The ²⁶Mg(p,n)²⁶Al and ²³Na(α,n)²⁶Al Reactions Citation Skelton, Robert Thomas (1985) The ²⁶Mg(p,n)²⁶Al and ²³Na(α,n)²⁶Al Reactions. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/z85k-2k90. https://resolver.caltech.edu/CaltechTHESIS:02012019-083752423 Abstract Cross sections for the 26 Mg (p ,n) 26 AI reaction have been measured from threshold at E p = 4.988 MeV to E p = 5.820 MeV. Cross sections for the 23 Na (α,n) 26 AI reaction have been measured from threshold at E α = 3.483 MeV to E α = 4.597 MeV. In each case separate measurements have been to the ground state and to the first and second excited states of 26 AI. Cross sections for the inverse reactions have been calculated and reaction rate factors relating to the destruction of 26 AI in a supernova environment have been determined. Astrophysical implications relating to the observation of live and extinct 26 AI are discussed. Excitation functions for several additional exit channels for the 26 Mg + p and 26 Na + α reactions are reported. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: Physics Degree Grantor: California Institute of Technology Division: Physics, Mathematics and Astronomy Major Option: Physics Thesis Availability: Public (worldwide access) Research Advisor(s): Kavanagh, Ralph William Thesis Committee: Koonin, Steven E. (chair) Leighton, Robert B. Gomez, Ricardo Kavanagh, Ralph William Defense Date: 10 October 1984 Funders: Funding Agency Grant Number NSF PHY79-23638 Record Number: CaltechTHESIS:02012019-083752423 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:02012019-083752423 DOI: 10.7907/z85k-2k90 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 11377 Collection: CaltechTHESIS Deposited By: Mel Ray Deposited On: 01 Feb 2019 19:39 Last Modified: 16 Apr 2021 22:16 Thesis Files Preview PDF - Final Version See Usage Policy. 21MB Repository Staff Only: item control page

THE 26 Mg(p,n) 26 AI AND 23 Na(cx,n) 26 AI REACTiONS thesis by Robert Thomas Skelton In Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy California lnstitute of Technology Pasadena, California 1985 (Submitted October 10, 1 984) -ii- AC Kf\JOW LEDG EMENTS I wish to express my appreciation to the faculty, students, and staff of the W. K. Kellogg Radiation Laboratory for providing an atmosphere wherein research has been not only Interesting and exciting, but also fun. In particular I wish to thank Professor R. W. Kavanagh for his patient instruction and guidance, especially when many aspects of this project took more time than anticipated. I am also grateful to Professor W. A. Fowler for his advice and informative discussions, and to Professors C. A. Barnes and S. E. Koonin for their support. Other individuals who have been of particular assistance to me are Professor D. G. Sargood, Dr. H. S. Wilson, Dr. J . L. Osborne, Dr. M. H. Mendenhall, and Dr. J . H. Thomas . Finally, I want to express my appreci ation to my parents, Robert and Mary Skelton, to my sisters , Susan, Rebecca, and Melissa, and t o my uncle and aunt, Ted and Louise Carmack, for their understanding and encouragement during this period. This research was supported in part by the National Science Foundation (PHY79-23638). -iii- ABSTRACT Cross sections for the 26 Mg (p ,n) 26 AI reaction have been measured from threshold at E 23 F =4.988 MeV to E F =5.820 MeV. Cross sections for the Na (cx,n) 26 AI reaction have been measured from threshold at E a =3.483 MeV to E a = 4.597 MeV. In each case separate measurements have been to the ground state and to the first and second excited states of 26 AI. Cross sections for the inverse reactions have been calculated and reaction rate factors relating to the destruction of 26 AI in a supernova environment have been determined. Astrophysical implications relating to the observation of live and extinct 26 AI are discussed. Excitation functions for several additional exit channeis for the 26 Mg + p and 23 Na + ex reactions are reported. -iv- TABLE OF CONTENTS page ACKNOWLEDGEMENTS ii ABSTRACT iii I. INTRODUCTION 1 A. 26 AI and the Early Solar System 1 B. Scope of this Experiment 3 C. Overview of Experimental Techniques 4 II. EXPERI MENTAL APPARATUS AND PROCEDURES 5 A. Tar gets 5 1. 26 Mg Targets 5 2. 23 Na Targets 8 B. Accelerator, Beam Transport, and Vacuum Systems 9 1. Negative lon Source for Proton Beams g 2. JN Accelerator for a -Particle Beams g 3. EN Tandem Accelerator 10 4. Beam Optics 10 5. Vacuum Systems 10 C. Sequ ence Timer 11 D. Neutron- Det ect ion Sy stem 11 E. {3+ and 7-Ray Detection Systems 13 -v- Ill. DATA ANALYSIS 16 A. Target Yield Formulae 16 1. Thin Target 16 2. Thick or Semi-Thick Target 16 B. Total Neutron Cross Sections 17 C. Cross Sections to the First Excited State 19 D. Cross Sections to the Second Excited State 22 IV. RESULTS AND CONCLUSIONS 24 A. Experimental Results 24 B. Comparison to Previous Experiment 24 1. 26 Mg(p,n) 26 AI Experiments 24 2. 23 Na (a,n ) 26 AI Experiments 26 C. Comparison to Theory 27 D. Astrophysical Implications 30 E. Conclusions 30 APPENDIX A: Additional Excitation Functions 3.2 REFERENCES 33 TABLES 37 1. 26 AJ(ni,pi 6 Mg Experimental Reaction Rate Factors 37 2. 26 AJ(ni,a) 23 Na Experimental Reaction Rate Factors 39 3. 26 AI Theoretical Reaction Rates 41 4. Summary of Excitation Functions 43 -vi- 45 FIGURES 1. Energy Level Structure and Decay Scheme of 26 AI 45 2. The Mg-AI Cycle 47 3. Water-Cooled Target Mount 49 4. Rutherford Backscattering for 26 Mg Target 51 Thickness Measurement 5. Rutherford Backscattering for 23 Na Target 53 Thickness Measurement 6 . Target Chamber 43 7. Output Spectrum from a 3 He Detector 57 8 . Output from the Priority Encoder 59 9. Arrangement of the Scint illator Detector for Counting 61 {:3+ Particles 10. Output from a Ge(Li) Detector Counting a a 152 Eu Source 63 11. Gamma-Ray Detection Efficiency Calibration 65 12. Typical Nal Spectrum from 67 26 Mg(p,n 1 ) 26 AI Measurements 13. Times in the Bombard-and-Count Cycle 69 14. Typical Ge(Li) Spectrum from 71 26 Mg (p ,n ) 26 AI Measurements 2 15. Cross Sections for 26 Mg (p ,ni ) 26 AI 73 16. Cross Sections for 23 Na (a,n t. ) 26 AI 75 17. Comparison to Previous 26 Mg (p,n) 26 AI (0) 77 Measurements 18. Comparison to Previous 26 Mg (p ,n 1 ) 26 AI Measurement 79 -vii- l~. Comparison to Previous 26 Mg (p ,n 2 ) 26 AI 81 Measurement 20. Comparison to Previous 26 Mg (p ,n) 26 AI 83 Measurement 21. Comparison to Previous 23 Na(a,n) 26 AI 85 Measurement 22. Comparison to Previous 23 Na(a,n 1 ) 26 AI 87 Measurement 23. Comparison to Previous 23 Na(a,n 2 ) 26 AI 89 Measurement 24. 26 AI (ni,p ) 26 Mg Cross Sections 91 25. 26 AI (ni,a) 23 Na Cross Sections 93 26. Ratios of Reaction Rates for 95 27. Ratios of Reaction Rates for 97 28. Reaction Rate Factors 99 29. Excitation Functions for 26 Mg(p,n) 26 AI 101 30. Excitation Functions for 23 Na(a,n) 26 AI 103 31. Excitation Functions for 26 Mg (p ,p ') 26 Mg • 105 32. Other Excitation Functions 107 I. INTRODUCTION A. 26AI and the Early Solar System In 1 977 Wasserburg and collaborators (Le77) reported large excesses in the 26 Mg j 24 Mg isotopic ratio in a Ca-AI rich inclusion in the Allende meteorite. The magnitudes of the excesses in several different chemical phases correlated linearly with the 27AI j 24 Mg ratio, which suggests that the 26 Mg resulted from in situ decay of 26AI. An alternative possibility is that fossil 26 Mg from 26AI decay was mixed into the meteorite from interstellar dust grains, but this would lead to the observed linear correlation only if all of the 27AI present came from the same source as the 26AI. Since this latter possibility is implausible, the conclusion is that tile observed excesses are indeed due to in situ decay of 26AI; this of course implies that solid objects of macroscopic size ( .... 1 em) condensed on a time scale not long compared to the half-life of 26AI, 7.2 x 10 5 y (Th84), after completion of nucleosynthesis. This discovery has generated much interest in models of 26AI production. Explosive nucleosynthesis in supernovae has been examined by Woosley et al. (Wo81) and Clayton ( Cl82). Their calculations indicate that although the 26AI j 27AI ratio in the hydrogen-burning shell of a supernova explosion could be as high as 1 o-2 , most of the mass of 26 AI is produced in explosive neon burning, so that the overall ratio of 26AI j 27AI is ~ 1 x 1 o-3 . This ratio is close to that previously obtained by Truran and Cameron (Tr78) and by Arnett and Wefel (Ar78), although in their calculations the 26AI was produced by explosive carbon burning. For both explosive neon burning and explosive carbon burning, the dominant productirn mechanism for 26AI was the 25 Mg (p ,,) 26Al reaction and the dominant -2destruction mechanism the 26AI (n,p ) 26 Mg reaction. Explosive nucleosynthesis in novae was examined by Woosley and Weaver (Wo80), by Arnauld et al. (Ar80), and by Hillebrandt and Thielemann (Hi82), who found that the amount of 26AI produced in novae is comparable to that in supernovae, with the lower mass ejected per nova event offset not only by the higher event rate but also by the higher 26AI j 27AI ratio calculated for novae. This higher ratio ( ~ 1, according to Hi82) would also permit greater dilution and/or decay prior to meteorite condensation. The possibility that the 26AI in the meteorite resulted after its condensation from spallation reactions from radiations from the early sun has been considered by Lee (Le78a) and found implausible. A particularly exciting development in the 26AI question has been the recent report of Mahoney et al . (Ma82) of detection of the 1809-keV -y-ray characteristic of 26AI decay (see Figure 1) using an orbiting ~-ray detection system aboard the High Energy Astronomical Observatory 3 (HEAO - 3). The strength of the line with the (4.8 ± 1.0) x 1 o- 4 ~3 M 0 detection system looking photonsjcm 2 -sec-sr (Ma84), of ambient 26AI at the galactic center was interpreted in the interstellar medium. as representing Clayton (CI84) has re- examined the poc3ibility that this quantity of 26AI arises from galactic supernova contributions. By incorporating among other considerations the latest measurements of the galactic metallicity gradient and time evolution of metallicity in general, he finds that supernovae would need an average 26AI j 27AI production ratio of ~30 x 1 o-3 , 30 times higher than the model estimate. He considers the possibility that the flux arises from a much smaller quantity of 26AI which is much closer, perhaps a single nearby nova or supernova of the recent past ( 1 0 4 -1 0 6 yr ). Such a supernova would have to have occurred around 1 4 parsees, and a nova around 1 parsec; either event would seem to be unlikely, and Clayton therefore concludes that the most probable source of the observed flux is dispersed nova contributions. -3- B. Scope of this Experiment As previously mentioned, the 26AI (n,p ) 26 Mg reaction is estimated to be a principal 26AI destruction mechanism in supernovae, but knowledge of the cross section as a function of energy is necessary to compute the reaction rates accurately. Direct measurement of this excitation function is difficult mainly because the target material must be made artificially. 26 However, the values for the AI (n0 ,p ) 26 Mg reaction can be extracted from those of the measurable 26 Mg (p ,n ) 26 AI reaction using t he principle of detail e d balance. (The subscript 0 0 on the neutron denotes that the nucleus associated with it, namely the 26AI, is in the ground state. Similarly, a subscript of 1 or 2 would denote the first or second excited state of 26AI . 26 Mg was used as a target in this experiment, so that only cross sections involving its ground state were studied; the p is therefore understood to be p 0 in this notation.) Reaction rates via the (p ,n0 ) channel calculated from the experimental data can be compared to those calculated from crosssection values from a theoretical model, such as the Hauser-Feshbach optical model. The extent of agreement can be used to judge the adequacy of the model. Cross 26 sections and reaction rates for the 26AI (n 1 ,p ) 26 Mg and AI (n2 ,p ) 26 Mg reactions, also of interest in nucleosynthesis calculations,· are inferred in a similar manner from their inverse reactions. Many of the same experimental techniques developed are equally applicable to the 23 Na(a,n) 26AI reaction, and that reaction was studied in a similar manner. Thus only those reactions involving the ground state of 26 Mg or 23 Na were accessible with the materials and techn iques available. Reactions involving the excited states of these nuclei are also of interest. Reactions involving the ground state of 26 AI can be studied using a target of 26 AI, but those involving excited states of nuclei in both channels can only be calculated theoretically. -4C. Overview of Experimental Techniques Figure 1 shows the energy level diagram of 26 AI and its decay scheme. Especially to be noted is the isomer level at 228 keV with rr=o+. This level is the analogue of the 26 Mg ground state; its de-excitation by M5 electromagnetic transition is estimated by Moszkowski (Mo55) to have a half-life of ~ 8 x 1 0 5 y, whereas its superallowed {3+ decay to the 26 Mg ground state has a half-life of only 6 .35 sec. Since any 26AI ejected in this state will decay to 26 Mg long before condensation is possible, it is clearly necessary to consider the firstexcited and ground states as separate species in the Mg-AI cycle, the reaction network caiculations relating to 26 AI production and destruction. Figure 2 shows the most important elements of this network. Among the complications is the possibility of transitions between these two states via inelastic collisions with pretons or other light particles. This network is treated by Ward and Fowler (Wa80), emphasizing th is last consideration. In this research project separate measu rements were therefore made of the excitation f unctions to the ground and first two excited states of 26Al in the 23 Na(a:,n) 26AI and 26 Mg(p,ni 6 Al reactions. -Cross sections were determined by bombarding a thin layer of evaporated target material on a substrate with protons or a-particles and counting the number of events leading to the state under examination. The cross section is obtained from the formula: u = 1 x 1 o27 Y- B tnt N where u is the cross section in mb; (I. 1 ) Y is the total number of events detected ; B is the background number of events; t is the detection efficiency; nt is the target thickness in atomsjcm 2 ; and N is the number of incident particles. Determination of absolute cross-section data for the various states of 26AI required measurement of the quantities in the above formula; for this several types of detectors and some special target evaporation procedures were used; these are described in detail in Chapter II. -5- II. A. EXPERIMENTAL APPARATUS AND PROCEDURES Targets 1. 26 Mg Targets Isotopically enriched 26 Mg targets were required in order to avoid difficulties with neutron background from the 25 Mg (p ,n) 25AI reaction. 99.7% 26 Mg was readily available as MgO, so that a chemical reduction was necessary. The procedure of Takayanagi et al . (Ta66) was used; in this procedure, powdered zirconium serves as the reducing agent because the reaction proceeds at "'1 200° C, a considerably lower temperature than alternative reducing agents permit. (Tantalum, for example, requires a temperature of "'2000° C.) The reduction was carried out under high vacuum ("' 1 o-7 torr) in a be!l jar. Even at the relatively moderate temperature, the close geometry necessary to utilize the separated isotope efficiently required that the backing be cooled in order that the evaporated magnesium condense on the backing. This was accomplished by maintaining a flow of cooling water on the reverse side of the backing, sealing the cooling water against the high vacuum with an a-ring, as shown in figure 3. The laboratory threshold energy for the 26 Mg (p ,n ) 26AI reaction is 4.99 MeV, which is above threshold for many other (p ,n) reactions; neutron background from the backing therefore had to be taken into account. The preferred backing material was high purity aluminum foil with a thickness of 0.25 mm, specifically, MARZ grade from Materials Research Inc. The yield from this material was 2500 neutrons/,uCoul. at 4.99 MeV. Natural aluminum is isotopically pure ( 27AI) with a (p ,n) threshold of 5.8 MeV, so that the background arose solely from impurities in it. To emphasize the importance of the choice of backing, clean high-purity tungsten was tested and found to yield 1 4 times as many neutrons for the same beam dose and energy, and at higher energies the disparity became even greater. Slight!y lower-purity aluminum (99.999%) yielded 2 to 3 times the neutron rate of the MARZ grade material. For measurements of the cross sections to the second -6excited state of 26 Mg, a backing of high atomic number became necessary to prevent the 417-keV ~-ray signal from being swamped by higher-energy ~-rays arising scattering and 1-ray from inelastic proton cascades from the 27AI(p,,) 28 Si reaction. The Coulomb barrier associated with .the high atomic number inhibits both types of processes. The target used to obtain relative cross sections to this second excited state had in fact been made several years earlier by other researchers in this laboratory (Da 79). It consisted of 8.2 I-Lgfcm 2 of 26 Mg on a Ta backing 0 .25 mm thick; the fact that it had become oxidized did not present any problem since the 26 Mg (p ,71z )26AI signature, a 417-keV 1-ray line, was well resolved from other 1-ray lines. The relative data were normalized with a different target described below. Absolute target thickness must be determined in order to obtain an absolute cross section. This was accomplished by Rutherford backscattering, a technique in which accelerated charged particles (a-particles for the cases under discussian) are scattered off the target into some well-defined solid angle and counted with a detector which measures their energy. The differen t ial c ross section in the laboratory system is given by Sargood (Sa82): da [z1 2 z2 e (a +cos'\J.)r dO = ~------------~~2 (11.1) 4 a [Etab sin '\J.r with the parameter a defined as (11.2) and the other quantities as follows: Z 1 , Z 2 , M 1 , and M 2 are the atomic numbers and nuclear masses of the incident particle and scattering material; e is the electron charge in Gaussian units; and '19- is the scattering angle in laboratory coordinates. The energy remaining after collision, El~b, is given in terms of the incident lab energy, Etab , by -7- El~b = [r (.M~ -.M? sin2 '!3) 112 +.M 1 cos19-1 2 Elab M1 + M2 ( 11.3) For the case of 26 Mg deposited on 27AI, the target mass is only one unit below the backing mass, so that the backscattering peak for the 26 Mg is difficult to separate from the 27AI backscattering edge; this difficulty is further compounded by energy loss in the 26 Mg layer. These problems were circumvented by manufacturing a special target on which a 275-JLgfcm 2 gold layer was deposited on the aluminum backing, and the 26 Mg was deposited on this gold layer. The gold layer was thick enough that energy loss in it reduced the maximum energy of the a-particles scattered by the aluminum below the energy of the a-particles scattered by the 26 Mg; at the same time, the gold layer was thin enough that the gold backscattering peak did not intrude onto the 26 Mg backscattering peak. The backscattering spectrum for this target is shown in figure 4. The thickness of other targets was determined by measuring the neutron yield at some convenient proton energy and comparing it to the yield of the special target described in the preceding paragraph. This simple procedure is valid as long as the contribution to the neutron yield from the backing and contaminants is known. This condition was satisfied for the targets on aluminum backings, but not for the one on theTa backing used for the 26 Mg (p ,n2 ) 26AI measurements. In order to normalize the data from this target (in effect, to determine the thickness of 8.2 JLgfcm 2 stated above), it was necessary to manufacture a separate target. Tungsten had been found to present a lower neutron back- ground than several other heavy metals tested, and a target was evaporated onto a tungsten backing. An identical backing with no 26 Mg was prepared and both were bombarded at the selected energy. With the contribution from the backing ( ~ 6%) known, the 26 Mg thickness was determined as described above. The energy selected was one at which the 26 Mg (p ,n ) 26 AI was at the maximum of a broad resonance, thus minimizing the fraction of the total yield contributed by the backing. The 417-keV yield from this target was then measured at a -8selected bombardment energy in a carefully controlled geometry to deduce the absolute cross section for the 26 Mg (p ,n2 ) 26AI reaction at that energy; this value was used to normalize the relative data described above. 2. Sodium Targets Preparation of the sodium targets was simpler than that of the magnesium targets. Natural sodium is isotopically pure ( 23 Na) so it was only necessary to evaporate the selected sodium compound onto the backing. A compound was preferred to avoid the difficulties associated with dealing with highly reactive sodium metal. The first two compounds tested were NaOH and NaCI. High-purity copper foil was selected for backings because both isotopes of copper have relatively high (a,n) thresholds. This combination proved unsatisfactory because both compounds were found to disperse into the copper, so that the energy resolution became extremely poor. Combinations which proved better were Na 4 P 2 0 7 (sodium pyrophosphate) on tungsten and Na 2 WO 4 (sodium tungstate) also on tungsten. The tendency to disperse into the backing material was still observed, but to a greatly reduced extent. One special target for normalizing the relative data by Rutherford backscattering was prepared; it consisted of Na 2 WO 4 on a gold backing thin enough (300 1-Lg 1 cm 2 ) that the gold backscattering peak did not extend so low in energy as to interfere with the sodium backscattering peak. Graphite was used to stop the transmitted ex beam for the Rutherford backscattering, since a's backscattered from it would not interfere with the sodium peak. Copper was used to stop the transmitted beam for the neutron yield measurement to avoid significant neutron contributions from reactions other than those on the target material. The Rutherford backscattering spectrum from this target is shown in figure 5. Preliminary investigation showed that the cross section to the o+ isomer state of 26AJ was generally much less than that to the ground state, in contrast to the situation with 26 Mg (p ,n )26 AJ. This should not be unexpected ; even -9though the transit ion to the ground state involves a higher angular momentum barrier (l =4 instead of l =2) , the statistical factor, 2J + 1, favors ground state formation by 26 Mg (p ,n ) 26 AI 1 an 11:1 ratio. No conclusion should be drawn from the data since this the target and product nuclei are analogue states. The low cross section necessitated measuring this excitation function with a rather thick target, so that considerable energy resolution was sacrificed. Its thickness was determined in a somewhat compiicated manner described in chapter 3. B. A ccelerator , Beam Transport, and Vacuum Syst ems 1. Negative lon Source for Proton Beams Protons are ionized in a Duo-Piasmatron source and accelerated toward an adder canal held at approximately 32 kV. Low pressure H2 in th is canal chargeexc hanges with the incident proton beam, and some of it emerges from the canal with a charge of -1, having captured two electrons. The 32 kV then further accelerat es these negative ions into a 20° magnet, which bends t he beam o nto the axis of the tandem accelerator. The proton beam is thus injected into the tandem accelerator w ith a kinetic energy of approximately 64 keV and a charg e of -1, i .e. , asH- ions. 2. JN Accelerator for a-Particle Beams The Negative lon Source described above is not well-suited to production of a-particle beams because of the cumbersome lithium oven necessary to produce He- ions. The a-particle source was instead a model JN single-ended Van de Graaff accelerator, which produces helium ions in a charge state of +1; these ions emerge with an energy of approximately 0.5 MeV and currents up to around 1 00 jJ.A can be obtained. Before they reach the EN tandem, the ions are neutralized in a canal inside the Negative lon Source enclosure. The a-particle be am is t hus injected into the tandem accelerator with a kinetic energy of approximat ely 0.5 - 10MeV and electrically neutral. 3. EN Tandem Accelerator The HVEC Model EN Tandem Accelerator is a Van de Graaff accelerator capable of reaching 6.5 MV at its center terminal. Gas in a stripper canal at this terminal strips electrons from the beam as it reaches that point. H- ions are therefore accelerated toward the terminal, stripped of both electrons, and accelerated further afterwards; thus they acquire 2 MeV for every MV of terminal voltage. The a-particles, being neutral at injection, are not accelerated approaching the terminal. They are stripped of one or both electrons; some therefore gain 1 MeV /MV and some 2 MeV /MV over their injection energy. Either beam can be used. 4. Beam Optics The principal element in the beam analyzing system is the 90° analyzing magnet. This magnet isolates only those particles having the correct momentumto-charge ratio so that the beam exiting the magnet will have a weil-defined energy. Several quadrupole and steering magnets are used to control and focus the beam at both high-energy and low-energy ends. At the low-energy end electrostatic elements are also used. 5. Vacuum Systems Several conventional diffusion pumps, backed by mechanical forepumps, maintain a vacuum of ~1 o-6 torr in the beamlines. Two large ion pumps, one at each end of the EN, maintain vacuum in the accelerator column with minimal carbon deposition. (Diffusion pump fluids contain carbon.) Carbon is a serious contaminant in a system where one is examining (p,n) and even more so (a,n) cross sections because of the low threshold and high cross section of 13 C for these reactions. The vacuum at the end of the beam line in which the target was mounted was therefore maintained with an ion pump; a cold trap cooled to liquid - 11 nitrogen temperature helped to trap any vapors containing carbon before they could be deposited on the target. A sorption pump, rather than a mechanical pump; was used as a roughing pump to prevent introduction of any vapors containing carbon. Figure 6 shows a schematic of the target chamber arrangement. C. Sequence Timer The signature for formation of 26 Mg in its o+ state is delayed {3+ particle emission with T 112 =6.35 s. Therefore it is possible to bombard the target for a short time with the {3+ detection system turned off, interrupt the beam, and then measure the {3+ activity for a period of time comparable to the half-life. This procedure avoids a large amount of beam-induced background while maintaining the ability to count a large fraction of the events producing 26AI in its o+ state. In practice, several cycles were run, typically 1 0. A sequence timer originally designed and built by F. M. Mann was used to control steps in the bombard-andcount cycle selected. This device controlled the beam-chopping magnet, a mechanical beam chopper, the neutron-counting scaler gating, the {3+ scaler and/or multichannel analyzer gating, and multichannel analyzer routing. It is described in detail in Mann's thesis (Ma75). D. Neutron-Detection System The neutron-detection system consists of a large graphite cube, 1 2 3 He proportional counters, and the associated electronic equipment. The graphite cube is approximately 1 .4 m on a side and weighs approximately 5000 kg. It is mounted on a cart which moves on rails so that it can be positioned over the end of the beam pipe to place the target at its center. The graphite serves as a neutron moderator; the common isotope of carbon, 12 c (98.9%) has a low thermal neutron capture cross section (3.4 mb) so that the thermalized neutrons diffuse around the cube with minimal absorption except by the detectors. (The capture cross section for 13 C is even lower, at 0.9 mb.) For - 12comparison, similar detectors have been constructed out of polyethylene, despite the 330-mb capture cross section of 1 H, one of its principal constituents. Such detectors can be made smaller, but their detection efficiency is more strongly dependent on neutron energy. The 12 3 He gas proportional counters are embedded in the cube near the outside symmetrically located with respect to the center. A gas proportional counter is a tube filled with some particular gas that has a wire running down its axis, the wire being electrically insulated from the tube. High positive voltage is placed on this wire so that electrons produced in the tube are accelerated toward it and positively charged ions toward the outer wall. In a proportional counter, the voltage is high enough that electrons are accelerated sufficiently between collisions to liberate other electrons; the amount of charge reaching the center electrode is therefore much larger than if no gas amplification occurred. The voltage is not so high as to cause the avalanche to saturate; the amount of charge collected is thus proportional to the original number of ion pairs produced by the ionizing event, which in turn is proportional to the energy deposited by the event. A 3 He counter detects neutrons via the 3 He (n,p ) 3 H reaction. This ;eaction has a cross section of 5300 b at thermal energy and liberates 782 keV to the two resulting charged particles; clearly the p emerges with 75% of this 782 keV and the 3 H with the remainder. If both particles deposit their energy within the active region of the volume, the output pulse will correspond to the full energy. If the (n,p) event occurs near the wall, it is possible for the recoiling proton to deposit its energy in the wall, so that only 25% of the energy is deposited in the active volume. The same can occur with the 3 H, resulting in deposition of 75% of the energy in the active volume; clearly, either particle could also deposit a fraction of its energy before entering the wall. The anticipated spectrum is therefore a continuous distribution between a threshold at 25% of maximum energy and a spike and cutoff at 100%, with a feature at 75%. Figure 7 shows a spectrum from one of these counters and confirms these expectations. -13Each counter is connected to a pre-amplifier which provides impedance matching and amplification to the charge pulse from each counter. Each of the 1 2 pre-amplifiers delivers its signal to a priority encoder; this device first compares the pulse to the preset threshold value for that particular counter/pre-amplifier combination. If the pulse exceeds the threshold, a pulse is generated which has a height proportional to the counter number. The output of the priority encoder is therefore a series of 12 spikes, the number of counts in a given spike being the number of pulses exceeding the threshold from the corresponding counter. This output could be delivered to a multichannel analyzer to inspect for asymmetries in the neutron distribution or any anomalies in a particular counter. Figure 8 shows the spectrum resulting. Normally, however, only the total number of counts w as of interest, and the priority encoder output was simply delivered to a scaler after verifying system performance with a multichannel analyzer. E. p+ and ')'-Ray Detection Systems A conventional Nal detector (with photomultiplier tube) was used to count the delayed {3+ particles from the 26 Mg (p ,n1 ) 26AI reaction, detecting the 511keV -y-rays resulting from annihilation of the {3+ particles. The target mounting arrangement included a beamtube wall thick enough ( ~4 mm of aluminum) to stop all the p+ particles emitted into it; over 90% of the solid angle was subtended; therefore very few {3+ particles annihilated at a large distance from the target. The signal from the photomultiplier was processed by a multichannel analyzer and stored on magnetic tape. The lower count-rates from the 23 Na ( cx,n 1 ) 2 6 AI reaction made a more efficient system desirable, and a polystyrene well scintillator to detect the {3+ particles directly was selected. The target was mounted at the end of a thin-walled (0.25 mm stainless steel) beam tube which fit into the well. A schematic of this arrangement is shown in figure 9 . The entire assembly was placed inside the graphite cube so that neutrons were counted during the "beam on" segments of the cycle in addition to delayed {3+ particles. A large fraction of -14the (3+ particles were emitted with sufficient energy to penetrate the wall and deposit a significant fraction of their energy in the polystyrene. The pulses from its photomultiplier were counted by a scaler with its threshold set to count the bulk of the (3 + distribution and simultaneously by a multichannel analyzer integrating the high energy tail. Use of the scaler data sacrifices some background rejection in favor of counting statistics compared to use of the multichannel analyzer data. A systematic variation was noted in the ratio of the count-rates, suggesting a drift in photomultiplier tube gain. Close analysis shows that the count rate from the bulk of the distribution would be much less sensitive to such a drift than that of the high-energy tail; for the magnitude of the drift calculated, ""'3%, it could be ignored compared to other uncertainties. In effect, taking the ratio of count rates for the tvJo different energy "cuts " was a sensitive --c.heck for gain drift; a 1% change in count-rate associated with gain drift corresponded to a 5% change in ratio. For both 26 Mg (p ,n1 ) 26 AI and 23 Na (cx,n 1 ) 26AI reactions, a Ge(Li) detection system was used in conjunction with a c alibrated 22 Na source to determine detection efficiency. Conventional Ge(Li) systems were also used to detect the 41 7-keV , -ray signature from the 23 Na (cx,n 2 ) 26AI and 26 Mg (p ,n2 ) 26AI reactions. A piece of thin (2 mm) lead sheet was used between the target and Ge(Li) detector; this thickness strongly attenuates low-energy r-rays, which are copiously emitted by the target under bombardment and by the calibration sources used, but it only moderately reduces ,-rays in the energy range of interest. The signals were processed by a multichannel analyzer and stored on magnetic tape. The Ge(Li) detector was located at 125° with respect to the beam axis in order to measure the total cross section provided that contributing terms in the Legendre polynomial expans ion include none above P 2 (cos v), as indicated by the data of Norman et al . (No81 a) . Detection efficiency was determined by counting calibration sources in a geometry identical to that of the cross-section measurement. Figure 10 show s a spectrum obtained from a 152 Eu calibration source, and figure 11 - 15shows a plot of photopeak (full-energy peak) efficiency as a function of -y-ray energy. - 16- Ill. DATA ANALYSIS A. Target Yield Formulae 1. Thin Target When the energy loss of the beam in the target is small compared to the typical resonance width, all interactions can be considered to occur at the same beam energy, and the yield is simply proportional to the target thickness. This state of affairs is the most desirable, as several potential sources of error, discussed below in connection with thick and semi-thick target s, are avoided. The thin-target formula for the cross section is given by equation (1.1 ); for comparison to the other cases, this formula is re-expressed as t; No f N1 ut Y-B=----- A (111.1) where Y- B is the number of events detected over background; t; is the detectioo efficiency; N o is Avogadro's number; f is the number of nuclei of the nuclide under study per molecule of target material; N 1 is the number of incident particles; u is the cross section; t is the thickness in mass per unit area; and A is the molecular weight of the target material. 2. Thiele or Semi-Thick Target A thick target is one which is thick enough that the beam loses sufficient energy within it that it is below threshold for the reaction under study. Typically, the target stops the beam altogether. The yield increases monotonically with increasing beam energy; the yield is proportional to the integral of the crosssection: _ y _ B- t; No f N1 Efinc u(E)dE A K,(E) Eth (111.2) - 17where the symbols are defined as above, with a few additions: Eth and Einc are threshold and incident energies; u must now be considered as a function of energy; and K; is the stopping power of the target material, expressed in energy per unit mass-density, e.g., keV/(g/cm 2 ). A semi-thick target is the intermediate case in which the energy loss in the target layer is not small compared to the resonance width, but not sufficient to stop the beam. The formula in this case is identical to equation (111.2) except that Eth is replaced by Eex, the energy at which the beam exits the back of the target layer. In either of these cases, determination of the actual cross-section values presents not only the mathematical intricacies of unfolding the integrals with the concomitant increased statistical uncertainties, but also an indeterminate uncertainty associated with the distribution of the target material within the target layer; i.e. if the distribution is not uniform, the above integrands should be weighted with a function describing the target material concentration within the target layer as a function of depth in the layer. B. Total Neutron Cross Sections Analysis of the data for the total neutron cross section was by application of the thin-target formula, equation (1.3). 2 6 Mg (p ,n) 26AI The background count rate for the reaction was determined by bombarding an aluminum foil identical to the backing at various energies. This count rate, ~ 31 0 counts (2500 neutrons) per ,uCoul., corresponded to a cross section of 0.35 mb. 23 Na (a,n ) 26AI For the reaction, bombardment of the target below threshold resulted in a yield of 1 60 counts per ,uCoul. Resonances in the excitation functions of two common contaminants, 18 0 and 13 c, were examined, and the amount of each was determined; within uncertainties, the contributions from these accounted for all of the yield below threshold. A computer subroutine which incorporated the excitation functions of these two nuclei was written to perform the background subtraction. Typically, the background was ~ 1 60 counts/ ,uCoul., corresponding to -180.5 mb; maximum values at a few isolated points were four times these amounts. The neutron-detection efficiency, t:, was determined by measuring the count rate from a 252 Cf source which had been calibrated indirectly against a source from the National Bureau of Standards. The detection efficiency. measured was (12.47 ± 0.40)% for the 252 Cf neutron spectrum, which has an average energy of 2.35 MeV. This value was checked by an activation technique. 89 Y was bombarded with protons and the neutrons from the 89 Y (p ,n ) 89 Zr reaction were counted. Subsequently, the 909-keV r-ray activity from the 89 Zr was measured with a Ge(Li) system. Since the fraction of 89 Zr decays emitting this 1-ray, (99.01 ± 0.04)% (Le78b), is accurately known, a straightforward analysis (Sk84) gives the neutron-detection efficiency. Considerable precautions were taken to minimize the possibility of systematic error and to reduce random uncertainties, as this measurement was principally in support of a high-precision measurement of the 478-keV ~-ray branching ratio in the decay of 7 Be by Skelton and Kavanagh (Sk84). The neutron-detection efficiency by this technique was (12.02 ± 0 .08)% for a neutron spectrum w ith an average energy of 450 keV. The efficiency used for calculations was 12.2%, assumed to be independent of neutron energy as supported by the work of Macklin (Ma57). The target thickness was measured by Rutherford backscattering of aparticles of 2 MeV incident energy from the special targets described in chapter II at an angle of 160°. The 26 Mg thickness was (36.6 ± 0.5) J.Lg 1 cm 2 ; the 23 Na thickness was (1.44 ± 0.07) J.LQ/cm 2 • An independent check for the 26 Mg was made in connection with the 26AI half-life measurement of Thomas et al . (Th84) by measuring the neutron yield from a thick natural magnesium target (99.8%) bombarded with protons at several energies below the threshold for the 25 Mg (p ,n) 25AI reaction; the principal source of neutrons was therefore the 26 Mg(p ,n) 26 AI reaction. The cross sections for (p,n) reactions for most poten- tial impurities chemical are roughly comparable to those measured for 26 Mg(p,n) 26 AI, so their contribution to the neutron yield should be .-...0.2%; even -19if lithium and beryllium were the principal contaminants, their contribution would still be ~ 4% of the total, but the rarity of these elements renders this possibility remote . This observed yield was compared to the expected yield, calculated by integrating the excitation function and applying the thick-target formula, equation (111.2). An error in the target thickness determined by Rutherford backscattering would result in an inversely proportional normalization error in the cross section, a(E), in this formula; thus the two results would differ by a factor proportional to the error. The observed and calculated yields agreed within 3%; the estimated uncertainty was 5%. C. Cross Sections to the First Excited State For the 26 Mg (p ,n 1 ) 26AI reaction, the excitation function was first measured in a constant geometry, but a close one difficult to reproduce to high precision. The resulting data therefore represented the relative cross sections and ne eded only the cross section measured at a single point to be converted to absolute cross sections . A sample Nai(TI) spectrum obtained in conjunction with the 26 Mg (p ,n ) 26 AI is shown in figure 12. The normalization to absolute cross sec1 tions was accomplished by bombarding a target with a large separation (15 em) between target and detector to minimize the effect of any difference between the positions of the beam spot and the calibration source as well as the effect of the distributed nature of the source. (Positrons have range of ~ 4mm in aluminum.) A Ge(Li) system was used to measure the annihilation radiation; its detection efficiency was determined with a calibrated 22 Na source. The choice of a positron-emitting calibration source, as opposed to a pure ~-ray source, minimized uncertainties arising from the distributed nature of the source and from annihilation in flight. The system detected (1 .68 ± 0.04) x 1 o-3 annihilation quanta per positron emitted from 22 Na. Since only 0 .6% of the 2 2 Na positrons annihilate in flight in a low-Z material compared to 4% for those of 26 mAI (Ma75), the detection efficiency was ( 1 .62 ± 0.04) x 1 o-3 counts in the annihilation photopeak per -20positron from 26 mAI. The target thickness was determined simply by measuring neutron yield at the peak of the resonance near EP =5.334 MeV. The yield of 3.00 x 10 4 counts per .ucoul. showed the target thickness to be 25.2 .ug 1 em 2 . At the peak of this resonance, the cross section was thus determined to be (62.0 ± 3.0) mb; the dominant source of uncertainty is the reproducibility from one determination to another. A similar approach was used for the 23 Na (o:,n 1 i 6 AI reaction. Target thickness was again determined by measuring the total neutron yield; however, a much thicker target was found necessary to obtain reasonable counting statistics above background, and the thin-target equation could no longer be used for correlation of the neutron yield to target thickness. This correlation was therefore made by the following procedure. The yield as a function of energy for total neutrons was measured simultaneously with that for the delayed {3+ -particles. Previously measured data for the total neutron excitation function from a thin target were integrated by computer over several different energy ranges in order to predict what the yield as a function of energy from this thin target would be if its total amount of 23 Na were kept fixed, but if it were distributed uniformly among other materials in the target layer at various concentrations so that energy loss in the target layer would be non-negligible. One result of the target material being distributed in this manner is to degrade the energy resolution. The observed semi-thick target neutron yield as a function of energy was compared to the various predicted functions, and the one presenting the most similar energy resolution was selected. The ratio of neutron yields was then used to infer the total amount of 23 Na on the semi-thick target; this amount was 8.9 .ug 1 em 2 of 23 Na alone, corresponding to 25.7 .ug 1 em 2 of Na 4 P 2 0 7 • This amount of Na 4 P 2 0 7 corresponds to an energy loss of 18.9 keV in the energy range under consideration; the estimated energy loss in the target was 60 keV, indicating that considerable intermixing of target and backing was occurring, a result not unexpected in view of the high beam currents necessary ( ~ 1 ,UA) to obtain - 21 satisfactory yield above background. The energy selected to normalize the relative data was 4.157 MeV, using the same target. The same procedure was used as for the 26 Mg (p ,n1 ) 26 AI described above, with the only difference being that the Ge(Li) detector was considerably closer to the target ( ~ 4 em) in order to allow for the lower yield. The cross section at this peak was (1.72 ± 0.17) mb. The detection efficiency was (6.2 ± 0.2) x 1 o-3 counts in the annihilation photopeak per 26 mAI positron. For the 23 Na (cx,n 1 ) 26AI excitation function, the thintarget formula was used even though the target was much thicker than typical resonances observed in the 23 Na (cx,n) 26AI reaction. This procedure can be justified for two reasons. First, the statistical uncertainties and uncertainties arising from the actual 23 Na distribution within the target layer are such that an attempt at a more sophisticated analysis would be more a mathematical exercise than a legitimate refinement of the data. Second, and more important, the primary goal in obtaining the data is satisfied nearly as well by making this assumption: to first order, the contribution to <av >,the thermally averaged reaction rate factor (see equation IV.2), from a given resonance depends only on the integral J a(E)dE; use of the thin-target formula for a semi-thick target in effect partially performs this integral so that the same reaction rate is obtained. One additional factor entered the normalization for the 26 Mg (p ,n1 ) 26AI and 23 Na (cx,n 1 i 6 AI reactions. In each case, delayed positrons were counted, either directly or via their 511-keV annihilation radiation. Since the detector was turned off while the beam was on, the observed number of counts in equation (111.1) is reduced by a factor fA, the fraction of the events which occur during the time that the detection system is sensitive. This factor is given by Bashkin et al. (Ba59): _ exp(-A.Tw) [1-exp(-A.T8 )] [1-exp(-A.Tc)] fAA.T8 [1 -exp( -\Tr)] X -22- r [1-exp(-'m.A.Tr)] 1 - ...._----,,--------.'----1 'm [exp(.A.Tr) -1] (111.3) where the times are defined in figure 13; .A. is the decay constant ; and 'm is the total number of cycles. This fraction was approximately 0.5 for all 26 Mg (p ,n ) 26AI and 23 Na (a,n ) 26AI measurements. 1 1 D. Cross Sections to the Second Excited State As with the first excited state, the approach was to obtain relative data in a close geometry, and then to normalize them in a wide geometry at the peak of a broad resonance. A sample Ge(Li) spectrum for the 26 Mg (p ,n2 ) 26AI excitation function measurement is shown in figure 1 4. For the 26 Mg, the energy selected for normalization was 5.545 MeV. The ,-ray detection efficiency as a function of ~-ray energy was determined using a 152 Eu source ; the spectrum and efficiency curve were similar to those shown in figures 1 0 and 11. The photopeak efficiency at £ 7 = 417 keV w as (0.1 0 4 ± 0.002)%. Target thickness was determined by measuring the total neutron yield and subtracting the background from the tungsten backing; the total yield was 5.5 x 10 5 neutrons per ,uCoul.; the yield from an identically prepared backing was 1.23 x 1 0 5 , 22% of the totaL The 26 Mg thickness was therefore 42.5 ,ug 1 cm 2 , 26 Mg (p ,n ) 26.A.I of (245 ± 7) mb at EP 2 resulting in a cross section for =5.545 MeV. An independent check was made again in connection with the 26AI half-life measurement of Thomas et al . (Th84) by measuring the 41 7 -keV ~-ray yield from a thick natural magnesium target bombarded with protons at energies near the top of the range measured previously. Observed and calculated yields again agreed w ithin 3% with an estimated uncertainty of 5%. For the 23 Na (a,n 2 ) 26AI reaction, the yield from the backing was much less, and the procedure correspondingly simpler. The Ge(Li) system efficiency was ( 1 .04 ± 0.02)% at E 23 Na was 1.65 ,ug 1 em 2 . 1 =41 7 keV, and the thickness of This led to an absolute cross section for the -2323 Na ( cx,n2 ) 26AI reaction of (16.1 ± 0 .6) mb at Ea.= 4.509 MeV. Multichannel analyzer spectra were integrated with the TEKHIST computer program. This program · allows the user to select three spectral ranges independently: background below and above the peak and the peak itself; the net area is then crosshatched on the screen and the gross and net integrals displayed and recorded. Further details of the program are given in the thesis of its author, J. L. Osborne (Os83). -24- IV. A. RESULTS AND CONCLUSIONS Experimental Results Figure 15 shows the results of the analysis of the 26 Mg (p ,n ~.i 6 AI data, a preliminary report of which has been made previously (Sk83). The estimated precision for the total neutron data is ± (5% + 0.1) mb; the 5% arises primarily from uncertainties in the overall normalization, while the 0.1 mb arises from uncertainties in background subtraction. The estimated precision for the first-excited- state data is ± (6% + 30 fib) ; for the second-excited-state data, it is ± (8% + 0.3mb). The excitation function for production of the ground state of 26AI was determined by subtract1ng the excitation functions for the other two states from the total, and, above the threshold to the first excited state, it is therefore subject to greater uncertainties, given by the quadrature sum of those from the three independent measurements. Figure 16 shows the results from 23 Na (cx ,ni 6ft.l. The estimated precision is similarly ± (5% + 0.3mb) for the total neutron data, ±(15% + 5 ,ub) for the firstexcited-state data, and ± (8% + 0.1 mb) for the second-excited-state data. The excitation function to the ground state was determined again by subtraction, and the comment about the uncertainty for the corresponding 26 Mg (p ,n )26AI case applies . B. Comparison to Previous Experiment 1. 26 Mg (p ,n) 26 AI Experiments The first study of the 26 Mg (p ,n) 26AI reaction was by Wong et al. (Wo67) who investigated it in conjunction with a study of quadrupole deformations; they used time-of-flight to distinguish the neutron groups. However, since their lowest incident proton energy was 8.25 MeV, their results cannot be compared directly to the present experiment. -25Furukawa et al. (Fu71) bombarded a stacked-foil 26 Mg target arrangement with a 52-MeV proton beam and subsequently counted the activity of the longlived · 26AI ( T 112 = 7.2 x 1 0 5 y) with a high-sensitivity detection system; in this manner they determined the cross section for production of the ground state of 26AI. Paul et al. (PaSO) bombarded stacked-foil targets at somewhat lower energies (5 to 7 MeV); they subsequently determined the 26AI content of their targets by accelerator mass spectrometry. In both of these experiments, cross sections were measured for production of the 26AI ground state, either directly or via some higher state which decays to the ground state. Within the energy range covered by the present experiment, the only excited state decaying to the ground state is the 417-keV state; these reports are thus to be compared to the sum of the ground state and 41 7 -keV state excitation functions of the present experiment. Figure 17 shows the results of this comparison; only one datum from the first paper and two from the second are within the energy range of the present experiment, but these are seen to agree quite well with the crosssection values measured in the present experiment. King and Cheng (Ki79) measured the cross section for the 26 Mg (p ,n1 ) 26 AI reaction in a manner similar to that of the present experiment. Figure 1 8 compares the values they reported to those of the present experiment; their first five points are clearly lower, by factors from 0.5 to 0.8; the sixth point agrees. Tile discrepancies are well outside estimated uncertainties, suggesting that additional determinations might be appropriate. Norman et al . (No81 a) have analyzed the y-ray yield from a 26 Mg target under proton bombardment, with the goal of measuring the total yield to the ground state. Within the energy range of the present experiment, the only contributing state is that of 417 keV; thus the data of their experiment are to be compared to the 26 Mg (p ,n2 ) 26AI data of the present one. Figure 19 presents both sets of data; the agreement is seen to be excellent. -26Norman et al . (No81 b) have also measured the total neutron yield by using a thick target and analyzing the differential yield to determine the excitation function for the total neutron yield. Figure 20 compares their data to the results of the present experiment; a few isolated points disagree, and it appears that the correction to the effective energy is inconsistent; nevertheless, the overall agreement is again very good. The thin targets used in the present technique clearly permit much better resolution than was obtained in any of the other experiments. It should however be pointed out that the other experiments spanned greater energy ranges. In general, good energy resolution is not essential in applications for astrophysics because the cross-section data will be averaged for reaction rate calc ulations; i .e. , one calculates the reaction rate factor, N 0 <uv >, where N 0 is Avogadro's number and <rrv > is given by Fowler et al . (Fo67): r s 11/2 <rrv> = l~ ~rr 3/2 co [Err(E)exp(-E !kT)dE. (IV.1) Here J.L is the system reduced mass; k is the Boltzmann constant; T is the ternperature; and E is the center-of-mass system energy. The units of N 0 <uv > are em 3 mole - 1 sec - 1 ; one calculates a reaction rate (em - 3 sec - 1 ) by multiplying this factor by the densities of the two reactants. However, for low values of T 9 , the lowest resonance (or lowest several resonances) can dominate the integral. ( T9 is the temperature in 1 0 9 K; T 9 =1 corresponds to a temperature of 1 0 9 K.) Examples will be given in paragraph C below. 2. 23 Na( o:,n) 26AI Experiments Norman et al . (No82) have measured excitation functions for the total neutron yield, the yield to the first excited state, and the yield of various -y-rays at a-particle energies up to 26 MeV using thick-target techniq ues. Figures 21, 22, and 23 compare cross sections for total neutron y ield, first-excited-state production, and second-excited state production respectively. The agreement is -27excellent for the total neutron data and for the second-excited-state data; the only point in the first-excited-state data that can be compared is roughly a factor of 2 low compared to the present experiment, suggesting that further investigation of this state may be warranted. C. Comparison to Theory The principle of detailed balance allows the cross section for a given reac- tion to be used to calculate the cross section for the inverse reaction. To invert the cross section for the reaction 0 + 1 --> 2 + 3, the formula is given by Fowler et al. (Fo67): 0"(23 --> 01) a( 01 -->23) 1 +623 gog1 AoA1 Eo1 1 +601 g2g3 A2A3 E23 (IV.2) where the 6ij are Kronecker deltas to accommodate the possibility that both particles in either the entrance of exit channel might be identical; the g i . are the spin multiplicities, i.e., 2J. + 1; the A. are the masses; and the E .. are the ~ ~ kinetic energies in the center-of-mass syste~. This equation was used to calculate the excitation functions for 26AI (ni,p ) 26 Mg leading to the ground state of 26 Mg from the lowest three states of 26AI. These results are shown in figure 24, along with the results of a Hauser-Feshbach optical model calculation for comparison. It is clear that the theoretical model considerably overestimates the 26AI (n 0 ,p ) 26 Mg 26AI ( n 1 ,p ) 26 Mg reaction. All cross sections seem to be considerably overes- cross section and generally underestimates that of the timated at low energies; since the energy denominator in equation (IV.2) can magnify any non-zero cross section arbitrarily, it is possible that 26 Mg (p ,n) 26 AI cross sections near threshold were below the level detectable and that the 26 AI (n,p i 6 Mg cross sections in fact might be much larger at very low energies. However, for energies in the 26 AI + n system above 5 keV, the sensitivity of the measurements was sufficient to exclude the theoretical values shown in figure 24. See also the comments below regarding contributions to the reaction rate -28factors. Figure 25 shows the results of applying the principle of detailed balance to the 23 Na(o:,n) 26AI data, along with the results of a Hauser-Feshbach calculation. The theory again overestimates the cross section at low energies for the two excited states; for the ground state, the theory underestimates the cross section at nearly all energies. Tables I and II show the reaction rate factors (equation IV.1) for the 26AI ( n . ,p ) 26 Mg and 26 AI (n .,o:) 23 Na reactions. "t "t integration was carried out numerically from E In calculating these values, the =0 to the upper end of the avail- able data. An asymptotic contribution was then added on; this contribution was caiculated by assuming a constant value of the cross section above the maximum tabulated value. The asymptotic values were selected by estimating the average cross section over the last 1 00 keV of experimental data. The values selected were 25, 500, 26 AI (n 2 and 50 mb for the 26 AI (n 0 ,p) 26 Mg, 26AI(n 1 ,pi 6 Mg, and ,p ) 26 Mg reactions respectively. For the corresponding 26AI (ni,a) 23 Na reactions the values were 40, 60, and 70 mb. Percentage contributions from the asymptotic term are given in parentheses when they become significant in these tables. One might suspect that an unlimited contribution to the reaction rate could arise from a small energy denominator in equation IV.2; this is not the case, as the energy denominator is cancelled by the factor of E in the integrand of equation IV. 1. Single unobserved resonances near the respective thresholds could add to the tabulated values for the 26AI (ni,p ) 26 Mg reaction rates (table 1) the amounts N A <CTi v > = 4. 7 X 10 4 T 9-312 , 1.6 X 104 T 9- 312 ' and 1.6 X 105 T 9- 3 / 2 fori = 0, 1, and 2 respectively. For the 26AI (n .,o:) 23 Na reaction rates (table 2) the "t corresponding coefficients of T 9 - 3 1 2 are 1.1 x 10 5 ,3.0 x 10 4 , and 6.1 x 104 respectively. Figures 26 and 27 show the ratios of the reaction rates calculated from the experimental data of figures 24 and 25 to the corresponding reaction rates -29calculated using the theoretical cross-section data. The ratios are not plotted for values of T 9 when the contribution from the asymptotic term of the "experimental" reaction rate factor exceeds that from the actual experimental data; this occurs for T e ~ 5. The desirability of good experimental resolution is illustrated by the fractional contributions to the 26AI (n 0 ,p 0 ) 26 Mg reaction rate factors from the two = 0 . 1, the resonance at 32 keV in figure 24a contributes approximat ely 60% of the integral; at T 9 =0.3, t he large resonance at 79 lowest resonances. At T 9 keV contributes a similar percentage. Thus at low temperatures, the exact position and strength of an individual resonance can essentially determine the reaction rate factor. Table 3 shows several relevant reaction rate factors calcu lated from the formulae given by Caughlan et al . (Ca84). Here the reactions 26A! (n 0 ,p t) 26 Mg and 2 6 AI (n 0 ,cxt )2 3 Na refer to all states of the pro duct, ground a nd excited; thus they would not necessarily be comparable to the data of tables 1 and 2 . One very significant comparison is however app ropriate: the experimental ly determined 26 AI (n 0 ,cx 0 ) 23 Na rate is several times the theoretically estimated rate for the 26AI ( n 0 ,cxt )23 Na reaction. In fact, this experimental 26AI ( n 0 ,0.0 ) 23 Na reaction rate is a very large fraction ( 40% to 65%) of the theoretically estimated 26 AI (n 0 ,p t ) 26 Mg rate, the supposed principal destruction mechanism. excited states of 23 Na contribute appreciably, it seems If higher possible that 26 AI (n,cx) 23 Na is in fact the principal destruction mechanism. 26 AI (n,cx) 2 3 Na reaction clearly contributes significantly to the destruction of 26 AI In any case, the in a neutron-rich environment. These four key reaction rates, the experimental 26 AI( n 0 ,p 0 ) 26 Mg , 26 AI (n 0 ,p t ) 26 Mg, and the theoretical 26AI (n 0 ,cxt )23 Na, are plotted as functions of T 9 in figure 28. the experimental 26 AI(n 0 ,a 0 ) 23 Na , the theoret ical -30D. Astrophysical Implications The 26AI (n 0 ,a:0 ) 23 Na reaction rates calculated from the data of the present experiment reinforce Clayton's statement (CI84) that supernovae have little chance of contributing the quantity of 26Ai, live and fossil, which has been observed. The alternative suggestion, that contributions from novae dominate, is correspondingly strengthened. E. Conclusions Further measurements of reactions involving 26 AI are clearly warranted to investigate possible mechanisms for its production and destruction. Several have recently been reported. Champagne (Ch82) has studied the possibility that 26 AI production by the 25 Mg (p ,[) 26 AI reaction might be enhanced by the existence of resonances at low proton energy. Since the Coulomb barrier makes direct study of this reaction infeasible, he has pursued it via the 25 Mg ( 3 He ,d) 26 AI reaction and has discovered one candidate level. The clearest specific need is for direct measurements on 26AI targets to determine the cross sections and reaction rates between various excited states of 26 Mg and the ground state of 26 AI. Production of such targets has been reported recently by Buchmann et al . (Bu84a); also reported has been the use of some of these targets to investigate the 26AI(p,[) 27 Si reaction (Bu84b), a potential destruction mechanism in a proton-rich environment. Kappeler 26 AI (n 0 (Tr84) have very recently reported Trautvetter and measurements of the ,p 1 ) 26 Mg reaction rate using a neutron spectrum which corresponds to T 9 = 0.29 on a target of 26AI. Reactions to this first excited state of 26 Mg (Jrr =2+, E = 1.809 MeV) are expected to dominate the rate for 26 AI (n ,p t ) 26 Mg. Their result is that N <av > = 6.2 x 10 5 cm 3 mole - 1 sec - 1 . 0 0 This value is remarkably low; it is only 2% of that predicted by Caughlan et al. (Ca84) 26 AI ( n 0 for 26AI(n ,pt) 26 Mg 0 and only 25% of the reaction rate for ,p 0 ) 26 Mg calculated from the data of the present experiment. This • 31 result, unless contraverted, would permit much greater quantities of 26AI to be produced in a neutron-rich environment, and may resurrect the candidacy of super"novae as the sites for production of the quantities observed. Further refinement of theoretical models will also be necessary inasmuch as reaction rates involving excited states in both entrance and exit channels are expected to play a significant role. Laboratory measurement of cross-section data between excited states of two nuclei is difficult and complex in favorable cases; for 26 Mg and 26AI it would seem to be impossible because of the short life (~ ps) of the 26 Mg excited states and the necessity of a free neutron target if one contemplated use of a beam of 26 mAI . One seems therefore obligated to depend on the theoretical calculations for these reactions. -32- APPENDIX A As was mentioned in the body of this thesis, when the 417-keV 1-ray yields representing reactions to the second excited state of 26 AI were collected, the 1-ray spectra were recorded on magnetic tape. These spectra spanned an energy range from "'300 to 2000 keV; therefore any exit channel from either 26 Mg + p or 23 Na + ex involving emission of a 1-ray in this energy range could be studied with a minor increment of effort. Table 4 lists the reactions for which this has been accomplished; figures 29 through 32 show the results; in each case, the cross section is for the production of the specified rray. Therefore, in order to calculate the cross section to a particular excited state, one must subtract off contributions reaching that state by cascading from a higher one. In all cases the bombarding energy has been converted to excitation energy in the 27 AI compound nucleus for use as the abscissa. The principal data of this experiment, the excitation functions for the 26 Mg(p,n.) 26 AI ~ and 23 Na(cx,n.) 26 AI ~ reactions, are repeated with this same abscissa. This abscissa was selected to facilitate comparison among all excitation functions measured. The experimental energy ranges covered were E P =3.965 to 4.597 MeV for the 26 Mg + p entrance channel and E a = 3.965 to 4.597 MeV for the 23 Na + ex entrance channel. The formulae for converting the excitation energy to laboratory energy are EP = 1.03879 Eex - 8.59151 (A.1) E a = 1.17 411 E ex - 11.8463 (A.2) and for the 26 Mg + p and 23 Na + ex entrance channels respectively, where all energies are in MeV. -33- REFERENCES Ar78 W. D. Arnett and J. P. Wefel, Astrophysical Journal (Letters) 224, L 139 (1 978). Ar80 M. Arnauld, H. N¢\rgaard, F.-K. Thielemann, and W. Hillebrandt, Astrophysical Journal237, 931 (1980). Ba59 S. Bashkin, R. W. Kavanagh, and P. D. Parker, Physical Review Letters 3, 518 (1 959). Bu84a L. Buchmann, H. Baumeister, and C. Rolfs, Nuclear Instruments and Methods, in press. Bu84b L. Buchmann, M .Hilgemaier, A. Krauss, A. Redder, C. Rolfs, H. P. Trautvetter, and T. R. Donoghue, Nuclear Physics A415, 93 (1 984). Ca84 G. R. Caughlan, W. A. Fowler, M. J. Harris, and B. A. Zimmerman, submitted to Atomic and Nuclear Data Tables (1 984). Ch82 A. E. Champagne, Ph.D. Thesis, Yale University (1 982). Cl82 D. D. Clayton, in Essays in Nuclear Astrophysics, edited by C. A. Barnes, D. D. Clayton, and D. N. Schramm (Cambridge: Cambridge University Press), 401 (1 982). Cl84 D. D. Clayton, Astrophysical Journal 280, 144 (1984). Da 79 J. M. Davidson, D. G. Sargood, and J. L. Zyskind, Bulletin of the American Physical Society 24, 593 (1 979). -34- Fo67 W. A. Fowler, G. R. Caughlan, and B. A. Zimmerman , Annual Review of Astronomy and As t rophysics 5, 525 ( 1 96 7). Fu71 M. Furukawa, K. Shizuri, K. Komura, K. Sakamoto, and S. Tanaka, Nuclear Physics A174, 539 (1971). Hi82 W. Hillebrandt and F.-K. Thielemann, Astrophysical Journal 255, 617 (1 982). Ki79 J. D. King and C. W. Cheng, Canadian Journal of Physics 57, 286 (1 979); erratum, Canadian Journal of Physics 57, 1063. Le77 Typhoon Lee, D. A. Papanastassiou, and G. J Wasserburg, Astrophysical Journal (Letters) 211, L107 (1977) . Le78a Typhoon Lee, Astrophysical Journal 224 , 21 7 ( 1 978). Le78b Table of the Isotopes (7th ed.), edited by C. M. Lederer and V. S. Shirley (New York: John Wiley and Sons) (1 978). Ma57 R. L. Macklin, Nuclear lnstuments 1, 335 (1957). Ma75 F. M. Mann, Ph.D. Thesis, California Institute of Technology (1 975). Ma82 W. A. Mahoney, J. C. Ling, A. S. Jacobson, and R. E. Lingenfelter, Astrophysical Journal 262, 7 42 ( 1 982). Ma84 W. A. Mahoney, J. C. Ling, W. A. Wheaton, and A. S. Jacobson, Astrophysical Journal, in press (1 984). -35- Me78 R. A. Meyer, MuLtigamma- Ray Calibration Sources (Booklet M-1 00), (Livermore, California: University of California) ( 1 978). Mo55 S. A. Moszkowski, in Beta- and Gamma- Ray Spectroscopy, ed. K. Siegbahn (New York: lnterscience), chap. 13, p. 391 (1 955). No81a E. B. Norman, K. T. Lesko, T. E. Chupp, and P. Schwalbach, Nuclear Physics A357, 228 ( 1981 ). No81b E. B. Norman, T. E. Chupp, K. T. Lesko, and P. J. Grant, Astrophysical Journal 251,834 (1981). No82 E. B. Norman, T. E. Chupp, K. T. Lesko, P. Schwalbach, and P. J. Grant, Nuclear Physics A390, 561 (1 982). Os83 J. L. Osborne, Ph.D. Thesis, California Institute of Technoicgy (1 983). Pa80 M. Paul, W. Henning, W. Kutschera, E. J. Stephenson, and J. L. Yntema, Physics Letters 948, 303 (1 980). Sa82 D. G. Sargood, Physics Reports 93, 62 ( 1 982). Sk83 R. T. Skelton, R. W. Kavanagh, and D. G. Sargood, Astrophysical Journal 271, 404 (1 983); erratum (submitted). Sk84 R. T. Skelton and R. W. Kavanagh, Nuclear Physics A414, 1 41 ( 1 984 ). Ta66 S. Takayanagi, M. Katsuta, K. Katori, and R. Chiba, Nuclear Instruments and Methods 45, 345 (1 966). -36- Th84 J. H. Thomas, R. L. Rau, R. T. Skelton, and R. W. Kavanagh, Physical Review C30, 385 (1 984). Tr78 J. W . Truran and A. G. W. Cameron, Astrophysical Journal 219, 226 (1 978). Tr84 H. P. Trautvetter and F. Kappeler, Zeitschrift fur Physik, in press. Wa80 R. A. Ward and W. A. Fowler, Astrophysical Journal 238, 266 (1 980). Wo67 C. Wong, J. D. Anderson, J. W. McClure, and B. Pohl, Physics Review 156, 1266 (1967). Wo80 S. E. Woosley and T. A. Weaver, Astrophysical Journal 238, 1017 (1 980). Wo81 S. E. Woosley, T. S. Axelrod, and T. A. Weaver, Comments on Nuclear and Particle Physics 9, 185 (1 981 ). -37- TABLE 1 26 AI (ni ,p 0 ) 26 Mg Experimental Reaction Rate Factors The reaction rate factors, N 0 <uiv >, for reactions from the three lowest states of 26AI to the ground state of 26 Mg. The values are calculated from data of the present experiment. Asymptotic cross sections are used for cross sections above the experimental range. The numbers in parentheses represent the percentage contributions from the asymptotic term. -38- TABLE 1 Tg 26AI (no ,po )26Mg 26AI (n1 >Po )26Mg 26AI (n ,p i 6Mg 2 0 0.10 2.32 E+05 2.64 E+07 1.25 E+07 0.15 4.95 E+05 4.10 E+07 2.22 E+07 0.20 8 .30 E+05 6.07 E+07 3.21 E+07 0.30 1.51 E+06 1.10E+08 5.03 E+07 0.40 2.05 E+06 1.57 E+08 6.53 E+07 0.50 2.46 E+06 1.94 E+08 7.60 E+07 0.60 2.79 E+06 2.22 E+08 8.28 E+07 0.70 3.07 E+06 2.44 E+08 8.65 E+07 0.80 3.31 E+06 2.60 E+08 8 .81 E+07 0.90 3 .53 E+06 2.74 E+08 8.83 E+07 (1) 1.00 3.73 E+06 2.85 E+08 8.75 E+07 (1) 1.50 4.49 E+06 (3) 3.26 E+08 (3) 7.84 E+07 (4) 2.00 5.21 E+06 (1 0) 3.53 E+08 (8) 6.93 E+07 (9) 2.50 6.04 E+06 (20) 3.71 E+08 (15) 6.27 E+07 (16) 3.00 6.98 E+06 (31) 3.84 E+08 (21) 5.80 E+07 (23) 3 .50 7.98 E+06 ( 41 ) 3.94 E+08 (28) 5.48 E+07 (30) 4 .00 9.02 E+06 (49) 4.03 E+08 (34) 5.26 E+07 (36) 4.50 1.00 E+07 (56) 4.11 E+08 (40) 5.11 E+07 (42) 5.00 1. 11 E+07 (62) 4.19 E+08 (45) 5 .02 E+07 (48) 6.00 1.30 E+07 (71) 4.35 E+08 (54) 4.93 E+07 (57) 7.00 1.48 E+07 (77) 4 .51 E+08 (61) 4.94 E+07 (65) 8.00 1.64 E+07 (81) 4.67 E+08 (67) 5 .00 E+07 (70) 9.00 1.80 E+07 (84) 4.83 E+08 (72) 5.09 E+07 (75) 10.00 1.94 E+07 (87) 5.00 E+08 (76) 5.20 E+07 (79) -39- TABLE 2 26 AI (ni ,a0 ) 26 Mg Experimental Reaction Rate Factors The reaction rate factors, N 0 <aiv >, for reactions from the three lowest states of 26AI to the ground state of 23 Na. The values are calculated from data of the present experiment. Asymptotic cross sections are used for cross sections above the experimental range. The numbers in parentheses represent the percentage contributions from the asymptotic term. -40- TABLE 2 Tg 26AI (n , CXo f 3 Na 0 26AI Cn, 'C:Xo )23Na 26AI (~' c:xo )23Na 0.10 2.08 E+07 2.37 E+06 4.10E+06 0.15 1.69 E+07 2.94 E+06 5.42 E+06 0.20 1.50 E+07 4.25 E+06 7.39 E+06 0 .30 1 .34 E+07 7.40 E+06 1.13E+07 0.40 1.31 E+07 1.00 E+07 1.42 E+07 0.50 1.31 E+07 1.18 E+07 1.63 E+07 0.60 1.33 E+07 1.31 E+07 1.79 E+07 0.70 1.36 E+07 1.40 E+07 1.92 E+07 0 .80 1.38 E+07 1.48 E+07 2.03 E+07 0.90 1.40 E+07 1.55 E+07 2.13E+07(1) 1.00 1.42 E+07 1 .61 E+07 2.22 E+07 (1) 1.50 1.53 E+07 (1) 1.92 E+07 (3) 2.59 E+07 (8) 2.00 1.66 E+07 (3) 2.22 E+07 (9) 2.92 E+07 (18) 2.50 1.80 E+07 (7) 2.50 E+07 ( 1 6) 3.22 E+07 (28) 3.00 1.95 E+07 (12) 2. 77 E+07 (25) 3.50 E+07 (38) 3.50 2.09 E+07 (18) 3.01 E+07 (33) 3.75 E+07 (45) 4.00 2.22 E+07 (24) 3.24 E+07 (40) 4.00 E+07 (54) 4.50 2.35 E+07 (30) 3.46 E+07 (46) 4.23 E+07 (59) 5.00 2.48 E+07 (36) 3.66 E+07 (52) 4.45 E+07 (64) 6.00 2.71 E+07 (46) 4.04 E+07 (61) 4.86 E+07 (72) 7.00 2.93 E+07 (54) 4.38 E+07 (68) 5.24 E+07 (77) 8.00 3.14 E+07 (61) 4. 70 E+07 (73) 5.59 E+07 (82) 9.00 3.33 E+07 (66) 5.00 E+07 (77) 5.93 E+07 (85) 10.00 3.52 E+07 (71) 5.28 E+07 (81) 6 .24 E+07 (87) - 41 - TABLE 3 26AI Theoretical Reaction Rate Factors The total reaction rate factors, N 0 <av >for reactions from the ground state and the first excited state of 26AI to any state of 26 Mg and 23 Na. These are the theoretical reaction rates from the parametrized formulation of Caughlan et al. (Ca84). -42- TABLE 3 26AI (n , ay_ 1 i 3 Na Tg 26AI(7lo •Pt )26Mg 26AI (n, •Pt )26Mg 26AI (no' ay_ )23Na 0.10 3.10E+07 1.30 E+07 6.98 E+06 1.44 E+07 0.15 3.12 E+07 2.30 E+07 6.46 E+06 1.44 E+07 0.20 3.13E+07 3.52 E+07 6.14 E+06 1.44 E+07 0.30 3.16E+07 6.74 E+07 5.87 E+06 1.44 E+07 0.40 3.19E+07 1.02 E+08 5 .90 E+06 1.44 E+07 0.50 3.22 E+07 1.32 E+08 6.11 E+06 1.44 E+07 0.60 3.24 E+07 1.56 E+08 6.45 E+06 1.44 E+07 0.70 3.26 E+07 1.76 E+08 6.89 E+06 1.44 E+07 0.80 3.27 E+07 1.91 E+08 7.40 E+06 1.44 E+07 0.90 3.28 E+07 2.04 E+08 7.98 E+06 1.44 E+07 1.00 3.29 E+07 2.13 E+08 8.61 E+06 1.44 E+07 1.50 3.34 E+07 2.37 E+08 1.23 E+07 1.45 E+07 2.00 3.49 E+07 2.43 E+08 1.67 E+07 1.53 E+07 2.50 3.77 E+07 2.42 E+08 2.15 E+07 1.73 E+07 3.00 4.17 E+07 2.38 E+08 2.65 E+07 2.07 E+07 3.50 4.69 E+07 2.33 E+08 3.17 E+07 2.56 E+07 4.00 5.29 E+07 2.29 E+08 3.69 E+07 3.21 E+07 4.50 5.99 E+07 2.24 E+08 4.22 E+07 4.00 E+07 5 .00 6.75 E+07 2.19 E+08 4.75 E+07 4.94 E+07 6.00 8.39 E+07 2. 10 E+08 5.81 E+07 7.21 E+07 7.00 9.94 E+07 2.02 E+08 6.86 E+07 9.90 E+07 8 .00 1.1 0 E+08 1.95 E+08 7.90 E+07 1.29 E+08 9 .00 1.12 E+08 1.88 E+08 8.95 E+07 1.61 E+08 10.00 1.02 E+08 1.83 E+08 9.99 E+07 1.94 E+08 -43- T AB LE 4 Summary of Excitation Functions Th is tabulation provides a summ ary and index for the excitation functions of ail exit channels analyzed from 26 Mg + p and 23 Na + n ; the 26AI + n exit channels are included for comparison. See Appendix A. -44- TABLE 4 Summary of Excitation Functions Reaction 1-Ray Energy (keV) Figure 26Mg (p ,no)26AI 29a 26Mg (p ,n 1)26 AI 29b 26Mg(p,n2)26AI 417 29c 26Mg (p ,n t )26 A! 29d 23Na (c:x,no)26AI 30a 23Na (c:x,n 1)26 AI 30b 23Na (c:x,n2)26 AI 417 23Na(c:x,nt)26AI 30c 30d 26Mg (p ,p' )26Mg * 1809 31a 26Mg (p ,p' )26Mg * 1130 31b 26Mg (p ,p' )26Mg * 1779 31c 26Mg (p ,p' )26Mg * 1003 31d 26Mg (p ,c:x1 )23Na * 440 32a 23Na (ex, a. ')23Na * 440 32b 23Na(c:x,p)26Mg * 1809 32c -45- FIGURE 1 Energy Level Structure and Decay Scheme of 26AI All energies are shown to scale. The entrance levels for the two reactions studied, 26 Mg (p, n ) 26 AI and 23 Na (a, n) 26AI, are shown at the right. The vertical scales show excitation energy in the center-of-mass system for each case; the energy regions for which data were obtained are indicated by the vertical bars. -46- FIGURE 1 1\. ;- <:)' 0.417 3++- _ _~~~~- 0.228 5 4 2 3 1 2 1 zsMg +p-n 12 -47- FIGURE 2 The Mg-AI Cycle The dominant net effect of the cycle is to convert 4 protons into the ex-particle, emerging from the 27AI (p, cx) 24 Mg reaction; the isotopes of Mg and AI act as catalysts. Nuclei reaching A =28 escape from the cycle. Half-lives for {3+ emis- sion are shown. _26AI (n,p ) 26 Mg paths are the same as those for {3+ emission by 26AI. (After Wa80). 25Mg + p . (3+ 7.2s ~~Mg + p....L...~.Al~ + p 'Y 'Y ~~Si 26 .Alo + p---'-1-~ 13 Excited ~g~.Alm + p 'Y ~ Str£ fj+ 215i +P 14 (3+ I 4.1s 2sMg + p....L._21 .Al + PI 12. 13. a -r 'Y 28p 15 fj+ I0.27s ., 2esi u ITI N :0 c: C) ., +::> co -49- FIGURE 3 Water-Cooled Target Mount This arrangement was used for manufacturing the 26 Mg targets by reduction of MgO with zirconium powder. A current of several hundred amperes flowing through the evaporation boat was used to heat the materials in it to a temperature sufficient for the reaction to proceed ("' 1200° C). The liberated 26 Mg would then evaporate and condense on the cooled target backing. To furnish an approximate size scale, the exposed aperture of the target backing was 13 mm. -50- FIGURE 3 ~~~~~--- Copper body ~~~~~~~------ Water passage '--------- Target backing Evaporation boat -51 - FIGURE 4 Rutherford Backscattering for 26 Mg Thickness Measurement Figure 4a was obtained from a target consisting of 26 Mg on a thin gold substrate on an aluminum backing bombarded with 2-MeV a-particles. The features of this spectrum are the backscattering edge from the aluminum backing (1 ), the peak from the 26 Mg (2), and the peaks from the gold (3 and 4). The main gold peak (3) represents backscattering of a-particles which traversed the 26 Mg layer; the minor peak (4) represents backscattering from gold on the front surface, probably indicating a pinhole in the 26 Mg layer. Figure 4b was obtained from a comparison target which had a gold layer on aluminum, but no 26 Mg. This spectrum was obtained with geometry and electronics identical to those of figure 4a. The two principal features are the aluminum edge (1) and the gold peak (2). Comparison of the two spectra shows the energy suppression of the gold edge by the 26 Mg as well as the further suppression of the aluminum edge by the 26 Mg. (Even in figure 4b the aluminum edge is being suppressed by energy loss in the gold. Backscattering from aluminum on the front surface would produce an edge at an energy slightly higher than that of the 26 Mg peak in figure 4a; in practice the two would merge because the resolution of the detector would not be sufficient to separate them.) -52- FIGURE 4 ~ Q) ~ (/) --+-) 10 2 0 ;:j 0 u 101 ...-I Q) 104 0 0 ro ..c: u 103 ~ Q) ~ (/) --+-) 10 2 0 ;:j 0 u 101 200 400 600 800 Channel Number -53- FIGURE 5 Rutherford Backscattering for 23 Na Thickness Measurement The target was Na 2 WO 4 on a thin gold foil with a graphite beam stop; it was bombarded with 2-MeV a-~articles. The features of this spectrum are the graphite beam-stop edge (1) and peaks from a small amount of surface carbon (2), from oxygen (3), from 23 Na (4), and from the gold and tungsten (5). -54- FIGURE 5 105 5 {/) .-+-) 0 ;:::1 0 u 103 200 400 600 Channel Number 800 -55- FIGURE 6 Target Chamber The cold trap minimized the amount of carbon-containing vapors entering from the upstream side. The beam was defined by the aperture, 5 mm in diameter. The last 77 em of beam tube acted as a Faraday cup. Aperture Ion pump ·Electrical insulator Target en :0 rrl c 5 ., I Ol (Jl -57- FIGURE 7 Output Spectrum from a 3 He Detector Features of this spectrum are the threshold at 25% of full energy associated with the proton entering the wall (1 ), the break associated with the 3 H entering the wall (2), and the full-energy peak (3). The threshold would be set around channel 100. (See text). -58- FIGURE 7 25 ,--.. (/) roj:f 3 ro 20 (/) ~ 0 ..c:t ~ '-" r--4 15 Q) j:f j:f ro ..c:t 0 10 $-! Q) ~ (/) ..p.) ~ ~ 0 5 1 0 100 200 300 Channel Number 400 500 -59- FIGURE 8 Output from the Priority Encoder Each "spike" represents one of the 12 counters. The pulses from channels 7 and 8 are more closely spaced because of details of the circuit design; since their separation still exceeds any reasonable requirement, no attempt to improve this was made. F 1001 0 2 u 101 0 ~ :::1 Vl 10 111 I 211 I 31\ I 411 511 II 6 711118 119 1110 1111 1112 II I 100 Ill Ill IMI !WI 300 II&AA.IIIIIIII 400 IIAU118pR1111!11PII WI Channel Number 200 !li P 1 500 18 11111811 1 1 03 ~ <D c :0 m S-4 C5 ., 104 6 1o3 <0 d d <D ~ 105r117~----,---:-,----,---,--- I 1 C!l 0 - 61 - FIGURE 9 Arrangement of the Scintillator for Counting (:3+ Particles The size of the plastic scintillator was just sufficient to stop the highest-energy (:3+ particles; this selection minimized background. The entire assembly shown was placed inside the graphite cube in order to count prompt neutrons and delayed (:3+ particles within the same bombard-and-count cycle. Beam Target Plastic scintillator Photomultiplier tube "T1 U) m ::::0 c C) 0) 1\) - 63- FIGU RE 10 Spectrum from a Ge(Li) Detector Counting a 152 Eu Source All lines marked originate from 152 Eu except the one noted; these lines have the following energies and relative intensities (Me78): Notes : Number Energy (keV) 1 244.7 359 2 344.3 1275 3 367.8 40.5 4 411.1 107 5 444.0 148 6 778.9 619 7 964.1 692 8 1085.9 475 9 1112.1 649 10 1408.0 1000 11 1460.8 12 1528.1 Intensity Note (1) (2) 12.7 ( 1) Includes contributions from unresolved lines at 1 084 keV (! and 1 089.7 keV (! = 82). (2) Background line from 4 °K =11. 7) -64- FIGURE 10 0 rrrrn..-r--mn.TT-r-.rrrrllr.--.m~rrr.-~~no~~C) co 0 0 <:0 0 0 C\2 -65- FIGURE 11 Gamma-Ray Detection Efficiency Calibration The peak efficiency occurs at a relatively high energy because a thin sheet of lead was used to attenuate the lower energy -y-rays. The lead was slightly thicker than would have been ideal, since the linear (power law) portion of the curve does not quite extend to 0.41 7 MeV; this slightly increases the uncertainty in detection efficiency. - 66- FIGURE 11 ~ 0.4 -67- FIGURE 12 Typical Nal Spectrum from 26 Mg (p, n 1 ) 26AI Measurements The prominent peak (1) is the photopeak from 511-keV annihilation radiation arising from the delayed 26 mAI positrons. -68- FIGURE 12 0 .----.----.---~~--~----~~~----~~ C\2 0 0 C\2 0 I 1..() (spu-gsnottL) 19UU'B118 .I9d SlUUO:J -69- FIGURE 13 Times in the Bombard-and-Count Cycle See equation 111.3. The cycle restarts after a time T T; several cycles (m) are run. Some representative values are as follows : Tc Tr m f.;.. 6.25 1.29 9.26 1 7.00 20 0.4 70 6.25 1.29 9.26 17.00 40 0.473 5.70 0.30 1 0.1 16.00 10 0.564 - 70 - FIGURE 13 - - - 71 - FIGURE 14 Typical Ge(Li) Spectrum from 26 Mg (p, n 2 ) 26AI Measurements The target was on a tantalum backing. (Natural tantalum is nearly 100% 181 Ta .) The peak of principal interest is that at 417 keV (5). The lines marked are identified as follows: Origint Number Energy (keV) 1 136 181 Ta excitation to 136 keV state 2 165 18 1Ta excitation to 302 keV state 3 302 181 Ta excitation to 302 keV state 4 366 181 Ta(p,n) 181 W to 366-keV state of 181 W 5 417 26Mg (p 'n 2 )26AI 6 440 26Mg (p, cx)23Na 7 511 annihilation radiation; dominant source 26 mAI positrons 8 1130 26Mg (p, p' ) 26 Mg • to 2938-keV state of 26 Mg 9 1809 26 Mg (p ,p' i 6Mg • to 1 089-keV state of 26 Mg - • to 440-keV state of 23 Na t In most cases it is possible that higher excited states than those mentioned are cascading to the state mentioned; this is obviously occurring for ( 1) and (9) in view the presence of (3) and (8) respectively. - 72- FIGURE 14 0 0 0 C\2 0 0 lO M 0 0 L.(.) - 73- FIGURE 15 Cross Sections for 26 Mg (p, n) 26AI Excitation 26 Mg (p, n functions 2 for (a) ) 26AI; (d) the total. 26 Mg(p,n 0) 26AI; (b) 26 Mg(p,n 1 ) 26AI; (c) In (d) the cross section from threshold to 5.22 MeV is magnified by a factor of 5 to improve visibility. -74- FIGURE 15 + 250 200 150 100 d 50 - 0 ..0 32oo ~ .....0 tCD 150 (/) (I) ~ 100 s.. u 50 0 100 50 0 100 50 0 5.0 5.1 5.2 5.4 5.3 5.5 5.6 Laboratory Proton Energy (MeV) 5.7 5.8 - 75- FIGURE 16 Cross Sections for 23 Na (ex, n i 6AI Experimental excitation functions for (a) 23 Na (ex, n 0 ) 26AI; (b) 23 Na (ex, n 1 ) 26AI; (c) 23 Na(ex,n 2 ) 26 AI; and (d) the total. Note that the ordinate scale for (b) is one-tenth that of the others, and note the obviously lower resolution. Generally, it would not be acceptable to have obtained the data of (a) by subtraction from (d) of the low-resolution data of (b); however, since in this case the crosssection values in (b) are such a small fraction of the total, the errors introduced are minimal. - 76- FIGURE 16 70 60 50 40 30 20 10 0 :a 20 s - c 10 -~ _, 0 ~ 0 Vl C/1 C/1 0 1-o u 1 0 70 60 50 d - 77- FIGURE 17 Comparison to Previous 26 Mg (p, n ) 26AI ( 0) Measurements Comparison of data from the present experiment (solid line) to data from Paul et al. (Pa80) (open circl.es) and to Furukawa et al. (Fu71) (solid circle). The data shown represent the total production of 26 AI in the ground state, either directly or via ,-ray emission from a higher state, in the 26 Mg (p, n) 26AI reaction. - 78- FIGURE 17 I I I I I I I I I I f- - f- A - f~ tJ 10 2 r- - 11 -r.~ \ 11 ,......,. ..0 - ~ 0 ., ·.-< () Q.) (/) C/l en 0 $..< u P' ~ \J s -- - - 10 1 -- - I I I r- - 10° - - -- - 1ft - - v I 5.0 5.1 I 5.2 5.3 I I 5.4 5.5 5.6 I I I 5.7 5.8 5.9 Laboratory Proton Energy (MeV) - 79- FIGURE 18 Comparison to Previous 26 Mg (p, n 1 ) 26AI Measurement Comparison of data from the present experiment (solid line) to that of King and Cheng (Ki79) (open circles) for the 26 Mg (p, n 1 ) 26AI reaction, determined by measuring delayed {3+ activity. The discrepancies are well outside of the estimated uncertainties for all except the point at 5.75 MeV. -80- FIGURE 18 + 1.':1 0 ...... ~ 0 ~ 10 1 Vl Vl 0 u'"' + 10° 5.2 5.3 5.4 5.5 5.6 5.7 5.8 Laboratory Proton Energy (MeV) 5.9 - 81 - FIGURE 19 Comparison to Previous 26 Mg (p, n 2 ) 26AI Measurement Comparison of data from the present experiment (solid line) to the data of Norman et al . (No81 a) (open circles) for yield to the 417-keV state. -82- FIGURE 19 + ,........ ..0 s ~ 0 ...... ....., 0 Q) {/) en en 0 ~ u 5.4 5.5 5.6 5.7 5.8 Laboratory Proton Energy (MeV) 5.9 -83- FIGURE 20 Comparison to Previous 26 Mg (p, n )26AI Measurement Comparison of data from the present experiment (solid line) to the data of Norman et al. (No81b) (open circles) for total neutron yield in the 26 Mg(p,n) 26 AI reaction. The results of the previous experiment were obtained by differentiating the yield from a thick target. -84- FIGURE 20 I ~ 0 ...... I 10 1 ~ 0 Q) (f) {/) {/) 0 ~ u 5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 Laboratory Proton Energy (MeV) 5.9 I - 85- FIG URE 21 Comparison to Previous 23 Na (ex, n ) 26AI Measurement Comparison of data from the present experiment (solid line) to the data of Norman et al. (No82) (circies) for the total neutron yield in the 23 Na (ex, n) 26 AI reaction. The results of the previous experiment were obtained by differentiating the yield from a thick target. -86- FIGURE 21 102 ~ I I I I I I I I I I I I I I - I - ~ ~ - ~ ~ -r _j_ A I~ ~ r- ,_ - '-If 10 1 r- - ~ .--... .0 s ......... 1=1 0 ...... - ~ 11- - ~ ~ ~ 0 Q) ~ I Cll Cll ~ 0 u'"' 100 r- ~ ~ 1~ ~ ~ - rr (/) l - ' - v ~ _- ~ ~ I 3.6 I 3.8 I I 4.0 I I 4.2 I I 4.4 I I 4.6 Laboratory Alpha Energy (MeV) I I 4.8 I -87- FIGURE 22 Comparison to Previous 23 Na(a,n 1 ) 26AI Measurement Comparison of data from the present experiment (solid line) to the data of Norman et al. (No82) (open circles) for the measuring the delayed positron yield. 23 Na (a, n 1 ) 26AI reaction, determined by -88- FIGURE 22 t:l 0 ...... ~ 0 Q) ifl 3.8 4.0 4.2 4.4 4.6 Laboratory .Alpha Energy (MeV) 4.8 -89- FIGURE 23 Comparison to Previous 23 Na(a, n) 26AI Measurement Comparison of data from present experiment (solid line) to the data of Norman et al. (No82) (open circles) for the 23 Na (a, n 2 ) 26AI reaction, determined by measuring the 417-keV ,-ray yield. -90- FIGURE 23 I I I I I I I I I I I 1- j ~ 1- ,l l..tl r~ \ --s - - ~ ..0 ~ ........., ~ 0 .,...; -<-) I I C) il) (/) (/) (/) 0 I-< u 10° - - - ~ - - I I II 4.0 I I 4.2 I I 4.4 I I I 4.6 Laboratory Alpha Energy (MeV) I 4.8 I - 91 - FIGURE 24 26 AI (ni ,p Experimental 26AI(n 1 excitation ? 6 Mg Cross Sections functions (solid) for (a) 26AI (n 6 0 ,p )Z Mg; (b) ,p) 26 Mg; and (c) 26AI(n 2 ,p) 26 Mg. These were calculated by the prin- ciple of detailed balance from the data of figures 15(a), (b), and (c) respectively. The results of a Hauser-feshbach optical model calculation (dashed) are also shown. Not e that the ordinate scale for (a) is one-tent h that of (b) and (c). The substantial theoretical overestimation of the 26AI (n 0 ,p )26 Mg cross section is apparent, as is the tendency of the theory to overestimate all cross sections at low energy. -92- FIGURE 24 ~ 0 :g 1000 ~ U1 [/] [/] 0 s... u 0.1 0.3 0.4 0.5 0.6 Center-of-Mass Energy (MeV) 0.7 0.8 -93- FIGURE 25 26 Experimental 26AI (n 1 excitation AI (ni , o:) 23 Na Cross Sections functions , o:) 23 Na; and (c) 26AI (n 2 (solid) , o:) 23 Na. for (a) 26AI (n 0 , o:) 23 Na; (b) These were calculated by the principle of detailed balance from the data of figures 16(a), (b), and (c) respectively. The fine dashed lines in (a) and (c) are the results of the present experiment reduced by a factor of 5 to fit on the plot. The results of a Hauser-Feshbach optical model calculation (coarse dashed) are also shown. The "kinks" in the dashed curve are strictly an artifact introduced by the fact that the computation was carried out over a rather coarse grid of bombardment energies. The substantial overestimation of 26 AI (n 2 , o:) 23 Na and underestimation of 26AI (n 0 , o:i 3 Na are apparent. -94- FIGURE 25 250 '' 200 c ' '' ' ' \ 150 \ 100 -------------- 50 ---,D. 0 ------------ 8 b d 100 .S ......, 0 Q) U1 50 en en ...0 (.) 0 a 250 200 150 100: 50 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Center-of-Mass Energy (MeV) 0.8 0.9 -95- FIGURE 26 Ratios of Reaction Rates for 26AI (ni ,p ) 26 Mg Ratios of reaction rates calculated from the theoretical cross-section values of the Hauser-Feshbach calculation (figure 15) to the reaction rates calculated from the cross-section data of the present experiment for (a) 26AI (n 0 ,p )Z 6 Mg; (b) 26AI(n 1 ,p) 26 Mg; and (c) 26AI(n 2 ,p) 26 Mg vs temperature. reactions are to the gmund state of 26 Mg. In each case, the -96- FIGURE 26 -97- FIGURE 27 Ratios of Reaction Rates for 26AI (ni , o:) 23 Na Ratios of reaction rates calculated from theoretical cross-section values of the Hauser-Feshbach calculation (figure 16) to the reaction rates calculated from the cross 26AI(n section 1 data of the present experiment for (a) 26 AI (n 0 , cx) 23 Na; (b) ,cx) 23 Na; and (c) 26AI(n 2 ,cx) 23 Na vs temperature. In each case, the reac- tions are to the ground state of 23 Na. -98- FIGURE 27 \ \ \ I \ I I \ I \! ~ j\ '\ I\ 'i 'I / I I I I I I I I ,I I / / I I I / o/ ~ '/ // // I ,I I / I . 0 T"""'' ~0 0 . -99- FIGURE 28 Reaction Rate Factors Reaction rate factors for (a) 26AI(n 0 ,p 0 ) 26 Mg (calculated from the data of the present experiment); (b) 26AI (n 0 , a 0 ) 23 Na (calculated from the data of the present experiment); (c) 26AI (n 0 ,p t ) 26 Mg (as tabulated by Caughlan et al.) (Ca84); and (d) 26AI (n 0 , at ) 23 Na (Ca84). The values represented by (c) are expected to be dominated by reactions to the excited states of 26 Mg; therefore it is not surprising that (c) should be so much higher than (a). What is surprising is that (b) should be higher than (d); the theory apparently underestimates significantly the 26AI (n 0 , eta )23 Na reaction rate. - 100- FIGURE 28 I I I I ol I I ro l'- ...-l ...-l 0 0 .IO'f:JBj 8'fBtJ 0 . - 101 - FIGURE 29 Excitation Functions for 26 Mg (p, n i 6 AI These are the same data as presented in figure 15, except that here they are plotted VS excitation energy in the compound nucleus e AI) to facilitate com7 parison with other excitation functions presented in figures 29 through 32. - 102- FIGURE 2 9 250 200 150 100 d 50 c 0 ~ 150 Q) en 0~--~-----r----+---~~--~----,_~~~~~-----r----+---~ 100 50 0~--~-----r----~--~~---+----4-----~--~----~----+---~ 100 - 103- FIGURE 30 Excitation Functions for 23 Na (a, n )26AI These are the same data as presented in figure 1 6, except that here they are plotted vs excitation energy in the compound nucleus ( 27AI) to facilitate comparison with other excitation functions presented in figures 29 through 32. - 104- FIGURE 30 0 20 :a 8 '-' d 0 :.;::; 10 . 0 CD en til til 0 .... u 1 0 70 60 50 40 30 20 10 0 13.1 13.2 13.3 27 AI. 13.4 13.5 Excitation 14.0 - 105- FIGURE 31 Excitation functions for 26 Mg (p ,p' i 6 Mg ~ Excitation functions for 26 Mg (p ,p' ) 26 Mg ~leading to (a) the 1809-keV -y-ray; (b) the 1130-keV ~-ray; (c) the 1780-keV ~-ray; and (d) the 1 004-keV 1-ray. Note the reduced scale for the last two, which represent respectively excitations to the third and fourth excited states of 26 Mg. - 106- FIGURE 31 10 0~---+----~----+---~----~----4-----~---+~~~----+---~ 200 -;a100 8 .._, 500 400 300 200 100 a - 107- FIGURE 32 . Other Excitation Functions Excitation functions for (a) 26 Mg (p, cx) 23 Na "leading to the 440-keV ;-ray; (b) 23 Na (ex, cx) 23 Na ~ leading to the 1809-keV ;-ray. to the 440-keV ;-ray; and (c) 23 Na (cx,p )26 Mg leading - 108- FIGURE 32 40 30 c 20 10 0 40 -!3o a .t:l 0 '(; 20 ~ Vl {II {II ,..0 10 (,) 0 50 40 30 20 10 0 b