This technique, described in the Charged Particle Section (page 62) I provides the bulk of the cross section data. Two radioactive nuclei, 16 o + 16 0 reactions. 30 P and 31 S, were produced by Cross sections for their production were measured by counting the emitted beta particles as a function of time after the beam was turned off. The decay curves were analyzed using the known halflives to separate the two activities. Experimen- tal details and results are given in the Activation Section (page 109 ). A cross check between the previous two methods was afforded by the set of channels 30 p +P +n 31S + n • In the Neutrons Section (page 141) is described a determination of the neutron production cross section using a flat response detector. The cross check 0-( 30 P) + 0-( 31 S) = 0- (d) + o-(n) is established and conclusions on the number of three body reactions are made .. - 16 The 12C + 20 Ne exit channel cannot be studied with the previous techniques. Its branching ratio is hard to estimate theo- retically because it may be a direct reaction, yet both 16 0 12C + 20 Ne and the inverse astrophysical interest. 12C + 20 Ne - + 16 0 may be of Thus, the angular distribution of the former 12 reaction leading to the ground states of ured using a coincidence technique (see Section, page 152). 16 0 + 16 0 _ C and 12 20 C + 20 Ne was meas- Ne Production No data on the total cross section to excited states were obtained. A number of important semiquantitative results were also obtained from the ,('s . 16 emltted in 0 Gammas Section (page 42 ) presents results which roughly verify the expected branching ratios. total '( emission from steps in the (~ E = 50 ke V) • cm 12 12 C + C 16 + 16 0 reactions. The In addition, measurements of the 0 + 16 0 were made at narrow energy No evidence for structure similar to that reactions was seen, so large steps in bombarding energy for the reaction cross section measurements were justified. All cross sections were measured relative to the elastic scattering cross section for 16 0 + 16 0, because direct current integration of heavy ion beams, especially in gas targets, always presents problems and was completely avoided except for the 12C + 20 Ne measurements. . In the 16 0 + 16 0 The ecm = 90 0 relative maximum Mott scattering angular distribution provided a convenient and easily reproducible point to use for the normalization. Although there are elastic scattering cross section data at this - 17 angle in the literature, a new. more precise determination was made for E cm = 7.35 - 14.35 MeV. The Elastic Scattering Section (page 18 ) describes these experiments. The large number of exit channels and energetically accessible excited states in the reaction products made it very difficult to exclude contaminant reactions. Therefore a differentially pumped gas target of high purity 02 was used whenever possible. The low target density was partly compensated for by the much higher beam currents possible in an open gas target. Also. energy losses and target uniformity are more easily controlled in such a system. The target design is described in the Elastic Scattering Section (page 21). Several examples of problems that can arise from solid targets are given in the Activation Section. Finally. two appendixes contain scattering data to compare with the 16 12 C + 12 ° + 16 ° C 'Y ray and elastic case. Striking differences can be seen between Figures 9 and 42 and in Figure 12. The final cross sections are contained in Table 15 of the Conclusions Section. - 18 ELASTIC SCATTERING Introd uction Some means of determining the number of incident and target 16 nuclei was necessary for measuring sections. + 16 0 reaction cross 0 Direct integration of the beam current is often used to obtain the number of incident particles. but this is difficult for heavy ion beams because of the uncertainty of the beam's charge state distribution after pas sing through the target. Thus the relationship between the current and the number of particles per second is poorly known. Another solution was to determine the heat deposited by the beam with a calorimeter. However. elastic scattering of the beam from the target region gives a mOre direct measurement of the combined beam intensity and target thickness. The reaction cross section can be written as II reaction roducts) elastically scattered particles ~)reaction ~~) d elastic scattering with the constant of proportionality depending on geometrical and kinematic factors only. nearly all the This method was used for determining 16 0 + 16 0 reaction cross sections. requiring a knowl- edge of the differential cross section for elastic scattering. The elastically scattered at Scm = 90 0 0 (Slab = 45 ). 16 0 nuclei were always detected This angle was chosen because the Mott - 19 scattering has a relative m.axim.um. there for all energies with a differential cross section just four Um.es the Rutherford value, and because the angle could be easily located experim.entally. As a test of the differentially pumped gas target systern.. the elastic scatter. 16 mg of 0 + 16 0 was measured at ecm = 90 0 • Our preliminary results disagreed with values in the literature (Bromley (1960, 1961» near the Coulomb barrier, so m.ore complete data with higher preci s ion were taken. In these experiments the 16 0 nuclei were scattered from a mixture of Oxygen and Argon gas and were detected with the sam.e counte rand collim.ation as in the other charged particle m.easurements. The ratio of 16 0 + 16 0 elastic scattering to pure Rutherford scattering (16 0 + 40 Ar) was obtained from a ratio of counts in the one detector at elab = 450 • . 16 tions for 0 + 16 0 and 16 The difference in the angular distribu- 0 + 40 Ar near elab = 45 0 required special precautions to keep the angle constant and to obtain reproducible data with good statistical accuracy. E cm Data were taken from. =7.3-14.4MeV instepsofl00-250keV(C.M.) and 0 5+ with 0 4+ beams of 3 to 7 )J.a from. the CIT - ONR tandem. accelerator. The energy distribution of the beam in the target region was estim.ated to have a FWHM of < 60 keY (C. M.) that arose from target thl.cknes s and straggling. The position and incident angle of the beam. were continuously monitored. 9. Final data are given in Table 1 and Figure Each data point in the region 9.5 - 11.5 MeV (C. M.) represents 4 to 6 different measurements of at least 40 m.inutes total counting - 20 - time. The results show that the 90 0 (C. M.) cross section is not as smooth near the Coulomb barrier as formerly thought. Previous elastic scattering data for 16 0 + 16 by Bromley, Kuehner and Almqvist (1960, 1961) fo r MeV at angles of 0 000 cm = 38 , 58 , and 90 0 E were taken cm • 5.0- 17.5 using a solid target. Over part of this energy range Carter, Stelson, Mehta and Bernard (1965) searched for fast changing structure in the tering at 0 000 cm gas target. = 48 • 58 , 80 , and 90 0 16 0 + 16 0 elastic scat- with a differentially pumped Carter, et al. ,reported general agreement with Bromley, but no new absolute differential cross sections were given. energies, E cm At higher = 10 - 35 MeV, Maher, Sachs, Siemssen, Weidinger and Bromley (see Siemssen (1967) and Maher (1969) made measurements of angular distributions and excitation functions and fOWld strong resonance structure. . Recently there has been theoretical lnterest in the elastic scattering. 16 0 + 16 0 Rickertsen, Block, Clark and Malik (1969) used a nuclear molecular potential to fit the differential cross sections at o 6 00 , 7 00 , 8 00 , and 90 0 for E 0=49, cm = 10to 22 MeV. Brueckner, Buchler and Kelley (1968) and Chatwin, Eck, Richter and Robson (1969, 1970) tried to fit the 90 distributions for E tal data of Bromley cm o excitation fWlction and some angular = 10 to 15 MeV. _re In both cases the experimen- used t.o compare to the theoretical fits, since no other data were available in this energy region at that time. Block and Malik (1967) discussed the resonance structure observed at higher energies in the data of Maher, ~ al., and the pro blem of - 21 the nuclear surface in connection with heavy lon scattering wal'l discussed by Gadioli- Erba and Sona (1969). The Differentially Purnped Gas Target The differentially pumped gas target system is shown in Figure 5. The target chamber was 29.3 cm I.D. with 6.4 mm thick steel walls. The first canal was between the chamber and the Roots pump and was 6.4 mm I.D. by 2.5 cm long. The second was 3.6 mm I. D. by 10.2 cm long and the third was 9.5 mm I. D. by 12.0 cm long. At each end of the second canal was an 0.5 mm thick tantalum collimator 2.5 mm in diameter which was responsible for determining the size of the beam in the chamber. Using the light produced by the beam in the gas, it was checked visually that the beam did not hit the sides of the first canal. A set of adjustable slits. set at a total width of 4.1 mm and separated from the second canal by 104 em, gave a maximum permissible angular deviation of ± 0.18 in the beam relative to the central axis of the system. o Initial align- ment of the canals was performed with a telescope zeroed on these slits. Attached to the first pumpout was a Roots pump with a pumping speed of about 70 liter/sec at 0.2 torr. The second pump was a 1200 liter/sec diffusion pump with a cold water baffle and the third one was a 750 liter/sec diffusion pump with Freon-22 baffle. The largest absolute pressure drop was across the first canal because of the high capacity of the Roots pump. get was measured by a 0 - 20 torr The pressure in the gas tar- Wallace and Tiernan precision - 22 - Figure 5 Schematic of the Differentially Pumped Gas Target. The parts of the differentially pumped system are drawn to the scale shown. The beam entered the target through three canals with typical pressures of slits, 10-5 torr in the region of the 10-4 torr between canals 2 and 3, canals 1 and 2, and 0.1 torr between 3 torr at the gas inlet. were normally in the target chamber. Several detectors The monitor (45 0 ) counter was mounted on the inner aluminum cylinder in the chamber bottom. A teflon sleeve and two O-rings permitted it to rotate without breaking the chamber vacuum. Another counter could be mounted on the brass rod which rotated inside this aluminum cylinder. The counter telescopes were rigidly connected to the 1ucite top, which could als~ be rotated without breaking the vacuum because of another teflon sleeve and pair of O-rings. I o I TO I I I I I 20 em. III STEEL D ALUMINUM o LUCITE E'J COPPER I DIFFUSION PUMP II BEAM - ~ BRASS I SLITS /\ V PUMPED TARGET DIFFERENTIALL V GAS PUMP TO ROOTS CANAL I TARGET CHAMBER TEFLON /SLEEVE ..... I N an. - 24 roid gauge. checked against a McLeod InanOIneter. The energy 108s of the beam before arriving at the target chamber center was estiInated by taking the full chamber pressure from the target region to the middle of the first canal and zero pressure beyond. With this approxim.ation. the beaIn traversed 7 cm. in the gas befo re reaching the center of the cham.ber. For pure 02 gas at a cham.ber pressure of 3 torr, using Northcliffe's (1963) energy loss curves. a 22 MeV before reaching the target. (FWHM). 16 ° beam. would lose about 320 keY The straggling would be about 40 keY For a target length of 3 InIn seen by the detector the target thickness would be about 14 keY (lab). The target length for the counter telescopes described in the Charged Particles Section was roughly an order of Inagnitude larger than this. In the m.easurement of reaction cross sections. ultra high purity (> 99.99 % by volUIne) 02 gas was flowed through the chaInber at about 20 liter atm./hr for a chamber pressure of 3 torr. SIn all leaks. outgassing. and pUInp oll backstreaIning were estim.ated at < 4 X 10 -3 liter atIn / hr total. The ratio of the nUInber of hydrogen atoInS to the num.ber of oxygen atom.s in the cham.ber was estiInated -3 16 1 0 + H Light was emitted as the beam. passed through the g,s. The to be < 5 X 10 from. the observed hydrogen recoils from. elastic scattering seen in forward angle proton spectra. current froIn a photomultiplier viewing this light was used as an indication of the beaIn intensity, especially for purposes of focusing - 25 and steering the beam into the target chamber. The photomultiplier current was propo rtional to the beam current within a facto r of two over the entire energy range used in these experiments. Direct current integration with gas in the chamber was not attempted. In a gas target there is an angle at which the nwnber of counts from Rutherford scattering is independent of angle for a given detector collimator configuration. This useful fact was employed in part for monitoring the beam's angle in the chamber during the elastic scatterlng measurements. It was also used for the experimental determina- tion of the ratio of geometrical factors for two different counters (see Charged Particle Section, page 70 ). In a gas target the number of counts N in a counter is pro- po rtio nal to N «(solid angle) • (gas length) • (current) • (cross section) dn L i dO"/dn· Two defining collimators are needed per counter to restrict the length of the beam path seen. For a counter at 9 with A = area of the back collimator, d lab = 90 o w = width of the front slit, = distance between collimators, and D = distance from the beam line to the far collimator. At other laboratory angles - 26 b0cause the path length seen by the counter increases. In the special case of pure Rutherford scattering of light particles by heavy targets S do- ex 1/ i 4 ( lab) dQ"" s n -2so the angular dependence of N is 1 N ~ ---------:::S~- sin Slab. sin 4( ~ab) and =0 dN dS lab o Slab = 132 • for Therefore, the number of counts for Slab ~ 132 0 N is nearly independent of angle and pure Rutherford scattering of light beam parti- cle s on heavy targets (8 ee Dwarakanath (1968». Making co rrections for the mass of the bombarding particle M , and of the target M , 1 2 the corresponding angle is a solution of the equation o = 5 - sln2 Blab • 4 + sin Blab· [9 + 20(~:tJ [24(~:t + 16 (~JJ • In the particular case of instead of 132 0 , 16 0 on 40 Ar the correct angle is 135.6 causing a difference in the number of CO\Ults of 0 - 27 - < 0.7 %. Figure 6 plots the value of 9 1ab as a function of M/M • 2 Experimental The 16 0 + 16 ° elastic scattering was measured using various mixtures of ultra high purity Oxygen and Argon gases in the differentially pumped target. 02 : A r = 3 : 1 to 1: 1. The ratio of pressures was typically A special gas mixing bottle was used to make sure that the gases were well mixed (to within ± 0.25%). Mixtures containing a larger percentage of 02 were employed especially at higher energies where the ratio of elastic to Mott scattering was less than 0.9. Heat deposited along the beam path may cause changes in the gas density and perhaps in composition. Since only a ratio of counts was used for elastic scattering cross sections, density changes were unimportant. The continuous gas flow in the chamber also reduced composition changes along the beam path.. chamber varied from 3 - 7 J.1a of 0 0.13 to 0.30 watts/cm. 4 Typical beams in the +, corresponding to a loss of It is estimated that these differences in heat loss could lead to «0.10/0 changes in the gas composition. The energy loss of the beam before reaching the target region was determined experimentally using elastic scattering. The scat- tered particles I energy was measured for chamber pressures of 3.0 and 0.5 torr. Correcting for the 10.8 cm of gas between the target and counter, and using the measured energy shift, the energy loss - 28 - Figure 6 Special Scattering Angle VB. ~/~. The laboratory angle at which the number of counts from pure Rutherford scattering in a gas target is independent of angle is plotted against the ratio of the incident to the target masses 1\~ (see the text page 26 angle exists for M:t./M:2 ~ 1.0. and Figure 7). No such - 29 - ~------~------~------~------~g ~------~--------------~----~~O 1500 13<1' - 30 of a 23 MeV 16 0 beam to the center of the target was found to be 330 ± 60 keV (lab). Using Northcliffe I s curves (1963) , the energy loss and straggling are 310 keV and 40 keV (FWHM, lab) respectively. The elastically scattered particles were observed simultaneously with three solid state counters (see Figure 7). Two were placed on one side of the beam to check on its position in the chamber: One counter was at 132 0 , where the number of counts is nearly inde- o pendent of angle, and the other was at a forward angle (Slab::::: 24 ), where the count rate is a strong function of angle. 16 The ratio of the o beam particles scattered from the Argon gas into the 240 cOWlter, o 0 0 N(Ar,24 ), to the number entering the 132 counter, N(Ar,132 ), changes by about 200/0/degree and is a good indicator of beam angle changes. Experimental values of this ratio agreed within the statis- tical fluctuations expected from the numbers N(A r, 132°). N(Ar,24 0 ) and The standard deviation in this ratio was ± 1.60/0. This indicated beam angle changes of less than ± 0.080/0, whereas the o geometrically allowed change was ± 0.18 • N(Ar, 24 )/N(Ar, 1320 ) 0 tering of energies. 16 0 Furthermore, provided a check on whether or not the scat- from Ar was purely Rutherford at higher bombarding Deviations were found above E 0 the ratio N(Ar,24 0 )/N(Ar,45 ) energies measured. 1ab = 27 MeV; however, did not change up to the highest Thus N(Ar, 45 0 ) was taken to follow the 1/E 2 law over the full range of energies used. The third silicon detector was at Slab = 45 of the beam from the 24 0 and 132 0 cOWlters .. 0 on the other side (This same cOWlter and - 31 - Figure 7 Arrangement Elastic of the Counters Scattering for the Measurements. The actual elastic scattering data were taken with the 4.s<' counter, but the other two detectors were used simultaneously to check for variations in the incident beam angle text page 30). Also shown is the relative number of scattered protons calculated for p + Ar Rutherford scattering as a function of laboratory angle in a gas target text pages 26 (see the and 70 )• (see the - 32 - en5 z 0 t- o 0:::4 Q.. LL RUTHERFORD SCATTERING OF PROTONS ON ARGON IN A GAS TARGET 0 3 1% RANGE I I 136.5 0 127 0 0::: L&.I CD ~ =>2 z l -, L&.I > ~ ..J L&.I 1200 90 0 0::: 0 COUNTER ANGLE FIRST STAGE fDlFF. PUMPING P.M. WINDOW ---------------------.~. ~~40 BEAM 132 0 ~ - JJ collimator arrangement was used to monitor the target thickness and beam intensity in the other charged particle meas urements.) ° Its collirn.ation was ± 0.67 • The correct angle of this counter ° steps over relative to the beam was determined by taking data in 1 alab = 45 o • a set of angles near the number of N(O,450) 16 0 In the Mott scattering of scattered from 16 0 nuclei into the 45 16 0 0 + 16 O. counter. exhibits a relative maximUIll when the counter is at 45° (see Figure 8). (The actual angle is about 44.9 o because of the variation in the center-ai-mass solid angle conversion factor with angle.) However N(Ar,450) varies monotonically with angle, so the ratio N(O,45°)/N(Ar,450), which gives the final data. has a o maximum at an angle slightly greater than 45.0 • This difference was found to be 0.50 , in good agreement with calculations. In order to decrease the influence oi small changes in the beam angle on the results~ the counter was set between the two maxima at 45.2 relative to the beam. o N(O,4S.20) differs from N(O,4S.00) by less than 1.3%. All elastic scattering and recoil peaks in the spectra were well separated. These spectra from each of the counters were stored in multi.channel analyzers, and the counts in the peaks were summed later and used in the data analysis. Results The theoretical angular distribution for pure Mott scattering is given by - 34 - Figure 8 Mott Scattering Calculated for Angular Distribution 160 + 160 • - .35 - "-az: > w w ~ I- ... ....<t -0 g III + II C) -0 0 CJ) t0 t- :e 0 0 0- 0 ~ ~ :2 v ~ v W 0 0 -0 C M CROSS z SECTION IN MB/SR - 36 1 { sin 4 "'e 2 ~)cm = + (-1) 21 1 + cos 4 e "2 cos 1. n tan ~) } 2 21 + 1 2 e 2 e (T) sin - cos 2 2 2 where T) = 2 2 Z e /h v re 1 e :: center of mass angle, and I:: nuclear spin = 0 in this case. The interference term causes relative maxima and minima in the angular distribution (see Figure 8), and these change in angle with energy. However, at ecm = 90 0 there is always a relative maximum and constructive interference, and the Mott prediction is just four times the pure Rutherford value there. That fact makes this particular angle ideal for monitoring beam intensity and target thickness in the case of the 16 0 + 16 0 reactions. The ratio of the 16 0 + 16 0 ing at elastic scattering to Mott scatter- ecm = 90 0 is shown in Figure 9. Almost all points are the average of 2 to 6 measurements, or about 5 - 80 minutes counting time. Data in the region E 4 to 6 such measurements. cm = 9.5 - 11.5 MeV are the results of These data were taken in several passes over the energy region covered to average out possible changes in the incident beam angle. A statisticaJ. analysis of all the results dem.onstrated that the beam angle was always within ± 0.08 o of the - 37 - Figure 9 160 + 160 Elastic Scattering. The ratio of the differential cross section for elastic scattering at section is plotted. acm = 90 0 160 + 160 to the Mott scattering cross All errors are total errors (see Table 1). Energy losses in the gas have been subtrac ted and produce an overall uncertainty in the energy scale of ±'O keV (C.M.). Data plotted as solid circles are exhibited on an expanded scale as well. - 38 -~-- 160 C + 160 Elastic S . M. Angle =90 0 coffering •o o o 01 c: o o .98 o .96 o .94 o .92 o o o .90 \I 12--f;;---1-- E . . (MeV) CM 13 14 15 correct value. - 39 Changes in the intensity distribution of the beam across the entrance collhnator, changes in the gas pressure, or rapid fluctuations in beam current affecting the dead time of the electronics, did not influence the results. N(O, 4 So) /N(Ar, 4So) This was because the ratio was obtained from one counter alone. There- fore, the error bars on the data of Figure 9 and Table 1 correspond only to statistical errors calculated from the total number of COWlts at each energy and the uncertainty in the normalization constant. The energy loss was taken to be the measured value of 330:1: 60 keV (lab) at E lab = 23 MeV and was extrapolated to other energies using Northc1iffe I s curves (1963). An overall uncertainty in the C. M. energy scale for all points of loss correction. :I: SO keV is estimated from the energy The elastic scattering results permitted another check on the energy loss to the 16 0 beam before reaching the target. o 0 The ratio N(02' 4S ) /N(Ar. 45 ) was measured with 3.1 torr and with 0.7 torr chamber pressures at E of the curve in Figure 9. cm = 11.7 MeV, on the steep portion The change in the ratio indicated a total energy loss before the target of 2S0:l: 100 keV, in agreement with the other. independent technique. o The average value of N(O,4S )/N(Ar.4S o ) for E cm ~ 10.0 MeV was used to normalize the data of Table 1 to 1.00 below the Coulomb barrier. The normalization factor agreed to within 2% with the value calculated for pure Coulomb and Mott scattering from the mixing ratio of the gases. The small difference is well within the Wlcertainty in the gas mixing percentages. - 40 The num.erical values of the data presented in the paper of Bromley, et al. (1961) are no longer available. Therefore, points were read off Figure 13 of that paper and then compared to values in Table 1. When this was done, the data of Bromley, et al. seem to be shifted up in energy by 150 - 250 keY (C.M.) from the gas target data for points above the Coulomb barrier. Part of this shift may be the result of reading the values from Figure 13. However 1 it is also believed that the values of Bromley et al. should be shifted to lower energies by 50 - 100 keY (C .. M.), or more. based on more recent energy loss information. quoted to be ,,- 100 P. gm/cm 2 thick" SiD foils with an estimated energy loss of ,,- 250 keV" (C. M.). The curves of NorthcHffe (1963) predict an energy loss of 350 keY (C.M.) at E targets. The targets were lab = 24 MeV for such With the larger energy los s estimate. the older data should be shifted down by 50 keY (C. M.) (half the error in the target thickness, since an average energy 108s over the target is used). If the 2 foils were actually 130 p. gm/cm , the predicted energy loss is 450 keY and the corresponding shift is 100 keY. Note that the data in Table 1 are shifted down in energy from the data of Bromley t et ale even without the correction for energy loss of the beam before reaching the target region. Moving the energy scale down by 100 keY for the data of Bromley, et ale gives agreement within one standard deviation with the gas target results at energies above E data are about 5 to 100/0 higher for E cm cm = 13 MeV; the older = 11.5 - 13 MeV. This is - 41 adequate agreement within their estimated errors, and the precision their values can be read from their Figure 13. 16 More recently, Maher, et al. (1969) measured the ecm = 90 o elastic scattering at SiO foil target. from E cm 0 + 16 0 = 10 to 35 MeV using a Both particles were detected in coincidence. A fairly thick target was used by Maher in order to get sufficient yield at higher energies. These values are systematically shifted up in energy by about 250 keV C. M. from the gas target data.. also shifted up in energy from Bromley's (1961) data. They are The reason for these discrepancies is not certain, but may be the result of poor knowledge of the solid target thickness and the energy loss. The gas target energy loss is believed to be well known. The 16 0 to the one for dix I). 12 + 16 0 C + 12 elastic scattering curve should be compared C taken with the same apparatus (see Appen- The elastic scattering minima in 12C + 12C correspond to maxima in the reaction cross section and in a, p, nand '( yields. The lack of such structure in for the single anomaly near E 16 0 + cm 16 0 elastic scattering (except = 10.5 MeV) suggests there may be a corresponding lack of fluctuations in the reaction cross section. See the Gamma Rays Section for a further indication that this is true. - 42 GAMMA RAYS Introduction Gammas emitted from j.6 0 + 16 0 reactions gave additional information on which exit channels are important and on the variation of the cross section with bombarding energy. Two different tech- niques were employed. In one case, several spectra were taken with Ge(Li) for 16 detectors o beams bombarding various targets containing Oxygen. specific energy '{'s Only were looked for, namely those from the first few excited states of nuclei formed in 16 0 + 16 0 reactions. Many levels can be populated in these nuclei; hundreds are energetically allowed in 31 P and 28 . Sl, for example. However, highly excited states will often decay by a cascade of '{'s, proceeding through one of the low lying levels to the ground state, so transitions from the first few states are expected to be strong. Although branching ratios to the various exit channels could not be obtained from these observations, semiquantitative information based on the intensities of the observed lines indicated that the most important exit channels are p + 31 p 2Q' + 24 and/or 2p + 30 S i, Mg, and Q'p + 27 AI. Q' + 28 Si , d + 30 P and/or pn + There was also evidence fo r 30 p. n + 31 s. Very rough estimates of the relative strength of these channels were made, but Doppler broadening of Hnes and similarities in characteristic '{ energies prevented more definite conclusions. The most - 43 important finding was the significant number of three body breakup reactions present and the sizeable increase in the two body reaction percentage at lower bombarding energies. The total "V yield as a function of C. M. energy in was measured in 50 keV (C. M.) steps with aNal (Tl) 16 0 + 16 0 scintillator placed just above the beam line in the differentially pumped target. The number of "V's emitted increases with the total reaction cross section, but a strict proportion is not expected because of cascades from highly excited states. significant changes in angular distributions, and possibly a preferential population of certain levels. The "V yield will be sensitive to fluctuations in the reaction cross section over restricted energy intervals, such as those observed in the 12 C + 12 C system (see Patterson, Winkler and Zaidins (1969) and Almqvist (1960, 1963)} since there are so many excited states that can be fed. The "V yield data suggest that the 16 0 + 16 0 total reaction cross section varies smoothly with energy and fluctuations, if present, are less than the errors for the charged particle measurements. Ge (Li) Detector Spectra . Several high resolution "V spectra were obtalned for reactions at E cm 16 0 + 16 0 = 12 MeV with 40 and 55 cc coaxial Ge (Li) detectors for a number of different targets. One spectrum in Figure 10 was taken usi.ng the differentially - 44 - Figure 10 160 + 02 Gas and 160 + NiO Gamma Spectra. These spectra were taken with a Ge(Li) counter at a bombarding energy of 24 MeV (E = 12 MeV). The targets were 02 gas at cm 1.S torr pressure in the differentially pumped system and a 2 90 p.gm/cm nickel foil oxidized by heating in an Oxygen atmosphere. The same gain was used in both spectra, and the energies of some identified lines are shown. broadening is especially noticeable in the spectrum. Doppler line 160 + 02 gas - 45 - I I l f- -8 ) .1 IL'I- ) -• CJ) - ~ 8 Z 0 - LZ'I - ," w.~ . . . :} 0 ~O·,- tiII·o - .,~.' •.. ') -~ " ,,> . ' \' ,/' " 'f IQ'O L" " ," f' 7 . Z Z -<:i ~ () '~f -§ 8 '" . !, , "r '" ~ ./T . -8 t . l'? ;rO ,f ; .. ...... .... ~ ):..I." /""~ . . I : ;" '., l ' "~ I I 0 80 § §Gi ) t ~( " } M .., . . .' ' ,. °0 ~ I ~ . 't I L ' O - •..... f ...) <~~ I. oC••• " ~. ~ ( Z 0 ,~ !E Z \~ L£'I- It) ) § 0 .- ,,'1 - " 'J... .> 0 8 ) It) 00 0 0 0 si It) COUNTS 0 0 0 It) 0 0 - 46 pumped gas target with a gas pressure of 1.5 torr. The front sur- face of the detector was placed about 5 cm from the beam path and 48 ern beyond the target chamber center. Shielding from yl s pro- duced upstream and downstream was 11 cm of lead arranged so the target length was about 15 cm or 340 keY (lab). The tantalum beam stop was 97 cm from the detector. Energy calibrations for this an d 0 th er spectra were rna d e us i ng 22N a, 137 Cs sources to an accuracy of 54Mn , 60 C 0, 88 y an d ± 5 keV. Most y lines in Figure 10 are much wider than expected from the actual detecto r resolution. The main contribution to the line width is Doppler broadening because the heavy reaction products have velocities relative to the detector when they decay. 16 case of 0 For the . + 16 0 --- a + 28 Sl.* (1.78) the Doppler shtft is expected to be up to 65 keY or 3.6%, and for it is up to 35 keY or 2.7%. 16 0 + 16 0 - p + 31p* (1. 27) The observed wi.dths (FWHM) of both lines are about 4.0% from Figure 10. The 70 keY (FWHM) straggling in the beam energy acquired from passage through 55 cm of O 2 gas to the target region caused no significant further broadening of the y Hnes. In a thick solid target the y energy resolution is better than for the gas target because the density is much higher, so the heavy nuclei are slowed down much more quickly and the Doppler broadening corresponds to the slower velocity at the time of the Since the lifetime of the 28 S1 y decay. 31 P * (1.27) level is O. 73 ± .07 ps and of * (1.78) is 0.63 ± .03 ps (Endt and van der Leun (1967», only - 47 about 10 -3 I.l gm / cm 2 of 02 gas is traversed before a from these states in the gas target. The corresponding thickness 2 for a solid target is on the 0 rder of 1 I.l gm/cm • The difference in '( line widths is apparent between the spectra of the bombarding 02 gas and a '( decay 16 ° beam NiO foil (made by oxidizing a 1000 A commercial Ni foil in a pure 02 atmosphere with a collimated light source) in Figure 10 and a thick piece of quartz shown in Figure 11. The advantage of better resolution resulting from thick solid targets is partly offset by the uncertainty in the origin of some '( lines. Since solid targets cannot be made of pure Oxygen, they are susceptible to the production of undesired other nuclei in the target. ° + °16 O'p + 27 from reactions with For example, with hydrocarbon contami- nants on the target surface, the reactions 16 '(I s 160 + 12C - P + 27 Al and Al would lead to the same characteristic '(I s and could not be distinguished. The Ge (Li) detector was always at right angles to the beam with at least a 1 cm thick cylindrical lead shield around the detecto r housing as some protection against background. The distance between the counter's front surface and the beam spot varied from spectrum to spectrum and ranged from 2 to 10 cm with about 1 mm of aluminum in between. of charge 5 + 16 The beam intensity was generally kept below 200 na ° because of both the high neutron fluxes and the high co unting rat e s • - 48 - Figure 11 160 + Quartz Gamma Ray Spectrum. This spectrum was taken with a 55 cc coaxial Ge (Li) detector for 24 MeV 160 (8i02 ) • nuclei bombarding a thick piece of quartz Energies of the more prominent peaks were determined from the energy calibration, which is good to about The ± 5 keV. 0.511 MeV Compton edge obscures most gamma lines below about 0.4 MeV. However, two strong low energy lines are present and are believed to be X-rays from lead. o o ~ Z f- CJ) 'I Ii' ,II i ! , I I' .\ 1 :\ ?Joo U'U'\ 12~ • =• : : :J ""- • " •• fi ii . .; .., ! ! 01 g~ • .. , " ~ ~ ... ! If) .. .. 15~O 16~ CHANNEL i; 01 ...,....~.., I~ I ,\ I I!., ~ '. '. ~ J! .7-.."-,,,...' oi !!! ". V ..:. ~~ i , ~':••~'\. ~........~~ ",-,' :.Ji_~,_~ .'1 !1. J:' "",NIl. I ! ...!Ij' I!i'I I' \ ~ . . ~ Y SPECTRUM 160 + QUARTZ ii/I , .; .., • 0; :. ; ., .~ ,.:,~..';;.I I ,. ~:~.;,: '-:fl" r,',t,I"... .,.,..~~...... ~ ID (-' 2o '" .1"1.".__."'" i..l xliS \... ""--...:' 1 I \ f\~i' d~ ' "'. . .;.' ' ,' ' ';.;;:;/<! . ' .,."".•j~rl··. I' : ........... ......" , '-."~ ~ d~' ii' ..., . • •.,; ,II, i !I~ I /! ~' ,,&, I':x, f4~ 1700 1800 1900 2000 - '.or....r"i : n ~ I f. r I,.\ ... ., ·\."'''''';'''N'''';\''~'''~''~~.';'O""""~>:<\,_,..~;",,_.~. .v>,,...,,'_''""'''"'I-.-~.-t--',,~ ~l ""! \J.! _. . : 1 500f-·iI • 1000 0"o 1000 2000 3000 4000 ~oo,r--------r--------~~----~--------~------~--------'-------~r--------r--------r--------r----' \Q ~ - 50 Table 2 lists the y energy, the relative detection efficiency, and the counts normalized to the number in the 2.23 MeV peak for 9 strong lines observed in all spectra. The estimated errors on the ratios range up to ± 20% because of problems in background subtraction. Note that the ratio of counts varies significantly. Some differences arise from the variety of circumstances under which the spectra were taken. Others probably carne from contaminants on the targets or from. 16 0 t Si reactions. Since all peaks in Table 2 are present in the gas target spectra, they are all believed to originate from 160 + 16 0 Th e re 1at i ve p h otopeak reac ti on pro d uc t s. efficiency of the detector was estimated from Paradellis and Hontzias (1969). Huang, Osman and Ophel (1969) and from direct m.easurement to roughly follow a power law Effic iency - E -Q' with Q'D! 1 .. 2 This quantity is also tabulated in Table 2. Estimates of branching ratios to the various 16 0 t 16 0 channels were made from the intensity of lines in Figure 11. exit Some conclusions were also implied by the absence of certain transitions. Table 3 gives a list of the y lines between 0.5 and 4.4 MeV from Figure 11, the most probable transition or transitions involved t and other possibilities that are considered less likely (for 16 0 t 16 0 reactions only). Some lines or contributions to some peaks may be from undes ired y's. Below 500 keV the annihilation peak and its Compton edge dominated, and above 4.4 MeV little structure was - .51 observed. Transition energies were taken from Endt and van der Leun (1967) and the y energies were obtained from the energy calibration with a number of source". The accuracy 1. about ± 5 keV except at the higher energies where no calibration lines were used. Several1ines remain unidentified. Identifications in Table 3 were required to be self consistent in a number of ways. Single and double escape peaks were always broader than the photopeaks of about the same energy. Strong lines between 1.5 and 2.5 MeV and al11ines above 2.5 Mev were required to have both. y decay schemes and branching ratios, where known. were taken into account. Thus if a transition between the third and second excited states was present, the level had to be seen as well. y's depopulating the second Finally, if a transition from the second excited state in a nucleus was identified, the one from the first excited state was also required to be present, etc. the latter was that 31 An exception to P (3-0) = 3.135 MeV was not observed. but decays from higher levels were. A number of conclusions can be drawn from Tables 2 and 3 . correspondmg to E em = 12 MeV. These follow for each 16 0 + 16 0 exit channel with Q > 11 MeV (see the energy level diagram Figure 1). Level energies and y branching ratios were taken from Endt and van de r Le un (1967) and Ajzenberg-Salove and Lauritsen (1959). All yields are stated as ratios to the 28 S1 yield and are generally based on results presented in Table 2. Limits on yields come from Figure 11. - 52 28 St + t + p, _ _ 28 S1 + 3 He + n. 26 M g + Q' + Zp, small because of Q values. All are expected to be No conclusions are possible from ,,-ray yields since no excited states can be populated at E crn = 12 MeV. 27 Si + 0' + n. Neither the transitions from the first nor from the second excited states of 27 Si were observed. A limit on the yield was derived to be < 0.05 (relative to 28 S1 == 1.0). 29 p + t. There is only marginal evidence for the 29 p (1- 0) trans ition, and none for the decay from the second exc ited state. The yield was estimated at .:5 0.03 times the yield at E cm = 12 MeV. The large negative Q 28 Si value and Coulomb barrier probably suppress this channel. 29 Si + 3 He • 29 S1 + P + d, 29 Si + 2p + n. No conclusions possible. The (1- 0) transition is masked by the 1.27 MeV 31 P, 30 Si. etc. ,,'s from The (2 - 0) transition is masked by the 3.05 MeV second escape peak, by 31p (4-1) and by 31g (4-1). 16 0 + 12C + 0'. The only energetically allowed state is the 4.43 MeV level of 12C ~ but it is not observed (see Figure 11). 20 Ne + 12 C and 20 Ne + 30'. Very little can be concluded. above background were detected at E 20 Ne (1_0) or at 4.43 MeV for y No counts = 1.63 MeV for 12C (i-O). The Q values indicate that these channels may proceed through the - 53 ground states most of the time ~ emitting, no -V's. See the 12C + 20 Ne Production Section (page 152 ) fo r a measurement of the cross section to the ground state. 30 p + d t 30 p + P_ + n. -V d ecays f rom t h efi r s t f our an d perh aps five levels of 30 p were identified. The 0.67 MeV line was * (1) is a T = 1 state. The number of weak because 30 P "{'sfrom 30 p is about the same as from 27 Al + P + a. Decays from the first three or four states in 27 Al are present. of 27 28 Si • The fourth is in question because of the absence Al (4-0), whereas the 1.727 line is broad and contains the single escape peak from 2.23 MeV -V's. presence of 16 0 The possible . + 12 C reactions must be considered, so the number of 27 Al formed by 16 0 + 16 0 reactions is ~ 0.5 times the number of 28 Si formed. 24Mg + 2 a. The (1 - or absent. 0) transition is strong, but others are weak However the second to fourth levels in 24 Mg > 2.7 MeV. Again there is the possibility of -V reactions, so the yield of 24 Mg is .!S 0.4 decay with E 16 0 + 12C ( relative to the 31 S + n. 28 Si yield == 1. 0) • This channel is very weak compared to others with similar Q values. 31S (1-0) was observed, but the (2-0) transition, if present, is obscured by the mirror transition 31p (2- 0) and others. the 31 Based on the 1.24 MeV -V's only, S yield is - 0.06 times the 28 S1 yield. - 54 31 P + P and 30 8i + 21'. The idea of taking -V spectra was originally conceived as a means of separating these channels. This failed because of a remarkable number of coincidences. The -V's involved are: 1.27 MeV. There are at least 5 different transitions within 5 keV of this energy. One is the 1.78 MeV first escape peak, expected to comprise only a small fraction of the counts in this line. The amount of 29 8i (1 - amount of 30 P (4 - 2) can be estimated using the known -V decay scheme of 30 P peak. 0) is uncertain, but the * {4} and the counts in the i.98 MeV Note that 3i p {i-O} and 30 8i (2-0) transition energies are identical within the errors and the detector resolution. 2.235 MeV. The 32 Four important transitions occur within ± 3 keV. 8(1-0) and 31 8{2-0) -V's are expected to com- prise only a small portion of the total from the lack of transitions from higher states in both and from the size of the 31 8 (1 -- 0) peak. That leaves 31p (2-0) and 30 8i (1-0), whose energies are within 2 keV. 3.505 MeV. 30 8i * (2) decays 55 % of the time through the 2.23 MeV level, and 45 % of the time directly to the ground state. However, there is evidence for decays in 31 P from its first six excited states (excluding the third state) ~ so there is a possibility of a contribution from 31p (6-0). The ixn- portance of the latter transition cannot be checked from the - 55 " decay scheme of 31 P is 2.239 MeV! * (6) because the energy of 31 P (6 - 1) Nevertheless, for only the counts 1n the, 1. 27 MeV line, the number of 30 S1 is < 0.2 and of 31p is > 0.7 (normalized to the number of 28 St == 1.0) from the strength of the 3.51 MeV peak. these lines for 28 Si + Q'. The combined strength of all 30 Si and 31p is 3.5. Decays from the first two excited states were observed. This is the only reaction producing a 1.78 Me V ", and there are many levels of 28 8i which cascade through 28 8i * (1.78). Thus the 1.78 MeV line was ideal to compare to other yields, and its strength was taken to be == 1. O. 32S. Unfortunately no conclusions can be reached. 32S (1 - 0) has an energy of 2.23 MeV, which is the same as several other strong transitions. (2) The observation of the decay from 32 S * is questionable because of the "line II shape (see Figure 11). Thus there is no evidence for or against a negligible yield in this channel from the " spectra. A summary is given in Table 4. These conclusions agree qualitatively with the preliminary analysis performed in the Introduction Section based on Q values and Coulomb barrier heights. Table 4 contains similar data for quartz at E 1ab = 20 and was subtracted from the 16 0 18 Mev as well. 18 MeV beams bombarding A background spectrum run, but was unnecesscu:y for the spectra taken at the other energies. The decrease in the fraction - 56 of three body exit channels can be noted from the fall in the relative branching ratios of 27 AI, 24 Mg and 30 p . Such information is quite important in relating the measured production cross sections for protons and alphas to reaction cross sections. A proton fron'l much as one from 31 P 30 Si + 2p should be counted only half as + P in the proton spectra, since two light particles are emitted per reaction in the former case. The uncer- tainty in the three body fraction will be reflected in the reaction cross section, because of the difference of a factor of 2 in the counting, and in any extrapolation of the cross section to energies below E cm = 7 MeV. See the Conclusions Section (page 171) for a further discuss ion of the above problem. y Yield vs. Energy Fluctuations in the total cross section should appear in the y yield as a function of bombarding energy, especially if many excited states are populated, as in exist in the 12C + 12C 16 0 + 16 ° reactions. Such fluctuations system and these data were taken to look for a similar behavior in 160 + 16 0 • The differentially pumped gas target, usually at a pressure of 1.5 torr of ultra high purity 02' was used for the measurements. The beam passed through about 16 cm of gas before reaching the center of the target region, losing about 400 keV (lab). was estimated at 40 keV (FWHM, lab). The straggling - 57 A 2 X 2" NaI (Tl) scintillator was located with its front face 2.2 cm above the beam line with 0.5 ern of aluminum between them. A 1.9 cm lead shield around the crystal restricted the target length to about 9 cm or 100 keV (C.M.). The attenuation to 0.51 MeV -V's was a factor of 110 and to 2.23 MeV -V's was 2.8. against undesired -V's were taken: Precautions inside the scattering chamber there was lead placed around the entrance and exit apertures, and the beam stop was moved 140 cm away from the target regiono Three discriminators were used to count all cutoff points of 0.6, 1.6, and 2.2 MeV. The monitor counter from elastic scattering measurements was set at for normalization. -V pulses above elab = 450 and was used The yield was determined from YIELD = CONST • (# y's - background rate· time) • ( +I monitor counts) (E cm 2) ratio of elaStiC) scattering to ( Mott The constant was chosen to normalize the yield to 100.0 at E cm = 10.0 MeV so data with different cutoff energies could be compared. Errors were estimated from statistical uncertainties on the number of counts and from a 3 % error for pressure changes. shifts in the cutoff energy, and errors in the elastic scattering cross section .. The results are given in Table 5. The background was found to be propo rtional to time (36 counts per minute for the 2.2 MeV cutoff and 410 for the 0.6 MeV cutoff). No additional background was observed from the canal of the gas target. 1 to 16 minutes. Counting times ranged from Energies were corrected for losses in the gas. The - 58 normalized yields for all three cutoff energies agree within ± 20 % over the whole energy range measured. with the lower cutoff energy data presenting a steeper energy dependence. diffe rence could result from cascaded y I s; This systematic a small fraction of such Y I S are detected with the higher cutoff than with the lower ones. ThuB, the variation with energy of the average number of cascade -v's per reaction influences the lower cutoff data more strongly. Furthermore, certain exit channels may be excluded by setting the cutoff too high, also influencing the energy dependence. In the energy range covered, the of nearly 10,000 (see Table 5). y yield changes by a factor To see small fluctuations, the barrier penetration effect can be factored out: YIE LD - Ffi- exp (- cm - g E cm ) and the results are plotted in Figure 12 for the 1.6 MeV cutoff. absolute normalization was used for No S, and the value of g was chosen somewhat arbitrarily (it corresponds to an interaction radius of 7.25 fm). Other g values would tilt the data one way or the other in the plot, but would not affect the presence of bumps. Small fluctu- ations may actually be present in Figure 12, but they could not be seen in the charged particle data with the larger measurement errors. This situation should be compared to similar results obtained for 12 C + 12 C reactions, also displayed in Figure 12. Charged - S9 - Figure 12 S for the Yield of Gamma Rays 160 + 16 0 and 12C + 12C. from 16 16 The differential~ pumped system was used for the 0 + 0 2 measurements and a 10 JJ-gm/cm carbon foil was used for the 12C + l2C data. In both cases the detector was NaI and elastic scattering monitored the combined target thickness and beam current (see the text pages 58 and 181 and Tables 5 and S for 160 + 160 are in arbitrary units (see Figure 41), whereas the 12C + 12C resul ts are norm:a.lized 18). at The values of Ecm = 4 MeV to the charged particle data of Patterson, Winkler and Zaidins (1969), which is also plotted. - 60 I I I I 16 0 +160 S~ -.--- (I). 3 ~ .. ' .....' I... ' - " ·:·..·I· . .. r 2~ ie.p(. 'H. I - gE) - '" 0.84 MeV-I 9 .... - Y -Yield Yield 4 ~ , I Ey > 1.6 MeV - '. .' - "''l '1' .... " . . .. . ....... .... ' H- 0 I I ~ I 7 8 9 10 " (MeV) ECM - "'}- I 1 " 12 Y - Yield a = iE eap(-1Z.2. ,T - 9 E) -~5 9 = 0.46 MeV-I Ey > 1.4 MeV , Charged Particle Data ~ • < OJ .,a ...:s " - I I -\ • 1 \1\ • . '. ".: o~ 3 I ", J, ' . II o J . ",.... w . "I, " it .! \ /' •\ ' .' • w /' ., .,. ________ ........ .0 ." " ~ 4 ______ ~ ________ ~ ________ 5 6 ECM (MeV) . • • •• w ~ 7 __ ~ " ____ 8 - 61 particle measurements from Patterson, Winkler and Zaidins (1969) and '{ yield data normalized to the former at described in Appendix II are plotted. E cm = 4 MeV as The agreement over the full energy range might have been worse if some other cutoff energy were employed. Such an effect was noticed in the A more detailed structure was seen with the it was easy to take fine energy steps. 16 0 + 160 case. '{ yield data because The sharp contrast between the two sets of data in Figure 12 is the main evidence for concluding that the 16 0 + 16 0 cross section is relatively smooth. One impor- tant consequence is that it is not necessary to take charged particle data for 16 0 + 16 0 in small energy steps. - 62 - CHARGED PARTICLEs Introduction Most of the 16 0 + 16 0 total reaction cross section comes from channels with at least one light charged particle emitted. The gamma spectra and the arguments in the Introduction, based on compound nucleus formation and Coulomb barriers, indicate that the most important of these exit channels are: 16 0 + 16 0 _ 28 S1 +Q Q = 9.592 MeV P +P 7.676 30 Si + 2p 0.388 24 Mg + 2a -0.390 27Al +p +a -1. 991 +d -2.412 29 Si + 3 He -2.510 +P +n -4.636 31 30 p 30 p Cross sections for the production of protons, deuterons and alphas were determined by measuring their yield at a number of angles. Two counter telescopes we re constructed to distinguish between these light charged particles. Particles of different masses could be distinguished by passing the particles through a transmission detector of thicknes s .6x to measure the energy los s, dE/dx • .6x, and then measuring the total energy E .6E = remaining with - 63 another counter. A number of purely experimental problems prevented the detection of all light charged particles down to the lowest energies at a given laboratory angle. Protection of the counter telescope from the very high elastic scattering count rates required a foil to stop the in the 16 ~E 0 nuclei. Furthermore, particles of low energy stopping detector of the telescope could not be identified properly and were not counted. It was important for the low energy cutoff for each type of particle to be as low as possible, so few counts would be lost. This requirement dictated that the protection foil thicknes s be kept to a minimum and suggested the use of a proportional counter for measuring ~E. A silicon surface barrier detector with the sanle energy loss for protons as the proportional counter constructed would have a thickness of 4J1. and was not commercially available. In addition. the high capacitance of such a detector would result in a resolution no better than that of the proportional counter. The foil necessary to retain the proportional counter gas introduced a small additional energy loss (equivalent to 4.2J1 of silicon). For many bombarding energies and angles it served as part of the protection foil needed against elastically scattered particles. One of the two counter telescopes used a 58J1 thick solid state detector in order to separate the deuterons from the protons, because the proportional counter resolution was not good enough for these particles. - 64 Although the total energy resolution of the counter telescope was $ 400 keV, only a few levels in actually resolved. 28 Si, 31 P and 30 P were One reason is that in the residual nuclei regions of excitation energy having a high density of states are energetically accessible. There are hundreds of such states in just the first two exit channels tabulated above. Furthermore, the low particle yields required large angular openings for the counter telescopes, resulting in kinematic broadening of the peak from a given excited state. Finally, the three body channels produce a continuum of particle energies for a given state in the residual nucleus. Under these circumstances. contaminant reactions could be completely masked by 16 0 + 16 0 reactions and still contribute a sizeable portion of the particle counts. alphas from 16 0 + 12 C or 16 0 + 14 N individual levels were not resolved. For example, protons or might go unnoticed because So it was necessary to use a very pure target material and to take precautions to prevent contaminants. A solid target containing Oxygen was not acceptible fo r this reason. The most satisfactory target was ultra high purity Oxygen gas in a differentially pumped system.. The beam intensity was not limited by the entrance foil needed for a "closed l' gas target, and the beam energy loss and straggling were well under control. Gas flowing through the target chamber swept out all impurities fronl outgass ing in the system t preventing buildup of target contaminants. Details of the differentially pumped gas target are given in the - 65 Elastic Scattering Section (page 21). Angular distributions of protons and alphas were taken at 8 energies between Ecm = 6.8 to 11.85 MeV with the counter telescope ( with a proportional counter to measure .6E) • Total production cross sections were derived from these measurements. However there was a problem relating these to 160 + 160 because of three body breakups. In two body exit channels only one reaction cross sections light particle is emitted per heavy ion reaction, whereas two are given off in each reaction for three boQy channels. A proton or alpha from the latter should thus be counted only half as much as 1n the two body cas,e. The uncertainties in the percentages of each ex! t channel was a serious source of error in deriving 160 + 160 reaction cross sections from the data. The deuteron yield was measured at similar fashion. Searches were made for energies, but none were detected. E = 20 and 24 MeV in a lab 3He and 3H at the same Limits on the latter cross sections were derived. Experimental All charged particle measurements were made using the differentially pumped gas target wi th ultra high purity Oxygen gas (> 99. 99i by volume) at a chamber pressure of 3.0 - 3.5 torr. The same 45 0 counter used for the elastic scattering measurements monitored the combined beam current and target thickness as described in the Elastic Scattering Section (page 30). Be:fore each series of runs, - 66 the angle of the monitor counter was set to the yield of elastically scattered oxygen. alab = 45 0 by maximizing Its geometrical factor was (OL) 90 0 = (6.2:±: 0.4) X 10- 5 cm sr and its angular opening was :±: 0.7 0 • The alpha and proton spectra were obtained with a counter telescope (Figure 12) composed of a proportional counter to measure .6E and a 2 mm thick lithium drifted silicon detector (110 mm area) to measure E of the particles. 2 in The gas tight housing of the telescope was rigidly connected to a lucite flange rotating in an O-ring in the lid of the scattering chamber. The cylindrical pro- portional counter was 2.9 cm in diameter by 3.8 cm long and was machined in a block of aluminum (see Rossi and Staub (1949) and Curran (1958) for the design of proportional counters). The high voltage electrode was a 0.1 mm diameter length of piano wire on the axis of the proportional counter.. It was supported by a cylindrical glass insulator on the end nearest the E counter, and by a Kovar glass feedthrough on the other end, bringing the electrical connection to the wire out of the counter housing. An Ortec 109 PC charge sensitive preamplifier with built in FET protection was connected to this point by a coaxial cable enclosed in stainless steel tubing. The tubing was open to the atmosphere on one side and epoxied onto the counter housing, over the Kovar feedthrough, on the other side. Thus all high voltage connections to the proportional counter were under atmospheric pressure. The total capacity of the counter wire and - 67 - Figure 13 Cross Sectional View of the Counter Telescope. This counter telescope consisted of a proportional counter to measure 6E and a 2 mm thick Si (Li) counter to measure E of the particle. The proportional counter consisted of a cylinder of Argon gas in the alwninum telescope housing. The high voltage wire was on the cylinder axis and was connected to a Kovar glass insulated feedthrough and then to a coaxial cable protected by stainless steel tubing (see the text page 66 ). The proportional counter gas continuously flowed through the counter at a pressure of about 120 torr. The whole counter telescope was rigidly mounted on the lucite top to the target chamber (see Figure 5). ~ BRASS ("::::.::.) ALUMINUM ~ LUCITE SLIT • ~- IN Ar GAS Ni FOIL 10,000 A ENTRANCE I" H.V. PROP. COUNTER COUNTER TELESCOPE OUT \ SIGNAL :'.j 1 I ····.1 ~COUNTER \ Si(Li) ~ Ar GAS Si (Li) DETECTOR 2 mm CD '" I - 69 cable t up to the preamplifier input, was 13 pf. Electrical break- down occurred at about 300 V in the Oxygen gas (at 3 torr chamber pres sure) when the high voltage connection was made without the tubing, whereas it occurred at about 600 V in the counter gas (120 torr) with the cable at atmospheric pres sure. The normal operating voltage was 550 V and the corresponding gas multiplication was roughly 100. A mixture of Argon and ;% Methane served as the proportional counter gas, and flowed continuously through the counter. A forepuITlp and two needle valves ITlaintained a constant pres sure of 100 - 130 torr as measured on a ITlanOITleter in parallel with the counter during the actual runs. Particles entered the telescope through a 1.6 ITlITl vertical slit in a 1.6 ITlITl thick brass disk. They then pas sed through the counter gas retaining foil of 10.000 A nickel. In order to protect the Si (Li) detector froITl heavy ions and the telescope froITl high elastic scattering count rates. espe dally at very forward angles, one of three different foils could be inserted in addition in front of the telescope without breaking the target vaCUUITl. nesses were 1,4 ITlg/CITl 2 and 3.4 mg/cITl and 0.0005 11 ) and 0.9 ITlg/cm 2 2 The foil thick- ::uuITlinUITl (0,0002" nickel (10 ,000 A). The thinnest foil needed to stop the elastically scattered Oxygen was used at each angle and energy. The detection liITlits with just the entrance foil alone, and with the 3.4 ITlg/cm 2 aluITlinuITl foil in addition, were respectively 0.6 and 1.3 MeV for protons and 2.5 and 5.0 MeV for alphas. For laboratory angles over 70 0 the telescope entrance foU - 70 was thick enough to stop all particles from 16 I:Icattering and no additional follH were used. 0 -I- 16 0 elastic The lowest possible detection limit was thus obtained for a region of angles where the reaction products have lower energies for kinematic reasons. The alphas were always stopped in the telescope, however protons above 18 MeV were not because the E detector was too thin. These counts were recorded by the electronics as having an energy (E) lower than they actually possessed, and they constituted less than 3% of all protons. Such conditions arose only at forward laboratory angles with high bombarding energies. The telescope angular resolution was ± 3.9 0 and its geometri- cal factor was (S1L) 900 = (1.28:1:: 0.05) X 10 -3 cm sr. An experimental check on the solid angle factors was performed by scattering 1.8 MeV protons from pure Argon gas in the differentially pumped system at a chamber pres sure of 2.0 torr. the scattering is pure Rutherford (at least for Dwarakanath (1968». were moved to At this energy alab < 140 0 , see Both the monitor and the counter telescope alab = 132o where the nUIllber of counts detected is independent of angle (s ee Elastic Scattering Section, page 26 ). ratio of the number of counts in the counter telescope and in the monitor counter gave The - 71 (nL) MONITOR, 90 0 <tiL) TELESCOPE, 90 0 = -2 (5.2±0.2)X10. The correction to account for the fact that the number of counts is not exactly independent of angle is < 1 %. rections are estimated to be < 10%. Multiple scattering cor- The same ratio from geometrical measurements is =(4.8±0.3)X10 A mean value of (5.0 ± 0.2) X 10- 2 -2 • was used for the evaluation of the data. A schematic of the electronics associated with the counter telescope is shown in Figure 14. After amplification, the 6E and E pulses were stored in the two coordinate directions of a two dimensional Nuclear Data 64 X 64 channel analyzer. The ADC processing the 6E pulses was coincidence gated from a low level discriminator set on the E pulses, thus eliminating much of the noise inherent in the proportional counter. A typical two dimensional spectrum is shown in Figure 15. The only background observed in the spectra was a continuum of counts with 6E "'" 0 and E:> 0, up to about E = 8 MeV. counts were identified as cutoff energy E 1ab ). )" s detected by the Si (Li) counter. The was independent of angle, but the number of counts varied with angle from 1/sin 9 These 9 lab = 20 to 150 o (approximately as Neutrons were excluded as the main contribution - 72 - Figure 14 Counter Telescope Electronics. [}- E c )UNTER PROP. C )UNTER v ( _ __ 1\ --_ .- BIAS ~ L_ AMPLIFIER 1416 ADC ..- NUCLEAR _ ORTEC SCA DELAY I~ DATA - NUCLEAR DATA ADC COINC. PULSE STRETCHER AMPLIFIER 1416 CANBERRA CANBERRA +300 v. TENNELEC IOOA PREAMP - BIAS ~ ...- + 600 v. ORTEC 109 PC PREAMP NUCLEAR DATA r-ANALYZER - ~ ...., - 74 - Figure 15 Two Dimensional Charged Particle Spectrum. 0 This spectrum was taken at Ecm = 11.85 MeV and Slab = 20 wi th the counter telescope of Figure 13. Note that the alpha (uppermost), proton and background separated. (6 E .. 0) lines are well Summing counts in the 6E direction gives the alpha and proton spectra of Figure 16. A cross section of the E = channel 7 is given in Figure 18. counts at (E"" 3.3 MeV) 0 z z fT1 ra; l> ~ 0 :u f\) fT1 UI -f cz 0 0 0 I· • • : • • • •• • •• • • •0 • • ••• • •o· • • • •• •• • I • ••• • • • . • • 16 32 DIMENSIONAL • •• o. ana", •••0. 00. o·O• i o •• ~ a2,3 E COUNTER 48 I • 64 CHANNEL • • ~ • •• 0 •• •• 00 •• •• ,0 a. a ~ CHARGED PARTICLE SPECTRUM TWO :. : ' " p cutoff •• . • ~·-i·----·-·--~~-- •• • • •• • • •• • • • •• • ••• •••• • •••• •• • •• •• • •• •• •• • •• ~. .;>~ :. ~.•• I t> ~-r:· fT1 (X) ~O • • • • 3 - 10 1-2 • 11-30 0 • 0 100-1000 31-99 • >1000 COUNTS 1; - 76 because the neutron production cross section was llleasured and waH too srn.]ll to account for the observed counts (see Neutrons Section, page 141). !3 Electrons fronl ionization process es in the target and decay electrons probably contributed sOTIlewhat to this backgrotuld. The proton line was generally separated froTIl these background COtults by a channel or TIlore, and the proton spectra showed no indications that extraneous counts were included. The efficiency and pos sible noise contributions in the two diTIlensional coincident .6E - E pulse recording systeTIl were checked by using different gains and time delays for the two channels. The energy scale in the E No anoTIlalies were found. direction was calibrated with the 31 protons and alphas corresponding to the lowest lying levels in and 28 lines. Si P respectively. s :nce these levels could be seen as separated Energy losses in the foils and gases (02 and Ar) were cal- culated froTIl tabulations by Whaling (1958), Marion (1968) and Northcliffe (1963). The two diTIlensional spectra were sUTIlTIled in the .6E direction to get particle spectra as shown in Figure 16. The Inagnitude of the particle energy in the Si (Li) counter, E = E t. coun er ' was deterInined froIn the energy calibration, and could be related to the energy of the light particles in the target region, E 3 , using the energy los ses calculated. Several experiInental checks on the calibration and energy losses were Inade. For example, the 1.8 MeV protons used for the solid angle facto r ratio Ineasurement afforded one check. Another - 77 - Figure 16 Alpha and Proton Spectra. These spectra are taken from the two dimensional spectrum of Figure 15. The peaks in the alpha spectrum are not the result of statistics The (see Figure 17 and the text page 79). E counter was not thick enough to stop the highest energy protons, so the lip cutoffl1 corresponds to the highest energy that can be deposited by protons in this counter. This situation occurred only at forward angles and the highest bombarding energies used. - 18 - .. I I CHARGED PARTICLE SPECTRA • • • • • N 0 0 0 0 c: z • • •• • •• ••• 0 N I - ..-. • • • - • ..... • • •• O ~ 1 I I •• ••• •• ...••• • • 16 p cutoff • .......- • •• 0 •• I 0 0 0 PROTONS ... • • -t (J) - • . ... 20 0 9 1ab • • 0 - Ecm= 11.85 MeV • • - • I I 32 E COUNTER - ALPHAS - .. ••.. , Q2,3 ... ·1 . ..e- 48 CHANNEL Q1 ~ ao ~ 6• • 64 - 79 was obtained frol1l. peaks scen in the alpha spectra. Thel:lc W(; re observed at l1l.any different angles and energies and were found to correspond to certain fixed excitation energies in of the alpha spectrum at E crn 28 St. A portion = 11.95 MeV and a 1a b = 20 0 was obtained using the 61 cm magnetic spectrometer (~a = ± 1 ± 4.5 0 ) and the 16 counter array in the focal plane. bombarded a SiO foil target. , ~<I> = An Oxygen beam The alphas were bent by the spectrom- eter and passed through 5.1 mg/cm entering the counters. 0 2 (0.00075") of aluminum before A monitor counter at alab = 45 0 detecting the elastically scattered Oxygen was used to normalize the runs, and relative efftctency corrections of up to 20% were applied to each counter of the array. The resulting spectrum is given in Figure 17. The range of alpha energies covered was (E exc = 8.2 to 16.5 Me V). E Q = 10. 7 to 21. 2 Me V A large contribution to the width of the observed peaks carne from kinematic broadening effects (~e • dE/de = ± 120 keY). The energy positions of the peaks were checked against the counter teles cope spectra denlOnstrating that the energy calibration had a precision of ± 400 keY for the whole spectrum. E3 or ± 300 keY for E exc over On the other hand, the energy resolution of the counter telescope was only about 400 keY for these experiments because of the kinematic broadening of the lines, limited resolution in the 64 channels used for recording the spectra, and straggling. Agreement of the energy calibration as derived from the protons and as derived from the alphas provided still another check that energy losses were correctly computed. - 80 - Figure 17 Alpha Spectrum Taken with These data were taken with a SiD the Spectrometer. foil target and the 16 counter array in the focal plane of the 61 cm spectrometer. The resolution was limited by kinematic broadening due to the large angular opening of the spectrometer entrance slits. Some peaks are shown with appropriate excitation energies. These were used to check the energy calibration of the counter telescope charged particle spectra. •••• I • • e •• \, . I 13 '. ,...: , '. .. 12 MeV I I:!.8 ..."', I 13.1 ... . '. " I 12.2 9 'ab = 20· Eem - . . '... . :'. , 12 I 11.5 I I!.O II (MeV) 160 + 160 .. a + 28Si 14.0 14 .'..: . . . .. '1\..'. ... . ::A. ... .. ... . .'. ,"".... '. 15 ENERGY 10 8.9 9 8 NMR FREQUENCY (Mhz) o·3Oo---------~--~----~--~~--~--~.'--~~--~1-J!~~~'~.L-~'~.~~ 35 40 850 ::) z U) ~ 16 EXCITATION ~ - 82 With the counte r tele scope of Figure 13 only a limit on the number of deuterons could be obtained because of the poor proportional counter resolution. counts for Figure 18 shows the .6E distribution of E count er = 3.3 MeV from Figure 15. energy scale is also shown. An approximate The width of the proton and alpha lines can be calculated assuming a Gaussian distribution of energy losses. The observed FWHM are 25 keY and 80 keY for protons and alphas respectively, whereas the calculated values are 20 keY and 40 keV. At this value of E t the multiple collisions determine the CoWl er energy los s distribution (a Gaussian) t but a Landau distribution (see Moya1 (1955) and Landau (1944}) must be used for proton energies above about 4 Me V, where single collisions appreciably influence the los ses. The expected position of deuterons, tritons and also shown in the figure. 3 He Isis The lack of a definite line at these points indicates that few of these particles are present. limits on the production of dIs, tIs and 3 He Is summing COWlts near the expected lines. Cross section were computed by The tails from the proton and alpha lines obscure any deuterons t etc. present t and in the data analysis all counts were assumed to be either protons or alphas. A second particle telescope was constructed specifically to separate deuterons from protons. The construction was similar to that of the other telescope, except that a 58 J-L (150 mm con transmission counter served to measure mm l 2 in area) sili- .6E and a 3 mm by 110 lithium drifted silicon detector measured E. The thicker .6E cOWlter was essential to obtain a better relative energy resolution so - 83 - Figure 18 Spectrum of t,. E Counts Charged Particle in the Spectra. The number of counts in the two dimensional spectrum of Figure IS at channel. E '" 3.3 MeV are plotted against the t,.E An approximate energy scale based on the expected proton. and alpha energy losses in the proportional counter is also shown. 3He,s The expected positions of deuterons, tritons and are indicated. o o ::> z p J, d t 1 x 1/20 , OF COUNTS , 3He ~E _ CHANNEL 40 + a (keV) 900 • • • ' ••••• •• •••••••••• 60 50 8 1ab =20· l1E 600 SCALE Ecounter t: 3.3 MeV Ecm t: 12MeV SPECTRUM 300 ENERGY o••• . .•••• " ••••••••• "•••••••••30 ••••• 20 10 o ~ 100 o APPROXIMATE +=- I (Xl - 85 the proton line would not obscure the deuterons. Both counters were kept under vacuum to prevent electrical breakdown of the counter bias of 500 V in the target gas. 2.1 mg/c:m 2 S1 (Li) The entrance foil was alu:mlnized :mylar and a 3.4 :mg/cm 2 alu:minu:m foil could be moved before the entrance slit to stop elastically scattered Oxygen. The angular opening was ± 4.9 o and the geometrical factor was <S1L) 900 = (1.23 ± 0.04) X 10 -3 c:m sr. No attempt was made to experimentally check the ratio of this value to the monitor counter solid angle factor. The ~E and E gains were matched to about 0.5% and the pulses then fed into an Ortec Particle Identifier (see Figure 19). of its outputs was the sum of the E One and ~E pulses, and the other was an identifier pulse proportional to (E + ~E) 1. 73 _ E 1 • 73, a quantity e:mpirically dependent only on the type of particle. Deuterons clearly separated from the protons were observed, however a search for at E 3 He and cm 3 H was again unsuccessful. = 11.85 MeV and 9 1a b = 250 that many levels in 30 P The spectrum of deuterons is given in Figure 20. Note are easily resolved, and there is no large increase in counts at the low particle energies characteristic of the proton and alpha spectra (Figure 16). Yields of protons and alphas leading to states of low excitation energy in the residual nuclei, as obtained from the two counter telescopes, agreed within experimental errors. - 86 - figure 19 Particle Identifier Electronics. This setup was used for the solid state counter telescope. It was also successfully employed to separate alphas from protons with the counter telescope illustrated in Figure 13, even though the E and ~E gains were not appropriately matched. COUNTER E COUNTER AE H --....I PREAMP CANBERRA 1416 AMPLIFIER DELAYED SCA DELAYED -....- • AE I (STRETCHER I LINEAR GATE SLOW ~ OUTtUT. ~OLNf· I ISTRETCHER I , E + AE COtNC. i MULTICHANNEL ANALYZER PARTIClE SPECTRUM SCA~'---....J IDENTIFIER OUTPUT ORTEC ~-'=':":"'::-=:-;:---, PARTICLE ENABLE IDENTIFIER J. SCA TIMING, , • i COINC. OUTPUT 1-.§~T~eEl SLOW LINEAR TIMING,. FAST CANBERRA 1416 AMPLIFIER OJ ~ - 88 - Figure 20 Deuteron Spectrum. The solid state counter telescope and the particle identifier were used to obtain this spectrum. It corresponds to the highest bombarding energy and most forward angle of all the deuteron data taken. Note that the number of counts does not strongly increase at low energies in contrast to the spectrum shape seen for alphas and protons in Figure 16. U) o (,) Z ::l I- o 50 100 o . .. •• • 50 • •• • • • .4Ia CHANNEL 100 MANY LEVELS , ..., 29Si+p 3Op • ... .'. ... •••• • ••••• • .....' • 10 dt.2 do 150 rl"'~ ~-9 d4 d3 DEUTERON SPECTRUM 24 MeV a'ab • 25· ••• • •• • Elab II 160 +160 5 Ecounter 15 200 MeV CXI \() - 90 The charged particle data taken using the counter telescope (proportional counter ~E) involved many days of running. Up to 14 angles were taken at one energy with runs lasting 15 nlinutes to 18 hours each. Beam currents were typically 4 to 12 f.La of 4+ 16 O. Counts in each spectrum varied from 47 alphas at E and cm = 6.8 MeV elab = 40 0 , up to 34,000 protons at Ecm = 11.85 MeV and 20 0 • Data Analysis From the spectra taken. angular distributions in the C. M. and laboratory systems were derived and total production cross sections were determined in two ways. The first method involved transforming all quantities to the C •.M. system using a computer program written for the purpose. 1) The analysis proceeded as follows: Energy losses were calculated for the foil thicknesses and gas pressures used in the proportional counter and target chanlber. 2) The energy calibration (E t vs. channel) and energy coun er losses gave the energy of the particle when emitted in the target region~ 3) E 3' for each channel. Knowledge of the bombarding energy E angle in , laboratory elab and E3 pernlitted calculation of the center- of-rnass angle ecm ,of the excitation energy in the cor- responding heavy particle ( 28 Si, 31 P, etc .. ) E exc • and of the conversion factor between the laboratory and C. M. differential cros s sections (C. M. Factor = do- /dS"l) cm / - 91 da/dS'2)lab) froITl relativistic kineITlatics. The three body decays, for which this stateITlent ITlight not be correct, will be discussed later. 4) FroIn m.easured quantities and counts in the spectra, differential cross sections were then computed froITl the relation ~) CITl =~)em • CMF' telescope. ) ( CMF monitor el. s c. . (S in Slab, te~esc<?£e) • ( :telescope) sin 45 « S2L) monitor, 90 0 monitor ) Note that these differential cross sections are integrated over the excitation energy span of the particular channel in the spectrum.. The energy calibration for the alpha spectra was checked at this point by plotting da-/dS'2) against E exc cm fo r several different laboratory angles, as in Figures 21-24. the saIne value of E The peaks in these spectra have exc as observed in the spectrum of Figure 17 taken with the spectrometer. The protons showed structure too, but the peaks were not as pronounced. 5) Differential c r08 s sections for larger intervals of E namely £01' Eexc:: 0-5,5-7.5,7.5-10, etc. exc MeV were , - 92 - Figures 21 - 24 Alpha and Proton Spectra vs. II dO' Eexc. " The values of djl)cm are plotted against the excitation energy, E ,for alphas and protons at E ::: 7.85 and em exc 11.85 MeV. Data from spectra taken at several different angles are presented in each figure to show that the peaks occur at fixed values of E At the lower bombarding exc energies the percentage of particles from these peaks II dO' II increases. Note that dll)cm corresponds to the integrated differential cross section over the particular channel in the spectrum. is also given. The region of extrapolated counts "'C b ~ "'C ....... E o - 0.5 .0 ....... -'".... 1.0 1,/ • •• • '2 2 IOi 6 Ecm CM ¥t- • I 15 I 20 ... .... 10 EXCITATION , =,--"]1 5 ENERGY 20· 7~ ( ... , I 0 (MeV) IC I 1.78 g.s. • • 40- • SPECTRA = 11.85 MeV ALPHA • 6.27 • • •• -6.89 4.61 ••• •• r1 4.97 n ... .... • ... . , .~. EXTRAPOLATED COUNTS • .... • .... :~ ·...:. . 2...· J\.. i • • •• • J4.2 •• • I I .r---.-------r-------,r------y-------r----, I \,() \,01 "'C b 1 I OJ ~ .001 E .c en "- " - .002 20 I 15 ~!l- I : I 7.0 .. 10 EXCITATION I 5 - 4.61 4.97 rI ENERGY • ~ •• • •• • • • • ·fII •.. .' ..•. ' 11 EXTRAPOLATE':} ~ .". COUNTS ~\ • 11.5 ~ 9.8 I 11.0 I. - ·.0 ~!t T Ecm SPECTRA 7.85 MeV eM ALPHA I o (MeV) I 1.78 9.5. • 20° • 40° .. 60° \() +=- I ° I / 20 .. _ -t 't al • • ,• ,. 15 *14\. '. .. ... 70· • 20· _ 40· 11.85 MeV EXCITATION 10 ENERGY 5 -u.. • • ... • 1~"1e ••,: Ecm - eM PROTON SPECTRA EXTRAPOLATED COUNTS } j I.O~ A i E ~ en ...... -... l - 2.0J- ••• • • •...... • • •• • 0 (MeV) I I I \r\. \0 "'C ~b - '"" In ...... ..Q E - 01 .002. .004r { Ctv1 I • 15 I 10 EXCITATION I I ENERGY 5 , I - . taM • 20° • 40° A 60° I I o (MeV) , SPECTRA 7.85 MeV PROTON Ecm = I V+ ..:.,\. I II. •[\. EXTRAPOLATED COUNTS 20 /11' H RECOILS ,. I 0- \() - 97 then computed by summing dcr/dS1) cm from step 4 over the appropriate channels and linearly interpolating the counts at the ends of the interval. 6) Relative errors on the differential cross sections as computed in step 5 were compo sed of: a) statistical errors on N b) an error associated with the variation of the C.M .. telescope and N i • mon tor Factor over the angular opening of the counter telescope (± 3.9 0 ). The change in the C. M. Facto r over this angle was typically 3-12% depending on the excitation energy and laboratory angle. c) an error to allow for uncertainties in the energy calibration. Since the calibrations were believed to be good to ± 0.5 channels, an additional error to the counts Nt 1 was assigned to be half the number of counts e escope in the channel at each end of the interval summed. corresponding uncertainty in E3 The is roughly ± 200 keV. The largest contributions to the relative error were normally the last two, but at the lowest energies the statistical uncertainties on the number of counts Nt 1 predominated. e escope Table 6 gives the results of these calculations along with the relative errors. At several bombarding energies and laboratory angles more than one run was taken, primar!.1y as a cross check between the many running days used to gather the data. Differential - 98 cross sections for each interval in E exc consistent within the appropriate errors. for these runs were always Instead of each individual measurement, weighted averages of such data are given in Table 6. The angular distributions were found to be symmetric about ecm = 90 o within the relative errors in almost all cases (see Figure 25). For identical beam and target particles, they should be strictly symmetric if the computation of the C.M. angle and C.M. Factor is correct (as it is for all two body reactions). For the interval E exc = 0 - 5 MeV the alphas, and to a lesser extent the protons as well, show structure in the angular distributions. The structure is not present at higher excitation energy intervals probably because of the larger number of excited states in these intervals. The protons have a generally shallower angular distribution than the alphas, but both are peaked in the forward and backward directions. Based on the symmetry about ecm = 90 o , too few low energy (close to the detection limit) proton and alpha counts were detected at backward angles compared to forward angles. This was mainly true for the first two or three channels in the particle spectra (E t < 1.5 MeV) coun er and was attributed to multiple scattering. Whenever particles corresponding to a certain range in E in channels 1 to 3 of the E appear spectrum at very backward laboratory angles, the same range of E energy at forward angles. exc exc will give particles of much higher This is for purely kinematic reasons. Since the low energy particles at the backward angles undergo fairly - 99 - Figure 25 Proton and Alpha Angular Distributions. Average differential cross sections for restricted exci.tation energy intervals are plotted for alphas and protons at Ecm = 8.85 MeV from Table 6. The average differential cross section (value of A, see the text page 102 ) from the Legendre polynomial fit is shown for each exci.tation energy interval. In general, the angular distributions are symmetric about ecm = 900 and are flatter at higher excitation energies. ~ - o a:: o (/) CJ') (f) W o t- z o ~ 0- 0- 0 JI .... .01 0 .02~~ I f- .0 >~ ~ • ~ E 0 I~ .D "- <J) ) ~ .25H- I 1 I I I 5 - 7.5 MeV I 1 90- 1 0 - 5 MeV . _ L __ Eexc = I I - - - - ~ - ~ .... - 0- o .005 I- o .01 o .05 o I- .06 f- o ... .05 ~ eM ANGLE teO- n I I I t I I I II - Eexc = hi f I I III I II I Eexc = 7.5 - 10 MeV II! I ! III I I ,II Eexc = 10 -12.5 MeV ..., i -i , ~ - - Ecm "" 8.85 MeV III I III 1 I I II I Eexc = 12.5 - 15 MeV I I I Jlflll I I I PROTONS o. T ; T y' I I I I ,I f I I Eexc 9(f fIi I I I = 0 - 5 MeV I I I I I - - - - - - - /" I 180- I I I - I I Ii ~ = 5 -7.5 MeV = 7.5-10 Me) f J I I I Eexc Eexc tfflIl1 II I I f II Eexc = 10-12.5 MeV IJIIIII 1 I Eexc = 12.5 -15 MeV llItl11 ~ ALPHAS I 8 I--' - 101 strong multiple scattering, whereas the higher energy ones do not, the angular distribution may be distorted (the backward angle data then being incorrect). The size of the loss of counts is difficult to calculate theoretically because of the complicated detection geometry and the presence of material all along the path from the target to the E counter. Outside the entrance slit to the counter telescope the particles lost by multiple scattering can be compensated by other particles scattering into the path through the telescope. However, multiple scattering in the 10,000 A nickel entrance foil or Argon gas may result in a net loss of particles detected. The counter telescope entrance slit could prevent compensating particles from scattering into the telescope. As suming that the Argon gas is concentrated at the nickel entrance foil and that the multiple scattering angular distribution is Gaussian (see Marion and Zimmerman (1967», the estimated loss of particles is 15% for 2.5 Me V. Intervals in E E exc t"'" 1.2 MeV and E p,coun er a,counter which contain counts from the first three channels in the particle spectra were not included in Table 6. The counts analyzed by this method were assumed to be totally the result of two body exit channels (31p + p, 28 m + a or 30 p + d). Particles from a three body breakup may have been incorrectly analyzed for obtaining production cross sections. If the three particles are ejected "instantaneously" after the reaction with no interactions between them, the analysis is correct. dence of ecm t E cm This follows from the depen- and the C. M. Factor - 102 - C.M. Factor ::. only on Slab' E system. lab dO"/dS1) cm dO" dn)lab d(cos Slab) = 7 = d(cos S cm'' and the velocity of the center-of-mass of the In the absence of final state interactions, these quantities do not depend on the variables of the other particles emitted. How- ever, in the pres ence of such interactions the quantities ,E C. M. Factor may be incorrect. 16 0 + 16 0 - 30 Si + 2p, S cm cm • For example. in the reaction if there is a compound nucleus formed which first emits one proton and later emits the second (the final state 30S1) t then the interaction being between the second proton and center-of-mass velocity for the second "evaporation" Is not the same as the center-of-mass velocity for the 16 0 + the program would derive the wrong values of Factor for the second particle emitted. 16 0 system. acm ' Hence Ecm t and C. M. The assigned exdtation energy E exc = Z· 1 E 16 +Q O. lab g.s. was not correct for the resulting nucleus 30 - E cm 51. Total cross sections for each interval in E exc were com- puted by fitting the angular distributions with Legendre polynomials fT production = 4'JTA - 103 Only even L values were used since the bombarding and target particles were identical. with k The number of terms taken was 5 or k - 2. the number of different angles. whichever was less. value of A The and its error from the fit also appear in Table 6. When- ever there were only three or fewer angles. the angular distribution was taken to be isotropic and an average was used for the differential cross section A. The assigned error on such values of A to cover the individual values of da-jdn) was larger. was taken or to be 20%. whichever cm For conditions typical of cases where data at only a few angles were available, nam.ely high excitation energies and low bom.barding energies, the angular distributions have a typical variation of ± 10 - 300/0 ove r all angles. The 20% error on A above was assigned from this variation in da/dO} cm mentioned with angle. To obtain total production cross sections, the number of low energy particles stopped in the target chamber gas. foils and proportional counter gas, and therefo re lost~ had to be estimated. This was done by making a linear extrapolation from Ntelescope (in chan- nel 2 or 3) counts at E3 counts at (channel 2 or 3) to The number of counts lost was taken to be addition, Hydrogen recoils from 16 0 + 1H (N 0 ext rap ± N E3 = o. ext rap ). In elastic scattering were identified as a contaminant at forward laboratory angles and lower bombarding energies (for an estimate of the Hydrogen contamination in the target gas, see the Elastic Scattering Section). these protons have a maximum energy of E lab Kinematically = 5.3 MeV at a 16 bombarding energy of 24 MeV and a maximum laboratory angle of 0 - 104 90 0 • The Hydrogen recoll peak was eas lly identifiable in the proton 16 spectra. and the number of protons from 0 + 16 0 reactions be- neath the peak was also determined by a linear extrapolation. From the extrapolated counts and counts in the spectrum above the hl.ghest interval in E exc was computed. , the differential cross section dO'/dU) The values 41TA and 41T do- IdO) marized in Table 7. cm, e xt cm.extrap rap are sum- The errors given include the fitted or estimated errors on the average differential cross sections, a 2% error on the Mott scattering cross section, an estimated 15% error for losses by multiple scattering,. and a 4% error for the solid angle factor ratio. The total production Cross sections are also given (see Figure 26). As an independent check on the precision of these cross sections, the data at 4 energies were analyzed using a different method. Laboratory cross sections were computed from ~) cm • (Sin el~bt telescope sin 45 el. sc. with N tot = N telescope + N extrap • • • CMFmonitor <OL) monitor! 90 0 ) • ( <nL) telescopt, 90 0 ) ( • Ntot ) Nmonitor The same errors as above were applied, except that in this case the variation of the C.M. Factor over the angular opening of the counter telescope and the energy calibration errors, 6c}. did not apply. At least 9 angles were taken at each of the energies and the results are given in Table 8. The total - 105 - Figure 26 Product.i.on Cross Alphas Sections for Protons, and Deuterons • The measured production cross sections and total errors are plotted as a function of E from Table 7. Smooth lines em have been drawn through the alpha and proton points. Energy losses have been taken into account and produce an overall uncertainty in the energy scale of ± 50 keV (C.M.). - 106 tOOO~--~----~--~----~---T----~--~ 500 200 100 ~ E 10 I z 0 t- o d l&J (f) 1.0 I (f) (f) 0 Q: 0 0.1 CHARGED PARTICLE FROM YIELDS 16 0 + 160 10 II .01 .001 6 7 8 9 eM ENERGY 12 (MeV) - 107 production cross sections were computed £I·orn a Legendre polynofnlal fit to the data do- dn lab = APO(cos Slab) + BPi + CP z + ••• 0- where all L Slab = 90 o production = 4n-A values up to L = 5 were included (no symmetry about is required). The production cross sections and the total errors are also given in Table 7. The agreement between the total cross sections from Tables 6 and 8 demonstrates that errors from the possible incorrect treatment of the three body reactions in the first method do not seriously affect the total production cross sections obtained. applies to any deuterons (or 3 He or 3 H The same conclusion counts) included in the charged particle spectra which would not have been analyzed correctly. Thus the cross sections at E crn = 6.80 and 7 .. 32 MeV are also ex- pected to be correct, even though data were taken at only a few angles. The production cross sections (for pIS etc.) are an upper limit to the actual reaction cross sections (for p + 31p, 2p + 30 5i , etc.). A lower limit is obtained by counting all protons or alphas with energies below the respective three body cutoffs as though they all came frOITl three body exit channels. (see Table 9, lower limit I). This was done at 4 energies A better estimate of the lower limit - 108 used the same procedure except that counts in the peaks of the alpha and proton spectra {see Figures 16, 17} were taken to be from two body reactions, giving the cross sections listed as "lower Bmit II. " The upper limit was reduced by subtracting out known three body decays. This is discussed in the Conclusions. - 109 ACTIVATION METHOD Introduction Cross sections for three exit channels in 16 0 + 16 0 reactions were measured by an activation method with 21T counting geometry. The nuclei 16 O{ 16 31 O,pn) Sand 30 P 30 P from 16 O( 16 O,n) 31 S, 16 O( 16 O,d) 30 P and were collected on a catcher foil on the surface of a f3 particles plastic scintillator. The beam was then turned off and from 31S and 30 p were detected in the scintillator as a function of time. The decay curves were analyzed using the halflives of these nuclei to separate the two activities. other Unfortunately, the presence of f3 activities from undesired reactions compllcated the analysis. Expe rim ental The experimental setup is shown in Figure 27. The 16 0 beam was passed through slits and a 1.1 cm diameter hole in a 5 cm thick lead block before hitting the SiO fall target. The lead shielded the scintillator from radioactivity on the defining slits. The heavy reaction products passed through the SiO foil and were collected on a gold covered aluminum foil in front of the scintillator. There were alternate bombarding periods when the photomultiplier was turned off, and counting periods when the number of j3' s from the radioactive decays were measured as a function of time. The combined beam intensity and target thicknes s was monitored by observing 16 0 + 16 0 - 110 - Figure 27 Experimental Setup for the Activation Method. The activation measurements were made by first bombarding the SiO foil target with the 160 + 160 160 beam. Heavy nuclei formed in reactions passed through the target and were collected on the aluminum catcher foil. Elastically scattered particles were counted in the solid state detector at 4SO. Then the beam was turned off and ~ particles from radioactive reaction products on the catcher foil were detected with the Pilot B scintiD_ator. Lead was used to shield against room background and radiation from the entrance slits. - III - "..Jo• 8w - 112 elastic scattering at ing Section. ecm = 90 0 as described in the Elastic Scatter- Typical beam currents were 300 to 500 na of 0 4+ , and total tim.es per measurement were 10 n1inutes to 5 hours. The targets used were 20 - 40 I-'- gm/em about 150 - 350 keV thick to 18 MeV 16 0 by evaporating optical grade on a glass slide. 2 SiO foils and were beams. They were made SiO onto a layer of 10 I-'- gm/cm 2 BaCl The amount of SiO deposited was estimated using a quartz crystal thickness monitor. Foils were then floated off in distilled water and mounted on tantalum target holders. The target thickness was measured with the 61 cm double focusing magnetic spectrometer. A very low intensity and diffuse 160 beam was passed through a pinhole in 0.012" tantalum and then analyzed by o the spectrometer set at 0.5 - 1.5 • When the between the pinhole and the magnet, the 16 0 SiO foil was placed beam had a lower energy which could be directly measured on the spectrometer. To measure the target thickness, the beam was first scattered from a nickel foil or from Argon gas in the differentially pumped gas target into a detecto r. Then the S10 foil was placed before the nickel or 16 Argon and the energy shift in the scattered 0 gave the target thickness. At the lowest bombarding energy, mum recoil tively. The 31 Sand 30 P E lab = 15 MeV, the mini- energies are 4.7 and 4.4 MeV respec- SiO target was < 3.2 MeV thick (estimated from Northcliffe (1963)) to such nuclei created at the front surface of the foU. Experimentally, no difference in yield was noted for the - 113 31 Sand 30 p different thickness foils used, confirming that the were not stopped before reaching the detector. The maximum reco i1 angle of was 14.0 0 31 S was 11 • 5 0 with respect to the incoming beam direction. deflections of 1 o could occur from 31 'Y decay of and of 30 P Maximum S or excited states while in flight, and the multiple scattering angle for 2 .1 0 <e >z < 24 • these nuclei in the SiO foil was These effects suggest that the heavy nuclei should be mostly confined to a cone of half angle < 30 0 • In the experiment, the aluminum. foil and scintillator subtended a cone of half angle 33 o as seen from the target. How- ever. the yield was checked as a function of the half angle subtended o by the scintillator and catcher foil over a range of 16.5 to 36.0 • Total 13 yields were found constant within 5%. Furthermore, it was experimentally demonstrated that more than half the radioactivity was emitted within a cone of half angle 6.2 0 • A cylindrical disk of tantalum. 0.8 cm in diameter by 0.4 em thick was placed at the center of the catcher foil. The disk was thick enough to stop all from radioactive nuclei deposited on it, and the by about 50% with this arrangement. and 30 p ~ i3 particles yields were lower Therefore, almost all 31 S were collected on the aluminum catcher foil. Commercial 0.0015" aluminum foil with about 0.6 mg/cm of gold evaporated on its surface served as the catcher foil. Z It was used as a light reflector for the scintillator and a beam stop as well. AI 0 layer on the aluminum surface is typically 40 - 100 A Z 3 2 16 (1.5 - 4 IJ.gm/cm ) thick. The gold insured that the 0 beam had The - 114 lost sufficient energy by the time it reached the A1 0 80 that the 2 3 16 16 Coulomb barrier prevented background counts from 0 j ° r(!a.ctions. Background activation runs with the beam in but the target out were taken after every target- in run (see Figure 30). An Oxygen buildup in the catcher foil from bombardment with the beam contributed to the background. Four hours of continuous bombardment with 300 na beam would build up 7 X 10 15 of the amount of Oxygen in a 20 p. gm/ cm atoms of Oxygen, or 10% 2 SiO foil. Buildup of hydrocarbons from the pump oil and of other substances on the gold surface also might add background counts. j3 To minimize background counts from these sources, the catcher foil was changed periodi- cally and measurements were made at decreasing bombarding energies. Higher energy 16 0 beams penetrated deeper into the gold and aluminum and could not be reached later by lower energy beams. Also, a liquid Nitrogen trap was installed beneath the SiO foil to decrease Carbon buildup. The scintillator was Pilot B optically bonded to an RCA - 8575 photomultiplier with Dow Corning #20-057 Optical Coupling Compound. The scintillator was 1.4 cm thick by 5.1 cm in diameter. The photomultiplier was chosen to fl.t inside the 61 cm scattering chamber, where the measurements were taken. The mounting of the scintillator on the photomultiplier was checked under vacuum for the presence of air bubbles which would affect the light collection efficiency. The scintillator and photomultipHer were shielded with - 115 1.2 to 2.5 cm of lead, and the whole assembly was mounted on one of the moveable arms in the scattering chamber. On the other arm was the monitor counter (usually a heavy ion surface barrier counter 75 1.1 thick and 100 mm typical solid angle of 3 X 10 target of ± 0.7 moved to 8 cm 0 • -4 2 in area) with a sr. and angle subtended from the Before each series of runs the detector was = 90 o relative to the beam by maximizing the yield of elastically scattered Oxygen. shown in Figure 28. A typical monitor spectrum. is The desired counts could be easily separated from the silicon recoils. The counts in the various peaks indicated that the ratio of Silicon to Oxygen in the target was nearly 1 to 1 and 1 remained essentially constant after "2 hour of continuous bombardmente The desired activities were formed by: 16 0 +16 0 _31 S + n _ Q E (3 +,max Tl 1.448 MeV 4.42 MeV 206 sec 3.22 2.50 min 30 p + d - 2. 412 30 p + P +n -4.636 ~ The ll1ajor contami.nant activity had a halflife of about 4 seconds and was probably 27 Si formed by -0 0 422 3.79 4.2 sec 27S1 + a + n -1.583 3.79 4.2 sec 29 p +t -1.478 3.93 Other possibilities are 16 0 + 16 0 - - 116 - Figure 28 Monitor Spectrum for This spectrum was taken at 160 + SiO. E:iab = 20 MeV, elab = 450 and shows that the desired 160 + 160 elastic counts were easily separated from 160 + 5i elastics or recoils the text page 115). (see - 117 - • • • o • co ~ • • •• • • .- '0 • • en U) U CD a:: • • •• ..J W 0 1ft 0 :l a:: 0 w Q. 0 .-en en Z a: c( ::E: ~ I- Z Z 0 0 -Zl- !e0 •• :E • •• 0 0 5000 COUNTS - 118 Carbon contamination and subsequent Carbon buildup on the SiO target were suspected to be the main causes of the undesired activity. The 4 second activity yield varied for different target foils and increased as a function of time for a particular foil, suggesting that it did not come from 16 0 + Si reactions. Measurements of the 12C (16 0 ,n) 27 Si cross section were made on Carbon fol.1s with the same apparatus. If the 4 second contaminant activity was completely from this reaction, it would indicate a typical Carbon thickness of 2 about 0 .. 5 J.L gm/cm • The contaminant yield was somewhat decreased by installing a cold trap beneath the SiO foil. Oxygen bombardment of natural Silicon could yield several 13 activities with halflives of seconds to minutes. Eth 14 res h ld< 18 MeV (lab) are: 29 0 Those with 17 P(Tl = 4.4 sec), 2 0 (71 sec), 15 0 (124 sec), and 30 p (2.50 min). 29 p (formed by a proton transfer to 28 Si) F (66 sec), The halflife of is very similar to that of 27 Si, and both would have been considered as the 4 second activity in the decay curve analysis. However, significant increases in the relative amount of this activity were noted as a function of bombard- . 12 16 27 Lng time on a glVen target, indicating that C ( 0, n) Si was probably responsible. There was no evidence for 13 emitters of about one minute halflife in any of the decay curves. The other two activities, 15 o and 30 P, were quite serious since they could have given the wrong cross section for duction. The reactions forming them would be: 30 P pro- - 119 16 0 16 0 + 28 Si _ 15 0 + 29 S1 _ 14N + 30 p Q = -7.2 MeV Ethreshold = 11.3 MeV -8.9 14.0 + 29 Si _ 15 0 + 30 Si -5.1 7.9 + 30 p -6.5 10.1 15 0 + 31 Si -9.1 14.0 _ 16 0 + 30 Si _ 15 N A conunercial 90 .... gm/cm 2 (tOOO.A) nickel foil oxidized by heating it in a pure Oxygen atmosphere was used as the target in some runs, . 30 At E cm = 12 MeV the cross section for production of P and 31 S agreed with the values obtained with SiO targets to within 10% • Furthermore, the Coulomb barrier for 160 + Si reactions is roughly 20 MeV C. M., which corresponds to bombarding energies of about 30 MeV. to 30 P The presence of an activity with a halflife similar was detected at lower bombarding energies. The (3 end- point energy for this activity is less than that for 30 p , and it was tentatively identified as reaction to Silicon. 15 0, possibly from a neutron transfer Although charged particle reactions will be greated suppressed far below the Coulomb barrier, there are no such barriers to be penetrated for a neutron transfer reaction, so they may have measureable yields there. A schematic of the electronics is shown in Figure 29. The sequence timer turned the beam on and off by way of a beam deflector magnet. The photomultiplier high voltage had to be turned off during bombardments, otherwise there would have been electrical breakdown from positive ion feedback in the tube due to the high count - 120 - Figure 29 Electronics for the Activation Method. All activation data were taken with basically this system. At tinYas, an internal (to the analyzer) time base generator was used to step the decay curve analyzer from one channel to the next. For very long bombardment and counting time runs the cycle was controlled manually and the sequence timer was not used (see the text page 119 ) • BIAS r?--1 PREAMP~ COUNTER MONITOR BETA DETECTOR II PM- r= IPREAMP SWITCH ON -OFF I H.V. +1300 V ~~NEERf.f~~ {3 SPECTRUM AMPHsCAI .. iSTRETCHERI EXTERNAL .. iSCALERI DECAY CURVE f-' N ANALYZER I f-' ~ RIDL START • ISE~:E~E ,....- RIDL ANALYZER -4 DE~k~~~~ON I BEAM - 122 rates. The photom.ultipller did not recover during the counting period unless it was turned off during the beam. on part of the cycle. Bom.bardm.ent and counting tim.es were varied. 31 The 8 and 27 8i lifetim.es are quite sim.i1ar, and at higher energies their yield is substantially less than the 30 P yield. Therefore bom.bardm.ent tim.es were typically 3 seconds and counting tim.es ranged from. 20 to 55 seconds in order to im.prove the data on the cross section. 16 O( 16 O,n) 31 S Longer bom.barding tim.es (60 - 180 sec) and count- ing times were used at lower energies to obtain the 30 P cros s sections. For the tim.e sequence spectra a lower level discrim.inator was set on the photom.ultipller pulses to reduce room. background counts. Usually the cutoff was above the 511 keY annihilation radi- ation Com.pton edge. Corrections for the true beta counts excluded were m.ade when cross sections were com.puted. Discrim.inator pulses were fed into a RIDL 400 channel analyzer in the tim.e sequence m.ode to give the decay curve. The dwell tim.e was 0.6 sec/channel with the analyzer internal oscillator, or 0 .. 25 to 4.0 sec/channel with an external oscillator. A typical decay curve and the corresponding background is shown in Figure 30. In addition to the tim.e sequence spectra, beta spectra were also taken during m.ost runs (see Figure 31). - 123 - Figure 30 Beta Decay Curve and Background. The beta decay curve with the target in and the corresponding curve for the target taken out of the beam were taken at E = 11.95 MeV. The curve with the background subtracted cm shows three activities (see the three straight lines drawn through the points). The bombarding time was 3.1 seconds, the counting time was 50.3 seconds, and the dwell time per channel was 0 .25 seconds. The curves represent a total of 20 cycles each (see the text page 122). o 40 t 70~ 1001- 400~"" 1000 t700'" • IN . • .... _.". ; . ...- I CHANNEL 100 ~ l NUMBER '..'..:........ 0..., " , ' •• '. ' .. . ' .,:.. TARGET OUT (BACKGROUND) ,. "I, _.".... ~: ... -.... ,. TARGET I\._'..".".._."".. :."".-....~,_,.I.',~•..,.,..~ • • ....."" •• .,~, .... • •...... " "'"'.... 4000~1--~----~--~--~----~--~--~ ~_ .:.. • ....... _e. 100 EOIII = 11.95 MeV CURVES 110+ 160 DECAY (0.25 seconds / channel ) o ~~ eI) ~ BACKGROUND SUBTRACTED ~ ~ I'\:) I f-' - 125 - Figure 31 Typical Beta Spectrum from 160 + 160 • The spectrum of counts from the plastic scintillator used in the activation measurements is shown for E = 9 MeV. A low em energy cutoff was necessary to discriminate against the gamma background (see Figure 32 and the text page 122). - 126 - ~ ~ :;:) ... 0 ~ .... a. U '" 1ft + 0 « - ... ~ -0 -0 III m o o ~ • CO II •• ~ .... u • •• • I • , ••• :, • • • •• • • • • •• • • • \ ••• •• •• • . • 1000 COUNTS •• •• • ,•• • I • • ., •: l ... ...z Z <t u % oI.f') - 127 Data Analysis A number of corrections had to be applied to derive final cross sections. The general expression used in the analysis follows: (# # radioactive) = 16 0 in). ( nuclei formed per sec • # 160 elaStiCallY) ( scattered at ecm = 90 0 (# 16 0 tar ets) • (cross seztion) • per cm in cm 2 (Time in) sec = NMON = (# 16 0 in) • (If 16 0 tar 2ets) • per sec per cm 60mon) ( dU") 2) • ( in sr • dn el. in cm jar • lab • (Time in) sec • Therefore U"TOT # radioactive) • ( nuclei formed NMON # radioactive ) where ( nuc 1e i £orme d was determined from # radioactive ) NCOUNTS:::. ( nuclei counted at end of bombardment (# radioactive ) = nuclei formed • (T!.m!.n g ) . ( Effic!.enc y ) Correction Correction • • (!3Correction. spectrum) - 128 The timing correction allowed for the nuclei fornled which decayed before the end of bombardment. It could also correct for deviations froni complete equUibrl.unl in the number of 30 p on the catcher foil. 31 Sand However. at least two or three cycles were taken before measurements were actually made, so corrections for nonequilibrium amounted to < 10% and they were not actually applied. The expression for the timing correction was Total # formed "ftatend of bombardment = T IT ) -T IT -T (1 - e o T c (1 - e O ) where T = mean life of the activity, cycle, and T c T o = bombardment time per = total time per cycle. The efficiency correction allowed for the positrons emitted but not absorbed in the scintillator. Even with a very large diameter plastic scintillator, only half the positrons would have been counted (2'1r instead of 4'1r solid angles). In addition, some more lost by going through the catcher foil. ing the 2'1r 141f factor) !3's were The total correction (includand was estirnated to be about a systernatic error can be associated with it. The !3 spectrurn correction allowed for counts rnissing in the decay curve because of the discrirninator setting. Its value was estirnated using a good statistics beta spectrurn (with background subtracted) at E cm = 12 MeV with a very low discriminator setting. The energy calibration was deterrnined front '( spectra of 22 Na, - 129 ThC" and 207 Bi. 31 activity t Starting with the highest 13+ endpoint energy S, a Fermi curve was fit to the high energy tail of the spectrum and subtracted off. Curves for 27 Si and 30 p successively subtracted in the same way. were used to estimate the f3 were These fitted curves spectrum correction. Note that it is different for each activity because of different 13 endpoint energies. The summed fitted and experimental curves used are shown in Figure 32. The areas differed by 20% with too many low energy counts experimentally. The 12 C( 16 O.n) 27 Si reaction on a Carbon foil produced a nearly pure 27 Si beta spectrum. The same pro- cedure was used on this spectrum., and the fitted and actual areas again differed by 20%. The excess low energy counts in the spectra were probably real 13 particles that had not been stopped in the scintillator because they were scattered out. or particles that were travelling nearly parallel to the scintillator surface and lost energy in the catcher foil before hitting the Pilot B plastic. corrections for the data varied from 0.7 - 330/0 for 1.5 - 360% for 30 P. j3 spectrum 31 S and from They could be estimated fairly well; this was demonstrated from the variety of discriminator settings giving agreement of cross sections within experimental errors (except for the low energy 30 P data). The number of radioactive nuclei left at the end of bombardment, NCOUNTS, was determined from the decay curves. First background counts were subtracted from the decay curve. N = (N Decay - N Background) ::I: -IN.Decay + N Backgroun d • - 130 - Figure 32 Beta Spectrum and Fi tted Curve. The experimental points are from a good statistics 160 + 160 beta spectrum with background subtracted at E :: 11.95 MeV. cm 31 The theoretical curve is the sum of beta spectra for S, p 30 and 27Si fitted to the high energy end of the observed spectrum (see the text page 129 for details of the fitting procedure), and was used to estimate the ~-spectrum correction. CIt ...Z oc n o o o w o o ~ ,,/~#~ 2 100 ECM BETA 3 0 + 160 SPECTRUM 4 200 = 11.95 MeV 16 ENERGY CHANNEL BETA , 5 (MeV) ~ I ~ - 132 During the background measurement with the beam in but target out it was attempted to keep the beam intens ity constant at all times. However, there is an error associated with the background subtraction because the beam intensity may have changed between the target-in and target-out runs. A three parameter least squares fit was made for N as a function of time, assuming three exponentially . 31 30 decaymg components with the known halflives of S, P The fit gave NCOUNTS for each activity_ sufficient to fit the data. 27 and Si. Two activities were not Since the backgro und was subtracted, the value s of NCOUNT S corresponded to reactions on the SiO target only, and not those on the catcher foil. Results The contaminant reaction on a 20 \.L gm/cm 2 16 0 + 12 C - 31 Si + n was studied Carbon foil to estimate the amount of Carbon necessary to account for the observed 4 second f3 activity. also used to estimate the f3 spectrum correction factor. monitor counter was left at Slab = 45 o It was The to the beam and the 16 0 + 12 C elastic scattering was used to no rmalize the results (see Appendix I). Total cross sections obtained are given in Table 10 and Figure 33. These data indicate a layer of Carbon about 0.5 \.L gm/cm 2 was present on the SiO target fons. The final cross sections for production of 31 S and 30 p given in Table 11 and Figures 34 and 35. energies are estimated to be ::t: The uncertainties in 50 keY C. M. from the energy are - 133 - Figure 33 Cross Sections for 16 0 + 12C -. n + 27si • The cross sections and total errors from Table 10 for 12C (16 0 ,n) 27Si measured by the activation method are plotted. A smooth curve is drawn through the pOints. Energy losses have been taken into account, resulting in an overall uncertainty in the energies of % 40 keV (C.M.). - 134 - lOO~--~-----r----~----r----'-----r--~ 70 40 10 - .Q E z 0 IU lLJ en en en 0 a:: u CROSS SECTION FOR 0.1 160 + 12C .... n + 27Si .01 .OOI~--~-- 12 14 ________4 -_ _ _ _ 16 18 160 LAB ~ _ _~ _ _ _ _~ _ _~ 20 ENERGY 22 24 (MeV) 26 - 135 - Figura 34 Cross Sections for 160 + 160 - n + 31S. The cross sections obtained by the activation method for 16 0 (16 0 ,n) 31S are plotted with total errors from Table 1I. A smooth curve is drawn through the points. A substantial fraction of the error results from the difficulty in separating 31S and 27Si in the decay curves. Energy losses have been taken into account and produce an uncertainty in the energy of each point of ± 50 keV (C.M.). - 136 100~--~----~--~----~----~--~--~ 70 40 10 CROSS SECTION FOR 160 + 180 --. n + 31S ..a - E z ..... o (,) l.&J CJ) CJ) ~ 0.1 0:: (,) .01 .00I~--~--------~----~--~--------~ 7 8 9 eM 10 ENERGY II 12 (MeV) - 1)'1 - Figure 35 Cross for 160 + 160 --d + 30p Sections or p + n + 30p • The cross sections obtained from the activation method for the production of 30p from 160 + 160 reactions are plotted Wi. th total errors (see Table 11). The values below E = 8.5 MeV are less certain because of a background em activity with a halflife similar to that of JOp (see the text page 119). Energy losses have been taken into account and produce an uncertainty in the energy of each point of ± 50 keV (C.M.). Also plotted are the cross sections for production of 31 s, neutrons and deuterons at E = 12 MeV. cm For a discussion of these, see the Neutrons Section (page 141 ). - 1.38 - 100 50 20 - 10 30 p d~b,S ACTIVITY .0 -- E ACTIVITY z 0 ~ (.) 1.0 d~ lLJ (/) (/) (/) 0 ~ 0.1 NEUTRON AND DEUTERON YIELDS FROM 160 +160 .01 .001 ____ ~ 7 ____ ~ __ ~ 8 9 eM ____ ~ __ 10 ENERGY ~ II ____ ~ __ ~ 12 (MeV) - 139 losses in the target foils. Errors on all three sets of cross sections consist of: A) Errors on the beta spectrum corrections :I: B) Tirning correction uncertainties ± 12 % C) Efficiency correction errors :I: 10 % D) Meas urement errors on the monito r solid angle :I: 5% E) Elastic scattering cross section errors :I: 2% F) Statistical uncertainty on NMON <3% G) Errors on background subtraction from an incorrect arnount of beam during the background run or errors resulting frorn changes in bearn intensity during the run caus ing a change in equilibriurn concentrations of 30p or 31 8 (estirnated) :I: H) 10 - 20 % 5 - 20 % Least squares fit uncertainties for . NCOUNT8 At higher energies the errors are generally larger for than for 30 p because it was difficult to separate the in the decay curves. The yield of of discrbninator cutoff above E cm " 30 31 8 and 31 8 278i P" did not change as a function = 9 MeV, so it was concluded that there was no contaminant activity with a halflife of about 2 to 3 minutes with a sizeable yield cornpared to the actual 30 p these energies. yield at The longer lived activity was studied with very high discriminator cutoffs, as well as the usual cutoffs, and with long bombardrnent (T E crn o 0< 3 min) and counting times = 8.45 and 7.95 MeV. for forming 30 P (T c = 10 rnin) at At the former energy the cross sections agreed at larger cutoffs. but increased with lower - 140 cutoffs, thus indicating the presence of a contaminant activity with a 2 to 3 minute halflife but lower f3 At E cm endpoint energy (such as = 7.95 MeV only a limit on the crOBS section could be obtained (8 ee Table 11). The 31 S eros B sections did not exhibit variations with discriminator cutoff. Average values of the cross sections at each energy are also given in Table 11. 30 P the 15 0 ). Note that the crOBS section falls much faster with decreasing energy than 31 S cross section. - 141 NEUTRONS Introduction The cross sections for the production of by counting 30 P as measured P particles. and for production of deuterons as measured with the counter telescope, differ by a factor of 11 at E cm = 12 MeV and a factor of 9 at 10 MeV. The difference is attributed to three body reactions. and as a check, a measurement of the neutron yield was performed at E cm = 12 MeV. Dis regarding exit channels with large negative Q values on the basis of Coulomb barriers to be penetrated, the most important modes of neutron production should be __ 30 p + p + n -- 27 Si + a + n The '( ray spectra taken indicated that other exit channels are negligible and that the 31 S yield. 27 Si yield was probably smaller than the Since a certain amount of Carbon contamination cannot be avoided when using foil targets t the reaction must also be taken into account. 16 0 + 12 C - 27 8i + n The activation data showed that Carbon buildup on the target was sufficiently slow to keep the neutron yield from this reaction lower than the yield from E cm 31 8 +n at = 12 MeV for many hours. In addition, a liquid Nitrogen trap - 142 was used at the entrance to the target chamber to reduce Carbon buildup. If the cross section determinations from either the radio- activity measurements or from the deuteron (charged particle) data were incorrect, and all 30 P were formed in the 30 P + d exit channel, then the nuznber of neutrons would be at znost 2 or 3 tiznes the nUInber of 31S forzned at E 16 was produced znai.n1y by be 11 to 13 tiznes the 31 0 ( 16 czn = 12 MeV. However, if 30 p O,pn) the nUInber of neutrons should S yield. Even with the usual uncertainties in measuring absolute neutron cross sections. the large factor between the two alternatives made the experiment feasible. It was concluded frozn the results of the neutron zneasureznents that both eros s section deterzninations are consistent and that 30 P is znainly produced by three body breakups. Experiznental A SiO foU target. siznilar to those eznployed in the activation zneasureznents. was boznbarded with a 24 MeV 16 0 beazn. The target thickness was 210 ± 60 keV (lab) (see the Activation Method Section, page 112). The low detector efficiency and difficulties in localizing the target region for taking angular distributions prevented the use of the gas target. The target chaznber was 10 czn I. D. with 3.2 mm thick brass walls. As usual, the cross section was nor- znalized to the Mott scattering at Slab = 45 with solid angle 0 using a znonitor counter - 143 dn MON = (3.6 ± 0.3) X 10 -4 sr. This value was obtained from purely geometrical measurelnents. A correction for the finite beam spot size « 2 rnrn square) to the monitor counts was estimated to be ~ 10 %. Precautions were taken to reduce the neutron background as much as possible. In addition to shields of boron loaded paraffl.n and cadmium against neutrons produced upstream from the target chamber, there were no slits or collimators near the target. the beam was first focused on slits 10 m from the target.. Instead, Passing through a magnetic quadrupole about 4.7 m from the target, the beam was then focused to a 1 X magnified image on a piece of quartz at the back of the chamber. The beam stop during the actual measure- ments was not the quartz, but a piece of tantalum with a Jayer of gold evaporated on it. The choice of detectors was limited by the large y flux. A standard long counter, similar to the shielded counter described by Hanson and McKibben (1947), was chosen because of its low y tivity and fairly flat neutron response (see Figure 36). sensi- The angular distribution of the neutrons was taken at a constant distanc e of 26 cm from the target to the front face of the long counter's inner wax cylinder. The neutron counter efficiency was determined with a "calibrated" (to about ± 10%) Pu-a-Be source in the place of the target. - 144 - Figure 36 "Long Counter" Response Neutron and the Predicted Spectrum. The response of a standard "long counter II for neutron energies up to En = 9 MeV was taken from unpublished data in Allen (1960). An extrapolation up to using an equation fitted to this data E = 18 MeV was made n (see page 150). The neutron spectrum calculated on the basis of a compound nucleus model is also shown (see the text page 150). Both were used to estj~ate a correction to the measured neutron production cross section to allow for a non-flat response for the "long counter". - 145 LONG COUNTER RESPONSE >u z ----- - w U I.J... I.J... W W > ~ 0.5 -.J --- - -- -- w 0::: TRUE EFFICIENCY RELATIVE TO EFFICIENCY FROM A Pu - a - Be SOURCE °O~----------~5-----------1~0----------~15~--------~20 Eneutron (MeV) OM. NEUTRON SPECTRUM Eem = 12 MeV w > i= « ...J w Q: °O~--------~5~--------~~======~--1~5----------~20 - 146 This source was tested against a "calibrated" (again to about :I: 10%) AC-Q-Be source and a 40% discrepancy in the number of neutrons detected by the long counter was found. From an average of the two sources, and the number of neutrons counted, the effic I.ency was Relative efficiency = Absolute efficiency • -IIdQ" = (1.10 :I: 0.22) X 10- 4 • 411' The uncertainty was as signed from the source calibration. However, the detector response was not perfectly flat, and the neutron spectrum from the reaction did not duplicate that from either source t so a correction to the efficiency had to be estimated. Following each measurement, a background run without the SiO foil was performed at each angle to allow for the nonisotropic neutron background. The beam intensity remained approxiInately constant throughout the experiment, and counting times ranged from' 10 to 25 minutes. The low count rate relative to background pre- vented lower energy measurements. Data Analysis The data were first analyzed assuming a perfectly flat long counter response, or alternately assuming that the source spectrum 16 and 0 + 16 0 neutron spectrum were identical. The differential cross section was computed from dO") • ( . NMON dn lab flat resp. N e1. sc. ). dQMON 411' • (Relative efficiency) of the long counte r - 147 The relative efficiency and ITlonitor solid angle were directly ITleasured, and the elastic scattering cross section was cOITlputed using the results of Figure 5 in the Elastic Scattering Section. Table 12 gives the observed values of N/NMON and their purely statistical errors. The total cross section is IT n flat response = 2lTS 1 d(cos 8 -1 ). dIT) lab dU lab flat resp. = 60 ± 1 7 ITlb. The error was cOITlputed assuITling 15% uncertainty in graphical integration and extrapolation of the angular distribution to backward angles (see Figure 37). 31 Taking the iITlportant exit channels as S +n and 30 in these ITleasureITlents, the following equality should hold at + np P E CITl = 11.95 MeV: IT( 30 P production) + IT( 31 S production) ? = IT(n production) + IT(d production) II II II (64 % 14 ITlb) + ? (6.2 ± 1.5 ITlb) = (60 ± 17 ITlb) +(5.4 ± 1.4 ITlb) = 66 ± 14 ITlb II 65 ± 17 ITlb The conclusion is that the three body breakups are responsible for ITlost of the 30 p forITlation. InforITlation froITl the activation ITlethod decay curves indicated that the left-hand side should perhaps be larger by 2 ± 1 rnb included. if the 16 0 + 12 C - 27 . Sl + n reactions were - 148 - Figure 37 Differential Cross Section for Neutron Production. The laboratory differential cross sections for neutron production measured with the long counter is plotted as a function of the laboratory angle. Even with the large active volume of the long counter, it had to be moved fairly close to the target because of its low absolute efficiency and the low neutron yield. Thus, the long counter subtended a large angle. The smooth curve drawn through the points was used to determine the total cross section. - l49 - • ~--------~----------~----~----~i - z - > -a:: a:0 2 0 t- e,') ::l Z III l- t:::l -a (/) a: ct ...J CD ~ (!) IC) en• LLI Z - IL. E 0 ::l 1&.1 o en II cID ~ u LLI C) Z ct ~ IS ____ z OC __________ ________ 10 S ~w.~ dv/dO) lab. corr. ~ (mb/.r.) ~O 0 0 - 150 In the previous analysis no correction was applied for the variation in detector response with neutron energy. made to estimate the size of such a correction. An attempt was First, some un- published results given in Allen (1960) show that the long counter efficiency relative to a PU-Cl:'-Be Relative efficiency = 0.3206 0" source 20"H +20" c H - 0.02167 E fitted the measured points to 1.5% RMS for Here 0" H and 0" c and Carbon. n (MeV) + 0.8406 En = 1.5 to 9 MeV. are the neutron total cross sections for Hydrogen Below about 1 MeV the efficiency drops off again, the precise values depending critically on the long countel" design. measurements could be located for E n No > 9 MeV, so the above expres- sion was used to extrapolate the response up to E n = 18 MeV (see Figure 36). Second, the neutron spectrum was estimated using the compound nucleus model of Blatt and Weisskopf {1952} as described in the Introduction. The density of states in all heavy nuclei of concern was taken to be that of a Fermi gas system with zero spin p = const2. exp (2 VJaE exc ) • E The value of a = 4 MeV -1 exc was again used. Both two and three body contributions were included and the result is also given in Figure 36. The C. M. neutron spectrum derived in this manner was transformed into the laboratory frame and then folded into the efficiency curve of - l5l Figure 36, yielding a correction of about 4% (see Table 12). well within experim.ental u.ncertainties. The total cross section for neutron production is then (J" n corrected It il!J = 62. ± 17 m.b o - 152 12C + 20 Ne PRODUCTION Introduction The 12C + 20 Ne exit channel could not be studied by the previous techniques (detecting 13 particles or light particles). Information was not even available from the peaks were identified as corning from 12 C spectra, since no "y * or 20 Ne, * and since a sizeable fraction of the yield in this channel may leave the reaction products in their ground states. Assum.ing this channel preceeds by a direct reaction mechanism with the Q' tunneling through the Coulomb barriers t Buchler (1969) estimated that the branching ratio to 12C + 20 Ne was < 200/0 at E cm = 10 MeV. In order to determine the cross section for forming 12C and 20 Ne in their ground states t the particles were detected in coincidence. Measurements were restricted at some angles by energy loss and multiple scattering in the SiO foil target and at others by high elastic scattering count rates. The angular distribution was thus obtained only for 35 0 < ecm < 1450 • However, these data were not sufficient to determine the cross section to within 500/0. An attempt was made to obtain data at more forward (or backward) C. M. angles using the 61 cm magnetic spectrometer. particles and the many charge states of 16 0 Elastically scattered only permitted the measurement of a lower limit to the total cross section of this channel. In addition, the cross sections fo r the reaction leading to - 153 excited states were not measured. Hence only a rough estimate of the 12C + 20Ne total cross section was obtained. E :: 11.95 MeV. cm All data were for Expe rim ental The discrimination against other reactions provided by the kinematic coincidence technique permitted the use of a soUd target. Such a technique would be difficult to perform for a gas target because of its low density and large counter solid angles. A SiO foil about 200 keV thick to a 24 MeV 16 0 beam was used. giving a high density of localized target nuclei. The presence of a Carbon contaminant was noted, but it did not affect the measurement. Two solid state detectors were used t one mounted on each IUoveable arIU in the 61 CIU scattering chaIUber. In these rlUlS the laboratory angle was calibrated and the proper cOlUlter height was determined with a telescope zeroed in on the chamber entrance slits. In addition. the numbe r of co incidence counts as a function of one counter angle, with the other detector fixed, showed a maximum within 0.5 o of the proper angle settings as determined above. Three independent sets of measurements were performed using different collimators and solid angles. The best data were obtained for one o cOlUlter with small (~e:: ± 0.5 • ~<j> = ± 1.40 • ~n = 7.9 X 10 -4 sr) o 0 and the other with large (~e = ± 1.8 , ~cf> = ::I: 3.2 • sr) solid angle and acceptance angles. ~n:: 6.9 X 10 -3 - 154 The beam passed through the foil into a Faraday cup. The beam intensity and target thicknes s were related to the integrated current in the cup by measuring the yield of Mott scattered e cm = 90 0 nuclei at with the two solid state counters. 16 0 The correct angle was determined as usual by maximizing the elastic scattering counts with angle t affording still another check on the angular calibration. As a result. the counter solid angle did not enter into the calculation of the differential cross section (see Data Analysis). The beam current was held approximately constant at about 200 na of 24 MeV 0 ± 0.4 0 5+ , and corrections to the data for beam angle changes of and the finite beam spot size « 3 mm square) to be less than 14 %. were estimated Counting times ranged from 5 to 40 minutes per point. Pulses from the two counters were amplified and fed into the Nuclear Data analyzer used in the two dimensional 64 X 64 channel mode. The signals were also sent into timing single channel analyzers and from there into an Ortec Fast Coincidence module (90 ns resolving time). Its output was stretched and delayed and then sent into the analyzer coincidence inputs. The energy scale for each counter was calibrated using elastic scattering peaks at several angles. A typical spectrum is shown in Figure 38. Each spectrum was screened for all peaks present. Random coincidences between two elastic scattering groups were often seen and were usually separated from the desired counts. True coinci- dences from elastic scattering of the beam from a Carbon contami- - 155 - figure 38 Two Dimensional Coincidence Spectrum £or 160 + 16 0 ... 12C + 20Ne • A typical coincidence spectrum with the forward counter at 340 and the backward counter at 500 contaminant group is the counts. 12C + 16 0 is shown. One elastic scattering A £ew counts £rom elastic scattering off other nuclei in the target are also present. At some pairs o£ angles" 160 + 160 elastic scattering counts were quite strong, but they were always separated £rom the desired group. - 156 - I I I ....en z :::> 0 <.:> 0 2 0 0 It) C\I It) II) I A C\I I <D I C\I • • • • ::) _..J <t 0 LLI ( /) (/) Z - Z LLI ~ a:: I- ~ -0 0 Q. « ~ I..... _(I)::> q-O ~vtf; . () - 0,.· 0 0 ..F~' .. Z (.) 0 (.) .. + I.&J 0 ""' JZ \vc" s~ LL.I . () Z o a: cr _N~ ttl CD Z + , (.) 0 -~ + 0 64 J I 1 48 32 16 BACKWARD COUNTER CHANNEL . • a:: o ... - 157 nant on the SiO foil gave a large nu.rn.ber of COWlts at some angles, 12 but these were always separated froln the C + 20 Ne group. Positions of all peaks from runs in one of the three sets of data is shown in Figure 39. 12 The 20 C + Ne counts were identifl.ed from the energy calibration, and random coincidences described above were excluded. the The separation of the two lines in Figure 39 reflects 16 - 2.4 MeV Q value for 0 to Q = 0 for elastic scattering. + 16 0 - 12 C + 20 Ne as compared This provides sti11 another check that the peaks were properly identified. A SiO foil target was used for the data taken with the mag- netic spectrometer (.6 8 = iO, .6 q, =± 10 ). The 16 counter array served as the detector. The ene rgy scale for each of the 16 counters was calibrated with 16 0 + S 1.0 and 12C , 0 elastic scattering at 8 of 12 C and 20 lab recoils from 0 = 10 and 21.5 • 16 0 + 12 C Different charge states Ne were tried, but the desired counts were always obscured by tails from 16 0 elastic scattering lines. The best upper limit on the diffe rential c ros s section was obtained by looking fo r 20 Ne at 8 1a b =7 0 (8 0 cm = 162.8 ). 16 was detected in a monitor COWl.ter at 8 0 + 16 0 . elastic scattermg = 90 0 and was used to cm 7+ integrate the beam intensity and measure the target thickness sbnultaneously. Data Analysis The differential cross section for the coincidence method was determined from the equation - 158 - Figure 39 Positions of Coincidence l2C + 20 Ne Peaks in Spectra. The channels at which peaks were observed in the coincidence spectra of one of the sets of 160 + 160 ~ 12 C + 20Ne runs is shown. Accidental coincidences between 0 + 0 and o + Si elastic scattering groups are excluded. Most of the coincident "elastic" points were from 0 + C or 0 + 0 elastic scattering. • o 0' .- 0 i -~ ::x: 0 "'0 :::u Z -I N c 0 0 0 :::u 0 ~(II ~ " I .0 ~ tv • 0 IN 10 + 30 .~ 40 50 12C (g.s.) + 2oNe(g.s.) ~ FORWARD COUNTER CHANNEL 20 OF PEAKS 12C SPECTRA 20Ne COINCIDENCE POSITIONS ... ? 0 12C(g.S.) + 2ONe(,.63) 60 , , I~ - 160 - ~) CIn =~) CIn N) ( 00 ) ( c. M. F ac to r ) " ( Q • NMON • C.M. Factor'MON el. sc. where dcr/dn) S CIn N = 90 o is the elastic scattering cross section at CIn el. sc. deterInined froIn Figure 9 (Elastic Scattering Section), is the nUInber of counts in the 12C + 20Ne peak and integrated current in the Faraday cup. The ratio 0 o 0 INMON is the Ineasured ratio of integrated current to Inonitor counts 90 0 and ) corresponding to the counter which defined the angles cJ> is the (8 8 CIn = CIn of the reaction, whereas the other counter was always wide enough to catch the second particle. A nUInber of corrections were applied. was near Slab = 90 0 t When one counter the foil was turned slightly, so the coincidence counts were adjusted for the increase in target nuclei. deadtiIne was always Inonitored and corrected for. The analyzer The effect of Inultiple scattering of the reaction products in the foil was difficult to estiInate. Under the assuInption that the angular distribution after scattering in the foil is purely Gaus sian and that the laboratory angular distribution was approxiInately Isotropic over an area larger than the counter, the ratio R if no multi Ie scatterin = # coincidences coincidences detected was compute d f or eac h po i n t t a k en. Values of <8 2) were deterInined ... 161 from Marion and Zimmerman (1967) for each particle and angle. The corrections we re < 5 % for the best fHclt of data, and werl~ typically 1 - 15 % for the other two sets. Coincidences lost by multiple scattering were som_ewhat compensated by particles scattered into the detectors, so R was always near 1. O. Marion and Zimmerman (1967) indicated that sizeable deviations from a Gaus sian distribution r--- 161 > 1.3..j <9 2) occur at dominant and 0 20 Ne where single scattering events become This mainly influences the correction for the higher J<6 2) is quite small « 0.2 energies, where 0 ) 12 C in any case. Table 13 presents the weighted average and relative errors for the differential cross sections. These errors are from statistical unce rtainties in the number of counts N, and from deadtime and m.ultiple scattering corrections (± 15 % since the num.ber of counts in the laboratory was not isotropic nor was the scattering pure Gaussian). In addition there is an overall error of ± 15 % estim.ated for the finite beam. spot size, for changes in the incident beam. angle, and for the charge integration. The identity of bom.barding and target particles requires the angular distributions to be sym.m.etric about 9 are plotted for 6 == 0 with 9 em < 35 0 o to 90 0 in Figure 40. for two reasons: 1) em. = 90 0 , so the data There is a lack of points at very forward angles the elastic scattering count rates becam.e prohibitively high. and 2) for these C. M. angles one particle has a very low laboratory energy, so energy losses and multiple scattering in the SiO foil becam.e - 162 - figure 40 Angular Distribution for 16o + 16 0 -+ 12C(g.s.) + 20 Ne(g.s.). The final differential cross sections for the 160 + 160 -. 12 20 C(g.s.) + Ne(g.s.) reaction are plotted from Table 13. The two curves drawn through the points are the "best" fits from Table 14, and they give quite different total cross sections • - 16) - N o 12C(g.S.) + 2ONe(g.s.) Eoftl • L = 2,4,6 -I cr 1I.9!5 MeV b L = 0,4,10 "• ~ o~.--~--~--~--~--~--~----------~ o 30· eM 60· ANGLE 90· - 164 excessive. 20Ne Note the presence of an isolated value for the (1.63) and a single limit for the 1ZC (gs) + ZONe 1ZC* (4.43) + ZONe (gs) 12C (ga) + * (4.25) and differential cross section. Results An attempt was made to determine the full angular distribution from just those measured values. Since all particles involved have spin 0, and since the incoming and target particles are identical, the angular distribution must be of the form (see DeBenedetti (1964» Z ~) cm AL complex. = even Classically L - 6 at E cm = 12 MeV, so L :S 10 was assumed. still left more parameters than points. This Therefore a least squares fit to the data with a function of the form or the corresponding function for three L Solutions were required to have A, C 2: ° values, was attempted. and B 2 :S 4A C etc. The best fits are given in Table 14, with the two best plotted in Figure 40. The total sections were computed from (TTOT 4 'IT' I ALI2 2L +1 - 165 The values of X 2 for the three parameter fits are very large, indicating that lTIore than two L values are necessary. Two fits with six paralTIeters seelTI satisfactory, but unfortunately give quite different cross sections. It appears that =4 L Is probably present, but this could be expected since the zeros of P 4 (cos e) occur at e = 30 .. 6 0 and 70.1 0 , close to the minima in the angular distribution .. The spectrometer data were used to chose between the two cross sections from the fits. ~) ClTI = %n) cm • ( The cross section was derived from N NMON CMF CMF MON ). • el. sc .. The limit to the desired counts N was estimated from the spectra of the 16 counters in the array. Solid angles were determined from the known monitor counter geolTIetry and the spectrolTIeter opening. A correction was applied for the ratio of the particles detected by the array to the number entering the spectrolTIeter (Eff). limit to the differential cross section was 0 162.8 (see Table 13). At this angle the L distribution gives do/dO) Table 14 give da-jdO) 6.5 mb/sr at cm cm The upper ecm = = 2,4,6 fit to the angular ,.., 14 mb/sr, whereas all other fits in < 2.5 mb/sr. Thus, it is concluded that the cross section for 160 + 16 0 - 12C (gs) + 20 Ne (gs) at E cm = 11.95 MeV is O"(C + Ne) = 8 ::I: 3 mb • - 166 A lower lirnit to thitO cross section 11\1 145 o-(Ne + C) > S 35 0 0 dO-) 21T d(cos eCITl)ocm . CITl = 5.2 ± 0.8 mb .. The error on the fitted cross section was chosen to cover the cross sections predicted froITl the best fits (excluding the solution). L = 2,4,6 No particular significance was placed on the L of the best fits except that L = 4 cross section for the 12C + 20 Ne . since reactions leaving 12 C is probably present. values Note that the exit channel was not obtained and/or 20 Ne in excited states were not ITleasured. The latter cros s sections cannot be large since no characteristic 'tIS or 20 Ne. were observed froITl excited states in either 12C - 167 - CONCLUSIONS The data from each of the sections are summarized below: A) Elastic Scattering + 16 0 1) All measured 16 0 to the 2} 16 0 + 16 0 elastic scattering data at ecm = 90 0 • The differential cros s section for 16 0 + 16 0 elastic ecm ::: 90 0 scattering at near E cm that in the is smooth except for a bump ::: 10.5 MeV. 12 C + as those in the 12 12 There is no structure similar to C case; thus, large variations, such C + 16 not expected in the B) cross sections are normalized 12 0 C reaction cross section~ are + 16 0 reaction cross sections. Gamma Rays 1) The important exit channels for 16 0 + 16 0 reactions at = 7 to 12 MeV are 31 P + p and/or 30 Si + 2p, cm 28 S1 +~, 24 Mg + 2a, 27 Al + a + p, 30 p + d and/or E 30 p 2) + P + nt 31S + n t and perhaps 12C + 20 Ne • The gamma yield as a function of bombarding energy was much smoother for 16 0 + 16 0 than for 12 C + 12 C t again suggesting that the large variations in the reaction cross section for case. for 12 C + 12 C are not present in the 16 0 + 16 0 Large steps in bombarding energy were justified 16 0 + 16 0 reaction cross section measurements. - 168 C) Charged Particles 1) The production cross section for alphas is about 2 to 3 times less than for protons from E cm = 7 to 12 MeV, and the production cros s section for deuterons is more than an order of magnitude less than for protons at E cm = 10 to 12 MeV. No 3 H or 3 He were definitely identified. 2) Three body events in the charged particle spectra may not have been properly analyzed, but the total production cross section was not significantly influenced and was approximately correct. This was demonstrated by evalu- ating some of the data by an independent method. D) Activation Method 1) The cross section for production of 30 P magnitude larger than for production of 12 MeV t and they are about equal at E 2) is an order of 31 cm S at E cm = = 8 MeV. The precision of these measurements suffered from contarninants in the SiO fo n target. E) Neutrons 1) Three body breakup reactions account for over the production of 30 p 2) at E cm 85 % of = 10 to 12 MeV. The production cross section for neutrons is about 5 to 8 times less than for protons from assuming the exit channel 30 p of the formation of 30 P E cm +P +n = 8 to 12 MeV, accounts for most at these energies. - 169 F) 12C + 20Ne Production 1) The c ros s section for + 16 0 - 16 0 12C (gs) + 20Ne (gs) was found to be 8 ± 3 mb, a factor of 40 below that for the production of protons at E crn = 11.95 Me V. The experimentally measured cross sections are given in Tables 7 and 11 and in Figures 26, 34 and 35. To obtain the total reaction cross section at the lowest bom30 p and 12C + 20Ne barding energies, estimates of the 32 S , 31 S, production cross sections are required. The following as sumptions were made for this purpose: 1) <r(30 p )=<r(31 S} below E cm =8MeV. The data at higher energies indicate that the two cross sections approach each other with decreasing energy, the two being approximately equal at E 2) cm '" 8 MeV (see Table 11). The cross section for 31S + n remains about 9% of the proton production cross section below E cm = 7.4 MeV. This is approximately the corresponding ratio at E cm = 8.85, 7.85 and 7.32 MeV. 3) The total cross section for assumed to be 16 0 10 ± 4 mb at E + 16 0 - cm 12C + 20Ne is = 11.85 MeV, slightly higher than the cross section measured for 20 12 C (gs) + Ne (gs) to allow for the formation of excited states in either 12 C or 20 Ne. The branching ratio for the 12C + 20Ne exit channel is assumed constant at the approximate value for E cm = 11.85 MeV. - 110 4) CT ( 32 any S) 0< 32 O. It is asswned that electrorn.agnetic decays of S forrn.ed (with an excitation energy of roughly 25 MeV) do not compete significantly with the strong decays (ernie sian of one or more particles). The first two assumptions will not seriously affect the extrapolation of the total reaction cross section to lower energies since the branching ratio for the srn.all. 31S + n, 30 p + d, and 30 p + p + n exit channels is The fourth assurn.ption could not be checked experirn.entally (see the Garn.rn.a Rays Section, page on general principles. 55), but is expected to be true Furthermore t the energy dependence of the cross sections for these four exit channels will be dominated by the Coulomb barrier penetration factor for 28 Si + 0', 0 + 16 0, as is also true + 2p, etc. channels. On the other hand, the third assumption is an attempt to include the 12C + ZONe for the 31 P + n, 16 30 Si exit channel without unneces sarily biasing the total reaction cross section. for the If a direct interaction (a-transfer) is largely responsible 12 C + 20 Ne yield, then the energy variation of the cross section could be different frorn. the other exit channels. Since the rn.ajor fraction of the total reaction cross section occurs in proton and alpha emitting channels t the activation rn.easurern.ents were interpolated down 100 keV (C.M.) to correspond to the sarn.e C.M. energy as the charged particle data. The interpolation was performed by drawing a smooth curve through the activation data (see Figures 34 and 35). The Wlcertainty assigned was taken to be the saxne as that of a typical measurement at an energy about - 171 100 keY (C. M.) higher. The central problem in deriving reaction cross sections from these data is the presence of three body breakup reactions. simple theoretical arguments (see page 14 From and Figures 2 to 4), and from the experimental results of the Gamma Rays and Neutrons sections, three body exit channels are important in reactions at the energies studied.. 16 0 + 16 0 Not only is the absolute percentage of three body reactions important, but the variation of this percentage with bombarding energy may significantly influence the extrapolation of the total reaction cross section to energies below those measured. Upper and lower limits to the total reaction cross section are + (O"( 30 P) + 0"( 31 S) = 0" (n) + 0" (d) ) with O"LIM(P) and O"LIM(a) the corresponding limits to the charged particle cross sections. These were discussed in the Charged Particles section (page 101).. The upper lim.it was derived by assuming a11 a and p counts were from two body exit channels. The lower limit was obtained by taking as three body breakup reaction products all counts that were not definitely from two body processes. These are given in Table 9. A better estimate of the upper limit can be obtained by subtracting off known three body reactions, namely 30 p +P +n events or IT ( all 30 30 P - 172 P). The Neutrons section dem.onstrated that over 85% of forlTled in channel at E cm. 16 0 + 16 0 reactions was produced by this exit = 10 and 12 MeV. The cross section for IT(d) , is not entirely neglected by this procedure. 30 P + d, In the charged particle spectra taken with the counter telescope of Figure 13, protons and deuterons could not be resolved. Any deuterons in the tail of the proton line were counted and analyzed as protons. How- evert an im.proper center-of-m.ass solid angle factor was therefore applied to such counts. On the other hand, the num.ber of deuterons was very sm.all com.pared to the num.ber of protons at higher energies, and no indications of a deuteron line were observed at lower energies in the two-dim.ensional charged particle spectra. Argum.ents in the Introduction based on Coulom.b barrier heights and Q values also suggest that the deuteron production cross section is sm.all com.pared to the total reaction cross section at lower energies. Furtherm.ore, the error introduced by incorrectly analyzing any deuterons did not seriously affect the production cross section for protons and deuterons. This was dem.onstrated by the agreem.ent of the cross sections obtained by analyzing the data with two independent m.ethods. Thus, it is con- cluded that a m.eaningful lim.it to the reaction cross section can be obtained in this way. The final total cross section lim.its were com.puted from. IT IT lower lim. upper lim. = IT10wer () +IT (0') tIT(30 p ) +IT(31 S ) +IT( 12 C +20 Ne ) Pow 1 er lilTl U lim. II = IT Production (p +d) t IT Production (0') +IT( 31 S) + IT( 12 C + 20 Ne) - 173 and the results are given in Table 15. the average of these two limits. The final cross sections are The total cross sections for the lowest two energies were derived from the upper limit only and the assumption of 17% to 200/0 three body reactions. These percentages were estimated from the three body fractions at the other four energies. Errors are estimated from the uncertainties in the three body percentage, errors on the measured cross sections, and uncer- 1:iainties in the extrapolated cross sections. The values of S for these cross sections are plotted in Figure 41 for g = 0 .. 84 Meyradius R = 7.24 fm; 1 (this corresponds to an interaction see the Introductiont page 5 ). A set of different values of the parameter g were tried~ but in no case was S a constant below about E cm = 9 MeY. The 16 0 + 16 0 gamma yield in Figure 12 uses the same value of g and exhibits an energy dependence similar to that for the total reaction cro ss section. '" the other hand, a constant S was not expected. On The measurements were made at energies close to the Coulomb barrier and there is a large angular momentum probably invo1ved~ neither of which are properly accounted for by the simple expression (T Cot S 179.1 E exp (- gE) • Furthermore, the variation in .fE S is less than a factor of 5, whereas the measured cross section changes by nearly a factor of 10 5 ! - 174 - Figure 41 160 + 160 Total Reaction The total reaction cross sections Cross for Sections. 160 + 16 0 and the total errors are plotted from Table IS. The barrier penetration factor has been factored out (see the text page 173). of The value of R;: 7.24 fm. g corresponds to an interaction radius Energy losses have been taken into account, resul ting in an overall uncertainty in the energy scale of ± So keV (C.M.). - 176 Attempts were also made to fit the cross sections with the expressions (j" i [S(0)+SI(0).E+SII(0).E2/2] exp ( _ ~~.l ) and (j .. S(E) E exp (The latter is the correct WKB angular momentum L=O. Here approximation expression for p.= , E • Eem , M:!.~ l\+~ radius, 2 Ec = ~ Z2e /R and 2 V(r) .. Zl Z28 /r.) R - interaction In no case was there an obvious method to reliably extrapolate the cross section down in energy to below E em = 6 MeV. On the other hand, the extrapolation is not so crucial since the measurements actually extend into the astrophysical region of interest. Therefore, much more detailed studies of nucleosynthesis during Oxygen burning should be permitted by the branching ratios and cross sections contained in Table 15. These are the first measurements of the total reaction cross section for 160 + 160 , the most complicated astrophysical nuclear reaction ever studied. - 117 APPENDIX I C + C AND C + 0 ELASTIC SCATTERING The elastic scattering of 12C + 12C and 12C + 16 0 ecm = 90 0 measured at using the differentially pumped gas target and the same counters as for the 16 0 mixture of high purity CH 4 12 + 16 0 measurements. A and Ar gases was used at a chamber For the pressure of 2.5 - 3.1 torr. energy loss to the were 12 C + 12 C scattering the C beam before reaching the target was computed from the curves in Northcliffe (1963) to be 150 ± 100 keV (lab). data are given in Table 16 and Figure 42. region E cm Most of the values in the 3.9 - 6.4 MeV consist of three or four different =. measurements. The minima in the curve correspond in energy to peaks in the total reaction cross section for yield (see Figure 12). 12 C + suggests that the total reaction cross section for smoother than for Bromley~· al. 12 12 C + 12 C. Almqvist~ al. (1961) also took data on the ecm = 90 o • 12 cm 16 C and in the 16 The lack of such structure in elastic scattering except for the anomaly near E scattering at The 0 + 16 0 = 10.5 MeV 0 + 16 0 is (1960, 1963) and C + 12 C elastic The energies of maxima and minima agree within the uncertainties quoted above for the data of Figure 42. is in contl"ast to the 16 0 This + 16 0 elastic scattering (see the Elastic Scattering section, page 36). The E 16 o 16 0 "y + 12 C elastic scattering was measured in steps of = 250 keV (lab) at several angles. These data were mainly - 178 - Figure 42 12C + 12C Elastic Scattering. The ratio of the differential cross section for 0 12C + 12C elastic scattering at ecm '" 90 to the )plott scattering cross seotion is plotted. All errors are total errors (see Table 16 and Appendix I). Energy losses in the gas have been subtracted and produce an overall uncertainty in the energy scale of ~ 50 keV (C.M.). 7 .8 ....o ~ .6 ca: 0:: .5 12C + 12C ELASTIC SCATTERING .4 .3 4 6 eM ENERGY 7 8 (MeV) - 180 taken in order to normalize the (see 16 0 + 12C - Activation Method, page132). 0 0 0 angles of Slab:= 27.3 , 45.0 t n + 27 S1 cross section The detectors were located at 55.0 • The energy loss to the beam. before reaching the target was estimated to be The results are given in Table 17. 230 ± 100 keY (lab). - 181 APPENDIX II THE 12C + 12C -y YIELD VS. Using a Carbon foll 10 J. l. gm/cm 0.6 J..l.a ( 12 + C, 3 ) t the 12 C + 12 2 E cm thick and Carbon beams of C -y yield was measured as a function of energy in 40 - 50 keY C.M. steps from 3 ...7 - 7.5 MeV. The com- bined beam intensity and target thickness were monitored by elastic scattering at acm ::: 90 0 t using the results of Appendix I. discrhninator cutoff was employed, E -y > 1.4 MeV. Only one The data were analyzed in the same way as in the Gamma Rays section (page 56 but the normalization was to 0.087 mb at E cm ::: 3.99 MeY. ), This permitted a direct comparison of the S variation with Ecm for the -y yield and for the charged particle measurements of Patterson, 12 Winkler and Zaidins (1969) for the C + 12 C reaction. The energy loss of the beam in the foU was estimated to be 60 keV (lab). results are given in Table 18 and in Figure 12. was taken from Patterson (1969). The The value of g used The agreement between the -y yield measurements and the charged particle data may have been poorer if some other discriminator cutoff had been used. example, the strong 0.44 MeV -y line from by the discriminator cutoff. 23 Na (1-0) was left out Significant changes in the relative intensities of lines in the '{ spectrum were noted for over changes in E cm For of roughly 100 keV as well. of these results relative to the 16 0 + 16 0 12 C + 12 C For a discussion reactions, see page 58. - 182 BIBLIOGRAPHY Ajzenberg-Selove, F., and Lauritsen, T., 1959, Nuc.~s., 11, 1. Allen, W.D., 1960, in ~ Neutron Physics part 1, edited by J.B. Marion and J.L. Fowler, (Interscience Publishers, New York), p361. Almqvist, E., Bromley, D.A., and Kuehner, J.A., 1960, Phys.Rev.Lett., !!, 515. Almqvist, E., Bromley, D.A., Kuehner, J.A., and Whalen, B., 1963, Phys •Rev ., 130, 1140. Arnett, W.D., 1969a ,in Supernovae and Their Remnants, edited by P.J. Brancazio and A.G.W. 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Chatwin, R.A., Eck, J.S., Robson, D., and Richter, A., 1970, Phys.Rev.C, 1, 795. .A., - 183 Chiu, H.Y., 1966, in Stellar Evolution, edited by R.F. Stein and A.G.W. Cameron, (Plenum Press, New York). Chiu, H.Y., 1968, in Nucleosynthesis, edited by W.D. Arnett, C.J. Hansen, J.W. Truran and A.G.W. CBJII8ron, (Gordon and Breach, New York). Curran, S.C., 1958, in Handbuch der Physik, volume 45, edited by S. Flttgge and E. Creutz, (Springer - Verlag, Berlin). Davis, R.H., 1960, Phys.Rev.Lett., ~,521. Also, see Proceedings of the Second Conference on Reactions Between Complex Nuclei, Gatlinburg, (John Wiley and Sons, New York), p297. DeBenedet ti, S., 1964, Nuclear Interactions, (John Wiley and Sons, New York). Dwaralcanath, M.R., 1968, Ph.D. thesis, California Institute of Technology. Endt, P.M., and van der Leun, C., 1967, Nuc.Phys., Al05, 1. Fowler, W.A. and Hoyle, F., 1964a,Ap.J.Supp number 91, 9, 201. 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Moyal, J.E., 1955, PhiI.Ma.g., 1:&, 263. Northcliffe, L.C., 196), Ann.Rev.Nuc.Sci., 13, 67. Paradellis, T. and Hontzias, s., 1969, Nuc.Instr.and Math., 73, 210. Patterson,J.R., Winkler, H., and Zaidins, C.S., 1969, Ap.J., 157, 367. Rakavy, G., 1967a, in High Energy Physics ~ Nuclear Structure, edited by G. Alexander, (North Holland, Amsterdam). Rakavy, G. and Shaviv, G., 1967b, Ap.J., 148, 803. Rakavy, G., Shaviv, G., and Z1namon, Z., 1967c, Ap.J., 150, 131. Rickertsen, L., Block, B., Clark, J.W., and Malik, F.B., 1969, pnys.Rev.Lett., 22, 951. Rossi, B.B. and Staub, H.H., 1949, Ionization Chambers and Counters; E:q?erimenta1 Techniques, (McGraw-Hill, New York). Siemssen, R.H., Maher, J.V., Weidinger, A., and Bromley, D.A., 1967, Pnya •Rev .Lett., 19, 369. Truran, J.W. and Arnett, W.D., 1970, Ap.J., 160, 18I. Tsuda, H., 1963, Prog.Theor.Phys., 29, 29. Vogt, E.W • and McManus, H., 1960, Phys .Rev .Lett., 1!" 518. Also, see Proceedings of the Second Conference on Reactions Between Complex Nuclei, Gatlinburg, (John Wiley and Sons, New York), p291. Whaling, W., 1958, in Handbuch ~ Physik, volume 34, edited by S.FlUgge and E. Creutz, (Springer - Verlag, Berlin). Wildermuth, K. and Caravi11ano, R.L., 1961, Nuc.Phys., 28, 636. - 185 Table 1 The Ratio of the Elastic Scattering to the Mott Scattering Cross 16 16 Section for 0 + 0 Energy losses have been included, but there is an overall uncertainty in the c. rn. energy scale of ± 50 1r: eV (c. rn. ) (See the text page 36 and figure 9 ). E crn 7.34 MeV 7.44 7.54 7.64 7. 74 7.84 7. 94 8.04 8. 14 8. 24 8.34 8.44 8.54 8.59 8.64 8. 74 8.85 8. 95 9. 05 9. 10 9. 15 9.25 9.35 9.45 9. 55 9.65 9. 75 9.85 9.95 10. 05 10. 15 10. 25 Ratio to Mott E O. 989 ± .006 10. 35 10.45 10.55 10.65 10. 75 10.85 10.95 11. 05 11. 15 11. 25 11. 36 11.46 11. 56 11. 66 11. 76 11. 86 11. 96 12.06 12. 16 12. 26 12.36 12.61 12.86 13. 11 13.37 13.62 13.87 14. 12 14.37 · 982 ± .018 .995±.O18 .996±.O17 1. 012 ± .018 • 991 ± . 006 1.016±.O17 • 984 ± .016 1. 002 ± .015 1. 006 ± .015 1. 000 ± .004 1.019±.O15 1. 008 ± .014 1. 002 ± .006 .974±.O13 • 977 ± .014 · 995 ± .004 1. 006 ± . 008 · 990 ± • 008 • 994 ± • 005 1. 004 ± .008 1. 003 ± .007 1. 003 ± .004 • 998 ± .005 1. 000 ± .005 1. 005 ± .005 1. 003 ± .004 1. 003 ± .004 1. 003 ± .004 • 995 ± • 004 .986 ± .004 • 975 ± • 004 crn Ratio to Mott O. 961 ± • 004 · 958 ± . 004 • 966 ± • 005 ,. 966 ± • 005 • 963 ± • 005 • 967 ± • 005 • 956 ± • 005 • 948 ± • 005 .915±.005 · 908 ± • 006 .886 ± . 005 .862 ± . 006 .833 ± • 006 · 774 ± . 005 • 735 ± • 006 .704 ± .006 · 663 ± • 006 .608 ± • 006 .579 ± • 005 .544 ± .005 .498 ± • 006 .416 ± • 005 • 363 ± • 005 • 318 ± • 005 · 280 ± • 005 .223 ± .004 · 198 ± . 004 · 149 ± • 003 · 115 ± • 003 - 186 Table 2 Relative Number of Counts in Gamma Spectrum Peaks (all numbers are normalized to E cm = 2. 23 MeV). y See figures 10 and 11. 1000 at E '" 12 MeV and all ratios are ± 20 %. Relative a y Counter Efficiency 0.511 5.86 . 71 3.94 Annihilation 30p .85 3. 18 27Al 270 170 220 400 1. 01 2.55 27Al 480 400 220 420 920 630 650 840 350 350 240 660 320 340 260 280 670 390 500 710 1000 1000 1000 1000 20700 13400 13100 3800 E 1. 27 1. 96 1. 37 1. 79 1. 46 1. 66 1. 78 1. 31 2. 23 1. 00 Nucleus 02 gas NiO Quartz SiO 7700 1000 10000 2300 870 920 550 530 31p 30 , 5 1, •• , 24 Mg 30p 28 Si 31p 30 ' S 1, •• , Total counts in 2. 23 MeV peak 2 a) A 20 p.gm/cm SiO foil was also used under the same conditions as the other solid targets (see page 50 of the text). Its spectrum is not shown. + Quartz Spectrum. 27 1. 020 1. 265 1. 248 1. 213 1. 135 27 .849 (1. 779 - .511 = 1. 268) 29 Si (1 _ 0) = 1. 2730 ± .0005 2) = 1. 267 ± .002 30 Si (2 _ 1) = 1. 275 ± . 009 P (4 - 30 ? 0) = 1. 0130 ± .0003 Transition Other Transitions (2.235 - 1. 022 = 1. 213) 31 S (1 _ 0) = L 242 ± . 020 31 P (1_ 0) = 1.2661 ± .0002 At (2 - Al (1 - 0) = .8429 ± . 003 (1. 779 - 1. 022 = .757) .757 P (2 _ 0) = . 709 ± . 001 .711 ? Annihilation Radiation = . 511 30 P (1 _ 0) = .678 ± . 001 Ide ntifica tion 30 .696 .680 -Y. 0.511 ±. 005 MeV E The y energies are from Figure 11 and the energy calibration is good to ± 5 KeV. energie s are from Endt and van der Leun (1967). See the text page 50. Identification of y Lines in the 16 0 Table 3 I -.J Q) j-J E P (3 _ 0) = 1. 455 ± . 002 2.235 2. 20 2. 15 2.03 30 Si (1 _ 0) = 2. 232 ± . 006 31 S (2 - 0) '= 2. 232 ± .015 32 S (1 _ 0) '= 2. 237 ± . 004 (3.05 - 1. 02 = 2.03) 31 P (5 - 1) = 2.1481 ± .0006 27 Al (3 _ 0) = 2. 2089 ± . 0006 31 P (2 _ 0) = 2. 2338 ± . 0005 28 Si (1 _ 0) = 1. 7787 ± .0002 30 P (4 _ 0) = 1. 976 ± . 002 31 P (4 - 1) = 2. 0288 ± . 0005 1. 783 1. 976 (2. 235 - . 5 11 = 1. 724) ? P (1_ 0) = 1.381 ± .005 0) = 1. 36857 ± .00004 30 Mg (1 - 29 24 Identification 1. 727 1. 533 1. 457 1. 372 ~ Table 3 con't. 1) = 1. 543 ± . 009 S (4 - 1) = 2. 045 ± .025 31 P (6 _ 1) = 2. 239 ± .010 29 . Sl (2 _ 0) = 2.0317 ± .0010 27 Si (3 - 0) = 2. 165 ± . 009 31 CD CD ..... 30 Si (3 _ 1) = 1. 535 ± .009 29 P (4 - 1) = 1. 721 ± .007 27 AI(4- 2)= 1.7190±.0009 I 32 S (2 - Other Transitions E 3.505 3.05 31 30 P (6 - 0) = 3.5055 ± .0010 Si (2 _ 0) = 3. 507 ± . 006 ? (3.505 - .511 = 2.996) 3.005 ? 2.56 28 Si (2 _ 1) = 2. 835 ± . 006 ? 2.535 2.845 (3.505 - 1. 022 = 2.493) Identification 2.49 -1. Table 3 con't. P (5 _ 0) = 2.539 ± . 002 (3. 05 - . 51 = 2.54) 30 Other Transitions \() f:, , - 190 Table 4 Estimated Branching Ratios for the All results are normalized to the page 55). Production of Heavy Nuclei. 28 Si yield = 1. 00 (see the text Relative Strengths y Decaying Nucleus 24 20 18 MeV Si 1. 00 1. 00 1. 00 Mg ~.4 ~. 1 ~.2 27Al 28 24 ~.5 :=. 3 ~. 2 30 p 1.0 •5 .2 27 Si <.05 29 p ~.03 31S • 06 . 1 •1 31p + 30 Si 3. 5 2.9 1.7 12C 20 , N e, 26 M g, 29 · 32S S 1, No Conclusions - 191 Table 5 16 . . o + 10 6 'V YIeld as a FunctlOn of Energy. The yields and relative errors of 'V's with energy above the indicated cutoffs are normalized to 100.0 at E = 10.0 MeV. The energies are corrected for losses in the gas a~Wthere is a ± 50 KeV (c. m.) uncertainty associated with this correction. See the text page 57. Normalized Gamma Yields E cm E y > 0.6 MeV 7.01 .06 E y > 1. 6 MeV · 16 · 21 .26 · 31 .36 .41 .46 .057 ± 5% .073 ± 5% .094 ± 5% .122 ± 5% . 154 ± 5% . 179 ± 5% .212 ± 5% .037 ± 5% .048 ± 5% .062±5% .074 ± 4% .097 ± 4% . 125 ± 4% . 157 ± 4% .181 ± 4% .224 ± 4% .264 ± 4% 7.51 .56 .61 .66 · 71 .76 .81 .86 .91 .96 .269 ± 5% .345 ± 5% .41 ± 5% .51 ± 5% .60 ± .5% .68 ± 5% .85 ± 4% .99 ± 5% 1. 19 ± 5% 1. 35 ± 5% .336 ± 4% .404 ± 4% .484 ± 3% .60 ± 4% .71 ± 4% .83 ± 4% .97 ± 4% 1. 16 ± 3% 1. 36 ± 4% 1. 62 ± 4% 8.01 .06 1. 72 1. 94 2.15 2.49 2.85 3. 15 3.47 3.90 4.50 4.97 .11 .11 · 16 .. 21 .26 · 31 .36 .41 .46 ± 5% ± 5% ± 5% ± 5% ± 5% ± 5% ±30,10 ± 4% ± 4% ± 4% 1. 91 2. 13 2.40 2.67 3.06 3.33 3.83 4.34 5.0 6.0 ± 4% ± 4% ± 3% ± 4% ± 4% ± 3% ± 3% ± 3% ± 3% ± 3% E y > 2. 2 MeV .080 ± 5% · 106 ± 5% · 126 ± 5% · 159 ± 5% .204 ± 5% · 240 ± 5o,to .284 ± 5% .321 ± 5% .414 ± 5% .445 ± 5% .60 ± 5% .70 ± 5% .82 ± 5% 1. 04 ± 4% 1. 17 ± 5% 1. 48 ± 5% 1. 71 ± 5% 2.11 2.28 2.54 3.03 3.38 3.58 4.07 4.66 5.2 5.8 ± 5% ± 5% ± 5% ± 5% ± 5% ± 5% ± 3% ± 4% ± 4% ± 4% - 192 Table 5 eon't. Normalized Gamma Yields E ern E 'Y > o. 6 MeV E y > 1. 6 MeV E Y > 2. 2 MeV 8.51 .56 .61 .66 · 71 .76 .81 .86 .91 .96 5.8 ± 4% 7. 1 ± 4% 7.8 ± 4% 8.1 ± 4% 9.0 ± 4% 9.8 ± 4% 12.2 ± 3% 14.8 ± 4% 17. 0 ± 4% 18.5 ± 4% 6.7 ± 3% 7.6 ± 4% 8.4 ± 4% 9.4 ± 4% 10.4 ± 4% 12.2±4% 13.8 ± 4% 15. 7 ± 4% 17.7 ± 4% 19.5 ± 4% 6.8 ± 4% 8.3 ± 4% 9.3 ± 4% 9.4 ± 4% 10. 7 ± 4% 11. 4 ± 4% 13.8 ± 3% 16.9 ± 4% 19.3±4% 21. a ± 4% 9.02 · 07 · 12 · 17 .22 .27 .32 .37 .42 .47 16.7 ± 4% 21. 8 ± 4% 23.9 ± 4% 27. 1 ± 4% 29.2 ± 4% 32.7 ± 4% 35.3 ± 3% 38.7 ± 4% 44.4 ± 4% 45.8 ± 4% 21. 0 ± 4% 23.6 ± 4% 24.9 ± 4% 27.4 ± 4% 30.1 ± 4% 33.4 ± 4% 35.5 ± 4% 39.0 ± 4% 42.5 ± 4% 45.7 ± 4% 22.2 ± 4% 24.2 ± 4% 26.5 ± 4% 29.9 ± 4% 31. 8 ± 4% 35.0 ± 4% 37.7 ± 3% 41. 0 ± 4% 47.3 ± 4% 48.8 ± 4% 9.52 .57 .62 .67 .72 .77 .82 .82 · 82 .82 .82 .87 .92 .97 49 56 56 6Q 68 74 83 80 80 81 79 84 94 99 49 52 58 61 66 71 80 ± 4% ± 4% ± 4% ± 5% ± 5% ± 5% ± 5% 86 93 96 ± 5% ± 5% ± 5% 52 59 58 63 70 77 86 84 83 84 81 85 96 100 ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% ± 3% ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% ± 3% ± 4% ± 4% ± 4% ± 40/0 - 193 Table 5 con't. E em 10.02 E y Normalized Gamma Yields > 0.6 MeV E > 1. 6 MeV E 100.0 ± 4% > 2. 2 MeV y y 100.0 ± 5% 100.0 ± 4% (normalization point) .07 .07 · 12 · 17 .22 .27 .32 .37 .42 .47 115 ± 4% 121 127 136 143 150 152 166 174 10.52 .57 .62 .67 .72 .77 .82 .87 .92 .97 ± 5% ± 5% ± 5% ± 5% ± 5% ± 5% ± 5% ± 5% ± 5% ± 5% 116 ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% 107 120 126 113 121 134 140 147 158 158 120 126 134 141 148 150 164 171 ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% 194 194 206 226 230 250 258 280 293 300 ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% ± 3% ± 4% ± 4% ± 4% 178 209 203 206 204 239 254 265 280 302 ± 5% ± 5% ± 5% ± 5% ± 5% ± 5% ± 5% ± 5% ± 5% ± 5% 189 190 201 220 221 240 244 263 277 283 ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% ± 3% ± 4%! ± 4% ± 4% 11. 02 .07 · 12 · 17 .22 .27 .33 .38 .43 .48 308 338 356 374 388 398 396 424 468 461 ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% 302 319 329 346 342 353 375 409 413 409 ± 5% ± 5% ± 5% ± 5% ± 5% ± 5% ± 5% ± 5% ± 5% ± 5% 289 318 331 347 359 362 359 381 387 404 ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% 11. 53 .58 .63 .68 .73 .78 .83 507 496 491 508 540 538 525 ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% 442 442 457 ± 5% ± 5% ± 5% 443 429 426 437 462 460 448 ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% ± 4% - 194 Table 6 C.M. Differential Cross Sections for Charged Particle Production. The coefficient A of po(cos e) in a least squares fit to the angular distribution with Legendre polynomials of even order is also given for each interval in excitation energy. The errors given are relative errors only (see page 97 of the text). eo .lIl. ,p dO" ) d1>, 0 .lIl. ,p ec .m. ,a Ec.m. = 11.85 MeV Eexe • 0 - 0.130 ± .038 mb/sr 0.102 ± .023 0.140 ± .026 0.126 ± .025 0.099 ± .019 0.110 ± .023 0.131 ± .027 0.145 ± .045 0.180 :i: .038 0.204 ± .046 A= 0.140 ± .012 61.9° 78.5 88.8 98.8 108.6 118.2 121.6 136.7 145.6 154.4 23.40 34.9 46.3 57.6 68.7 79.3 89.8 100.0 109.8 119.4 128.5 137.6 146.4 154.9 25.9° 38.7 51.0 63.5 75.0 86.4 97.2 107.6 117.2 126.1 134.9 143.3 151.0 158.6 dO" ) ern. c .m. ,a 5 MeV * 0.240 .032 mb/sr 0.103 * .016 0.112 * .018 0.053 :i: .011 0.036 ± .009 0.100 ± .011 0.018 * .014 0.063 ± .012 0.081 :t .015 0.103 :i: .021 0.076 :t .016 0.104 ± .034 0.205 ± .051 0.174 ± .040 A = 0.087 :i: .001 EO.lIl. m 11.85 MeV Eexo .. 5 - 1.5 MeV 0.57 :t .10 mb/sr 0.54 ± .09 0.46 :t .07 0.41 t .08 0.33 :t .06 0.36 :t .07 0.39 ± .01 0.36 :t .01 0.34 ± .06 0.37 :t .08 0.35 ± .06 0.41 :t .10 0.41 ± .08 0.43 :t .09 26.6° 39.7 52.6 64.9 17.0 88.3 99.5 109.6 119.3 128.5 137.0 144.9 152.5 159.6 0.34 :t .05 mb/sr 0.27 :t .04 0.27 :t .04 0.29 :t .06 0.21 ± .03 0.18 :t .04 0.26 ± .05 0.25 :i: .06 0.24 ± .07 0.30 :t .06 0.31 ± .05 0.29 :t .09 0.25 :t .07 0.27 ± .13 - 195 Table 6 cont. A • 0.42 ~ .0) c.m. - 11.85 MeV E 23.8 0 35.5 47.0 58.3 69.3 80.2 90.8 101.1 1ll.0 120.5 129.6 138.5 147.1 155.5 1. 77 :I: .31 mb/sr 1.54 :t .24 1.27 ± .19 1.21 :t .25 1.09 ± .17 1.09 ± .23 1.01 :t .18 1.17 ± .26 1.06 :t .17 1.15 :t .25 1.07 :t .19 1.21 :t .27 1.20 ± .23 1.24 ± .24 A = 1.19 ± .07 c.m. = 11.85 MeV E 24.3 0 36.3 48.2 59.7 70.9 81.7 92.5 102.6 112.3 121.7 131.0 139.8 148.0 156.3 4.0 :t .7 mb/sr 3.5 :t .5 3.1 :i: .5 3.1 :t .6 2.9 :t .4 2.9 :t .5 2.8 :t .5 2.9 :t .6 2.7 :t .4 2.9 :t .6 2.7 :t .4 2.9 ± .7 3.0 :i: .5 3.1 :t .6 A = 3.00 :i: .16 A - 0.26 ± .015 Eexc .. 7.5 - 10 MeV 27.2 0 40.5 53.8 66.4 78.7 90.3 101.3 111.6 121.4 130.2 138.6 146.3 153.6 160.7 1.00 ± .22 mb/sr 0.79 ± .12 0.66 :t .10 0.67 ± .11 0.58 ± .12 0.43 ± .12 0.61 :t .16 0.73:t .15 0.70:t .14 0.67 ± .16 0.52 ± .09 0.54 :t .20 0.55 ± .20 0.53 :t .28 A .. 0.65 ± .05 exc = 10 - 12.5 MeV E 28.2 0 41.8 55.3 68.3 81.0 93.0 103.9 114.3 123.6 133.1 140.7 148.5 155.4 161.9 2.7:t .5 mb/sr 2.3 :t .3 1.8 :i: .3 1.6 ± .3 1.6 :t .3 1.6 :t .3 1.5 :t .3 1.4 :i: .3 1.6 ± .3 1.6 :t .3 1.5 :i: .3 1.6 :i: .4 1.9 :i: .4 2.2 ± .5 A = 1.66 :i: .10 - 196 Table 6 cont. 25.3° 37.3 49.7 61.7 73.2 83.7 94.9 105.7 114.8 124.2 133.2 141.9 149.7 157.7 Ec.m. - 11.85 MeV Eexc a 12.5 - 15 MeV 8 •.3 ± 1.4 mb/sr 7.2 ± 1.1 6.5 ± .9 29.3° 43.9 58.1 6.6 ± 1.1 6.1 ± .9 6.5 ± 1.1 5.9 ± .9 6.4 ± 1.2 6.2 ± .9 6.5 ± 1.3 6.5 ± .9 6.7 ± 1.4 6.7 ± 1.5 6.9 ± 1.5 A = 6.5 ± 26.8° 40.7 52.6 66.0 77.6 89.3 100.6 1ll.3 119.7 129.4 137.0 145.1 152.8 160.1 71.5 84.3 96.9 108.2 118.2 128.4 136.1 5.0 ± .8 mb/sr 4.1 ± .6 3.5 ± .6 3.3 ± .5 3.1 :I: .5 2.9 ± .5 2.7 ± .5 2.7 :I: .5 2.7 :I: .5 3.0 :I: .4 A .,. 3.14 ± .3 .18 E c.m. = 11.85 MeV Eexc = 15 - 17.5 MeV 14.3 ± 2.1 mb/sr 13.1 ± 1.7 31.4° 46.7 62.4 76.4 89.9 12.4 ± 1.6 10.8 :i: 1.6 10.5 ± 1.6 10.3 ± 1.6 10.0 ± 1.6 9.9 ± 1.5 102.7 li5.1 6.7 ± .9 mb/sr 5.4 ± .8 4.4 ± .6 3.9 ± .6 4.0 ± .6 3.9 ± .6 4.0 ± .6 9.8 ± 1.6 9.5 :I: 1.5 8.4 ± 1.2 10.6 :I: 1.8 10.4 ± 1.7 9.9 :I: 1. 7 A '" 10.6:1: * 4 parameter .fit .5 A = 4.1 ± .4 * - 197 Table 6 oont. Ec.m. m 9.85 MeV 23.10 28.6 34.5 0.075 ± .010 mb/sr 0.070 ± .010 0.054 :I: .008 45.7 0.064 :I: .008 67.4 0.041 :I: .006 88.4 0.041 :I: .006 108.5 0.035 ± .009 127.3 0.053 ± .011 145.4 0.069 ± .013 154.2 0.082 :I: .012 A a 0.057 ± .0045 c.m. = 9.85 MeV E 23.40 29.0 34.9 46.4 68.4 89.8 109.7 128.5 146.4 154.9 0.J14 '" .019 mb/sr 0.130 ± .019 0.128 ± .018 0.123 ± .016 0.104 :I: .015 0.095 :t: .015 0.099 ± .019 0.103 ± .021 0.110 ± .023 0.125 ± .021 A = 0.114 ± .007 * 3 parameter fit E exc · 0 - 5 MeV 25. f' 32.0 38.5 50.7 74.4 96.6 116.9 134.3 150.7 158.3 Eexc 0.033 :t: .004 mb/sr 0.027 ± .004 0.019 ± .003 0.030 ± .004 0.010 ± .002 0.016 :t: .003 0.015 :I: .OC)7 0.029 :I: .011 0.035 ± .011 0.033 :t .006 A = 0.020 ± .003 * = 5 - 7.5 MeV 26.SO 33.0 39.5 52.2 76.5 98.8 118.8 136.4 152.2 159.5 0.140 * .018 mb/sr 0.105 :t .014 0.076 ± .010 0.043 :I: .005 0.056 ± .008 0.049 ± .008 0.030 ± .011 0.055 :I: .020 0.101 ± .028 0.088 ± .018 A = 0.052 ± .00$ * - 198 Table 6 cont. Ec.m. = 9.85 MeV 23.8° 29.5 35.6 47.1 69.7 90.9 111.1 129.5 147.1 155.6 0.39 :t: .05 mb/ar 0.34 :t .05 0.33 z .05 0.34 ± .04 0.30 ± .04 0.30 ± .05 0.29 ± .05 0.31 ± .06 0.32 ± .06 0.34 ± .05 A = 0.333 ± .018 Ec •m• = 9.85 MeV 24.s<' 30.3 36.6 48.4 71.4 93.0 113.2 131.6 148.3 156.5 0.90 ± .11 mb/ar 0.80 ± .11 0.78 ;I: .11 0.81 :t: .10 0.75 :I: .10 0.76 :I: .11 0.71 ± .10 0.78 :I: .13 0.83 :I: .15 0.86 :I: .14 A = 0.80 ;I: .06 E exc · 7.5 - 10 MeV 27.2° 33.9 40.6 53.7 78.5 101.2 121.2 138.0 153.6 160.5 0.215 :t: .028 mb/ar 0.202 ± .027 0.149 :t: .021 0.194 ;I: .024 0.136 :I: .022 0.110 ± .025 0.116 ± .026 0.166 ± .053 0.123 ;I: .034 0.119 :I: .022 A = 0.146 ± .014 Eexc = 10 - 12.5 MeV 28.2° 35.2 42.0 55.6 81.3 104.6 124.2 141.2 0.40 ± .05 mb/sr 0.38 ± .05 0.29 :t .04 0.33 :t: .04 0.34 :I: .06 0.32 ;I: .06 0.29 ± .05 0.29 ± .07 A = 0.318 :I: .021 - 199 Table 6 cont. 25.9° 32.4 39.0 50.9 75.4 96.9 117.4 135.1 151.4 159.0 Ec.m. • 9.85 MeV Eexc = 12.5 - 15 MeV 1.85 :j: .23 mb/sr 1.71 :I: .23 1.53 :I: .20 1.59 :I: .19 1.59 :j: .20 1.36 :t .18 30.0 0 44.7 58.9 86.0 109.8 0.60 :i: .08 mb/sr 0.44 :j: .06 0.46 :t .06 0.46 :I: .08 0.41 :I: .07 1.41 :t .22 1.58 :I: .29 1.59 :i: .29 1.40 :I: .22 A = 1.60 :I: .11 A '" 0.49 :I: .0) - 200 Table 6 cont. c.m. = 8.85 MeV E 22.9° 28.5 34.3 45.5 56.5 67.4 77.9 88.4 98.5 117.8 136.5 145.4 154.2 0.0074 :t .0017 mb/sr 0.0124 ± .0018 0.0120 :t .0024 0.0156 ± .0023 0.0158 :t .0026 0.0133 :I: .0021 0.0112 :t .0020 0.0101 :t .0018 0.0093 ± .0022 0.0110 :t .0024 0.0149 :t .0030 0.0134 :t .0026 0.0137 ± .0026 A = 0.0108 ± .0007 Ec.m. = 8.85 MeV 23.3° 29.0 34.9 46.4 57.4 68.5 79.3 89.6 0.030 :t .005 mb/sr 0.026 ± .004 0.028 ± .005 0.027 ± .004 0.028 ± .004 0.026 ± .004 0.029 :t .005 0.026 ± .005 0.026 :I: .006 99.7 119.3 0.027 ± .006 137.4 0.027 ± .006 146.3 0.023 :t .004 154.9 0.024 ± .005 A = 0.0263 ± .0018 Eexc - 0 - 5 MeV 0.0086 :t .0012 mb/sr 0.0045 :t .0008 0.0055 ± .0013 0.0030 ± .0005 0.0028 ± .0007 0.0018 :t .0004 0.0019 ± .0006 0.0019 ± .0005 0.0022 ± .0009 0.0035 :t .0015 0.0037 :I: .0012 0.0060 :t .0017 0.0077 :!: .0020 A = 0.0032 ± .0005 25.5° 32.0 38.1 50.5 62.7 74.0 85.3 96.1 106.6 125.3 142.5 150.5 158.1 Eexc = 5 - 7.5 MeV 26.4° 0.0166 ± .0023 mb/sr 32.9 0.0148 :!: .0021 0.0109 ± .0022 39.3 52.0 0.0136 ± .0019 64.4 0.0093 :!: .0016 76.2 0.0064 ± .0014 0.0070 :t .0020 87.8 0.0062 :t .0018 98.6 108.8 0.0050 :t .0017 127.8 0.0115 ± .0032 0.0066 ± .0023 144.4 152.0 0.0138 :t .0033 159.5 0.0149 :I: .0058 A = 0.0102 :t .0015 - 201 Table 6 Ec.m. :: 8.85 MeV 23.9 0 29.6 35.7 47.3 58.8 69.8 80.7 91.2 101.5 120.7 138.8 147.2 155.6 0.075 ± .010 mb/sr 0.067 :t: .009 0.074 :t: .012 0.063 ± .008 0.060 :t: .009 0.065 :t: .009 0.060 :t: .009 0.067 :t .009 0.069 :t: .011 0.071 :t: .013 0.063 :I; .011 0.075 :t: .014 0.066 ± .014 A = 0.067 ± .003 E c.m. 24.70 30.7 36.8 49.1 60.5 ::I 8.85 MeV 0.146 ± .019 mb/sr 0.134 :t .018 0.148 ± .024 0.133 :t: .017 0.131 :t: .018 72.2 0.124 ± .016 83.2 0.125 :t: .018 0.122 ± .016 93.8 104.0 0.135 :t: .022 123.2 0.138 ± .025 140.5 0.145 :t: .027 148.6 0.142 ± .027 156.9 0.135 :t: .028 A :: 0.133 ± .007 cont. E axc' " 7.5 - 10 MeV 27.2 0 0.043 :t: .006 mb/sr 0.048 :t: .006 0.030 :t: .005 0.026 :t: .005 0.030 :f: .005 66.3 0.027 ± .005 78.6 90.0 0.030 ± .006 101.3 0.029 :f: .005 111.6 0.029 :t .005 0.019 ± .005 130.3 146.2 0.024 ± .005 153.7 0.020 ± .004 160.5 0.026 ± .007 A = 0.0315 ± .0020 33.9 40.5 53.6 axc '" 10 - 12.5 Me V E 28.40 42.3 56.0 69.1 81.5 93.9 105.2 115.1 133.7 0.066 ± .010 mb/sr 0.060 ± .009 0.060 :t .009 0.067 ± .010 0.054 :t .008 0.055 :t: .009 0.051 :t .009 0.049 :t .008 0.061 :t .010 A = 0.057 :t: .006 - 202 - Table 6 cont. Ec.m. • 8.85 MeV 26.9° 39.7 52.3 64.8 77.0 88.6 99.0 109.2 128.7 145.4 1.52.4 Eexc • 12.5 - 15 MeV 0.28 oJ:: .04 mb/sr )o.so 0.054 ~ .008 mb/sr 0.26 :t .04 0.23 :t: .04 45.4 0.051. ;t .007 0.22 ~ .03 0.21 :t .03 0.22 ~ .03 0.21 ± .03 0.19 ± .03 0.20 oJ:: .03 0.20 ~ .0) 0.20 ± .03 A = 0.226 ± .012 60.1 74.1 87.6 100.8 112.3 0.048 :t: .007 0.047 ;t .007 0.049 :t .007 0.053 :t: .008 0.052 ± .009 A :z 0.0,0 :i: .003 - 203 Table 6 cont. Ec.m. .. 7.8.5 MeV 22.8° 34.l 4.5.4 67.1 88.3 108.0 127.1 14.5.2 1.54.1 0.001.51 :t .00023 mb/sr 0.OOl82 ± .00034 0.00088 ± .00018 0.00117 ± .00023 0.00128 :t .00024 0.00117 ± .00041 0.00131 :t .00046 0.00179 t .000.5.5 0.00189 :t .000.56 A '" 0.00127 :t .00010 c .m. = 7.8.5 MeV E 24.8° 0.0032 ± .0005 mb/sr 36.8 0.0036 t .0007 49.0 0.0028 ± .000.5 73.3 0.0024 :t .0004 93.9 0.0028 :t .0005 113.9 0.0027 ± .0008 132.8 0.0030 :t .0011 149.3 0.0032 :t .0009 157.3 0.0029 :t .0009 A = 0.0030 t .0003 c.m. = 7.8.5 MeV E 23.3° 34.9 46.2 68.4 89.6 109 •.5 128.4 146.2 154.8 0.0066 .: .0009 mb/sr 0.0086 ± .0016 0.0064 ± .0010 0.0068 :t .0011 0.0070 :t .0011 0.006.5 ± .0016 0.0077 :t .0022 0.00.58 :I: .0016 0.0057 :t .0017 A = 0.0067 ± .0005 * 3 parameter fit Eexc .. 0 - .5 MeV 0.000.58 :t .00011 mb/sr 0.00038 ± .000l2 0.000.54 :t .00012 0.00030 ± .00008 0.00033 t .0001l 0.00047 :t .00026 0.00038 :t .00026 0.00061 t .00034 0.00046 t .00029 A = 0.00040 ± .00014 2.5.3° 31.9 .50.1 73.8 96.0 116.1 133 •.5 1.50.1 1.58.0 Eexc = .5 - 7 •.5 MeV 26.3° 39.2 52.0 16.1 98.2 118.4 136.1 151.9 159.3 0.0010 ± .0002 mb/sr 0.0010 :t .0002 0.0011 ± .0002 0.0013 :t .0003 0.0015 :t .0003 0.0001 ± .0004 0.0006 :t .0004 0.000.5 :t .0003 0.0004 :t .0003 A '" 0 .0013 ± .0002 * Eexc • 1 •.5 - 10 MeV 27.1° 40.6 .53 •.5 78.2 101.2 121.1 138.3 153.4 160..5 0.0032 :t .0005 mb/sr 0.0027 :t .0004 0.002.5 :t .0004 0.0021 •• 0006 0.0024 :t .000.5 0.0023 :t .0008 0.0012 :t .0001 0.0017 :I: .0001 0.0021 t .0009 A '" 0.0026 :t .0003 - 204 Table 6 oont. Ec.m. a 1.85 MeV 23.7° 35.5 47.2 69.8 91.2 111.3 130.0 147.4 155.7 0.0135 % .0018 mb/sr 0.0158 ± .0026 0.0129 ± .0018 0.0124 ± .0018 0.0128 ± .0019 0.0126 ± .0026 0.0125 ± .0029 0.0132 ± .0027 0.0143 ± .0033 A = 0.0133 ± .0010 Ec.m. = 7.85 MeV Eexc • 10 - 12.5 MeV 28.s<' 42.6 56.2 81.5 104.9 125.5 0.0049 :t .0007 mb/sr 0.0040 ± .0006 0.0045 ± .0007 0.0039 ± .0007 0.0033 :t .0006 0.0044 ± .0011 A = 0.0036 ± .0007 Eexc • 12.5 - 15 MeV 31.2° 46.6 61.6 0.0021:t .0004 mb/sr 0.0015 :t .0003 0.0016 :t .0003 A = 0.0017 :t .00C1t - 205 - Table 6 cont. 23.0° 45.4 67.3 88.2 E .. 9.35 MeV C.m. Eexc • 0 - 5 MeV 0.052 :t .007 mb/sr 0.046 ± .007 50.6 0.034 :t .006 74.4 96.3 0.039 ± .006 25.6° A = 0.042 ± .003 c.m. = 9.35 MeV E 23.4° 46.3 68.5 89.7 0.082 ± .011 mb/sr 0.071 ± .012 0.066 ;I; .011 0.064 ± .011 A = 0.071 ± .006 c.m. = 9.35 MeV E 23.8° 47.2 69.6 91.2 0.23 ± .03 ab/ar 0.21 :J: .03 0.21 :t .03 0.19 ± .03 A = 0.209 ± .015 c.m. = 9.35 MeV E 24.7° 48.7 71.8 93.3 A ~ 0.0111 :J: .0010 Eexc • 5 - 7.5 MeV 26.4° 52.1 76.5 0.049 ± .006 mb/sr 0.039 ± .006 0.045 ± .007 A = 0.044 ± .009 exc = 7.5 - 10 MeV E 27.1 53.6 0.100 ± .013 0.111 ± .016 A = 0.105 ± .021 E = 10 - 12.5 MeV exc 0.46 ± .06 mb/sr 0.41 ± .06 0.39 ± .06 0.37 ± .05 A ... 0.41 ± .03 Ec.m. m 9.35 MeV 26.5° 52.2 0.014 :J: .002 JIlb/sr 0.008 :t .002 0.014 ± .003 0.018 ± .004 0.90 ;I; .11 mb/sr 0.84 ± .12 A .. 0.86 ± .17 exc '" 12.5 - 15 MeV E - 206 Table 6 cont. Ec.m. - 8.35 MeV 22.9° 45.3 66.8 88.2 0.0051 ± .0008 Jflb/sr 0.0044 ± .0009 0.0040 ± .0009 0.0043 :t .0009 A :z 0.0045 ± .0005 c.m. :z 8.35 MeV E 23.3° 46.3 68.2 89.5 0.0095 ± .0014 mb/sr 0.0098 ± .0017 0.0099 :t .0018 0.0072 ± .0014 A = 0.0089 ± .0008 c.m. .. 8.35 MeV E 23.8° 47.2 69.8 90.9 0.026 :t .004 mb/sr 0.025 ± .004 0.023 ± .004 0.024 ± .004 A + 0.025 :i: .002 c.m. ... 8.35 MeV E 24.,a 49.0 12.3 94.0 0.053 ± .001 mb/sr 0.047 ~ .001 0.045 ± .007 0.046 ± .007 A ... 0.048 ± .005 Eexc - 0 - 25.6° 50.4 14.0 5 MeV 0.0016:t .0003 mb/sr 0.0009 ± .0003 0.0013 ± .0004 A ... 0.0013 ± .0003 Eexc ... 5 - 1.5 MeV 26.4° 51.9 0.0032 ± .0005 mb/sr 0.0052 ± .0010 A = 0.0042 ± .0010 exc ... 7.5 - 10 MeV E 27.2° 0.015 :t .002 mb/sr Eexc • 10 - 12.5 MeV - 201 Table 6 cont. Ec.m. - 7.32 MeV 22.70 45.2 0.00019 ;i: .00004 mb/sr 0.00020 ;i: .00004 0.00009 :t .00003 66.9 A ... 0.00015 ± .00006 E c.m. .. 1.32 MeV 0.00040 :t .00001 mb/sr 0.00029 :t .00005 0.00033 ;i: .00008 A .. 0.00033 :t .00001 Ec.m. • 7.32 MeV 23.8° 41.3 69.9 0.00102 ± .00014 mb/sr 0.00074 ± .00012 0.00102 ;i: .00018 A '" 0.00088 :I: .00018 Ec.m. = 1.32 MeV 25.1° 0.00161 ± .00022 mb/sr 49.5 0.00132 ± .00019 73.2 0.00191 ± .00030 A = 0.00153 :t .00<»8 Eexc - 0 - 5 MeV 25.3° 50.0 73.6 0.00012:t .00002 mb/sr 0.00009 ± .00002 0.00014 :I: .00004 A • 0.00011 ± .00003 Eexc • 5 - 1.5 MeV 26.2° 51.7 A • 0.00037;i:.OOOO6 mb/sr 0.00024 ± .00004 0.00028 ± .000(9 Eexe - 7.5 - 10 M!lV 27.1° 53.3 0.00028;i: .00005 mb/sr 0.00032;i:.OOOO6 A a 0.00030 ± .00006 Eexe ... 10 - 12.5 MeV 28.4° 56.5 0.00032 ± .00005 ab/er 0.00028 ± .00006 A = 0.00030 ;i: .00006 - 206 Table 6 cont. Ec.m. = 6.60 MeV 22.7° 45.2 A • Eexc .. 0 - 5 MeV 0.000028. .000009 rrio/sr 0.000017 ± .000006 0.000021 ± .000007 E c.m. = 6.80 MeV 23.2° 46.1 0.000045 ± .000011 rrio/sr 0.000020 :t: .000008 A = 0.000028 ± .000017 Ec.m. = 6.80 MeV 23.9° 47.2 0.000066 ± .000014 mb/sr 0.000060 ± .000015 A = 0.000063 ± .000013 c.m. = 6.80 MeV E 25.2° 0.000147 ± .000024 mb/sr 49.5 0.000106 ± .000023 A = 0.000125 ± .000022 0.000015 :i: .000005 ab/er 0.000008 ± .000004 A • Eexc - 0.000010 :i: .000005 5 - 7.5 MeV 26.1° 51.5 0.000023 ± .000007 mb/sr 0.000014 ± .000005 A • 0.000017 ± .000006 Eexc = 7.5 - 10 MeV 0.000036 ± .000008 _/ar 0.000037 ± .000009 A • 0.000036 ± .000001 27.0° 53.2 Eexc = 10 - 12.5 MeV 28.7° 0.000017:i: .000005 mb/sr 56.6 0.000021 ± .000006 A = 0.000019 ± .000004 - 209 Table 6 cont. (Deuterons) c.m. = 11.85 MeV E 35° 56 82 Eexc "" 0 - 1 MeV 0.348 ± .008 mb/sr 0.324 ± .010 0.342 ~ .010 A = 0.34 :t .01 Ec.m. = 9.85 MeV 34° 54 80 exe = 0 - 5 MeV E 0.0565 ± .0018 mb/sr 0.0485 ± .0016 0.0516 ± .0018 A D 0.052 ± .010 Production Cross Sections for Charged Particles. 38 * 6 81 :t 13 133 ± 21 274 ± 42 12.5-15 15-17.5 SUM 36.5 :t $.7 20 :t 3 1.68 :t .21 -3.7 20.0 ± 5.83 t .89 10.9 ± 2.7 2.8 ± .5 10.1:t 1.7 5.1 ± .9 0.84 t .13 2.6 ±.5 15.0 ± 2.4 4.2 ±.7 7.5-10 10-12.5 0.33:t .06 .89 * .15 5.3 %.9 1.44 ± .23 .048 O.3~ :t 0.0016:t .0004 .0077 •()(X)6O 0.0363:t 0.00297:t .006 .028 1.08 '* .17 0.019:t 0.167 ± O.Olll:t 0.00079 % .0028 .00020 0.0041 ± 0.00035:t .0010 .00022 .10 0.084 t .014 0.037:t .007 -6.80 0.0019:t 0.00026:t .0008 .00010 7.32 0.60 :t .0$ 0.31 :t 0.112 * .020 .003 0.016 :t 0.056 t .010 0.136 ± .53 ± .09 .023 7.85 8.35 8.85 PROTONS 9.35 5-1.5 0-5 MeV Eexc E = 11.85 MeV 9.85 em 1.8 :t.3 .72:t .12 The total cross sections for intervals in excitation energy are taken from Table 6. The method for determining the extrapolated cross section is described on page 103 of the text. C1 is the total tot production crOBS section obtained by evaluating the data in the C.M. frame. C1 is the total 1ab production cross section from Table 8 (obtained by evaluating the data in the Lab frame). All errors are total errors; thus J the error on C1 is not just the square root of the sum of the squares of tot the errors in the columes above it. All cross sections are in mb. Total Table 7 '" o I-' 310 :t 50 mb 47 ± 7 45 ± 7 310 :t 47 O'lab Adopted Value 49 ± 6 310 ± 44 O'tot 6.5 ± 1.0 0.46 :t .08 0.45 ± .07 6.4 ± 1.0 .03 0.46 ± .08 ± 0.045 ± .010 0.0037 ± .0008 0.045 ± .010 0.0037:i: .0008 0.009 ± .004 0.0007 ± .0003 6.80 0.16 1.32 0.00297 ± .00060 7.85 0.304 ± .048 0.0363 :i: .0071 cont. 6.6 ± 1.0 0.73 ± .20 12.8 ± 2.9 38 ± 13 5.83 ± .89 8.85 214 :i: 42 mb 36.$ ± 5.7 9.85 EX TRAP • SUM E = 11.85 MeV em PROTONS Table 1 f\) f-J f-J 0.63 :t; .10 6.2 ± 1.0 39 ± 6 51 z 9 124 :i: 20 12.5-15 15-11.5 SUM 13.0 :i: 2.0 0.72 ± .14 4.0 ± .7 21 ± 3 10-12.5 1.91 :t; .30 0.40 ± .07 1.3± .3 1.8 ± .3 8.1 ± 1.4 7.5-10 0.19 ± .05 0.052 ± .014 0.128 ± .027 0.120 ± .021 0.021 ± .006 0.045 ± .011 0.032 ± .006 0.017 ± .003 0.0049 :t .0019 0.016 :t .005 0.040 z .009 0.55 z .14 0-5 MeV 0.66 :t .12 1.85 8.35 8.85 3.3 :t .5 9.35 5-1.5 11.85 MeV 9.85 0.147 :t .025 a 0.26 :t .05 em E 1.09 :t .19 Eexe ALPHAS Table 1 eont. 6.80 0.0124 ± 0.00104 ~ .0025 .00020 0.0038:t 0.00024 ± ~ .0010 .00006 I I\) 0.0037 ± 0.00045 ± .0010 .00010 I 0.0035 ± 0.00022 ± .0012 .00008 0.0014:t 0.00013:t .00006 .0004 7.32 150 ± 25 (Tlab Adopted 17 ± 3 15.9 t 2.5 152 t 24 Value 2.31 ± .38 17.6 ± 2.9 149 ± 24 (Ttot 2.2 ± .4 2.17 ± .34 0.40 ± .10 4.6 ± 1.1 25 ± 5 1.91 :t .30 8.85 124 z 20 mb 13.0 z 2.0 9.85 EITRAP. SUM Ecm = 11.85 MeV ALPHAS 7.85 7.32 6.80 0.14 :t .025 0.132 ± .021 0.017 :t .0035 O.OOll2 :t .00023 I I-' N w 0.153 ± .028 0.0169 ± .0034 O.OOill ± .00023 0.033 ± .010 0.0045 :t .0015 0.00008 ± .00008 0.120 :t .021 0.0124 :t .0025 0.00104:t .00020 Table 7 cont. a(3He ) * < 6 mb <OS < 0.1 < 0.003 ac3H) * < 3 mb < 0.2 < 0.05 < 0.002 * Three standard deviation upper limits. 11.85 MeV 9.85 8.85 7.85 Eem 0.75:t .18 mb 5.4 :t IS mb atot 3H and 3He 0.10 :t .10 1.1 :I: 1.1 0.65 :t .16 mb 9.85 EXTRAP. -- ,. 11.85 MeV 4.3 :t 1.1 mb cm E 0-7 o - 5 MeV Eexc c~nt. DEUTERONS Table 7 I\) I-' f:"' - 215 - Table 8 Laboratory Differential Charged Particle Cross Seotions Produotion. for All errors listed are relative errors only (see page 104 of the text) • The coeffioient A of Po (oos e) in a least squares .fit to the angular distribution with Legendre polynomials is also given. da) * ern 1ab,p+d E = 11.85 MeV o.m. 200 30 40 50 60 10 80 90 100 110 120 120 130 140 150 55.8 ± 41.1 ± 40.$ ± 35.1 ± 31.0 ± .4 21.6 ± .6 .8 41.1 ± 1.4 mb/sr 31.4 :t 1.3 23.9 ± 1.5 19.4 :t 1.1 11.1 :t 1.9 13.6 ± 1.8 24.4 ± .8 11.5 :t 2.0 21.5 ± .8 9.1 :t 2.1 .4 mb/sr .5 .6 l8.8:t .9 16.8 :t 1.0 13.$:t .9 14.8:t .6 14.5 ± .6 l3.6:.t: .1 12.8:t .6 A = 24.8 :t 0.2 1.2 :.t: 2.1 5.1 :t 1.5 3.8 :t 1.4 4.0 :t 1.4 3.4 ± 1.2 3.0 :t 1.2 2.9 :t 1.2 A • 12.2 :t 0.$ * The extrapolated oounts are included in the calculation of these cross sections and the errors quoted. - 216 Table 8 cont. Ec.m. .. 9.85 MeV 200 20 30 30 30 40 40 &J 80 100 120 140 150 150 7.62 ~ .16 mb/sr 8.02 :t .08 7.04 ~ .18 6.13 :I: .14 5.52 ~ .12 6.36 ± .19 5.92 :I: .16 4.91 :I: .19 3.58 :I: .07 2.81 ± .09 2.44 ~ .14 2.03 .:t .10 1.90 .:t .10 1.80 ~ .20 A = 3.58 :I: .04 3.79 :I: .1$ mb/sr 3.97 .:t .19 3.11 :I: .19 2.68 :I: .23 2.37 :I: .19 2.56 :t .21 2.38 :t .23 1.87 :I: .13 1.26 :I: .18 0.17 ± .16 0.50 :I: .13 0.38 ± .13 0.34 .:I: .13 0.26 :t .10 A .. 1.26 ± .05 Ec.m. .. 8.85 MeV 200 30 40 50 &J 70 80 90 110 130 140 150 1.053 :I: .027 ab/sr 0.901 :I: .037 0.788 ~ .023 0.758:t .018 0.740 :I: .060 0.600 :I: .021 0.516 :I: .013 0.441 :I: .015 0.372 .:t .016 0.313 .:I: .016 0.293 :I: .016 0.258 ~ .011 A .. 0.514 :I: .006 0.432 .:I: .025 mb/sr 0.392 ~ .048 0.325 :I: .023 0.309 ± .033 0.256 :I: .037 0.220 :I: .036 0.171 :I: .023 0.136 ± .024 0.100 ± .028 0.066 :I: .026 0.044 :I: .012 0.051 :I: .018 A '" 0.173 .:I: .008 - 217 Table 8 cont. Ec.m. • 7.85 MeV 200 30 40 60 80 100 120 140 150 0.066* ± .019 mb/sr 0.065* ± .014 0.054 *± .010 0.0456 :t: .0044 0.0361 :t .0015 0.0291 :t .0015 0.0251 ± .0015 0.0207 :t: .0013 0.0206 ± .0014 A = 0.0362 ± .0016 0.0256 ± .0025 mb/sr 0.0198 ± .0022 0.0195 ± .0019 0.0145 :t: .0013 0.0102 :t .0011 0.0086 :t: .0020 0.0059 :t: .0021 0.0036 :I: .0014 0.0032 :t .0013 A = 0.0105 :I: .0006 * These values have such large errors because of the large number of Hydrogen recoils contaminating the spectra. - 21B Table 9 Limits on the Reaction Cross Sections. Limits for the reaction cross section for 160 + 160 to exit channels emitting alphas or protons are given. The upper limit is the production cross section. Lower limi ts were determined by counting all protons or alphas as coming from three body breakup reactions except those which were definitely from two body exit channels (see the text page 101). Typical total errors are 15 - 20 %. cm = 11.B5 MeV E 9.B5 B.B5 1.B5 Protons Upper Limit Lower Lim t I Lower Lim t II 312 mb 160 161 45.0 mb 23.1 24.0 6.45 rob 3.51 3.59 0.455 mb .261 .210 Alpr.a.s Upper Limit Lower Limit I Lower 1imit II 153 92 93 15.9 2.11 1.63 1.66 .132 .112 .115 10.B 11.0 - 219 Table 10 Total Cross Section for 160 + 12C __ n + 27Si • Cross sections and total errors for 160 + 12C -. n + 27Si were determined using the activation method (see the ActiVation Method Section). Fnergy losses have been subtracted and produce an overall uncertainty in the energy of ~ 100 keV (lab). E 160z1ab 23.9 ~ .1 MeV 21.9 19.9 E em 10.24 ,., .04 MeV 9.38 8.53 E ~ cutoff 0.5 MeV .5 .5 " " " If " .8 18.9 17.9 16.9 15.9 14.9 13.9 12.9 8.10 7.67 7.24 6.81 6.39 5.96 5.53 .5 .5 .5 .5 .5 .5 .5 a(27Si) 36 ~ 7 nab 29 ± 6 16 ± 3 19 ± 4 19 ~ 4 10.4 ± 2.1 7.5 :t 1.5 2.8 :t .6 1.23 :t .27 0.36 :t .09 0.084 :t .021 0.016 :1: .005 - 220 Table II Total Cross Sections for the Production of J1S and JOp • Cross sections and total errors for the production of J1s and 30p by 160 + 16 0 reactions were determined using the activation method (see the Activation Method Section). Energy losses have been subtracted and produce an uncertainty in the energy of each point of % 50 keV (C.M.). The average cross sections are plotted in Figures 3)~ and 35. Individual Runs Errors O'~31S) O'~30p ~ + Relative E em E~ cutoff 12.00 HaV 0.5 MeV 11.98 1.4 11.96 1.3 11.95 .7 .5 " 11 .5 11 .5 tJ .4 1\ .5 fI 2.0 11.93 1.8 .3 " 11.92 1.4 6.5 ± 1.1 mb 69 ± 11 mb 6.7 ± 1.5 83 ± 17 5.0 :I: 1.2 51 ± 10 6.J ;I; 1.6 95 :I: 19 6.0 ± 1.2 60 ± 10 4.1;1;1.3 64 ± 10 72 ;I; 12 5.5 :I: 1.1 9.96 9.95 1.9 ± .4 II " 9.92 1.3 .4 1.1 2.0 .6 6.3 % 1.6 5.9 ;I; 1.0 6.5 :t. 1.4 2.6 :t .5 59 ;I; 9 58 % 9 61 ;I; 15 91 ;I; 22 66 ± 10 69 :t. 14 7.6 :t 1.5 8.2 ± 1.3 7.0 ;I; 1.4 7.4 :t 1.8 8.8 :t 1.8 Averages + Total Errors O'( 31 S) O'(30p ) 6.5 :t 1.4 mb 69 :t llpnb 6.7 ± 1.7 83 ± 19 5.0 :t 1.3 51 ± 12 5.5 ±.1 63;1; 9 6.0 :t 1.1 70 ± 13 6.5 :t 1.6 69 ± 16 1.9:t.5 7.6 :t 1.1 1.6 :t. 1.2 2.6 ±.6 8.8 ± 2.0 - 221 Table 11 E E@ cutoff em 8.97 MeV 1.4 MeV 8.96 1.3 ae 1 S) cont. a(30p ) 0.72 :t .18mb 1.4 :t; .3 mb 0.9 :t; .2 0.42 :I: .16 " 1.3 1.1 :t .2 8.95 .4 1.2 :t .2 8.91 1.4 0.67 :t .16 1.2:t .3 " 1.3 0.59 ± .15 0.8 :t .2 8.45 .5 0.11 :t; .06 0.47 :t .09 II 1.1 0.20 :t .05 " 2.0 0.25 :t; .07 B.41 1.3 0.14 :t .04 0.20 :t; .05 II 1.3 0.15 :t; .06 0.20 :t; .05 8.05 2.0 7.95 .8 0.034 :t; .018 0.091 :t .026 " 1.1 0.037 :t .033 0.054 ± .015 7.91 1.3 0.041 :t .017 7.45 .8 II 1.1 0.019 :t .016 0.010 :t; .003 7.41 1.3 0.011 :t .009 0.004 :t .003 ae 1 S) a(30p ) 0.72 :t; .20 mb 1.4 :t .4 1.0:t; .2 0.42 :t; .17 1.2:t .2 0.63 t .13 0.9 t .2 0.11 :t; .06 0.25 :t; .10a 0.14 :t .04 0.20 :t; .08 0.10 :t .03 b 0.06 :t .02 c 0.07 :t .02 0.07 :t .05 0.034 :t .018 <O.09 0.039 :t .012 0.041 :t .018 <o.06 0.023 :t .008 0.019 :t .016 a a 0.011 :t; .009 a) Variation in the cross section with the beta cutoff energy gives uncertain results. See the text page 139. b) Same data analyzed with a contaminant of half1ife 400 sec. c) Same data analyzed with a contaminant of haInife 1200 sec. a a 12 0.0272 ±. 0019 0.0135±.0012 0.0096 ± .0011 0 0 90 1300 O. 0294 ± . 0030 45 0 0.0373 ± .0028 00 28 N NMON Slab lab flat res. 2.8 ± . 3 3.9 ± .4 7.8±.6 8.4 ± • 9 10.7±.8 mb/sr da' ) d.n Angular Distribution of Neutrons at E 1. 039 1. 039 1.042 1. 041 1. 041 Correction Factor lab corr. 2. 9 ± .3 4. 0 ± .4 8.1 ± .6 8. 8 ± • 9 I\) I\) I\) 11.1±.8 mb/sr dcr ) dlf = 11. 95 MeV. cm All errors are relative errors. In addition there is a 20 % error associated with the monitor counter solid angle, the relative efficiency of the long counter, and the elastic scattering cross section on all points (see page 1470f the text). Table - 223 - Table 13 Differential Crosa Sections for E f) 12 C , 12 f) 20 lab C(g.s.) + 20 ern N e, lab 0 + 16 0 _ 12 C 1- 20 Ne at 11. 95 Me V. := f) ern, 12 C dO" dQ) ern ± Relative Error Ne(g . s.) ° ° 20. 0° 25. 0° 30. 0° 35. 0° 40. 0° 45. 0° 50. 0° 55. 0° 57. 0° 60. 0° 65. 0° 70.0° 75. 0° 80.0° 85. 0° 16 43.0 43. 8° 43. 1 41. 6° 39.4° 36. 9° 34. 1 31.2° 30. 0° 28. 2° 25. 2° 22. 2° 19.4° 16.7° 14.3° ° (spectrometer data) _ 7.0° 37. 3° 46. 5° 55. 7° 64. 9° 73. 9° 82.9° 91. 7° 100.3° 103. 7° 108. 8° 116.9° 124. 7° 132. 0° 138. 7° 144.8° 0.25 ± . as mb/sr .53 ± . 09 .66 ± . 12 .24 ± . as · 13 ± . 03 · 78 ± . 14 1. 43 ± . 23 .47 ± . 08 .23 ± . 04 .12±.03 . 33 ± . 06 .51 ± . 09 .59±.10 . 48 ± • Oq · 13 ± . 03 ( 18%) ( 17%) ( 18%) (19%) (21%) ( 18%) (16%) (17%) (19%) (21%) ( 17%) ( 17%) ( 17%) (18%) (21%) < 6. 5 12C (g. s.) + 20Ne~c(1. 63) · 07 ± . 02 12 C (g. s.) + 20 .:' 12 ':. 20 Ne (4. 25) and C (4.43) + Ne (g. s. ) <. 03 (29%) - 224 Table 14 Best Fits to the 16 0 + 16 E 0 _ em 12 C + 20 . . . Ne Angular Dlstrlbuhons at = 11. 95 Me V. 2 L Values X 0,4 4,8 2,4 28 32 46 6.6 ± .4 mb 7.4 ± .4 7.9±.6 2,4,6 0,4, 10 4, 8, 1O 4.4 4.4 24.5 2.5 ± 6 7.8±.5 7.5 ± .5 IJ' TOT ± Fitted Errol' .0001* .0()()3* .0003* .0011 Extrapolated or estimated cross sections .0031 6.80 .002* .004* .004* .017 .045 7.32 .029 .03* .12 .14 .27 .46 7.85 .48 (see the text page 169). <.002 <.05 .2* .01* < .2 <3 0'(3H) 1* 10 .82 1.9 5.1 1.7 2.2 3.6 6.5 8.85 6.6 58 11 93 17 O'(C+Ne) 24 0'(31 S ) 150 0'(30p ) 161 41 310 O'rr(a) O'prod(a) O'rr(p) 9.85 11.85 MeV O'prod(P) uncertainties in the extrapolated cross sections. <.003 < .1 < .5 <6 a(3 He ) uncertainties in the three body reaction percentage J errors on the measured cross sections, and E em * and the errors on the measured cross sections are given in Tables 7 and 11. O'II(P) and O'rr(a) are the values of Lower Limit n from Table 9. The total cross sections are averages of a. and 0' (see the text page 107 and Figure 41) and 1 ower upper they are tabulated below. The errors on the total cross sections were estimated from the All cross sections are given in mb 16o + 160 Total Reaction Cross Sections. Table 15 N N VI. .0052 6.80 * O'total at two energies was obtained from 0'upper body percentage. .23 .28 .25 .27 .30 .38 O'total O'prod(a) .13 .13 .11 .16 .15 .16 0'pro d(n+d) O'total .17* .20* .22 .26 .31 .34 0'3 body O'tota1 and the estimated values of the three .79 .75 0.060 ± .021 .068 7.32 0.0047 ± .0017 .84 0.55 ± .17 .64 .46 7.85 .80 9.4 6.8 8.85 8.1 ± 2.0 67 45 9.85 .84 O'total 56 :t 14 O'total O'prod(P) .78 0'upper 400 :t 100 mb 328 a.lower 476 11.85 MeV E em Table 15 cont. I ()'\ I\) I\) - 221 Table 16 The Ratio of the Elastic Scattering to the Mott Scattering Cross . 12 12 Section for C + C Energy losses have been included, but there is an overall uncertainty in the c. m. energy scale of ± 50 KeV (c. m. ) (See the text page 117 and figure 42 ). E crn 3.89 ± . 05 MeV 4. 14 4.39 4.64 4.89 5.02 5. 14 5.27 5.33 5.39 5.46 5.52 5.58 5.64 5. 71 5.77 5.80 5.83 5.89 5.92 5.96 6.02 6.05 6.08 6. 14 6. 21 6.27 6.33 6.39 6.41 6.46 6.48 6.52 Ratio to Mott O. 996 ± .007 1. 000 ± . 006 1. 004 ± .005 • 992 ± .007 1. 007 ± .006 .996 ± .012 1. 008 ± .007 · 985 ± • 009 1.002±.012 1. 007 ± • 007 1. 021 ± • 012 1. 024 ± .007 • 995 ± .008 • 967 ± .006 · 993 ± . 008 1. 012 ± .006 1.002±.012 1. 004 ± .007 • 940 ± • 006 .937±.012 · 937 ± .008 • 959 ± • 007 • 981 ± . 012 • 977 ± .007 • 938 ± .006 · 914 ± .007 .914 ± .006 .985 ± .006 .939±.007 .930±.017 • 865 ± .012 .845±.015 .816 ± .012 E cm 6.54 6.60 6.64 6.66 6. 73 6.77 6.79 6.85 6.89 6. 91 6.98 7.02 7.04 7. 10 7. 14 7. 16 7. 23 7. 29 7.35 7.41 7.48 7.54 7.60 7.66 7. 73 7. 79 7.85 7. 91 7. 98 Ratio to Mott .776±.014 .701±.013 .685 ± • 006 • 733 ± . 014 .808±.015 · 753 ± • 008 .696 ± • 013 • 728 ± • 014 · 723 ± .007 .651±.013 · 506 ± • 010 .477 ± • 006 .474 ± .010 .455 ± • 009 .418 ± • 005 .424 ± • 008 · 420 ± • 008 · 356 ± . 007 · 358 ± . 007 · 317 ± . 006 • 265 ± .006 · 267 ± • 007 · 281 ± • 006 · 298 ± . 007 .400 ± . 007 .422 ± .008 · 461 ± • 010 .417 ± • 008 .402 ± • 009 Ratio of the Elastic Scattering the Rutherford 160 + 12C. to Scattering Cross Section for 160 ,lab .999 ± .003 1.001 :I; .004 1.002 ± .004 1.008 ± .004 1.000 ± .004 1.004 ± .004 1.001 ± .004 16.02 16.27 16.52 1.001 ± .003 .993 ± .004 1.002 :t .004 1.012 ± .009 1.008 ± .009 1.001 ± .009 .994 ± .009 1.028 ± .018 .981 ± .009 .919 :t .009 .968 ± .009 1.000 ± .008 1.000 ± .008 1.006 ± .008 1.021 ± .018 .991 ± .009 .988 ± .009 1.003 :I; .009 .968 ± .015 .995 ± .008 1.001 ± .008 1.001 :I; .008 1.011 ± .008 1.000 ± .008 1.005 ± .008 .999 :I; .008 .987 ± .007 1.002 ± .012 .996 ± .003 1.004 ± .003 0 1.008 ± .018 1.000 :t .009 .992 :t .009 LOll :t .020 90 Ratios to Rutherford 1.011 ± .007 10 0 1.005 ± .005 eem =- 65 0 15.02 15.27 15.52 15.11 15.81 14.81 14.77 13.81 14.27 14.52 12.11 MeV 12.81 13.21 13.71 13.81 E 0 .981 ± .010 .910 ± .009 .967 ± .010 1.004 ± .009 .998 ± .010 .988 ± .010 .990 ± .010 1.014 ± .019 .992 :t .019 1.006 ± .009 .992 ± .009 .980 ± .009 .967 ± .016 1.037 ± .019 1.017 ± .009 1.002 ± .009 1.004 ± .021 116 .980 ± .008 .973 :I; .008 .936 :I; .008 .993 :I; .008 .987 ± .008 .982 ± .008 .980 ± .008 1.005 ± .008 .992 :I; .008 .998 ± .008 .997 ± .008 1.012 ± .008 1.015 :I; .012 12~ Energy losses have been subtracted from the quoted energies and result in an overall uncertainty in the energy scale of ± 50 keV (c .M.) (see Appendix I). The Table 17 I\) I\) (X) 0 .927 ± .008 .889 $ .008 .856 ± .008 .844 :t .008 .821 :t .008 .777 :i: .006 .739 :t .008 .699 :I: .007 .694 :t .007 .653 :i: .007 .573 :I: .007 .581 :I: .007 .548 :I: .006 .530:t .006 .510 :t .006 .424 :I: .005 .381 :I: .005 .968 :I: .010 .985 :t .017 .950 ± .010 .921 :t .010 .904 ± .009 .898 ± .010 .846 :t .016 .861 :I: .009 .805 :t .009 .768 :t .009 .762 :t .009 .767 :t .015 .732 :I: .009 .643 :I: .008 .624 :I: .007 .637 :I: .007 .578 ± .014 .576 :I: .007 .540 :I: .007 .495 :I: .006 .449 :t .005 .244 :I: .008 .169 :I: .006 .964 :I: .010 .964 :I: .016 .965 :t .009 .983 ± .010 .969 :t .010 .934 ± .010 .960 :t .018 .948 :i: .010 .939 :t .010 .911 :t .010 .868 :I: .009 .899 :t .015 .872 :t .009 .843 :t .009 .837 :t .009 .760 :I: .008 .761 :t .015 .773 :t .008 .757 :t .008 .715 :t .007 .699 :t .008 .601 ± .012 .443 ± .009 1.009 $ .008 1.017 :t .008 1.009 ± .008 .992 :t .008 1.008 :t .009 1.031 ± .009 1.032 :t .009 1.045 ± .009 1.039 ± .009 1.027 ± .009 1.043 ± .009 1.034 ± .009 .999 :I: .008 1.001 :I: .008 1.015 :t .008 1.014 ± .008 1.005 ± .004 1.006 :t .004 1.007 ± .004 1.009 :t .004 1.017 :I: .004 1.006 :I: .004 1.007 :t .004 1.010 :t .004 1.015 •. 004 1.026 :I: .004 1.022 :t .004 1.029 :I: .004 1.026 :t .004 1.013 :I: .004 1.010 :t .004 1.027 :I: .004 17.02 17.27 17.52 17.77 17.81 18.02 18.27 18.52 18.77 18.81 19.02 19.27 19.52 19.77 19.81 20.02 20.27 20.52 20.77 21.81 23.81 1.007 :I: .008 1250 1.006 :I: .004 0 -116 16.77 MeV 16.81 90 70 6~ ~ab 0 Table 17 cont. \0 I\) I\) - 230 Table 18 12C + 12C Gamma Yield The yield and relative error of . as y's a Func t,ion with energy of Energy. E > 1.4 MeV y is cm .. 3.99 MeV to the data of Patterson, Winkler and Zaidins (1969). The energies are corrected for losses in the gas normalized at E and there is a : 50 keV (C.M.) uncertainty in the energy scale associated with this correction (see Appendix II). Ecm Normalized Yield 7.485 MeV 7.435 7.385 7.335 7.285 7.235 7.185 7.135 7.085 7.035 420 :t 4% 411 :t 4% 385 :t: 4% 424 ± 4% 457 : 4% 363 :t 4% 399 ± 4% 360 ± 4% 328 ± 4% 367 ± 4% 6.160 ~V 6.135 6.110 6.085 6.035 5.985 6.985 6.935 6.885 6.835 6.785 6.735 6.720 6.710 6.685 6.635 406 :t 4% 334 ± 4% 349 :t 4% 353 ± 4% 321 : 4% 265 :t 4% 249 :t 4% 254 : 4% 261 :t 4% 292 ± 4% 5.185 5.135 5.685 6.585 6.535 6.485 6.435 6.385 6.335 6.285 6.235 6.210 6.185 184 :t 4% 163 :t 4% 196 :t: 4% 163 :t 4% 159 : 4% 174 ± 4% 200 ± 4% 179 ± 4% 158 :t 4% 136 :t 4% 5.435 5.425 5.385 E cm II 5.935 5.885 5.835 II 5.635 5.585 5.535 5.505 5.485 5.460 " " 5.350 5.335 5.310 5.285 5.270 Normalized Yield 124 ± 4% 124 ± 4% 88.7 :t 4% 81.9 :t 4% 82.5 :t 4% 130 ± 4% 129 ± 4% 104 :t 4% 64.9 :i: 4% 42.6 ± 4% 47.2 : 4% 48.9 ± 4% 75.3 ± 4% 74.2 ± 4% 97.1±4% 68.6 : 4% 35.0 ± 5% 25.7 ± 4% 22.7 ± 5% 19.9 ± 4% 17.7 :t 5% 17.2 ± 4% 17.8 :t 5% 18.1 :t: 5% 16.7 : 4% 14.1 :t 4% 14.2 :t 5% 12.9 ± 4% 13.3 ± 5% 12.9 ± 4% - 231 Table 18 cont. Normalized Yield Eem Normalized Yield 12.9 :I: 5% 12.6 ± 4% 10.6 :I: 4% 9.9 :t 5% 9.0 ± 4% 8.6 ± 5% 8.4 ± 4% 8.0 ± 5% 7.7 :t: 4% 7.8 ± 4% 4.335 MeV 4.300 4.260 4.220 4.180 4.145 4.105 4.065 4.030 0.58 ± 5% .58 ± 5% .62 ± 5% .54 :t 5% .52 ± 5% .369 ± 5% .228 ± 5% .148 ± 5% .119 ± 5% .113 ± 6% 3.990 .087 ± 6% 5.000 4.985 4.960 4.920 4.880 4.845 4.805 4.765 11.1 ± 4% 10.8 ± 5% 13.1 ± 4% 12.4 ± 5% 9.3 ± 4% 7.4 :t: 4% 8.2 ± 4% 7.1 ± 4% 5.4 :t: 5% 4.1 :I: 5% 4.730 4.690 4.650 4.610 4.575 4.535 4.495 4.455 4.415 4.375 2.11 :I: 5% 1.52 ± 5% 1.49 :I: 5% 1.80 :I: 5% 1.82 ± 5% 1.25 ± 5% 1.52 :I: 5% 1.54 ± 5% .91 ± 5% .65 :t 5% 11 Ecm 5.235 MeV 5.230 5.190 5.185 5.155 5.135 5.115 5.085 5.075 " 5.035 II " (normalization point) 3.950 3.910 3.870 3.835 " 3.795 . 3.755 3.715 " 3.675 .052 ± 6% .034 ± 6% .0254 :t: 7% .0195 ± 7% .0175 :I: 7% .0175 ± 7% .0190 :t: 7% .0149 ± 7% .0201 :I: 7% .0125 :I: 7% .0166 ± 7% .0105 ± 7%