Mass Measurements of Some Proton-Rich Nuclei Citation Miller, Richard Graham (1966) Mass Measurements of Some Proton-Rich Nuclei. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/YTVX-HS04. https://resolver.caltech.edu/CaltechTHESIS:10122015-082232803 Abstract The Q values and 0 o cross sections of (He 3 , n) reactions forming seven proton-rich nuclei have been measured with accuracies varying from 6 to 18 keV. The Q values (in keV) are: Si 26 (85), S 30 (-573), Ar 34 (-759), Ti 42 (-2865), Cr 48 (5550), Ni 56 (4513) and Zn 60 (818). At least one excited state was found for all but Ti 42 . The first four nuclei complete isotopic spin triplets; the results obtained agree well with charge-symmetry predictions. The last three, all multiples of the α particle, are important in the α and e-process theories of nucleo-synthesis in stars. The energy available for β decay of these three was found by magnetic spectrometer measurements of the (He 3 , p) Q values of reactions leading to V 48 , Co 56 , and Cu 60 . Many excited states were seen: V 48 (3), Co 56 (15), Cu 60 (23). The first two states of S 30 are probably 0 + and 2 + from (He 3 , n) angular distribution measurements. Two NaI γ-ray measurements are described: the decay of Ar 34 (measured Ƭ 1/2 = 1.2 ± 0.3s) and the prompt γ-ray spectrum from Fe 54 (He 3 , nγ)Ni 56 . Possible collective structure in Ni 56 and Ca 40 , both doubly magic, is discussed. The (He 3 , n) neutron energy and yield measurements utilized neutron-induced nuclear reactions in a silicon semiconductor detector. Cross sections for the most important detection processes, Si 28 (n, α) Mg 25 and Si 28 (n, p) Al 28 , are presented for reactions leading to the first four states of both residual nuclei for neutron energies from 7.3 to 16.4 MeV. Resolution and pulse-height anomalies associated with recoil Mg 25 and Al 28 ions are discussed. The 0 o cross section for Be 9 (α, n) C 12 , used to provide calibration neutrons, has been measured with a stilbene spectrometer for n o (5.0 ≤ E α ≤ 12 MeV), n 1 (4.3 ≤ E α ≤ 12.0 MeV) and n 2 (6.0 ≤ E α ≤ 10.1 MeV). Resonances seen in the n o yield may correspond to nine new levels in C 13 . Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Physics and Biophysics) Degree Grantor: California Institute of Technology Division: Physics, Mathematics and Astronomy Major Option: Physics Minor Option: Biology Thesis Availability: Public (worldwide access) Research Advisor(s): Kavanagh, Ralph William Thesis Committee: Unknown, Unknown Defense Date: 14 March 1966 Funders: Funding Agency Grant Number Office of Naval Research Nonr-220(47) Record Number: CaltechTHESIS:10122015-082232803 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:10122015-082232803 DOI: 10.7907/YTVX-HS04 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 9210 Collection: CaltechTHESIS Deposited By: INVALID USER Deposited On: 13 Oct 2015 20:28 Last Modified: 05 Mar 2024 22:31 Thesis Files Preview PDF - Final Version See Usage Policy. 40MB Repository Staff Only: item control page

MASS MEASUREMENTS OF SOME PROTON-RICH NUCLEI Thesis by Richard Graham Miller In Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1966 (Submitted March 14, 1966) ii ACKNOWLEDGMENTS The author wishes to thank all the faculty and technical staff of Kellogg and Sloan Radiation Laboratories without whose help this thesis would not have been possible. Particular thanks are due to Dr. R. Vv. Kavanagh who is the other half of the "we" used throughout this thesis. It was a long, hard struggle, but he may finally have taught me the meaning of the word "precision". I would also like to thank Dr. W. A. Fowler who wanted to know 56 the mass of Ni and thereby instigated this project. This research was supported by the Office of Naval Research [Nonr - 220(47) J. / iii ABSTRACT 3 The Q values and 0° cross sectfons of (He , n) reactions forming seven proton- rich nuclei have been measured with accuracies varying 26 30 · from 6 to 18 keV. The Q values (in keV) are: Si (85), s (-573), 42 48 56 60 34 Ar (-759), Ti (-2865), Cr (5550), Ni (4513) and zn (818). At 42 least one excited state was found for all but Ti . The first four nuclei complete isotopic spin triplets; the results obtained agree well with charge-symmetry predictions. The last three, all multiples of of the a. particle, are important in the a. and e-process theories of The energy available for !3 decay of these . . 3 three was found by magnetic spectrometer measurements of the (He , p) 48 60 56 Q values of reactions leading to v , Co and Cu . Many excited 48 56 60 . states were seen: V (3), Co (15), Cu (23). The first two states 30 3 of s are probably o+ and 2+ from (He , n) angular distribution measure34 ments. Two Nal Y- ray measurements are described: the decay of Ar nucleo-synthesis in stars. (measured T = 1. 2 ± 0. 3s) and the prompt Y- ray spectrum from 11 2 3 54 40 56 Fe (He , nY)Ni 56 . Possible collective structure in Ni and Ca , both doubly magic, is discussed. 3 The (He , n) neutron energy and yield measurements utilized neutron-induced nuclear reactions in a silicon semiconductor detector. 8 25 Cross sections for the most important detection processes, st (n~ u)Mg 28 28 and Si (n, p)AI , are presented for reactions leading to the first four states of both residual nuclei for neutron energies from 7. 3 to 16. 4 MeV. Resolution and pulse-height anomalies associated with recoil 0 28 Mg25 and AI ions are discussed. The o cross section for Be 9 (a., n)c 12 , used to provide calibration neutrons, has been measured with a stilbene spectrometer for n 0 (5. 0 .:S Ea.::: 12 MeV), n 1(4.3 ~Ea. .S 12. 0 MeV) and n (6. 0 :5 E .::; 10. 1 MeV). Resonances seen in the n a. 0 2 13 yield may correspond to nine new levels in C . · iv TABLE OF CONTENTS Part -I-.II. ID. Page INTRODUCTION 56 ASTROPHYSICS AND Ni 9 12 THE REACTION Be (a, n)c 1. hltroduction 2. Procedure 3~ Analysis of the stilbene spectra 3. 1 The integral- sum method 3. 2 The initial- step-height method 4. Results and discussion 4. 1 The n 0 yield curve 4.2 The n 1 yield curve 4.3 The n 2 yield curve 4.4 Levels of C 13 IV. 7 14 14 14 15 17 19 21 21 21 22 22 SEMICONDUCTOR DETECTOR AS A FAST NEUTRON SPECTROMETER 25 1. Introduction 25 2. General description of the spectrometer 26 3. Neutron energy measurement 29 4. Detection efficiency and neutro.:i yield measurement 33 5. Pulse-height and resolution anomalies 38 6.. Comparison with other methods V. -r 3 43 THE (He ,n) MEASUREMENTS 48 1. Introduction 48 2. 49 Procedure 3. Results 26 3. 1 The Si nucleus 30 3. 2 The s nucleus 51 53 55 v Page Part 34 3,3 The Ar nucleus 42 3.4 The Ti nucleus 48 nucleus 3. 5 The Cr 56 3.6 The Ni nucleus 60 3. 7 The Zn nucleus VI. VII. 55 56 57 59 63 4, Discussion 30 28 3 . 5. The Si (He , n)s angular distribution THE (He 3 , p) MEASUREMENTS . 67 1. Introduction 67 2. Procedure 67 3. Results and discussion 70 63 65 THE GAMMA-RAY MEASUREMENTS 73 1. Introduction 73 2. Decay of Ar 3, 34 Gamma rays from Ni 74 56 77 4. Discussion: Evidence for collective structure in doubly magic nuclei APPENDIX 1 78 Sample Calculations of the Si 28 (n, a )Mg25 0 Cross Section 81 1. Correction factors 81 .· 3 2. Cross section from D(d, n)He data 9 12 3.. Cross section from Be (a, n )c data 0 APPENDIX 2 82 83 Some Observations Concerning Negative Ion Beams 85 REFERENCES 91 TABLES 96 FIGURES 109 . 1 I. The nucleus Ni 56 INTRODUCTION ha s several properties which make it unusual and pa rticularly interesting. It is doubly magic (Z = N = 28, shell closure) and is the most tightly bound of all nuclei con712 taining equal numbers of protons and neutrons. Despite its unusual 56 nuclear stability, it beta decays to Co which in turn beta decays to Fe 56 , n early the most bound of all nuclei. There is a very large f peak in the cosmic element abundance centered at Fe 56 and, if one accepts the view that the elements are synthe sized inside stars, one must find a mechanism to produce this peak. The a, - and e - process theories of Fowler and Hoyle (1964) provide such a · mechanism: In the advanced evolution of a massive star just before 56 it becomes a supernova, Ni is made from lighter elements by 56 a- particle capture (the a - process). Some of the Ni decays by 56 · electron capture to Co before the explosion and is rapidly. trans~ 56 muted to other iron group elements, including Fe (the e-process ). 56 56 The remainder of the Ni decays to Fe after the explosion. The result is that the relative abundances of the iron group elements are 56 largely determined by the half life of the Ni decay. Chapter II gives a more detailed outline of these theories. 56 The stellar value of the Ni half life , which is much shorter than the terrestrial value be cause of the increased ele ctron density at the nucleus, is mainly determined by the amount of ene rgy 56 available in the Ni de cay i.e. the Ni 56 · - Go 56 mass difference. The work de scribed in this thes is began as an attempt to measure 56 56 the Ni mass , the Co mas s being alrea dy known. This mas s 56 had not been m easured previous ly for two r ea sons :. Ni is two positions from the line of s tability on the protofr·rich s ide which .2 I makes direct study via nuclear reactions duficult, and it appears to decay entirely by electron capture (see e.g. Wells, Blatt and · Meyerhof (1961)) so that !3 endpoint energy m easurements cannot be made. According to Wells et al., the gamma rays seen following the decay indicate that electron capture proceeds to a 56 state in c o at 1. 74 MeV with possible branches to lower-lying 56 56 states. Thus the Ni - Co mass duference must be greater than 1. 74 MeV and, since no positrons are seen, cannot be much more than 2 MeV. 56 In our study, the mass of Ni was deduced from the Q 54 3 56 value :measured for the reaction Fe (He , n)Ni . To overcome 3 the Coulomb barrier, the He beam energy must be 10 MeV or more and the reaction Q value was estimated to be about 5 MeV. Thus it was necessary to measure the energy of a 15-MeV neutron - too high to be able to achieve the desired resolution with neutron time-of-flight techniques. Following a suggestion by Dr. G. Goldring, the neutron energy was measured by m eans of charged-particle-producing reactions induced by neutrons in the silicon of the active volume of a semiconductor detector. In this way, the problem of measuring the neutron energy was reduced to the much simpler problem of measuring a charged particle energy. cations remain. Howeve r, several compli- The spectrum produced by a monoene rgetic neutron in a semiconductor detector is very complex because of the different isotopes of silicon present, the duferent reactions possible with each, and the many final states populated in each residual nucleus. The strongest groups observed are due to the 28 25 28 28 reactions Si (n, a)Mg and Si (n, p)Al . Cross sections for . these reactions leading to the fir s t four states of the two residual 3 . nuclei were measured in steps of 25 to 50 keV over the neutron energy range 7. 3 to 16. 4 MeV. The methods involved are described in detail in Chapter IV. Also discussed are a differ- ential pulse-height defect. observed when comparing peaks from 28 25 28 28 the reactions Si (n, a)Mg with peaks from Si (n, p)A.1 and the anomalously poor resolution of these peaks when compared with the resolutions of a particles or protons alone. 56 The Ni nucleus is composed of an integral. number of alpha particles (14), which is one reason for its large binding energy. Although all such nuclei possess large nuclear stability 40 compared to their neighbors, Ca is .the heaviest alpha nucleus . 24 stable against beta decay. The alpha nuclei above Mg are . 56 important stepping stones on the way to Ni in the a- process. . . 48 No mass measurement had been made on one of them (Cr ) nor 60 56 48 on the first alpha nucleus above Ni (zn ). Since both Cr and 60 3 Zn could be made by (He , n) reactions, they were. investigated 56 using the techniques developed for the Ni measurement~ The data obtained for all three nuclei were used to locate excited states and obtain an estimate of the 0 ° reaction cross section as well as to measure masses. In the course of the Zn 60 measurements, two unknown contaminants were observed to build up on the target during bombardment. Kinematic considerations eliminated all but two 28 elements which might reasonably be expected: Si (from 0- ring 32 grease) arid s (from 0-rings). However, neither the mass of . 30 .28 3 . 34 32 3 S (from S1 (He , n))nor Ar (from S (He , n)) was known. Targets of 0- ring grease and natural silicon were bombarded and 28 the identification of Si as one of the contaminant peaks was confirmed. At the same time an accurate measurement of the s30 mass was obtained. Next, targets of natural sulfur and Sb 2 s3 34 were bombarded and the mass of Ar was determined. The result 32 was such as to preclude s being the second contaminant. The 3 periodic· table was searched again, this time (He , n) reactions on all stable nuclei being considered. All possibilities were eliminated 24 3 26 kinematically except the reaction Mg (He , n)Si , but again no 26 accurate measure ment of the Si mass existed. Natural magnesium 26 targets were bombarded and the mass of Si determined, the 24 measurements indicating that Mg was indeed responsible for the second contaminant peak. How did it get there? It turns out that all commercial aluminum is alloyed with a small amount of magnesium 6 (R::1 1%). Further, at low pressures (,.,,, 5xl0- mm Hg) and high temperatures ( ~ 500° C), the magnesium may readily evaporate 60 from the alloy. The target holde r used for the Zn measurements was made of aluminum and the target was observed to become red 56 hot under bombardment. The Ni data was obtained using the same target holder and upon re- examination also showed peaks from 30 26 26 Si (and s too). Other accurate measurements of both the Si 30 and s masses were published at about this time and agree well with the values found here. The search of the nuclides made while trying to identify the contaminants discussed above suggested that 42 one more new isotope could easily be m ade : Ti via the reaction 26 30 4 3 2 34 1 . Th"is was d one. The f our nuc1e1. s·1 . , s . , A r C a. o(He , n )T.4 42 and Ti - all complete isotopic spin triplets of which they are the proton-rich members. The results obtained agree well with the predictions of charge symmetry. An additional measurement was 28 3 30 made on the Si (He , n)s reaction: the angular distributions of neutrons to the ground and first excited states were measured in a semiconductor detector. made. Probable spin and parity assignments are 5 . . 3 The procedure and results for all the (He , n) measurements are given in Chapter V. One detail of the procedure should be 9 12 mentioned here: The reaction Be (a., n)c was used to provide neutrons of known energy for calibration purposes, thus avoiding the problem of absolute energy measurement. Calibration spectra obtained in this way could also be used to unfold complex spectra by subtracting out the family of peaks associated with each neutron group, starting with the group of highest energy. Many excited states were found by this method. As well as being used for energy calibration purposes, the 12 9 Be (a., n)c reaction was used to provide 10. 6 to 16. 4-·MeV neutrons for the semiconductor-detector- efficiency measurements (see Chapter IV, section 4). For these reasons, it was investigated in 0 some detail. Absolute cross sections at o were measured for n , nl' and n 2 over most of the bombarding energy range of 4 to 0 12 MeV using a stilbene crystal as the neutron detector. . The n 0 yield curve has prominent resonances which may correspond to up 13 to nine new levels of C . These measurements are described in Chapter II. As already mentioned, one of the most important para56 56 meters in the e-process theory is the Ni - Co mass difference. 56 With this in mind, it was decided to check the Co mass, a 54 3 measurement which could be made with the reaction Fe (He , p)Co 56 using the same target material and even the same targets as used 56 56 for the Ni experiment. Fifteen excited states of Co were found, most of them verifying earlier work. At the same time mass and 60 48 level measurements were made on Cu and v which are the 60 48 . 13-decay daughters of Zn and Cr , the other two alpha nuclei whose masses had been measured. Twenty-three levels were seen 6 60 in Cu , all previously unreported. 3 ·. The (He ~ p) measurements are described in Chapter VI. The last chapter, Chapter VII, describes two gamma-ray 34 measurements. First, the half life of Ar ~1as found, a measurement made possible by the discovery of an allowed ~ -decay branch 34 to the O. 67-MeV level of c1 which takes place in addition to the 34 superallowed transition to the ground state of Cl . Second, the prompt gamma- ray spectrum from the reaction Fe 54 (He 3, n)Ni 56 was measured and the gamma rays seen identified with levels of 3 56 Ni found in the (He ,n) Q-value measurements. The data are consistent with a collective interpretation of the levels of Ni 56 discussed in section 4 of the chapter. 54 3 Before the Fe (He , n) reaction was tried, attempts were 56 made to produce Ni with reactions using a heavy ion beam of 20 32 either Ne or s . To get a beam of high enough energy to surmount the Coulomb barriers involved, it was first necessary to produce a negatively- charged beam from the negative ion source of the ONR-CIT tandem. These attempts were not successful but some useful information about heavy-ion-beam production was obtained and is given in appendix 2. 7 II. ASTROPHYSICS AND :l'n The importance of Ni 56 56 to astrophysics can best be explained by giving a brief life history of a massive star (mass thirty times that of the sun) as envisioned by Fowler and Hoyle (1964). The star comes into existence through the condensation of a large ·gas cloud, composed mostly of hydrogen, and is slowly warmed by the release of gravitational energy. Neglecting radiation pressure, exactly one half the gravitational energy released is radiated away and the other half converted into internal energy. 5 After about 3x l0 years, the temperature near the center of the cloud becomes so high that protons there have sufficient kinetic energy to undergo nuclear reactions. Hydrogen is transformed to helium with the release of energy. · Gravitational contraction ceases ·and the core temperature remains essentially constant (about 4x10 7 degrees) until all the hydrogen is converted to helium, a process 7 which takes about 3xl0 years. When the hydrogen is exhausted, the core again shrinks, warming further as it does so. At a temper._ 8 ature of about 2x10 degrees, helium burning commences and the . . 16 . 5 core is converted to 0 , a process taking about 3x10 years . . Further contraction and heating take place and in about one day the oxygen is burned by nuclear fusion r eactions at a temperature 9 32 of about 2x l0 degrees to form heavi_e r nuclei, primarily s . Up to this point, the nuclear evolution of the star has been cyclic in character. As long as a particular fuel is being burned, the star remains quite stable in gross structure. Small changes in the physical condition of the star's core regulate the nuclear energy generation rate so that it just balances radiation losses . In the brief interval between fuels, energy balance is maintained by gravitational 8 contraction which also increases the core temperature to the point where the product of the last process can become the fuel of the next. A fuel is first exhausted in the core of the star where the temperature is highest; the same fuel continues to be burned in a shell around the core even after the core has switched to a heavier fuel. During oxygen burning, two qualitatively new features become important: energy loss by neutrino emission and photodisintegration reactions. Anytime a neutrino is produced, it is almost certain to escape from the star without further interaction. Such an energy loss must be made up by an increase in the nuclear reaction rate. The eve theory suggests the existence of the reaction e+ + e - - v + -v and allows one to calculate the rate, a calculation which shows that this reaction, if it exists, is by far the most important source of neutrinos in massive stars at high temperatures and that its rate increases very rapidly with temper8 ature. At temperatures above 5xl0 degrees, neutrino losses exceed photon losses and in fact shorten the oxygen burning time 7 scale by a factor of 10 . Almost all the nuclear energy generated is now being used to balance the neutrino loss and this loss rate will therefore determine the evolutionary time scale. The second new feature is that at the higher temperatures now present many electromagnetic photons will have energies high enough to produce photodissociation reactions. Toward the end of 32 9 oxygen burning (T = 2. 5 x 10 degrees), some of the s produced will be photodisintegrated, primarily by (Y, p) reactions but occasionally by (Y, a ) or (Y, n) reactions. The residual nuclei are 28 rapidly broken down by further (Y, n) and (Y, p) reactions to Si , a nucleus which is too stable to photodisintegrate at the prevailing 9 temperature. The protons and neutrons released recombine into a particles because of the large energy release. The se, in turn, 32 36 . . are captured by S to form Ar . The total effe ct is summed up by 2s 32 -+ 28 Si + Ar 36 - 0. 31 MeV and forms a slight energy dra in on the star. The reverse reaction also occurs and the syste m comes into equilibrium with the number 32 28 36 approximately equal to that of Si + Ar • Note 36 32 28 that s and Ar can exist only because Si is stable against 44 4 photodisintegration. Small amounts of Ca o and Ti may also be density of s made by a capture but the temperature is not high enough for this to be very significant. This cycle of reactions marks the first ste p of the a-process. After oxygen burning, the core contracts until a tempera9 28 ture is reached (~ 3 x 10 degrees) at which Si is photodisinte24 24 grated and is effectively transformed into Mg + a.. The Mg 28 lifetime to effective a -particle loss is less than 10% that of Si ; 8 16 12 20 Ne , 0 and c have even shorter lifetimes and Be is spon28 taneously unstable. Thus, once the Si structure is broken, it is almost immediately transformed into seven a particles. Most of these a. particles will be captured by the remaining heavy nuclei to form heavier nuclei and the center of the mass distribution will shift to ever-higher values of atomic weight. Although the analogy is not very accurate, one could view the core of the star as being a vast sea of a. particles making up a Maxwell - Boltzmann statistical ensemble. The a. particles will group into clusters (nuclei) of varying size, the number of clusters of a given size being 10 proportional to exp(B/kT) where B is the bL1ding energy of the cluster. Of course the clusters are being conth~'lally broken up by photodissociation reactions but there will be some equilibrium distribution determined by the Boltzmann factor. That combination of a particles which has the most binding energy per nucleon (and is 56 therefore most abundantly produced) is Ni . Thus the main effect of the a- process may be summed up as 2Si 28 _. Ni 56 + 11. 0 MeV . The very complicated chain of reactionp implied by this expression produces enough energy to maintain stellar equilibrium but the neutrino drain is so great at the existing tempe ratures (3 - 3. 5 x 10 9 degrees) that the fuel is exhausted in about one hour. At this point, energy generation by nuclear reactions ceases 56 since Ni has tl~e maximum binding energy per nucleon in a medium in which the number of protons-and neutrons is equal. One source of energy remains: the beta decay of the heavier elements to the line of stability, in particular the transformation of tightly bound isobar, 28 Ni~~ to the more the 27co~~·9 After slight core contraction, .. temperature rises to 3. 8x 10 degrees and this and s u bsequent reactions are able to maintain equilibrium, This is the e- process . . 56 56 On earth, Ni decays to Co by electron capture with a half life of 6. 1 days. In the stellar core, the electron density at the nucleus is much greater than on earth because of the high temperature and pressure so that the decay rate is greatly enhanced 56 (by a factor of about 300 for our particular star). Once Co is formed, it is immediately transmuted to more s table nuclei by rapid nuclear reactions e. g. , 11 2Co 56 _, Fe 54 + Ni 58 + 4. 45 MeV. These two nuclei, although both stable, can capture electrons to 58 54 form Mn and Co which 1n turn a~e immediately transmuted to · more stable nuclei e. g .. ' 2Fe 54 + 2e- _, 2Mn 54 . - 1. 39 MeV _, Cr 52 + Fe 56 + 3. 53 MeV (net release), 2Ni 58 + 2e- _, 2Co 58 - 0. 78 MeV _, Fe 56 + Ni60 + 4. 62 MeV (net release) and so on. Once the stellar core has converted to Fe energy reserves are n early exhausted, 56 , its nuclear The attempt to balance neutrino energy losse s by cor e contraction only brings on a worse 9 56 fate: at temperature s above 4x 10 degrees, the Fe is photodisintegrated, first into a particles and neutrons and finally into protons and neutrons. Gravitational contraction can provide no where near enough energy t o balance this enormous ener gy drain. The inner core goes into fr ee fall and completely implodes in less than a second. thereafter. The mantle and envelope of the star explode soon The result - a supernova. Much of the stellar material immediately outside the imploded inne r core will be expelled from the star. It will have undergone the ·e-process but will not have suffered photodisinte gration. ' . The implosive instability, once . started, develops so rapidly that there is insufficient time for it to consume the whole core. This ejected material (about two solar masses) is presumably the source of the large peak in .cosmic 56 . element abundance centered at Fe • Two tests of the theory immediately suggest themselves: 12 1) Can the a- and e-processes produce the correct relative abundances of the elements in the iron group? 2) If the answer to 1) is "yes" (it is), is there sufficient time for the e-process to operate before the star blows up? This second question is considerably more complicated. The time available for the e-process to operate is set by the neutrino loss rate and is about 6000 sec for the star being considered. The rate of the e- process is largely determined by the rate of the 56 56 Ni -• Co electron capture. This in turn depends sensitively on 56 56 the Ni - Co mass difference, a number which was not experimentally available when Fowler and Hoyle first performed their calculations. Using nuclear and beta decay systematics, they guessed a value of 2. 1 MeV. The initial stimulus for the work described in this thesis was to measure this value. In Chapters V and VI, experiments are described in which it was found to be 2. 115 ± 0. 017 MeV - amazingly close to the original guess! This mass difference leads to a mean electron capture life time, r, of 56 2700 sec for the ground state of Ni in the e-process. The presence 56 of a state in Ni at 2. 69 MeV which is probably 2+ may enhance the decay by 20- 50%. Fowler and Hoyle adopted r == 2000 sec. The influence of this number on the relative abundances of the iron group elements may be seen in the following way. Suppose 56 the Ni lifetime were very long (several days). Then very little 56 Ni would decay before the star exploded. The expelled material 56 cools very rapidly and all nuclear reactions cease. Thus the Ni 56 beta decays entirely to Fe . The result would be a very sharp peak . 56 56 111 the abundance curve at Fe , and Fe only, contrary to obser56 vation. A very short Ni lifetime (a few seconds) would produce a different effect. There would be enough time before the explosion 13 for electron captures and subsequent fast 11uch.' 2 r reactions to move the nuclear materia l to positions of greater neutron excess and 58 slightly greater stability e; g. , the relative abundance of Fe 56 (which is slightly more stable than Fe ) would increase relative 56 56 to Fe • On the other hand, if the Ni mean life were about equal to the time available for the e-process to operate, there would be a 56 sharp fall in the final Fe abundance and a sharp rise in the 54 58 abundances of elements such as Fe and Ni (see reactions given above). Using this chain of reasoning and some computer calcu- lations performed by Clifford and Tayler (1965), Fowler and Hoyle made estimates of the final relative abundances of the different ·isotopes of iron as a function of the time available for electron 56 capture using the calculated Ni lifetime. Their calculations reproduce the cosmic abundance curve if the time available for 4 electron captures is 3. 2xl0 sec. This is about five times longer than the time given above for the operation of the e- process. How- ever, the two time scales can be brought into agreement in a variety of ways e. g. , by assuming the e-process material responsible for the iron group elements to have come from stars slightly less massive tha n the thirty- solar- mass star ass umed in the calculation or by making reasonable (and small} changes in the model of the physical structure of the star. 14 III. 9 12 THE REACTION Be (a, n)c 1. Introduction 12 9 The reaction Be (a, n)C (Q = 5. 704 MeV) is a convenient source of fast neutrons for calibration purposes. The neutron 12 group leading to the ground state of C is well separated in energy from the neutron group leading to the first excited state (at 4. 43-Me V excitation) and the gamma ray from the decay of this state is the only gamma ray present. Pure targets are readily available since beryllium is monoisotopic and are easily made using standard belljar evaporation techniques. Furthermore, the targets are quite rugged whether used as self- supporting foils or on thick backings. 0 This chapter reports o cross- section measurements performed with a stilbene detector for the production of the first three 9 12 12 levels of c : Be (a, n )c (gnd) for 5. 0 .:5 E :S 12. 0 MeV 9 ° 12 a (section 4. 1); Be (a, n )c (4. 43) for 4. 3 ~ E ::; 12. 0. MeV · 91 12 a (section 4. 2); and Be (a, n )C (7. 66) for 6. 0 :S Ea :S 10. 1 MeV 2 13 (section 4. 3). Deduced levels in C are given in section 4. 4. 2. Procedure 0 The neutron and gamma-ray yield at o was measured in a stilbene crystal for alpha-particle bombarding energies from 4 to 12 MeV. From the spectra obtained, it was possible to deduce 12 the neutron yield to the ground state of c from 5 to 12 MeV and 12 the neutron yield to the first and second excited states of C over much of the same range, although with much less precision. The step size was 100 keV except in the region of a narrov,r resonance at 11. 70 MeV where the step size was red1.1ced to 25 keV. The 15 ONR-CIT tandem accelerator was used to provide an a++ beam magnetically analyzed to a precision of 0. 2% . . Targets were made 9 by evaporation of Be onto tungsten backings 0, 018 cm thick. Target thickness was determined using a magnetic spectrometer to measure the difference in energies of 1-MeV protons scattered from the tungsten backing with and without penetration through the beryllium layer. See figure 21 for two typical target thickness measurements. The entire yield curve was measured with targets 2 2 of two different thicknesses: 40 ± 8 µg/cm and 88 ± 14 µg/cm . The stilbene crystal used was cylindrical, 3. 81 cm in 0 diameter and 3. 81 cm long. It was located at o with respect to the beam axis with its front face 5, 71 cm from the target. The crystal was mounted on a phototube-preamplifier combination whose output was connected to the internal amplifier of a 400-channel pulseheight analyzer. 3. . Analysis of the stilbene spectra A typical spectrum is shown in figure 1. Neutrons are H CH CH c H ) through elastic 6 5 6 5 collisions with protons so that each neutron group of discrete energy detected indirectly in stilbene (C is represented in the spectrum by a continuous distribution of protons from zero energy to the full neutron energy, all proton energies occurring with approximately equal probability. Thus, one might expect a monoenergetic neutron to produce a rectangularshaped spectrum in stilbene as recorded in a multichannel analyzer (equal number of counts in all channels up to the channel number corresponding to the incident neutron energy and no counts thereafter). However, the light output of stilbene is a non-linear function of proton energy, low- energy protons be ing less effective light 16 producers. Thus, instead of being flat, the spectrum slowly rises as one goes toward lower channels. Swartz and Owen (1960) present tables from which the detection efficiency and spectrum shape for a monoenergetic neutron may be calculated. They also give a detailed de scription of the use of organic scintillators, in particular stilbene, for the detection of neutrons by their proton recoils. Gamma rays are also detected in a stilbene crystal, again indirectly, through processes which transfer energy to electrons, primarily Compton scattering in the energy range of interest here. In figure 1, the double-peaked structure near channel 80 was produced by the 4. 43-MeV gamma ray of c 12 . The upper peak is the Compton edge of the gamma ray and the lower peak is due to conversion of the gamma ray into an electron pair which is totally stopped in the crystal, but with loss of both annihilation quanta. The light output of stilbene is a nearly linear function of electron energy and is considerably larger than the light output for a proton of the same energy. For example, pulses from the Compton edge of the 4. 43-MeV gamma ray have about the same amplitude as pulses produced by a 9. 7-MeV proton. We have used two methods for obtaining absolute n eutron yield from the observed proton pulse-height distributions. The first of these, the integral - sum method, was used to analyze all the n . data and part of the n data. The second, the initial- step- height 1 method, was used to analyze the n data. 2 0 17 3. 1. The :integral- sum method The raw · spectra for the entire neutron energy range examined were used to obtain a graph of channel number vs. protonrecoil energy, assuming that the channel number of the half-height point on the shoulder at the end of the proton recoil group (channel 117. 8 for n 0 in figure 1) corresponds to a proton energy equal to the incident neutron energy. Next, for each spectrum, the sum of all counts above a fixed channel, corresponding to an energy E (channel c 105 for n in figure 1, corresponding to a proton energy of 10. 23 MeV), 0 was found. From this, the number of ground-state neutrons per 0 steradian at o could be calculated by multiplying by E /(4n(E - E ) e) n where E n n c! is the incident neutron energy and E: is the detection efficiency calcula ted using table I from the articl e by Swartz and Owen. Figure 2 shows a plot of detection efficiency vs. neutron energy for the particular geometry used in this experiment. A sample calculation of the absolute cross section is given in the caption of figure 1. When finding the n yield by this method, we had first to 1 allow for the underlying n structure. This was done by fitting the 0 theoretical shape of the n 0 distribution (which was calculated using table ill with kB == 0. 0120 from Swartz and Owen's article) to the visible portion of the curve and subtracting n from beneath n . The 0 1 n yiel~ was then determined precisely as above. This method of 1 analysis avoids problems due to the front edges of the pulse -height · distributions being not well defined and is also amenable to computer programming. The validity of tlie integral- sum method of analysis depends upon three assumptions: 18 i) The n-p scattering cross section is isotropic in the center-ofmass system. This is certainly true for low- energy neutrons but the distribution becomes anisotropic as the neutron energy is increased although at first remaining roughly symmetrical about 90° (CM). For 17-MeV neutrons (the maximum energy of interest 0 here), · the anisotropy (ratio of o to 90° cross sections in the CM) is about 1. 07 according to Gammel (1960), but the effect on the integral sum is always smaller and has been neglected. (It amom1ts to about 5% for the 1 7- Me V point. ) ii) All of the recoil protons are stopped in the crystal. Actually, some recoil protons produced near the edges of the crystal will escape, thus moving some counts from high channels to low channels. The effect becomes more serious as the neutron energy is increased. For 17-MeV neutrons and for the E c chosen, this effect results in . the integral sum being about 7% low. It is nearly cancelled by the artificial increase in the number of counts resulting from neglecting the effects of anisotropy. iii) Neutrons are detected entirely by single-scatter event~. Double- scatter events are of two types: a neutron may scatter first from carbon (an event which by itself, produces too small a light pulse for us to have detected) and then from hydrogen; or a neutron may doublescatter from hydrogen. The first type of event may change the detection efficiency but will not seriously affect the spectrum shape; the second moves events from low channels to high channels. n 0 For the group of figure 1 and for the cut-off energy chosen, the integral sum contams less than a 5% contribution from carbon-hydrogen scattering and iess than a 10% contribution from counts moved into the summed region by hydrogen-hydrogen scattering. Both these effects have been neglected because of the difficulty in computing them exactly. 19 It has been found empiriCally (see e. g. , Swartz and Owen) that the single- scatter detection efficiency calculated assuming no carbon scattering events is slightly larger and is closer to the true multiple- scatter detection efficiency i. e. , this calculation accounts fairly accurately for events in which a neutron is scattered first from carbon and then from hydrogen. The physical meaning of this observation is that the effective path length of the neutron in the crystal is little affected by carbon scattering events. However, this argument is useful only when analysis is based on the full recoilproton spectrum (which was not possible with our data) because carbon scattering lowers the neutron energy and therefore changes the sha pe of the spectrum. Figure 2 shows plots of the single- scatter dete ction efficiency allowing for attenuation of the primary neutron beam by both carbon .and hydrogen (the efficiency curve used here), and hydrogen scattering only. Broek and Anderson (1960) have de rived an approximate expression which corrects the initial step height of the proton recoil distribution for both double scattering from hydrogen and edge effects. For our crystal, the correction factors are 1. 07, 1. 03 and 0. 995 respectively for 5-MeV, 10-MeV and 15-MeV incident neutrons, giving us some justification for neglecting wall effects and double scatter from hydrogen. Note that d ouble scatter from carbon and the effects of an anisotropic n-p scattering cross section are not included in their expression. 3. 2. The initial-step-height method The distortion of the spectrum produced by multiple- .scattering events increases as the neutron energy is de creased because the detection efficiency i s increasing. Thus the integral- 20 sum method becomes of dubious validity for "low" energy neutrons to a degree that is determined by the shape and size of stilbene crystal used. For our crystal, we have assumed the integral- sum method to be valid down to a neutron energy of about 10. 5 MeV; distortions of the spectrum due to multiple scattering become plainly visible at lower neutron energies. A possible way to avoid many of the difficulties introduced by multiple scattering is based on the following properties. The non- linear response of stilbene results in a proton of given energy producing a larger pulse than two protons in coincidence with the same total energy. Also, the neutron energy is lowered 15% on the average in a carbon- scattering event, the energy of the recoil carbon atom being mostly lost in a non-luminescent way. Thus the highest- energy portion of the proton- recoil spectrum should be produced predominantly by single- scatter events. The shape of the n of figure 1 is suggestive of this interpretation. peak 1 Below the shoulder, there is a short flat region, then a bump, presumably due to multiple scattering, in which the number of counts increases about 10%. The n yield was found by using the height of the peak just 2 below the shoulder and calculating the cross section from this assuming the single- scatter efficiencies. To get the total number of counts in the distribution, the step height was multiplied by E/(4ne: t.E), where E is the incident neutron energy, l'.E the energy width of the channel just below the step and e the efficiency. We call this method the initial- step-height method; its validity depends upon the same assumptions as were made for the integral-sum method. 21 4. Results and discussion 4. 1. The n 0 yield curve . Then yield curve was analyzed entirely by the integralo sum method and is displayed in figure 3. The analysis could not be extended below a bombarding energy of 5 Me V because of the increa sing de gree of overla p of n pulses with y . 43 pulses. Errors 4 0 introduced by this overlap are proba bly responsible for the large scatter apparent in the lowest few points of the yield curve. The uncertainty due to negle ct of the possi ble effects of multiple neutron scattering in the stilbene along with uncertainty in the target thickness leads to an estimate of 20% for the standard deviation of the absolute value of the cross section. The statistical error on each point is 2% or l ess for the points above 5. 5 MeV. 4. 2. The n 1 yield curve The n yield curve mft.y either be measured directly or be 1 obtained from the yield of the 4. 43-Me V gamma ray since reactions 12 leading to the 4. 43-MeV level of c are the only significant source of this gamma ray. (All highe r levels are particle unstable.) We used the gamma ray to obtain most of the yield curve , measuring the height of the Compton shoulder relative to underlying structure. . Some spectra taken of the rea ction N 15 . 12 (p, a y . 43 )C gave very clear 4 spectra-for comparison purposes. The n 1 group itself was . Y. 4 43 analyzed by the integral-sum method for Ea::=: 11. 3 MeV to find the absolute cross s e ction. The yield curve obtained from Y4 . 43 was then scaled to this portion of the curve. Cross sections for several points lowe r on the yield curves were found directly by the initial. step-he i ght m ethod and agreed with the scal ed values t o within 30%. 22 Figure 4 displays the results. The absolute values of the cross sections are assigned standard devia tions of 30%; the relative error on each point is 5% or less. The dotted portion of the curve is the shoulder is passing through the y . 1 4 43 shoulder, making accurate separation of the two unfeasible. How- region in which the n ever, the yield does not deviate more than 20% from the position indicated by the dotted line. 4. 3. The n yield curve 2 The energy of this neutron group is so low over the whole range measured (En= 3. 25 to 7. 00 MeV) that. multiple scattering greatly distorts the spectrum. Thus the initial-step-height method of analysis was used throughout. figure 4. The results are presented in The absolute value of the cross section is correct to within 40%. The statistical error on each point is 10% or less. Below Ea,= 6. 0 MeV, the n group could not be clearly identified; 2 above Ea= 10. 0 MeV, the n shoulder is merging with Y . . 2 4 43 4. 4. 13 Levels of C · Assuming the nine peaks in then yield curve correspond 0 13 to nine resonant levels in the compound nucleus, C , the parameters listed in table 1 were determined. Many of the resonances are also present in the n 1 and n 2 yield curves. The large rise in the n yield 1 curve between 4. 0 and 6. 0-MeV bombarding energy appears to be composed of several additional levels, but our data are not sufficiently good to perform an accurate separation. The results of two previous studies partially covering the 13 same region of C , both of which utiliz ed the same reaction, are included in the table. Gibbons and Macklin (1959) meas ured the total 23 neutron cross section summed over all angles for bombarding energies be tween 2. 58 and 8. 2 MeV and identified four l evels in = 4. 5, 5. 0 and a. 5. 75 MeV, can be associated with the pronounced rise we see in the the regibn we have covered. The first three, at E n yield curve in this region as well as with the resonance at 1 E = 5. 40 MeV in the n yield curve. Their fourth level, at a. 0 Ea.= 7. 8 MeV, may correspond to the prominent resonance at = 7. 95 MeV in our n yield curve and to a poorly-resolved a. 0 . structure at about the same energy in the n yield curve . The 1 resonances they see are fairly small (.S 10%) variations in the E total mention cross section which rises nearly uniformly from a value of about 400 mb at 4. 5 MeV to around 600 mb at 5. 5 MeV after which it stays fairly constant. 0 Seaborn et al. (1963) measured the o and 90° y yield 4• 43 0 for 3. 4 .: : Ea. :S 10. 1 MeV. Their 0 Y4 . 43 curve closely r esembles ours in the region of overlap except that the higher resonances (above E = 7. 8 Me V) we see are masked in their data by resonances in C 12 (a.~a.' y . ). They also measured thirteen angular distri4 43 butions between 3. 3 and 7. 6-MeV bombarding energy in an attempt to understand the broad rise in the n yield. All the angular distri1 butions were symmetric about 90°. After fitting the distributions with Legendre polynomials up to P , they concluded that the rise is 4 probably due to several (maybe four) broad overlapping levels, t wo of which are in agreement with the res ults of Gibbons and Macklin. Above the broad resonance they identified two more levels : an uncertain one at E a. = 7. 1 MeV in agreement with a resonance. in our n 0 yield curve (and perhaps our n curve as well), and another at . 1 E a. = 7. 7 MeV which may correspond to our n 0 resonance at Ea.. = 7. 95 MeV and to the l evel seen at Ea = 7. 8 MeV by Gi bbon~ and Macklin. 24 As pointed out by Seaborn et -:il. , the total neutron cross section measured by Gibbons and Macklin can be almost entirely accounted for by n up to about E a = 5 Me V. Beyond this point, a . 1 large pa rt of the cross s e ction is probably from low energy neutrons arising from the various possible mechanisms which leave 3a. + n in the final state. (Our n group is the most energetic neutron group . . 2 produced in this way.) In our data, it is rather surprising that the n 0 yield curve . has so many resonances which show up only weakly or not at all in the n and n yield curves. It is equally surprising that the large 1 2 rise between Ea= 4 and 6 MeV in the n yield should not show up 1 more clearly in the n yield. Some of the structure we have attributed 0 13 to resonating C levels may in fact be interference effects or fluctuations involving two or more overlapping nuclear levels. Thus, for example, the n "resonances" at Ea.= 9. 7 and 10. 2 MeV may well · 0 be an interference anomaly from a single level. The level at Ea. = 11. 70 Me V is, however, almost certain to be real. It is well defined and appears clearly in both the n and n yield curves. 0 1 25 IV~ SEMICONDUCTOR DETECTOR AS A FAST NEUTRON SPECTROMETER 1. Introduction A silicon semiconductor particle detector niay be used to obtain precision neutron energy measurements, the neutrons being detected by means of charged-particle-producing nuclear reactions with the silicon of the active volume of the detector. Neutron energy measurements have been made in this way over the range 6 to 17 MeV and higher- energy measurements are possible. The method is primarily useful for measuring the energy of the most energetic neutron produced in a reaction. Usually, lower-energy neutrons can also be measured, but with less precision. Measurements of neutron yield are also possible. Deuchars and Lawrence (1961) were the first to observe neutron-induced reactions in a silicon semiconductor detector and many other groups have observed them since, several of them recognizing the neutron-detection possibilities. Among the first of these were Birk, Goldring and Hillman (1963) and Mainsbridge, Bonner and Rabson (1963). Mainsbridge et al., and Colli, Jori, Marcazzan and Milazzo (1963) used the technique to measure yield curves for neutron-induced reactions in silicon. Except for these measurements, a semiconductor det e ctor has not previously been used for either neutron ene rgy or neutron yield determinations. This chapter will discuss the problems involved and their solution. The next chapter contains applications of the method. 26 2. General description of the spectrometer . Figure 5 shows pa rt of the spectrum pr oduced by a 9. 83-MeV neutron in a semiconductor detector. The neutron is represented by a whole family of charged particles which are the result of the different isotope s of silicon present, the different reactions possible with each isotope (the most important being (n, a) and (n, p) reactions), and the many states av~ilable in each residual nucleus. Note that the energies of the light charged particle and the heavy recoil nucleus produced in the r eaction are summed by the detector. Table 2 lists all possible (n, a) and (n, p) reactions. Those marked with an asterisk are the only ones of pra ctical importance in natural silicon. Among the factors to consider when choosing a semiconductor detector for measuring neutrons of a particular energy are detection efficiency, resolution, and the possible effects of gamma rays. The detection· efficiency is determined by the cross s ections for the various neutron-absorption processes which can take place. Some of these have been meas ured and are given in section 4. As an 4 example of their application , about 1 in 1. 4x10 15-MeV neutrons 28 25 passing through 1 mm of sili con will react via the Si (n, a. )Mg 0 reaction. Clearly, a detector with large active volume is desirable. Good resolution is also desirable, but in practice, as active volume increases, resolution decreases. If one is studying neutrons from a reaction induced by an accelerator beam, well defined in both energy and position, there is little point in increasing the volume by increasing the area - - the resolution will soon be limited by the kinematic energy spread of the outgoing neutrons. The detector will have to be.moved further away, thus reducing the maximum possible absolute efficiency to that of a smaller detector (with better intrinsic resolution) located closer t o the t ar get. It is the depth of the detector which should be a s gr eat as possibl e. 27 The resolution of a semiconductor detector when used to detect neutrons is always much worse than when used to detect either ex. particies or protons alone. The best FVIHM neutron resolution we 25 28 have obtained for the Si (n, cx. )Mg peak is about 125 keV, even for 0 detectors whose resolution for a. particles alone is less than 25 keV. This phenomenon, as well as a difference in amplitude for equal. .28( )M 25 d energy pulses produ~ed by the reactions 8.1 n, a. g an Si28(n, p)Al28 , both appear to be due to effects associated with the 28 25 heavy recoil ions (Mg and Al ) and are discussed in detail in section 5. A semiconductor detector will also detect gamma rays, primarily by Compton scattering. Such gamma rays can come from two sources: gamma rays following the neutron-induced reactions in the detector itself and gamma rays from the nuclear reaction being studied. The first source is of little importance because of its very low intensity (the flux is comparable to the number of neutrons detected per second) and the fact that most of these gamma rays escape without interaction. For example, a 1-MeV gamma ray has a mean atte:q.:uation length in silicon of 6. 7 cm and typically the detector dimensions are no greater than 1 cm. The only exception is the 31-keV gamma ray from 28 the first excited-to ground state of Al which has a mean attenuation length of only 0. 36 cm. Thus the p 01 double peak (see figure 5) cannot be resolved, even in principle. Gamma rays from the reaction being studied may, however, be a serious problem. The ratio of the Compton plus pair cross section to 28 25 the Si (n, a. )Mg cross section for a gamma ray and neutron each 0 . . having an energy of 10 MeV is about 10 to 1 and the incident gamma-ray flux often exceeds the neutron flux. Fortunately, the amount of energy which an electron can lose in the detector is limited by the detector 28 dimensions and is less than 4. 5 MeV if the largest dimension is 1 cm (a length sufficient to stop a 45-MeV proton or 200-MeV a. particle). Thus, if high-energy gamma rays are present, they set a lower limit on the neutron energy which may be accurately . measured. When necessary, this problem may sometimes be avoided by using a detector smaller than would otherwise be desirable. At this time, the deepest semiconductor detectors are made using the lithium-drift technique of Pell (1960). We have usually used such detectors obtained from Technical Measurement Corp. , San Mateo, California. These detectors had cylindrical shape with an active diameter of 1 cm and depth of 5 mm. All the discussion of the remainder of this section is based on Li-drifted detectors with these dimensions. Resolution is much improved by cooling. For one detector 28 25 tested, the resolution of the Si (n, a. )Mg peak impr~ved from 190 0 keV at room temperature to 145 keV when cooled with liquid nitrogen · and, for some detectors, neutron resolutions as low as 125 keV, apparently the best obtainable with any silicon semiconductor detector (see section 5), have been obtained after cooling. We routinely check detectors with an O. 23- ·me. calibrated Cs 137 gamma-ray source. The 0;662-MeV gamma ray is detected primarily by Compton scattering for which the cross section is known. Thus the volume of the detector may be measured directly. At the same time, a very small fraction of the gamma rays is totally absorbed by the detector and produces a peak analogous to the photopeak of a Na! crystal. The resolution of this peak provides a figure-of-merit for the uniformity and quality of the entire active volume of the detector. Figure 6 shows a typical spectrum. A good 29 detector has, when chilled, a gamma-ray resolution of less than 20 keV. (Our ultimate resolution was limited to about 7 keV by the electronics. ) However, a detector which has good resolution for gamma rays may not have good neutron resolution. One detector tested had, when chilled, a gamma-ray resolution of less than 10 keV but a neutron resolution of 230 keV. One possible explanation is that the silicon crystal contains many local inhomogeneities, such as droplets of lithium: fluctuations in the rate of energy loss of an electron due to these inhomogeneities are averaged out over the range .of the electron whereas a heavy particle is brought to rest via only one or a few inhomogeneous regions. Detectors often suffer from a second kind of defect: prominent low- energy tails on all the peaks of the neutron spectrum. These tails tend to wash out peak structure, making it difficult to find excited states in the reaction being studied. It appears that a detector can have fairly good resolution and still show such tails. A detector is considered suitable as a neutron detector if: i) The neutron resolution, when chilled, is 150 keV or better. ii) The ratio of the a. peak height to the valley height just above a. 0 is 15 to 1 or better. 3. 1 (The best we have observed is 22 to 1.) Neutron energy measurement Figure 7 shows one of several similar mounting arrangements used for the semiconductor detector. The principal function of the mount is to enable the detector to be chilled in such a way that ice frozen out from the atmosphere does not form on the detector or its external electrical connections. Such ice formation greatly increases the noise output of the detector. It is, of course, not necessary to have the detector mounted inside the target chamber since almost all 30 the fast neutrons produced pass through the target chamber wall and the front face of the detector mount without interaction. Having the detector outside the target chamber greatly simplifies any moving of the detector which must be performed during the course of an experiment. All precision neutron-energy measurements have been made 0 with the detector at o because kinematic energy spread is a minimum at this angle. The spectrum produced by the neutron being measured was compared with a calibration peak produced by a neutron of known energy as nearly equal to the unknown neutron energy as possible. This minimizes errors due to possible non-linearities of the detector or electronic equipment and makes possible the unfolding of complex spectra by the subtraction of the calibration spectrum from the unknown spectrum. The calibration spectra were obtained using the 9 12 reaction Be (a., n )C which, for this reason, was investigated in 0 some detail (see chapter III). 13 16 be C (a, n)o . Another good calibration reaction would 28 All quantitative calculatio~s have been based on the Si (n,a. ) 0 peak. Two methods have been used for finding peak position from the raw data : the centroid method and the intercept method. The first method is intrinsically the more accurate but requires that the target thickness and target- counter geometry be accurately .k nown whereas the second does not. · Before discussing the two methods in detail, let us consider 28 the shape of the Si (n, a. ) peak produced by a cylindrical detector 0 which has perfect resolution. Take the detector to be head-on, i.e. , the neutrons are incident normal to the circular face. The neutron peak will be broadened by two effects: the spread in beam energy due to finite target thickness, and the kinematic spread in the energy of 31 the outgoing neutrons due to the finite solid angle subtended by the detector. If the cross section as a function of beam energy is constant, the effect of target thickness alone is to produce a rectangular peak shape. The effect of kinematic spread is slightly more complicated. If the detector (located at 0°) subtends an angle sufficiently small that sin 8 ~ 8, the neutron energy as a function of angle, E ( 8), is n given by 2 E (8) -;:; E (0) - K(A, Eb ) 8 . n n earn (1) The quantity K increases as A decreases or Eb increases. If earn the cross section as a function of angle and energy is constant, the probability of a particular count occurring in the cone defined by 8 and G + d8 is approximately given by 2 P( 8) d 8 -;:; 2TT h 8 d8 2 2 h TT 9 = 2a d8 e2 0 (2) 0 The quantities h and 8 are defined in figure 8a. · Let P( 6) be the 0 probability of a deviation 6 from E (0). From (1), o = K 82. n Therefore, P(o)d6 = P( 8)d 8 and s:) = P ( e) d8 do ~ ( Pu 1 8 2 K • 0 Thus P(o) is constant and kinematic energy shifts alone will also produce a square peak. (3) 32 The two effects taken together, target-thickness shift and kinematic shift, will in general produce a peak shaped like a truncated triangle. Note in particular that the leading edge of this peak should be a straight line whose intercept with the axis gives a m easure of the zero-degree neutron energy independent of both target thickness and solid angle. This is the basis of the intercept method. The effect of imperfect detector resolution is to round out the peak. However, it is found that if only those points between 10% and 90% of maximum peak height are used, a very good fit to a straight line is obtained. The intercept with t,he axis is found to be the same to within a few keV for neutron peaks of the same energy taken under differing experimental conditions. This method should probably be used whenever the counting statistics are sufficiently good to allow discarding the data provided by the rest of the counts in the peak. In the centroid method, one simply calculates the centroid of the peak. In a real detector, the low energy side of the peak has a long tail. The method used to treat this tail was to fit a straight line to the back side of the peak above the tail, extend the line to the axis, and artif ically lower points in the tail to fit it. Both the incident beam energy and the outgoing neutron energy require corrections if a Q value is t o be calculated. To first order, these corrections can be made in the following way: The effective beam energy is taken to be the incident beam energy lowered by half the target thickness. This corrects for energy loss in the target. The energy of the neutron group detected is taken to 0 be the energy the neutron would have at o minus the average . kinematic energy spread of the. n eutron group due to the finite solid angle subtended by the detector. As a result of equation (3), this last correction is just half the maximum kinematic energy spread 2 2 2 of neutrons incident on the detector, i.e., Kr /2h ~ K8 /2. 0 If the detector being used has a radius greater than or equal to the depth (the usual case), one may get about 40% greater efficiency with the same average kinematic energy spread (i.e., average devi0 ation from the o value of the neutron energy) by using the detector side-on (see figure 8b}. In this case, the average kine matic spread 2 4 4 2 is approx imately K/8h (t + 4r ) l/ which for r ;(:. t, is approximately 2 2 2 Kr /4h -;;- K 80 /4 . The errors assigned to the Q values we measured with the spectrometer have the following sources: uncertainty in the exact value of the incident beam energy, errors in the corrections for energy loss in the target and kinematic energy spread of the outgoing neutrons, and counting statistics. The first source of error was always the largest, ranging from 10 to 20 keV for each inde pendent measurement; it was set by the geometrical precision of the magnetic analysis of the beam energy. discussion. See Pearson (1963) for a detailed In our experience, the beam energy was usually confined to within 1/2 to 2/5 the range calculated from the slit widths at the entrance and exit of the analyzing magnet when the total slit widths were 0. 100" to 0. 150" providing there was steady tandem operation and good beam alignment. 4. Detection efficiency and neutron yield measurement The charged-particle spectra produced by known numbers of neutrons bombarding a Li-drifted silicon semiconductor detector have been obtained for neutron energies from 7. 3 to 16. 4 MeV in steps of 50 keV or l ess. The purpose of the measurements was to 34 obtain cross section curves for the neutron-induced reactions in silicon sufficient to enable the dete rmination of unknown neutron 9 3 12 yields. Two nuclear reactions, D(d, n)He and Be (a., n)c , were used as sources of monoene rgetic neutrons, the first providing neutrons from 7. 3 to 12. 0 MeV, and the second, from 10. 6 to 16. 5 MeV. The ONR-CIT tandem provided deute rium and a -pa rticle beams magnetically analyzed to a precision of O. 2%. A deuterium gas target was used. The beam came in one end of a tantalum- lined, stainless steel cylinder 3. 69 cm long through a nickel foil 5000 A thick and was stopped in tantalum at the other end. At the lowest bombarding energy used, 4. 00 MeV, the deuterium beam lost 37 keV in the entrance foil and 5. 4 keV in the target chamber gas. 9 2 The Be target was 72 ± 14 µg/cm thick. At the lowest a.-particle bombarding energy used, 5. 1 MeV, the beam lost 51 keV in the target. Figure 11 shows the detection geometry used for both beams. Once the data were obtained, there was some question as to the best method of analysis. As already stated, the objective was to obtain curves which would be useful for the determination of neutron yield when using a semiconduCtor detector as a neutron spectrometer. 28 Only peaks from Si + n reactions are prominent and only these were considered (but see the last paragraph of this section regarding 29 Si (n, a.)). Obtaining the maximum amount of information would involve extracting cross sections for each of the separate processes 28 which occur such as the cross section for Si (n, a.3)Mg25 . However, several of the peaks are often difficult to separate. Further, the detectors used for. these measurements were Li-drift detectors and often the peaks in the spectra obtained with such detectors have prominent low-energy ta ils as compared with, for example, the results obtained in a surface-barrier det ector (see section 2). Thus a peak such as a. is not only difficult to separate from p01 but ha s 3 35 tails beneath it from all higher peaks (a , a , a 2 , and p01 ). There 1 0 is no way of measuring the exact shape of these tails and a small error in estimating their magnitude could lead to a very large error in the deduced cross section. For these reasons, cross sections were found for all 28 Si + n reactions above three well-defined valleys in the spectra: the valleys between a and a , a. and p , and p and p (or a if 1 2 01 23 4 5 0 visible). These represent the cross sections for a (the highest 0 28 energy Si peak), a. - a (first three peaks) , and a - p (first 23 0 0 2 seven resolved peaks). Figures 9 and 10 show two typical spectra, 9 one from the D(d, n) portion and one from the Be (a, n) portion of the yield curve. The numbers given on the detection geometry figure, figure 11, pertain to these two spectra. In appendix 1, a detailed 28 calculation of the Si (n, a ) cross section is given for the same two 0 spectra. The entire yield curves are plotted in figures 12 - 15. Possible contributions from tails extending outside the summed region were at least partly taken into account by correcting the sums for particle escape through the edge of the detector (see appendix 1). The error from this source is largest for the a sum but is 2 estimated to be always less than 10% and usually less than 5%. The error on the a 0 0 - a sum from this source is less than 2%. Peaks from reactions with other isotopes of silicon may be included in the summed regions. Such peaks were not seen and no correction has been made for them. The standard deviation on the absolute cross sections is estimated to be about 10% for neutron energies below 12 MeV but may increase to as much as 20% in the 16-MeV region. of the clearly-resolvable resonances in the a 0 Table 3 is a list cross section for neutron energies between 7. 2 and 11. 2 MeV. These all appear to 29 correspond t o levels in Si but, at slightly higher neutron energies, 36 curve structure is more likely due to Ericson fluctuations (see Colli et al. (1963)). -. 9 The spectra of the Be (a., n) portion of the yield curve were also analyzed in terms of the first seven resolved peaks: a , a , 1 0 a. , P , a , a and p . A computer was used to sum each peak 2 01 3 4 23 and subtract from beneath it fixed fractions of all higher peaks to allow for the contribution of tails beneath the peak. The fractions used were determined empirically by careful hand analysis of several spectra distributed along the yield curve. all but a 0 The results for (already given in figure 13) are shown in figures 16 to 18. The standard deviation is estimated to be less than 30%. The integral sum cross sections of figures 12 - 15 may be directly used to correct for variations in detection efficiency due to variations in neutron energy. Note that the particular integral sums chosen are not very sensitive to the quality of the detector. As a . 0 9 12 check on the curves, the cross section at 0 for Be (a, n)C was measured in a semiconductor detector for bombarding energies between 2 and 6 Me V. The same results are obtained independent of which of the integral cross sections is used. the curve obtained from analysis of the a 0 Figure 19 displays peak. The absolute cross section agrees with figure 2 in the region of overlap and with the measurements of Risser et al. (1957). This one curve ties together all the absolute cross s ection measurements of Chapters . III and IV. Its consistency with other curves and with published data is very reassuring. Two other groups have made extensive cross section 28 measurements for Si + n reactions in a semiconductor detector. Mainsbridge, Bonner and Rabson (1963) measured separate cross sections for a , a , a , a , p , p , p and p for neutron 1 2 3 01 45 0 23 678 37 energies between 4. 6 and 8. 5 MeV, and quote an error of 30% on the absolute cross section. Our data ove rlap the last 1. 2 MeV of their curves and agree well in relative shape if corr ection is made for the fact that the a 0 curve of figure 4 of their paper has been accidently transposed upwards in energy about 200 keV (Rabson (1965)). Their absolute cross section normalization is about 1. 8 times higher than ours. Colli et al. (1963), who were investigating Ericson fluctuations, measured s e parate cross sections for a. , a , a. , a , 1 2 0 3 a. , and two higher a groups for neutron energies between 12. 15 and 4 18. 5 MeV and quote an error of 30% on the result. Comparison of our a 0 yield curve with theirs in the region of overlap (12. 15 to 16. 4 MeV) indicates fair agreement as to relative shape but there are differences in both peak location and peak height. Peaks on their curve occur at neutron energies from 50 to 150 keV higher than peaks on our curve as the neutron energy is increased from 12 to 16 MeV. Our absolute cross sections vary from being 1. 4 to 1. 8 times higher than theirs over the same range. Part of the yield difference is explainable. They used a small (25 mm area, O. 3 mm deep) semiconductor detector as both target and detector and made no correction for escape through the edges, which they assumed produced at most a 20% error. However, we find that the correction factor varies from 1. 25 to 1. 44 as the neutron energy is increased from 12 to 16 MeV. (See the formula for f and the discussion following it in appendiX 1). Forward or backward peaking in the a- particle angular distribution could easily make this correction much larger. In using their data, care must be taken in deciding which curve belongs with a particular reaction since the curves are unlabell~.d and the captions are misleading (largely becaus e their curves have been r educed so much in 38 publication that the different kinds of points they used are indistinguishable). The a.0 peak is usually the most convenient peak to use for . determining either n eutron energy or neutron yield. At a neutron energy of 6 MeV, the cross section for its forma tion is less than · 10 mb but rises r a pidly to as much as 150 mb for neutron energies of 7. 5 to 8. 0 MeV as the a. particles acquire sufficient energy to overcome the Coulomb barrier of the compound nucleus. As the neutron energy is further increased, the cross section slowly falls, sinking to a value of about 10 mb at 16 MeV, the fall being probably due to the increased number of final states available to the compound nucleus. Arbitrarily taking 10 mb as the smallest acceptable cross section, a semiconductor detector made of natural silicon is useful as a neutron spectrometer for neutron energies between 6 and 16 MeV. As pointed out (and pa tented) by Birk, Goldring, and Hillman . 29 (1963), a semiconductor detector made of Si would enable useful measurements to be made at lower neutron energies as the Q value 26 29 of the Si (n, a. )Mg reaction is -36 keV compared with -2655 for 29 2 28 Si (n, a. )Mg §>. Mainsbridge et al. find the Si (n, a. ) cross section 0 -- 0 to be about 70 mb for a neutron energy of 5. 0 MeV. . A further advantage in simplifying the spectrum accrues from the greater 26 excitation energy, 1. 81 MeV, of the first excited state in Mg 25 (compared to the value 0. 58 MeV in Mg ). 5. Pulse-height and resolution anomalies Peaks from the reactions Si 28 (n, a.)Mg 25 and Si 28 (n, p)Al 28 show a differential pulse- height defect, i. e. , peaks produced in the 28 28 reaction Si (n, p)A1 always fall below the amplitude predicted for 28 25 them by a calibration obtained from the Si (n, a.)Mg peaks. In 39 figure 5, the quantity ti.E (equal to 78 ± 10 keV) indicates the differential pulse-height defect measured for this spectrum. The defect is a function of neutron energy and increases with it in an approximately linear fashion over the region measured (see figure 20). 28 29 A similar defect is not seen on comparing Si (n, a) and Si (n, a) peak amplitudes. For example, in figure 5, the a. 1 peak is within 1 28 6 keV of the position predicted for it by the Si (n, a) peaks and, for all spectra examined, its position is always consistent with zero differential pulse-height defect independent of neutron energy. Clearly, the defect is associated principally with differences in electron- cloud structure rather than mass alone. The resolution we observe for peaks such as Si 28 (n, a. ) is 0 always three or more times worse than one might expect on the basis of a particles alone being stopped. In fact, we have never obtained a "neutron" resolution of less than 125 keV full width at half maximum, even with detectors whose a-particle resolution is 30 keV or less. Neutron resolution appears to get slightly worse as the neutron energy is increased. The resolution of the aluminum and magnesium peaks appears to be about the same but it is hard to make exact comparisons because of the difficulty in subtracting the correct amount of background from beneath the aluminum recoil peaks. The emphasis of the following discussion is on explaining the differential pulse-height defect. However, the two effects, differential defect and poor resolution, appear to have a common origin and will end up being explained together. Generally speaking, a pulse- height defect could arise either from reduced charge collection, e. g. , recombination losses, or from reduced charge production. For a particular detector, such as the 40 Li-drift detector used to obtain the spectrum of figure 5, the magnitude of the defect is independent of both bias and temperature. For low biases, the whole spectrum shifts down and the resolution decreases due to poorer charge collection, but the differential defect is unchanged. Reducing the temperature from room temperature to near liquid nitrogen temperature may improve the resolution as much as 50%, but again the differential defect is unchanged. For neutrons of fixed energy, the defect is the same independent of the detector used. We have checked this with Lidrifted detectors and both high and low resistivity surface- barrier detectors obtained from seyeral different ma1:m facturers. It is hard · to believe the defect is the result of recombination losses when it is unaffected by so many factors which should change such losses. Apparently, the defect is the result of reduced charge production and is an intrinsic property of aluminum and rrIBoonesium ions being brought to rest in silicon. To test this directly, we bombarded thin foils of aluminum and magnesium with a particles from the ONR-CIT tandem. The momenta of the recoil ions (energies of 1 to 3 MeV) were measured with a magnetic spectrometer and the pulse heights they produced were measured with a surface- barrier detector at the focal plane of the magnet. Both ions had a pulse- height defect relative to a cali- bration obtained with scattered a. particles, the aluminum ions having the .larger defect as expected. However, the dead layer on the front of the detector would produce the same sort of differences and different detectors produced different relative defects. Unfortunately, we were unable to separate an intrinsic defect from the effects of the dead layer. 41 It has been known for some time that fission-fragment spectra observed in a semiconductor detector show an absolute pulse-height defect variously reported as being from 4 to 20 MeV. The defect is greater for heavier particles but most observers have found it to be independent of the type of semiconductor detector used and of the conditions, such as bias voltage, under which it is used. Two theories have been advanced to explain the defect: It is caused by recombination of electron-hole pairs in the dense plasma produced in the first part of the track (i. e. , charge loss), and that it is the result of screened atomic collisions near the end of the track which are relatively inefficient at producing ionization (i. e. , decreased charge production). Axtmann and Kedem (1965) have performed an experiment which discriminates between the two theories. They measured the defect for fission fragments whose energies were degraded in air and found it to be approximately constant for both median heavy (defect R:j 13 MeV) and median light (defect ~ 11 MeV) fission fragments over the energy range 25 to 100 MeV. They concluded that the defect arises at the end of the fragment track and is the result of reduced charge production. Aitken and Dixon (1965) have seen an absolute pulse-height defect in both silicon and germanium semiconductor detectors. They 28 73 found that the Si (n, a.) and Ge (n, a.) peaks produced by 14. 1-MeV neutrons were shifted 250 keV and 400 keV respectively relative to 241 the callbration obtained using an Am alpha source and that the defects were independent of detector bias. Sattler (1965) measured the maximum pulse height of recoil silicon atoms in the reaction Si(n, n) as a function of neutron energy using a silicon semiconductor detector as both target and detector, and using internal- conversion electrons to obtain an energy cali- 42 bration. He found the maximum pulse height of the recoil silicon atoms·to be less than expected on the basis of the electron calibration and obtained a direct measure of the fraction of the silicon recoil energy lost to ionization. His data vary in roughly the same manner as the Al - Mg differential defect plotted in figure 20. Note that in figure 20 ions of different energies are compared, the aluminum recoils always having lower average energies than the magnesium recoils, and both having energies distributed from zero to some maximum value. However, on the basis of the silicon recoil data of Sattler, the absolute defect is expected to increase with energy; the differential defect would be even larger if the two ions had the same energy. On comparing our data with that of Aitken and Dixon, and Sattler, it is seen that the absolute magnitude of the defect may be inversely correlated with the first ionization potential of the recoil ion; i.e., silicon has the largest ionization potential and the smallest defect. It is also true that for low ion energies (E ,$ 3 MeV) and at fixed velocity, the aluminum ion will always have the highest average charge. Flicker (1963) was the first person to suggest that atomic collisions might compete significantly with ionization as a mode of energy loss but he performed no quantitative calculations. Haines and Whitehead (1965) have made such calculations and compare their results with observed absolute pulse-height defects, obtaining good agreement with many measurements for both light and heavy ions in both germanium and silicon detectors. Their calculations were performed in the following manner: first, the fraction of the incident ion's energy which is transferred to other ions by atomic collisions was determined. They find that the lower the ion's energy, the 43 greater the fraction of its energy lost in this way. Most of the recoil ions will have energies much lower than the primary and will lose all or almost all their energy in further atomic collisions. However, the occasional recoil will have sufficient energy to lose a significant fraction by ionization. Thus they extended their calculation to "second order" and found the fractional loss of energy through atomic collisions for the recoils as well (a number equal to one for most recoils). All further energy loss was assumed to take place entirely by atomic collisions. They used differential energy losses and scattering cross sections based on the Thomas- Fermi model of the atom without corrections for atomic shell structure. Thus their theory cannot and does not explain the differential pulse-height defect we see. Haines and Whitehead also calculated the average dispersion in the energy lost by atomic collision processes. Their results are largely successful in explaining the poor resolution we find for peaks 28 25 such as Si (n, a. )Mg , a resolution which is never better than about 0 125 keV. After subtracting by quadrature the resolution due to the 25 spread in energy of the recoil Mg ( : : : : 35 keV), the spread in the incident neutron energy ( < 40 keV) and the electronics resolution ( < 15 keV), one is left with an intrinsic resolution of about 110 keV. From figure 2 of their paper, the intrinsic resolution is predicted to be 75 keV in fair agreement with our observations. 6. Comparison with other methods The ideal neutron detector would have the following properties: i) High energy resolution preferably with each neutron of different energy being represented by a single peak rather than a continuous pulse-height distribution or a family of peaks. 44 ii) A detection efficiency which is approximately constant (or at least smoothly varying) over a broad range of neutron energy and is large enough so that the experiment may be performed in a reasonable length of time. iii) Insensitivity to other radiations, particularly gamma. rays, which may also be present. No detector exists which meets all of the above criteria and the particular detector chosen for a given application will depend upon the yields and energies of the neutrons present, whether a yield or energy measurement is wanted and on the presence or absence of 54 3 .56 gamma rays. For our measurement of the Fe (He , n)N1 Q value, we wanted a detector which could measure the energy of a 15-MeV neutron with- a precision of at least 2 5 ke V and furthermore, could 0 3 do this in a reasonable length of time. The o (He , n) cross section is about O. 1 mb/sr . To obtain the necessary resolution, target thickness and detector solid angle must be restricted. The target 3 was chosen to be about 25 keV thick for an 11 to 12-MeV He beam and the detector was allowed to subt~nd no more than 19° in order that the average kinematic energy spread be less than 25 keV. Thus, 3 with a maximum beam current of 1 µa of He ++, the expected neutron flux through the detector is 140 per second. If the minimum acceptable count rate is taken to be one per minute, the detector must detect at least 1 in 8400 neutrons incident on it The only technique we could find which could achieve the necessary resolution with the above efficiency was the silicon- semiconductor-detector nuclearreaction method (hereafter abbreviated as the silicon spectrometer method). A 5 mm deep detector has an efficiency about three times 28 25 the above minimum for detection in the Si (n, a. )Mg peak and the 0 precision obtainable is limited by uncertainty in the bombarding energy ( ~ 10 to 20 keV) r ather than the spectrometer itself. 45 Some of the other techniques which might have been used but were found wanting for one reason or another are proton- recoil counters, time-of-flight, organic scintillators and nuclear emulsions. These and other systems are discussed in detail elsewhere (see e.g., Marion and Fowler (1960)). The proton-recoil counter technique (see e.g., Johnson and Trail (1956)) in which knock-on protons are produced in a polyethylene radiator and detected externally meets all the criteria listed in the first paragraph except that of efficiency 4 3 which is 10 to 10 times less than the silicon spectrometer method. Time-of-flight techniques may compete in energy resolution with the silicon spectrometer at the very bottom of the latter : s useful energy range, but even here, the precision of typical time-of-flight measurements is usually about five times worse. To maintain resolution at higher neutron energies, the flight path must be increased and the count rate soon becomes too small to make the measurement feasible. Most of the problems associated with neutron-detection systems arise from the necessity of converting neutrons to charged particles before they are detected. One of the most widely used conversion methods is neutron- proton scattering for which the cross section is both well known and smoothly varying. However, the recoil protons are distributed from zero energy to the full neutron energy. Fortunately, the distribution is approximately uniform, at least for neutron energeis below 20 MeV. Other conversion methods utilize neutron-induced nuclear reactions such as the silicon spectro28 meter method (Si (n, a.)Mg25) , the BF -filled proportional count er 3 10 7 3 3 (B (n, a.)Li ) and the He -filled proportional col.mter (He (n, p)T), although the latter two methods have extremely low efficiency for dete_cting neutrons in the energy range of interest here. 46 No matter how the neutrons are converted, the detectors fall into roughly two classes: those for which the conversion takes place within the active volume of the detector and those for which it takes place in an external radiator. Thus, for example, in detectors utilizing n-p scattering, protons are produced throughout the volume of an organic scintillator but in a proton-recoil counter they are produced in an external radiator, e. g. , polyethylene, from which they must escape before being detected (in, e.g., a semiconductor detector). In either case , it is the volume of the region in which the protons are produced that determines the detection efficiency. The first type has a large and smoothly-varying efficiency but poor energy resolution and high sensitivity to gamma rays. The second type has low efficiency because of the restricted size of the radiator but may have better energy resolution if only protons scattered in one direction are accepted in which case neutrons of different energies produce discrete peaks. The gamma ray sensitivity is low. The silicon spectrometer method combines the advantages of both the above types in that neutrons are detected throughout the active volume of the detector and neutrons of a particular energy . produce discrete peaks. Gamma rays are seldom a problem. The disadvantages are ·that the detection efficiency is rapidly varying and a monoenergetic neutron produces more than one peak. The silicon spectrometer method is in some respects similar to the use of a 3 He -filled proportional counter. One widely-used method remains: the use of nuclear emulsions. They contain a great deal of hydrogen (mostly in water) so that neutrons may be detected by internally produced protons as well as by particles from an external radiator. Since the direction of the incident neutrons is usually known, the neutron energy may be 47 . determined from a single track. However, for proton recoils above 5 MeV, range straggle sets a lower limit of about 1%on the accuracy of this kind of measurement. In practice, precision as good as 50 keV is seldom obtained. Neutron yields may be obtained fairly accurately. In conclusion, the silicon spectrometer method appears to be a valuable addition to the large number of neutron detectors available, making possible neutron energy measurements of low intensity, 6 to 16-MeV netitron groups with a precision not ea sily obtainable before. 48 · V. 3 THE (He , n) MEASURENIENTS 1. Introduction This chapter might better be titled "Applications of a Semiconductor Detector as a Fast Neutron Spectrometern as it contains all the results obtained with this technique. However, that would be putting the emphasis on the wrong part of the investigation as the spectrometer was specifically developed to measure the mass of 3 54 56 56 Ni via the reaction Fe (He , n)Ni . Once the technique was understood, it was a simple matter to perform additional measurements. All the neutron energy measurements were Q-value deter3 minations of (He , n) reactions. This reaction mechanism is a powerful tool for studying proton- rich nuclei as it effectively enables the addition of two protons to the target nucleus, leaving the residual nucleus as far as two positions away from the line of beta stability. The use of a semiconductor detector for measuring the neutron energy allows exploitation of this reaction mechanism, not easily done previously because of the high neutron energies (10 to 17 MeV) typically involved. poorly known. All of the nuclei described in this section were 34 48 .56 60 Four of them (Ar , Cr , N1 and Zn ) had previously not even had their ground states located experimentally. - Also included are some neutron yield measurements. 3 Absolute cross sections derived from the (He , n) data are given with the Q values in section 3. The angular distributions of neutrons to 30 . the ground and first excited states of s in the reaction 28 3 30 Si (He , n)s were measured and are given in section 5. 49 . 2. Procedure The ONR-CIT tandem accelerator was used to produce a 3 He ++ beam up to an energy of 12. 1 MeV. The uncertainty in the beam energy was approximately 0. 15 to 0. 20% depending on the settings of the regulation slits of the analyzing magnet. Neutron energies were measured with a semiconductor detector by the method described in Chapter IV. All but one of the targets were made by evaporating pure element of the substance to be bombarded onto tungsten backings O. 018 cm thick. The backings were washed in acetone and either heated to white heat in an evacuated tube in an induction furnace or etched in a 3 to 1 mixture of HN0 and HF; both processes appeared 3 to be equally effective. 48 60 56 The targets used for studying Cr , Ni and zn were 46 54 made from isotopically enriched Ti (84. 5%), :Fe (97%), and 58 Ni (99%) supplied by Oak Ridge National Laboratory. Natural 24 28 32 magnesium (73. 3% Mg ), silicon (92. 2% Si ), sulfur (95. 0% s ) 40 and calcium (96. 9% Ca ) were used as targets for the investigation .26 ,8 30 o f Si , A r34 a n d T.42 i. The sulfur target presented s pecial problems because of the very low melting point of sulfur (113° C). A tungsten target backing was silver-soldered to a block of copper and sulfur was evaporated on half the front face, the other half being left for background runs. The block of copper was screwed to a second block of copper which was water cooled during beam bombardment. Though there was still some. sulfur evaporation, it was possible to make a measurement of 34 3 the s32 (He , n)Ar Q value, .but the change in thickness made it impossible to locate the excited states r eliably. A target of 50 Sb s (mp = 550° C) was made by evaporation and showed no 2 3 deterior.ation under bombardment when water cooled. This target 34 enabled ~s to find one excited state in Ar • The thickness of each target was measured to within about 20% by comparing the energies of 1-MeV protons scattered from the tungsten on the front and back sides of the target. All targets had a 3 thickness such that, at the He beam energy used, they were about 25 (and always less than 45) keV thick. The be ryllium target used for calibration was chosen to give a neutron energy spread due to target thickness about equal to that from the target being studied. Figure 21 shows the thickne ss m easurements for two targets that were one of three pa irs of t a rgets used to measure the 54 54 3 56 Fe (He , n)Ni Q value. The Fe bombardment was performed at E = 11. 50 MeV with the target a t an angle of 45°. Using the He 3 data of the graph and the dE/dx curves of Whaling (1958), its thick9 ness was deduced to be 21 ± 4 keV. The Be (a, n) calibration was = 10. 80 MeV with the beam normally incident; the a target thickness was 26 ± 5 keV. performed at E The detector was located outside the vacuum system of the accelerator at an angle of 0° and at a distance such that the average kinematic energy spread of the incident n eutrons was about 25 keV over the face of the detector. Its output was connected through a charge- sensitive preamplifier to the internal amplifier of a 400- channel pulse-height analyzer. The gain of the whole system was continuously ' monitored with a pulser and, in. turn, the pulser voltage was periodica lly checked with a potentiometer. Calibration runs and runs on the unknown were alternated fre quently to check gain and target stability and to monitor the build up of contaminants on the t arget. Additional runs at 30° ensured that the peaks observed m oved an amount appropriate to the mass of the system under investigation . . 51 3. Results .All our Q-value analysis has been based on the a 0 0 peak of spectra taken at o , the neutron energy being found by comparing unknown and calibration spectra. Peak position was found by both · the centroid and intercept methods (see Chapter IV, section 3). If the two numbers did not agree, the data were rejected. This happened only once, probably because one of the targets was too thick. In all the reactions studied, reactions other than the one of 48 interest were observed. Except perhaps in the Cr ~easurements where other chromium isotopes may have contributed, these were always from contaminants on the target rather than other isotopes of the element being bombarded. This was determined directly by calculating where such isotopes would produce peaks and observing . . 12 3 14 that they were not there. The react10ns C (He , n)O and 16 3 18 . . . 0 (He , n}Ne were always observed. Some of the carbon was introduced during the manufacture of the target and more was deposited during the bombardment. The presence of oxygen was undoubtedly the result of target oxidation in air since the precautions 12 taken to prevent this were not very stringent. Peaks from the C and 0 16 reactions were not troublesome since their Q values are more negative than all those measured (except Ca 40 3 42 (He , n)Ti , for which these contaminants were used to provide an internal 13 17 18 calibration). Peaks from C , 0 and 0 would have been more troublesome but were not observed. For example, in one check, the . 12 13 relative number of C to C events observed was greater than 200 to 1. In addition to the carbon and oxygen contaminants, peaks due . 56 60 to silicon and magnesium were observed in the Ni and Zn data. (This observation was the initial incentive for measuring the 52 26 28 3 30 2 3 Mg \He ,n)Si and Si (He ,n)s Q values.) These contaminants were observed to build up from an initially unobservable concentration during the course of the bombardment. The silicon is undoubtedly from 0- ring grease and the magnesium is probably from the magnesium- containing ( ~ 1%) aluminum alloy used for the target holder and the beam pipe. As a check on the method of analysis, one of the spectra in which carbon was present as a contaminant was analyzed in detail. A Q value of -1152 ± 14 keV was obtained for the reaction 3 12 14 C (He , n)o . The weighted mean of all previous measurements 3 is Q = -1148. 1 ± . 4 keV. All our (He , n) Q value and excited state measurements are listed in table 4. In figure 27 three excited states of Ni 56 show themselves quite clearly in the raw data but usually excited states are masked by the family of peaks produced by the ground- state neutron and are seen clearly only after subtracting out these peaks. For this 9 purpose, the Be (a, n) calibration spectra were used. The spectrum used .for subtraction must be very close in energy to that of the ground state neutron because of the very rapid fluctuations in cross section for the neutron absorption events; the difference was usually less than 10 keV. Rough estimates of the zero-degree cross sections were . 3 made for all the (He , n) reactions observed. The ground-state neutron cross section was obtained by comparing the yieid of the 9 · (He 3 , n) reaction with the yield from the best Be (a, n) calibration spectrum. The cross section may then be found by using the known 9 Be (a, n ) cross section (figure 3), target thicknesses, detection 0 geometries and integrated beam current. Cross sections for excitedstate neutrons were found by de termining the ratio of their yield in 53 28 (n, a. ) peak to the ground-state yield in the same peak using 8 the known. Si'2 (n, a. ) cros s s ection (see figure s 12 and 13). These the Si 0 ratios, along with the ground-state cross sections are presented in table 5. 3 On the basis of what is known about (He , n) stripping theory (see, for example , Henley a nd Yu (1964)), the angula r distribution of the neutrons l eading t o the ground state of all the nuclei studied here should be strongly forward peaked s ince both t a r get and residual nuclei have o+ ground states. This is certainly true for 28 3 the only angular dis tribution we have measured, that of Si (He , n)slO (see page 65 and figure 30). With this in mind, table 5 also include s the half angle, 8 , subtended by the face of the detector. 0 The remainder of this s ection will give the detailed results obtained for each nucleus studied and compare them with previous work. 3. 1 26 The Si nucleus Figure 22 shows the spe ctrum obtained, from which a ground-state Q value of 85 + 18 keV was calculated. Centroid and intercept methods of analysis gave answers differing by only 2 keV. 26 The subtraction spectrum shows two excited states of Si , 12 at 1787 ± 27 keV and 2803 ± 28 keV, as well as peaks due to c and 26 16 . All peaks a ssigned to neutron groups leading to Si had the 0 0 correct kinematics (checked at o and 30°) and could not be produced by any known contaminants. The pronounced dip just below channel 250 (just below the a peak of the ground- state neutron group) 4 illustrates one of the major problems encountered in unfolding the neutron s pectra . For the beam energies used, the ber yllium target wa s 13 k eV thicker than the magnesium t a rget (which v.ras 32 ke V 54 thick) and in addition, the most energetic neutrons from the beryllium target w.ere 6 keV lower in energy than those from the magnesium target. There is a strong resonance in the a yield just below the 4 2 3 Mg \He , n ) neutron energy, and neutrons from the calibration 0 reaction extended further into it than neutrons from the magnesium reaction. The nucleus Si 26 was first reported by Tyren and Tove {1954) although they obtained no direct evidence for its existence. 27 They bombarded A1 with 23-MeV protons and found a 1. 7-second 26 activity which they attributed to Si formed in the reaction 27 26 A1 (p, 2n)Si . Since then, three other groups have investigated 24 3 26 26 Si , all of them using the reaction Mg (He , n)Si • The first positive identification was made by Ajzenberg-Selove and Dunning (1960), who detected the outgoing neutrons by means of proton recoils in nuclear emulsions and saw groups corresponding to the ground state, first excited state and second excited state, obtaining Q = 80 ± 80 keV for the ground-state transition. ·Robinson and Johnson (1960) used an NaI (Tl ) crystal to detect the gamma rays 26 produced following th~ decay ~f Si and identified two positron ' 26 branches leading to the 0. 229 MeV and 1. 059 MeV levels of Al . They measured a half life of 2. 1 ± O. 3 seconds. Frick et al., (1963), using a magnetic spectrometer to measure the positron spectrum and an NaI (Tl) crystal to detect gamma rays, confirmed the above decay . scheme. ' They determined the relative intensity of the two branches and found an end-point energy of 3. 828 ± 0. 013 MeV for the branch to 26 the O. 229 MeV level of AI . They found a half life of 2. 1±O.1 3 . seconds. From their numbers, the (He , n) Q value is found to be 58 ± 13 keV. 55 3. 2 The s 30 nucleus . The Si 28 30 (He 3 , n)s spectrum is shown in figure 23. From two independent sets of runs, the Q value was dete rmined to be -573 + 15 keV. One excited state was seen at an energy of 2190 ± 40 keV. 30 Three groups have previously investigated s , "all of them 28 3 30 using the reaction Si (He , n)s . The first measurements were made simulta neously by Jd:mson et al. , (1960) and Robinson et al., {1961), both of whom used scintillation techniques to look for positrons and gamma rays. Johnson et al. , found a 1. 5 ± O. 1- second- half-life positron activity with an endpoint energy of 4. 22 ± O. 15 MeV in coincidence with a 0. 676-MeV gamma ray. They attributed this 30 30 . to the decay of S to the T = 1, 0. 684-MeV state of P . Robmson et al. , identified the same branch, m easured the 13+ end point to be 4. 30 ± O. 15 MeV and the half life to be 1. 35 ± 0. 1 second. In addition, they dete cted the direct decay to the ground state, who se end point they measured as 4. 98 ± O. 15 MeV. More recently, Frick et al. , {1963) have measured the positron spectrum with a m agnetic s pectrometer, obtaining a half life of 1. 4 ± 0. 1 seconds and pos itron end points of 5. 085 ± 0. 026 and 4. 422 ± 0. 022 MeV. From the numbers 3 of Frick et al. , the (He , n) Q value is found to be - 540 + 27 ke V. 3. 3 . . 34 The Ar nucleus Figure 24 shows the s 32 3 34 (He , n)Ar spectrum obtained with the Sb s target. A Q value of -759 ± 15 keV was determined from 2 3 this spectrum and another series of runs in which a pure sulfur target was u sed. One excited state was seen, located at an energy of 20 58 ± 3 5 keV. 56 The data of figure 24 could be used to determine the s 32 3 (He , n ) Q value by a third method in addition to the centroid and 0 intercept methods. This was for two reasons: the beryllium and Sb s targets were of almost identical thickness (about 21 keV) and, 2 3 for the particular neutron energy produced here, the cross sections of the silicon reactions which produce peaks a. to a. and Poi all 0 2 varied linearly with neutron energy.. With the aid of a series of calibration runs taken with a spacing of 5 keV in neutron energy, the 34 energy of the ground- state neutron of the Ar spectrum could be found to within 2 keV relative to the calibration neutron energy by comparing the relative yields of a.0 to a.2 and Poi in the unknown and calibration spectra. Of course the ever- present uncertainties in the 3 4 He and He beam energies remained. All three methods of analysis gave the same result for the ground-state .Q value. 3. 4 The Ti 42 nucleus Figure 25 shows one of five similar spectra used to obtain 3 42 the Ca (He , n)Ti Q value which was determined as -2865 ± 6 keV. 9 Rather than calibrating separately with Be (a., n) as was done for all 40 the other Q values measured, we used the carbon and oxygen contaminants on the target, assuming Q values (taken from Mattauch et al., (i965)) of -1148. i ± 0. 4 keV and -3i96. 0 ± 4. 7 keV for -12 3 i4 i6 3 18 . . C (He ·, n )0 and 0 (He , n )Ne respectively. This pro_c edure 0 0 eliminated most of the error due to uncertainty in the beam energy. On all five spectra, the location of the a peaks due to the ground stat es of 0 i4 , T1.42 and Ne i8 were calculated. Structure ° underlying the ci. peaks of Ti 42 and Ne i 3 was subtracted out, a computer being ~sed to find the · best Be (a., n) subtraction spectrum 14 42 among several t aken for 0 and Ti . and to calculate peak positions. 9 57 The linearity of the 400- channel analyzer. was checked separately 18 14 with a pulser. The o -Ne separation was used to find the numbe r of keV per channel and the energy of the neutron to the ground state 14 42 of Ti was calculated relative to the 0 neutron. 42 The isotope Ti has also been observed by Oberholtzer 3 40 42 {1962) using the reaction Ca (He , n)Ti . Plastic scintillator was He meas ured a half life of O. 25 ± O. 04 used to detect the positrons. sec and an end point energy of 6. 0 ± 0 , 6 MeV. 3. 5 The Cr 48 nucleus Figure 26 shows one of two runs, the other being at a bombarding energy of 10. 2 MeV, from which the Q value of 46 3 48 Ti (He ,n )Cr was determined to be 5550 ± 18 keV. This Q value 0 was the highest and therefore the most difficult to me asure. As the beam energy is raised in order to get further over the Coulomb barrier, the neutron cross sections .in the silicon fall which suggests the existence of an optimum bombarding energy. Even at this energy, low cross ·section and detection efficiency plus the thin targets required for energy resolution prevented getting good statistics in a running time of practical duration. In particula r, it was impossible to obtain a good kinematics check. With the detector at 30°, it was 28 possible to verify that the Si (n, a. ) peak of the neutron to the ground 0 48 state of Cr (then0 -a0 peak) shilted approximately the right amount (and certainly not enough to be a light contaminant) but it was impossible to resolve any of the other groups seen at 0 °. The small peaks above and below then -a peak (in channels 387, 375 and 363) 0 0 shift in a different manne r with bombarding energy than the n 0 - a 0 . peak and are probably fr om a light contaminant which we were not able to identify. 58 There is a prominent peak in channel 360 which we interpret 48 as being the n-a. peak of a state in Cr at O. 72 MeV. Its position 0 3 15 17 also agrees with it being the a. peak of N (He ,n )F but there are 0 0 several arguments against this identification: This peak and the n - a. peak show up with about the same relative yields in the two 0 0 runs which were made at different energies with different targets made at different times. If the titanium of the target were totally 17 48 nitrided, the F n -a. peak would be about 50% larger than the Cr 0 n -a. peak. 0 0 0 However, the targets used were silver- colored both before and after bombardment instead of the yellow- bronze color of 46 48 3 titanium nitride. In the targets used for the Ti (He , p)v measure3 16 1 ments, it was possible to see protons from N \He , p)o ; their yield suggested about 2% nitration. The standard subtraction technique reveals another state at 2. 37 MeV and suggests the possible existence of several more at energies of 2. 79, 3. 11 and 3. 51 MeV. We feel that our identification of the ground state of Cr 48 is quite certain but the excited states mentioned above are all questionable because of the poor statistics, our inability to obtain a kinematics check, and the presence of an unidentified light contaminant. One other feature adds to the uncertainty: the targets 46 47 used were only 84. 5% Ti , the remainder being Ti - 5o. In 48 3 particular the targets were 11. 1% Ti which has a (He , n ) Q value 0 50 of 8. 627 MeV so that states in Cr could well contribute to the spectrum. The nucleus Cr (1952). 48 was first identified by Rudstam et al. , They bombarded iron targets with 340-MeV protons to study the cross section for the formation of different spallation and fission products. The target wa s dissolved and chemically separated into the different elements produced. In the chromium fraction, after 59 subtraction of a 26. 5 day Cr 51 activity, they found a new activity 48 by the with a half life of 23. 5 hours. This was identified as Cr 48 48 growth and decay of v . From the relative activities of Cr and 48 . 48 . V , they were able to deduce that Cr decays mostly, if not 48 entirely, by electron capture. Lieshout et al., (1955) made Cr by bombarding nickel with 300-MeV protons and chemically separating the chromium produced. They saw no positron decay and estimated it to be less than 2%. Two gamma rays of approxi- mately equal intensity were seen in the decay. Their internal- conversion coefficients were measured to determine their multiplicity. 48 48 Then, using beta-decay systematics, they estimated the Cr - v mass difference to be 1. 45 ± 0. 2 MeV. Sheline and Wilkinson (1955) chemically separated the chromium produced in the reaction .46 . 48 T1 (50-MeV a, 2n}Cr and saw the same gamma-ray spectrum as Lieshout et al. Using the internal-conversion data of Lieshout et al., 48 48 they estimated the mass difference Cr -v as 1. 724 ± 0. 200 Me-V.Our measured value for the mass difference is 1. 657 ± 0. 019 MeV. 3. 6 The Ni 56 nucleus The Q value for the reaction Fe be 4513 ± 14 keV. 54 3 56 (He ,n )Ni was found to 0 This result is the average of three independent sets of runs, one of which is shown in figure 27. The error quoted was calculated from estimations of the experimental uncertainties, the largest of which was the exact value of the beam energy; the standard deviation computed from the three independent measurements is also about 14 keV. Three (and perhaps five) excited states of Ni the data of figure 27. 56 are visible in In the raw spectrum (top), the fir s t three pea ks of the n 1 f amily i.e. , the a 0 , a 1 and a 2 peaks of the first exci ted 60 state of Ni 56 (at 2. 69 MeV excitation) are clea rly visible. The n -p peak looks abnormally high and, as can be seen from the 1 01 .middle spectrum (n and n 1 subtracted), coincides with the a. peak 0 0 of an excited sta te at 3. 95 MeV. Two subtractions were performed to obtain the middle spectrum. The n family of peaks was subtracted with one of the 0 9 56 Be (a, n) calibration spectra taken for the Ni ground state. Unfortunately, the n subtr_a ction could not be performed a s easily 1 since none of the n calibration spectra was sufficiently close in 1 neutron energy to provide a good subtraction. However, the data of figures 13 and 16 to 18 could be used to deduce the relative ratios of the peaks produced by a neutron with the same energy as n . 1 individual peaks of the calibration spe ctrum closest to n were 1 scaled using these ratios and the resultant spectrum shifted in The channel number for optimum match and subtracted out. In the bottom spe ctrum, peaks due to Mg 24 3 .26 (He , n )S1 , ° The 30 12 3 14 .28 3 81 (He , n )S and C (He , n )0 have been subtracted. 0 0 magnesium, silicon and carbon were present on the target as 56 contaminants. The subtractions reveal another state in Ni and 26 the first excited state of Si . 14 The 0 subtraction spectrum was obtained by bombarding 26 a carbon target but we did not have good calibrations for the Si 30 .. 9 12 and S peaks. However, we had taken a large number of Be (a,n)C calibra~ion spectra for the ground state of Ni 56 and, fortuitously, we found that among these spectra there were ones in which the neutron 12 to the first excited state of c (hereafter called nl) had an energy 26 30 very close to then0 energies of Si and s . The height of. the n 1 peaks is 10-15 times larger than then peaks, both because of a 0 la rger cross section for the neutron absorption events in silicon and 61 9 because the reaction Be (a., n) populates the first excited state of c 12 more strongly than the ground state. The Si28 + n yield curve spectra of Chapter IV, section 4,were exa mined to estimate how much n structure was under the n spectrum. It was small enough 1 0 relative to the n structure to be ignored. 1 From the data of figure 27, the excitation energy of the 26 first excited state in Si , whose a. peak is revealed clearly only 0 after five subtractions, is found to be 1. 78 MeV. This compa res with the value 1. 787 ± O. 027 found in section 3. 1. As in all cases studied, a long run was m ade with the detector at 30°. All of the peaks in figure 27 underwent a kinematic shift consistent with the identificatiJns made (ex cept the two peaks labelled 56 Ni in the top spectrum between channels 200 and 225 which were not seen in the 30° run and are discussed later). Many groups have investigated the decay of Ni found a half life of about 6 days. 56 . They all Sheline and Stoughton (1952), and Wells et al. , (1963) both put an upper limit of 1%on any positron emission. Thus the deca y appears to take place entirely by electron capture. Wells et al., the first group to have constructed a decay scheme, give a summary of work done previous to theirs. It all 56 involved chemical separation of Ni produced by beam activation of a metal foil, and study of the gamma rays produced in the decay. Wells et al. bombarded natural iron foils with 30-MeV alpha particles. After allowing one to two weeks for the short-lived activities to decay, 56 the Ni was chemically separated from the target and the gamma- ray spectrum resulting from its decay examined with NaI (Tl) scintillation gamma- ray spectrometers, singly, in coincidence and in delayed coincidence. These measurements, along with angular-correlation m easurements, permitted the construction of a decay scheme and 62 the assignment of spin and parity values to an the states of Co populated by the decay. 56 More recently, Ohnuma et al. , (1965) have performed almost the same experiment and obtained very similar results. They measured internal- conversion electrons and angular- correlation functions for all coincident gamma- ray pairs. 56 The first determinations of the mass of Ni were made simultaneously by Hoot, Kondo and Rickey (1963, 1965) and Miller, Kavanagh and Goldring (1963). Our work has been described above. 58 56 Hoot et al. investigated the reaction Ni (p, t)Ni at a proton energy of 28 MeV using a (dE/dx)-E counter telescope. They meas ured a 56 Q value of -13. 987 ± O. 018 MeV and found excited states of Ni .at 2. 71, 3. 94, 4. 97, 5. 35, and 6. 62 MeV. By measuring the triton angular distribution, they were able to deduce that the ground and 56 first excited states of Ni probably have spin and parity of o+ and 2+ respectively. The levels at 2. 71, 3. 94 and 6. 62 MeV seen by Hoot et al. agree well with our work. In addition, we have weak evidence in support of the 4. 97 and 5. 35 MeV states. Using their numbers, the a. peaks of these states should lie in channels 224 and 213 in the data 0 of figure 27 and indeed weak peaks are apparent at both these locations. They are, however, washed out in the subtractions. The two other sets of Ni56 runs show similar weak peaks in the correct locations. Knowing where to look, we can see that these states might be present but otherwise we would not have attached any significance to the small anomalies observed at these locations. 63 60 The Zn nucleus 3. 7 Figures 28 and 29 present one of two sets of independent 58 3 60 runs in which the Ni (He , n) Zn Q value was found to be 818 ± 18 keV. An excited state is seen at an energy of 1019 ± 25 keV. The very strong groups produced by carbon contamination prevente d the location of higher excited states. Lindner and Brinkman (1955) observed Zn 60 obtained from chemical separation of natural nickel bombarded with 52-MeV alpha particles. Using a liquid scintillator, a new gamma- ray activity with a half life of 2. 1 ± 0.1 minutes was found. This they attributed 60 58 60 to the decay of zn formed by the reaction Ni (a., 2n)zn • Gamma61 62 ray activities resulting from the decay of Zn and Zn were also observed. Using a scintillation dete ctor, weak gamma rays were observed from O. 5 to 3 MeV. They were unable to decide if these 60 61 resulted from the decay of Zn or Zn . 4. Discussion This section compares the mass and excitation- energy measurements with theoretical a nd semi-empirical predictions. 26 30 34 42 The four nuclei Si , s , Ar , and Ti are the proton-rich members of isotopic- spin triplets the other two members of which are well known. Thus, assuming cha rge symmetry of nuclear forces, their masses may be estimated by calculating the Coulombenergy correction. If one assumes that the Coulomb energy is proportional to Z(Z-1)/R and further assumes that R is constant for i sobars , one obtains 6M = A ( ilM' + o. 782 ) A - 2 o. 782 64 where 6M and 6M' are respectively the mass differences (in MeV) between the proton-rich and center isobars, and the center and neutron- rich isobars. For the center (Z = N) isobar, one actually uses the mass of the nucleus in its lowest T = 1 state. Our results are compared with this formula in table 6. Included in the table is a comparison of the excited states of the proton- rich and neutronrich isobars. The measurements agree well with the predictions of charge symmetry, as is usually the case. 48 60 56 The three ~uclei Cr , Ni and Zn are even. This makes it very difficult to estimate their mass because the only consistently reliable technique for estimating unknown masses is the use of charge symmetry and that cannot be applied here. (The above three nuclei are charge symmetric with themselves and themselves only.) However, Everling (1963b) was able to obtain 48 56 mass estimates for Cr and Ni by considering the mass trend of all even nuclei in the f shell. He first observed (Everling 712 (1963a)) that a plot of the mass defect (plus a term proportional to 20 28 24 A) vs. A for even nuclei in the d shell (Ne , Mg , Si ) was 512 nearly a straight line and that an extrapolation of this line towards . 16 lower A gave a value for the mass defect of 0 (doubly magic, p 112 shell closure) corresponding to the nucleus being in its first- excited state, the o+ state at 6. 05 MeV. He then made a similar plot for the 44 48 52 56 even nuclei of the f shell (Ti , Cr , Fe , Ni ), the line being 712 4 drawn from the first-excited, 3. 35-MeV, o+ state of Ca o (doubly 52 44 magic, ct shell closure) up through Fe . The nucleus Ti falls 312 20 slightly below the line (as did Ne for the ct shell plot) but he 512 24 48 56 expected that Cr and Ni should lie on the line (as did Mg and Si2 ~) and read off values for their mass excesses. His estimates of ·the energy available for beta decay (the number of interest in the 65 e-process) are given in table 7 along with values deduced by combining 3 3 the (He , n) Q values of this chapter with the (He , p) Q values of the next chapter. Everling's estimates agree very well with the experi- mental values. 5. The Si 28 30 3 (He , n) s angular distribution The angular distributions of neutrons to the ground and first 30 excited states of s were measured at a bombarding energy of 11. 6 0 MeV in steps of 10° from o to 50° with a semiconductor detedor 1 cm in diameter. At each angle, the detector subtended an angle of 0 10. o • The yield was determined by summing the number of counts 28 in the Si (n, a.0 ) peak and correcting the result for variations in the a. cross section using the data of figures 12 and 13. A series of B~ 9 (a., n) calibration spectra covering the same neutron- energy range 30 as the s ground- state neutron was also taken to facilitate sub- traction of counts ·due to the ground-state neutron from beneath the .28 30 Si (n , a. ) peak of S . 1 0 The angular distributions found for n and n resemble 0 1 typical stripping patterns (see figure 30). With this in mind, the ground-and excited-state distributions were fitted with spherical 2 2 Bessel functions, the best fits being obtained with j (kR) and j (kR) . 0 2 respectively where k is the momentum transfer and R is the interaction radius taken as 5. 0 fm to obtain the best fit. A justification for this procedure may be found in the work of Glendenning (1962) who has considered the similar case of (a., d) stripping. These fits, normalized 0 to the experimental points .at o , are indicated by the solid lines in the figure. If one assumes a small probability for spin-flip, the two 3 protons captured in the (He , n) reaction must be in a singlet state 28 because this is their state in He 3 • Since the ground state of Si is o+, 66 the spins and parities of the levels populated in s 30 are given directly by the ,f,....value of the angular distribution. Thus the ground and first 30 excited states of s are o+ and 2+ respectively as is expected on the 30 basis of charge symmetry (see levels of Si in Endt and Van der . Leun (1962)). 67 VI. 1. 3 THE. (He , p) MEAS{JREMENTS Introduction 3 This chapter describes the results of (He , p) Q-value 48 60 56 measurements for reactions leaving v , Co and cu in the 3 final state. Upon combining these with the (He , n) Q values obtained 48 56 60 in the preceding chapter for Cr , Ni and Zn , one can accurately establish the energy available in, for example, the decay of Ni 56 to co 56 • Thus, the Ni 56 -co 56 mass difference, tiM, is related to the 3 54 56 ground state Q values Q and Q of Fe (He , p)Co and Fe 54 (He 3, n)Ni 56 by P n . tiM = Q - O - (M - M ) p l1 n H a result which does not require knowing the masses of anything other than hydrogen and the neutron. Also, the advantage of being able to use the same target material (and even the same target) for both Q-value measurements eliminates many possible sources of systematic error. The mass differences obtained, particularly the 56 56 Ni -co difference, are important parameters in the e-process 3 (see Chapter II). The emphasis during the (He , p) measurements was to obtain accurate ground state Q values but with very little additional effort it was also possible to find many excited states. 2. Procedure 46 54 58 Targets of Ti , Fe and Ni were bombarded with an 3 11. 5 to 12. 0-MeV He ++ beam from the ONR- CIT tandem accelerator and the protons produced wer e analyzed with the ONR-CIT 61- cm 68 magnetic spectrometer. · The protons analyzed always had an energy of 12 MeV or more. They were detected in an array of, 16 semi- conductor detectors located in the focal plane of the magnet. Before being detected, the particles traversed approximately 1/2 mm ·of aluminum, a thickness sufficient to remove all particles other than protons. In particular, this removed deuterons, an important 54 3 58 3 consideration since the reactions Fe (He , d) and Ni (He , d) were 3 observed to compete strongly with the (He , p) reactions being investigated. 58 The targets consisted of isotopically enrich~d Ni (99%), 54 46 Fe (97%) and Ti (84. 5%) evaporated respectively to thicknesses 2 of 150, 50 and 20 µg/m/cm onto gold foils approximately 2000 A thick: The gold foils were prepared by evaporating gold onto glass slides on which barium iodide (which is very water soluble) had been previously evaporated. The foils were then cut up, floated off in distilled water, caught on tantalum frames and glued down with glyptal. Measurements were made at three angles to facilitate the separation of the proton groups of interest from contaminants. Small angles (15° - 45°) were chosen on the assumption that stripping is the dominant reaction mechanism, in which case the yield should be greater in the forward direction. This appeared to be true for the limited. number of angles checked. A nuclear magnetic resonance probe was used to measure the magnetic field and the results are presented graphically versus the frequency of this magnetometer. Jn addition, the ground- state proton groups were calibrated with the 9 3 11 reaction Be (He , p)B (Q = 10325. 1 ± 0. 7 keV). The two different evaluations of the ground- state proton energ~es agreed to within a few keV. . 69 The first measurement of the Co 56 mass was done in a manner ·slightly different than described above. The target was 54 3 56 one of those previously used to measure the Fe (He , n)Ni Q value. It was possible to find a single bombarding energy (8. 213 MeV) and angle (90°) such that the calibration and unknown proton 56 groups had the same energy. Thus both the Co measurement and the calibration were made without changes in beam alignment which greatly reduced error. However, at this bombarding energy, the yield was many times lower than at 12 Me V. The spectrum, which was taken without a .foil over the array detectors, showed some poorly-resolved structure between 150 and · 56 450 ke V excitation in Co possibly due in part to three low-lying 56 levels in Co reported by Nelson et al. (1962) but not seen by other groups. It was decided to repeat the experiment with better resolution. The desired resolution could not be achieved with the 16 counter array and to repeat the experiment with a single detector collimated tightly enough to give this resolution would have taken too much running time. Therefore, it was decided to use nuclear emulsions as the detector in the focal plane of the spectrometer. Ilford K2 nuclear emulsions 100µ thick on glass plates 1" x 6'' were obtained. (These should be ordered "with extra plasticizer". Otherwise the emulsion cracks and peels from its glass backing when put in vacuum - a phenomenon discovered the hard way!) A device was built which holds three plates in the spectrometer chamber and allows them to be rotated into the focal plane one at a time from outside the vacuum system. A sheet of aluminum, 0, 08 mm thick, was wrapped around the holder and served as a light shield. This aluminum should not touch the emulsion surface as it produces rapid blackening. Three exposures 70 were made lengthwise on e a ch plate. The central exposure was 9 Fe 54 (He 3 , p)Co 56 and the two sid~ exposure s were Be (He 3 , p)B 11 to be used for calibration. The emulsions were developed following directions given by Barkas (1963) and scanned using a microscope. Except for better resolution of the previously-re solved peaks, the spectrum In was identical to the one obtained with the 16 counter array. particular, the poorly-re s olved structure fooked little different than before. Late r, it was discovered that this structure is probably due to deuterons as it disappears when a sufficiently thick foil is put in front of the array. Fe 54 The structure is not due to groups from 55 3 (He , d)Co although groups from this reaction are visible In any case, the low-lying Co at lower proton energies. 56 levels reported by Nelson et al. are probably spurious. 3. Results and discussion Figures 31 and 32 show sample proton spe ctra obtained in 58 54 3 the He bombardment of Fe and Ni • Tables 9 and 10 list the energy levels found. The same lettering (i. e. , A for the highest energy proton group) is used in both figures and tables. Errors were assigned by comparing the spe ctra obtained at different angles. Table 11 lists the ground-state Q values measured. The . error is primarily due to uncertainty in the beam energy. Table 7 lists the mass differences which are of interest in the e-process. Figures 33 and 34 summarize the work done on mass numbers 56 and 60. Our results on v 48 are very incomplete: the targets were very thin which prevented obtaining a r ea sonable c ount rate ex ce pt .·· . . 48 at very forward angles and at these angles the groun d state of V 71 14 3 16 was obscured by peaks from N (He , p)O . The excited states we see (table 8) agree well with other measurements and since the mass 48 excess of v is known to an accuracy of 3. 4 keV, we did not pursue the matter further. There are variations of nearly two orders of magnitude in 54 3 56 the yields of various proton groups in the reaction Fe (He , p)Co as may be seen in figure 31. (Note in particular the scale change at f = 39. 25.) This was true at the three different angle s examined (15 0 , 300 , and 90 0 ). . ( From the work of several authors see table 9 footnotes), it is probable that levels A, B, D, G, K, and M have spins and parities of 4+, 3+, 5+, 2+, 1- (2-:) and 1+ respectively. By comparing the yield to each state with its spin, it is seen to be generally true that the higher the spin, the lower the yield. 56 The nucleus Co is one neutron over and one proton under . the double shell closure at Z = N = 28. The expected low-lying shell- r model configurations for the odd particle and hole are (lf \2%; ) 2 1 712 (giving rise to 2+, 3+, 4+, and 5+ states) and (lf (1f ; )(giving 5 2 712 rise to 1+, 2+, 3+, 4+, 5+ and 6+ states). Wells (1965) has performed r some shell- model calculations which indicate that levels A, B, D and G belong to (and complete) the (lf r \2 p ; ) configuration. He 3 2 712 1 (1f ; ) also makes a partial assignment of levels to the (lf 5 2 712 configuration. However, peak K, which Wells assumes to be 2+ and r uses as· a parameter in his calculations has been measured to be 1- (2-) by Ohnuma and Hashimoto _(1965). (Wells et al. (1963) had deduced experimentally that this level was (1 "."°, ~).) On the basis of the yield considerations mentioned above, levels F, I, J and L might be the high- spin members of the configuration. 60 is 2(+) from beta-decay studies. . The ground state of Cu No other information is a vailable as the l evel structur e has not been 72 previously investigated. The approximate number of low-lying 60 states can be readily explained using the shell model. The Cu nucleus may be pictured as three neutrons and one proton outside an inert core bounded by the completely filled £ shell. Two of 712 these neutrons will be paired with a binding energy of about 1. 5 Me V. 56 Thus, on the basis of the Co structure, the lowest shell- model 1 1 60 configuration of Cu is (2p /~) (2p ) giving rise to four states 312 (O+ - 3+). Again using the Co 6-1data, a:Out O. 8 MeV is required 3 to move a 2p312 particle to the 1f512 shell. This gives rise to two sets of four states (1+ - 4+} depending upon whether the odd proton or neutron is excited. The next grmtp of states will start around 1. 5 Me V and will arise from breaking the coupled pair of neutrons (many states), exciting the pair to the lf shell (4 states, o+ - 3+), 512 or excited both uncoupled particles to the 1f shell (6 states, o+ - 6+). 512 One conclusion is that 12 states are expected below 1. 5 Me V, in fair agreement with the data. Note in figure 34 the rather well defined group of 10 states (including the. gro~md state) ranging up to 940 keV. Two states could have been easily missed in this interval. 73 VII. THE GAMMA-RAY MEASUREMENTS 1. Introduction This chapter reports two measurements of gamma- ray spectra which are only indirectly related to the main theme of the thesis but which produced some interesting results. 34 Section 2 describes a measurement of the Ar half life. 34 34 34 The ground states of Ar , c1 , and s form a o+, T = 1 isotopic34 34 spin triplet. Thus the ground- state beta decays of Ar and Cl (both positron emitters) should be superallowed and, according to . 34 the CVC theory, have identical log ft values. The mass of Ar had already been measured (see page 55) and, since this nucleus has never been reported, it was decided to investigate its decay. 32 3 34 34 The Ar was produced in the reaction s (He , n)Ar . Its decay 34 32 3 34 produces c1 which is also produced via s (He , p)C1 . One expects the two isotopes to have similar half lives, making them difficult to separate. For the measurement to succeed by the 34 method used, it was essential that Ar have a detectable decay 34 branch to an excited state of c1 . The subsequent gamma ray 34 could then be used as a signature for Ar . Such a gamma ray was found. Section 3 describes the gamma- ray spectrum obtained from the de-e.x citation of excited states in Ni56 populated by the reaction F'e 54 56 3 (He , n)Ni . Section 4 gives a brief discussion of the evidence 56 40 16 in favor of collective structure in Ni , Ca and 0 , all of which are doubly magic. 74 2. Decay of Ar 34 · The half life of Ar 34 (estimated to be about 1 sec) was 34 measured by looking for gamma rays from c1 following the decay 3 34 32 34 of Ar produced in the reaction s (He , n)Ar . A 7. 6 cm x 7. 6 cm NaI (Tl) crystal was located 2 cm from the target at 90° in the laboratory. The bombarding energy was 10 MeV and the target . consisted of Sb s pressed into a hole in a beryllium cylinder 2 3 2. 54 cm in diameter and 2. 54 cm l ong. The experiment was performed in a beryllium environment for two reasons: the low atomic number of beryllium reduces bremsstrahlung produced by ~ rays and none of the reaction products of He 3 on beryllium produce delayed y rays. An electronic sequence timer initiated the following series of operations: the beam was allowed to strike the target for a time ,.. and was then chopped. After a short delay (150 ms) to ensure that the beam had died away, gamma rays were successively stored in the first and second halves of the memory of a pulse-height analyzer for the same time 'I" in each half. Then the analyz er was blocked, the beam turned on again and the cycle repeated. The ratio of the numbers of counts, corrected for background, in the t wo halves of the memory allows one to estimate the half lives of the gamma rays seen. The timing interval was varied from 1 to 5 34 times the expected Ar half life. Figure 3 5 shows the delayed-gamma- ray spectrum obtained with one- second timing. Most of the large peaks in the top spectrum (total yield of delayed gamma rays in the first two seconds after 34 beam turn-off) are due to gamma rays from s which follow the 34 beta decay of the i som eric state of c1 at 0. 143 MeV (see Endt and 34 Van de r L eun (1962) and figure 36). The c1 m is formed 75 predominantly by the reaction s 32 3 34 (He , p)C1 . Its half life was measured .by monitoring the target activity for 45 minutes after the beam was removed and found to be 32 ± 1 min in good agreement with the accepted value of 32. 40 ± O. 04 min. The relative yields 34 of the s gamma rays were m easured and are listed in table 12. 34 Once the s gamma rays were positively identified both · by virtue of their half life and their energy (determined with a 60 calibration using Co and RdTh sources), they were used as an internal energy calibration. This enabled the energies of the other gamma rays seen to be determined with a precision of 14 keV or better. The bottom spectrum of figure 35 shows the yield difference between the first and second seconds after beam turn-off. Note that 34 the s gamma rays have entirely disappeared, illustrating the advantages of this method for finding gamma rays produced in the decay of short-lived radioisotopes. Only three statistically significant peaks rema in. O. 51, 0. 67 and 1. 02. They are located at energies (in MeV) of The O. 51 and 1. 02 peaks are due to annihilation quanta, singly and in random coincidence. The remaining peak, at 0. 67 MeV, was found to have a half life of 1. 2 ± O. 3 s and is most . 34 34 likely due to the beta decay of Ar to the O. 67-MeV state of Cl . The large uncertainty in the m easured half life was due to difficulty in determining the background beneath the peak. Note that an 0. 51-Me V gamma ray in either true or random coincidence with the backscatter photon of another 0. 51-MeV gamma ray would produce a peak at O. 68 MeV very close to the peak seen. This possibility was eliminated by observing that the 0. 67-MeV peak had a unique half life, the same for 1, 1. 5, 3 and 6 second timing intervals, whereas the 0. 51-MeV peak did not. As a further check, 76 the spectrum produced by a Na 22 source in~erted in the beryllium chamber was examined using detection geometry similar to that of the actual experiment. No backscatter-sum peak was seen; its intensity was at least ten times weaker than the 0. 67-MeV peak seen in the experiment. A lower limit on the intensity of the beta branch to the O. 67MeV level may be obtained by comparing the yields of the O. 67-MeV and 0. 51-MeV gamma rays in the difference spectrum. This is only a lower limit because much of the short-half-life O. 51-MeV radiation comes from other sources such as the beta decay of the ground state 34 of c1 . The limit obtained is 1. 4 ± O. 2%. This has already been corrected for the gamma-ray branching ratio of the 0. 67-MeV level which, according to Glaudemans et al. (1964) decays directly to the ground state 80% of the time and cascades through the O. 14-MeV level 20% of the time. In our experiment, the O. 53-MeV gamma ray was swamped by annihilation radiation and the O. 14-MeV gamma ray was below the analyzer cut-off. In any case, the O. 14-MeV gamma 34 ray is useless for measuring the half life of Ar because the 0. 1434 MeV state of c1 is the isomeric state. 34 34 Using our values for the Ar - c1 mass difference and 34 . 34 Ar half hfe, we calculate log ft == 3. 59 ± O. 11 for the Ar decay. This value confirms that the decay is superallowed and agrees well . 34 with the value of log ft == 3. 508 ± O. 010 calculated for the Cl groundstate qecay. Both these values have been calculated using a computer 34 program for f developed by Bahcall (1965). Our Ar measurements, particularly the half-life measurement, are not sufficiently accurate to really test the eve theory. Using the lower limit obtained for the branching ratio of the . 34 Ar decay to the 0. 67-MeV state of Cl , we calculate l og ft ~ 5. 5 for 34 this transition. Therefore, the 0. 67-MeV level of c1 is 1+. 34 77 The results on mass 34 are summarized in figure 36. 3. Gamma rays from Ni 56 Gamma rays produced in the reaction Fe 54 3 56 (He , ny)Ni at a bombarding energy of 11. 6 MeV were studied in a 10. 2 cm x 10. 2 56 cm NaI (Tl) crystal. Unfortunately, gamma rays from Co , 54 3 produced by Fe (He , p), as well as gamma rays from reactions involving- target contaminants swamped the gamma-ray spectrum as seen in a single NaI crystal so that it was necessary to use an n- y coincidence system. 0 The neutron detector was placed at o where the neutron yield is expected to be largest on the basis of stripping theory, and the gamma-ray detector was located at 90°. Coincidences between the two detectors were used to gate the gamma- ray event into a 100 channel pulse-height analyzer. The biggest problem was to obtain a neutron-detection system which did not respond to gamma rays. We first tried to stilbene crystal with pulse shape discrimination but were unable to get satisfactory neutron- gamma- ray separation over the broad range of neutron energies present (up to 16 MeV). Our eventual solution was to "range limit" the gamma rays by using a small cylinder (1. 27 cm diameter, O. 63 cm thick) of NE102 plastic scintillator (supplied by Nuclear Enterprises Ltd., Winnipeg, Canada) and make u·se of the fact that the rate of energy loss for proton recoils is greater than for Compton scattered electrons. Thus, in this piece of scintillator, the maximum pulse height that an electron could produce was less than that proton recoils . of the more energetic . produced by n (6. 60-MeV state), which had an energy of 9. 4 MeV 5 and was the least energetic neutron of inte rest. The reaction 9 . . Be (a., nY . ) was used to test the apparatus and to set the integral 4 43 78 bias on the neutron detector. This was chosen as the half-height point in .the spectrum of a 9- Me V neutron. The gamma-ray spectrum obtained with the n-Y coincidence arrangement is shown in figure 37. Despite the poor statistics, due to the extreme inefficiency of the neutron detector, two gamma rays are seen, of energies 1. 28 ± 0. 06 MeV and 2. 66 ± O. 10 MeV. These gamma rays are consistent with a collective interpretation of the 56 levels of Ni given in the next section. 4. Discussion: Evidence for collective structure in doubly magic nuclei Recent experimental evidence suggests that the doubly magic 16 40 56 nuclei 0 , Ca , and Ni have pronounced collective properties. 16 The nucleus 0 shows several well-developed rotational bands (see, e. g. , Borysowicz and Sheline (19G4)), the lowest of these being based on the o+ first excited state at 6. 06 MeV. As outlined below, it is possible to construct a rotational band on the o+ first excited state 56 40 of Ca at 3. 35 MeV and it appears that the levels of Ni may separate into vibrational bands. Work by Everling (1963a, 1963b) on the mass systematics of the ld ; 2 and u shells suggests that the 40 712 16 5 o+ first excited states in 0 and Ca represent rearrangements of the nuclear structure necessary for adding more particles outside a doubly- closed shell (see the last paragraph of Chapter N, section 4 for a discussion of Everling's work). It is then perhaps not too surprising that these states might be highly distorted and show collective propertie s. The known states of Ni 56 appear to separate into two vibrational bands or (less likely from the energy spacing) a vibrational band and a r ot a tional band (see figure 38). Hoot et al.. (1965) have 79 weak evidence in support of the o+ and 2+ assignments for the ground and 2. 69-MeV states; the remaining. assignments are conjecture. Note that the separation of the two o+ ·states is close to being 1. 5 times the intra ba nd spacing (which is about 2. 7 Me V for both bands). Our gamma-ray data (see figure 37) are consistent with the vibrational interpretation of figure 38, the 2. 66-MeV gamma ray being a superposition of all the intraband transitions and the 1. 26Me V gamma ray being the inter band transition between the states at 3. 95 MeV and 2. 69 MeV. 40 The nucleus Ca appears to have a rotational band built on the o+ state at 3. 343 MeV (see figure 39), the formula E(J) = O. 092 J(J + 1) MeV fitting the levels chosen reasonably well. Recent papers by Springer (1965) and Bauer et al. (1965) provide most of the known spin and parity assignments. Both works were cyclotron studies of the angular distribution of alpha particles inelastically scattered 40 from Ca • Let us examine the experimental information on the levels in the postulated rotational band one level at a time. The states at 3. 348 MeV and 3. 900 MeV are definitely o+ and 2+ respectively. The lev_e l required to be 4+ could be any one of a closely spaced triplet around 5. 25 MeV, although the one at 5. 202 MeV fits best. This 40 triplet was clearly identified by Braams (1956) who studied Ca (p, p') with a magnetic spectrometer using a proton beam from an electrostatic generator. studies. This triplet could not be resolved in the cyclotron Bauer et al. , with a resolution of 120 keV, saw a single weakly excited level at 5. 27 MeV which they assigned as 3 or 1-. 80 Springer observed a single weak group at 5. 25 MeV whose angular distribution oscillated only fee bly but with a phase corresponding to a negative parity state. Since, in general, positive parity states were weakly excited in the cyclotron studies; it is possible that a 4+ state would be masked by a nearby negative parity state. If indeed the o+, 3. 35 MeV state represents an overall rearrangement of the internal structure as suggested in the first paragraph, members of a rotational band based on this state would be excited only weakly by (a., a.') because of the small overlap with the ground state wave function. The state at 7. 12 MeV was seen by both groups, again only weakly excited. Bauer et al. estimate its spin and parity as 2: 6+. A test of the suggested rotational band would be to see if a member of the triplet at 5. 25 MeV were indeed 4+. · Probably the 40 simplest experiment is to measure the Ca (a., a!) angular distribution. One way to achieve the necessary resolution would be to use a tandem accelerator and a magnetic spectrometer. 81 APPENDIX 1 Sample Calculations of the Si 28 (n, a. )Mg 0 25 Cross Section 1. Correction factors This appendix presents two sample calculations of the Si 28 (n, a. ) cross section: one in which the neutron source was °3 9 12 . . D(d, n)He ; the other, Be (a., n )C . The complete yield curves 0 28 for all the Si + n reactions measured are given in figures 12 to 18. One of the largest sources of error in the measured cross section is uncertainty in the actual active volume of the semiconductor detector (which served as both target and detector). Different . 9 detectors were used for the D(d, n) and Be (a., n ) data; the volume of 137 0 each was ·measured periodically using a Cs gamma-ray source of known strength. One of the spectra, from which the volume of the detector used for the D(d, n) data was deduced, is shown in figure 6. Another large source of error arises from uncertainty in the neutron-production absolute cross section. Values of the D(d, n) 0 cross section at o were taken from Fowler and Brolley (1956) and 9 have a standard deviation of 7% or less. Values of the Be (a., n ) 0 0 cross section at o were measured by the methods described in Chapter Ill. The results, which are plotted in figure 3, have a standard deviation of about 20%. Figures 9 and 10 show typical spectra from the D(d, n) and 9 Be (a, n) data respectively. Figure 11 shows the detection geometries and other details relevant to the analysis of these spectra, an analysis · which proceeded in the following way. . First the a 0 peaks were . summed over the r egions indicated in the figures and the sum obtained, S, multiplied by a factor f which corrects for a particles which 82 escape through the edges of the detector and a factor D to correct for the analyzer dead time. One can show that f :,;; 1 + (t + r) R/(2t r) where t and r are the detector thickness and radius and R is the range of the particle being stopped. This formula assumes both uniform and isotropic particle production throughout the detector volume. For 10-MeV neutrons detected in the a a correction of little importance. 0 peak, f ';;;;; 1. 02, However, f is much more important for the proton groups. Further evaluation of the absolute cross section will be considered for the two neutron sources separately. 2. 3 Cross section from D(d, n)He data In the following calculation, numbers are taken as needed from figures 9 and 11 where the symbols used are defined unless they have been defined above or are obvious. cr(a. ) = SfD/(N N N ) 1 2 3 0 = 92. 7 ± 9. 5 mb The separate quantities in this expression have the following meanings and values: SfD = (3578 ± 60) x 1. 013 x 1. 023 = 3705 ± .62 N 1 = Number of D atoms/mb = 2P x 2a/kT 83 . x (43. 2 ± O. 4 mm Hg) x 3. 69 cm -8 = 1. 043 ± 0. 010 x 10 atoms/mb 28 = Number of Si atoms in detector 28 = Nop/A x abundance (Si /Si) x volume of detector 22 3 3 = 4. 80 x 10 atoms/cm x (O. 275 ± O. 020 cm ) 22 = 1. 322 ± 0. 096 x 10 atoms = 6. 55 x 10 -21 = Number of neutrons incident on detector per atom of target gas = Q/e x do/dO[O0 , D(d, n)He 3 ] x nr 2/(h2 - a 2) = 1. 687 x 10 14 x (7tl. 7 ± 5. 4 x 10-27) x 2. 21 x 10 -2 = 2. 90 ± O. 20 x 10 -13 neutrons/atom 2 2 2 The expression nr /(h - a ) in N is the effective solid angle 3 subtended by the detector. This formula, which is proved by Evans (1955), assumes that the neutron source has no radial extension, an assumption which introduces an error of less than 0. 5%. 3. 9 12 Cross section from Be (a., n )c data 0 hl the following calculation, numbers are again taken as needed from figures 10 and 11. The form of the calculation is the same as in the preceding section. cr(a. ) = SfD/(N N N ) 1 2 3 0 = SID 25.6~ 7.2 mb = (1103 ± 35) x 1. 019 x 1. 082 = 1217 ± 39 = Number of Be atoms/mb = 5. 90 ± O. 94 x 10 -9 atomsI mb = Numbe r of Si = 4. 80 x 10 22 28 atoms in detector 3 3 atoms/ cm x (O. 40 ± 0. 06 cm ) 84 == 1. 92 ± O. 29 x 10 22 atoms Number of neutrons incident on detector per atom of Be. 9 12 2 2 = Q/2e x da/d0[0°, Be (a., n )c J x TTr /h . 14 ° -27) x (0. 20 ± o. 02) = 4. 68 x 10 x (4. 47 ± o. 90 x 10 == 4. 19 + 0. 94 x 10-13 neutronsI atom == 9 Overlapping Be (a., n) and D(d, n) ·data were taken·for En 9 ranging from 11 to 12 MeV. The Be (a., n) data were about 9% higher 9 throughout this range. Therefore, the entire Be (a., n) curve has been normalized to the D(d, n) curve by multiplication by O. 918. 85 APPENDIX 2 Some Observation Concerning Negative Ion Beams The production of negative ion beams is an essential part of the operation of a tandem accelerator. Negative beams of hydrogen and deuterium are routinely produced, an oxygen beam is fairly simple to obtain, and helium, carbon and sulfur beams are possible. This appendix will describe some investigations performed helping J. DeBoer develop techniques for obtaining a high energy oxygen beam (which was used for Coulomb excitation studies), and some attempts to produce negative neon and sulfur 56 beams (which were to be used for the production of Ni via the . C a 40(Ne 20 , a )N.56 react 10ns i and 8 i.28(S32 , a )N.56) i • The negative ion source of the ONR-CIT tandem consists of two units: a positive ion source; and a system consisting of an extraction electrode, focus electrode (Einzel lens), and charge exchange canal. To produce a negative hydrogen beam, hydrogen gas is bled into the positive ion source. Electrons emitted by a tungsten filament ionize the gas and magnetic fields promote the formation of a plasma consisting of ions ·such as H+, J:I +, H +, and electrons. 2 3 Some of this plasma is extracted from a small hole in the source and is accelerated through 40 keV by the extraction electrode and focussed with the Einzel lens. ~ext the beam passes through a narrow canal, the exchange canal, which has hydrogen gas continually leaked into it. A sinall fraction of the beam becomes negatively ionized upon collision with this gas and is again accelerated through 40 keV upon leaving the exchange canal. A magnet (the 20° magnet) is used to select the particular negative beam desired and the beam is 86 accelerated to the tandem terminal. Inside the terminal, it goes through another narrow, gas-filled canal (the stripper canal) where a large fraction of the beam is stripped to a positive charge state and re-accelerated upon leaving the terminal. The beam then passes through a 90° analyzing magnet, a set of energy regulation slits, and on into the target room. In our first attempts to make a negative oxygen beam, we put a mixture of 7% o and 93 % H in the source. We were able to 2 2 6 obtain up to 1/4 µa of 0 + beam on target at an accelerating voltage of 6 MeV. The purpose of the hydrogen was to reduce wear on the tungsten filament in the ion source. lasted only about one day. Even so, the filament usually In an attempt to determine which was the best of the many different negative oxygen beams coming from the source, we measured 20° magnet current vs beam intensity at the Faraday cup near the low energy end of the tandem (i. e. , at the low energy tee or LET). One of the curves obtained is shown in figure 40. All of the peaks below a magnet current of 100 ma are due to hydrogen beams since the same curve is obtained with only hydrogen in the source. The relative magnitude of the different peaks depends upon the lens s ettings, in particular the setting of the Einzel lens mentioned above. The largest hydrogen beam was always found to be that.corresponding to H + coming out of the source and H- coming 3 around the 20° magnet (the H +/H- beam), in agreement with a note 3 in the INEC instruction manual. The identification of the other peaks . is given in the figure. These identifications were made using the fact that the 20° magnet current should be proportional to the square root of the ion energy times ion mass (I ;:::,; /EA) if one assumes that all the beam which goes through the 20° mag11et has only one negative 87 charge. With deuterium in the source, the whole spectrum shifts up J2 in magnet current as expected. Later, the energy of the different hydrogen peaks was measured with an electrostatic analyzer located at the exit of the 20° magnet. Energies of 80 keV, 60 keV, 53. 3 keV and 40 keV were found respectively for the H+/H- , H2+ /H- , + 0 H /H and H /H beams as expected. 3 The peaks above a magnet current of 200 ma in figure 40 are at least partly due to oxygen or oxygen-hydrogen combinations; some of them are explicitly identified in the figure. However, many of these peaks persist with no oxygen in the source and have never been identified. They may be due to various comb:i,nations of carbon, nitrogen and hydrogen. We usually used the peak at about 370 ma It is most likely o ++/ 0-. Measurements with 3 the electrostatic analyzer established that the peaks at 300 ma and for an oxygen beam. 410 ma predominately have energies of 40 keV and 80 keV and are therefore 0 0 / 0 - and 0 +/ 0 - respectively although either member of each pair may have one or more hydrogen atoms attached which may explain the large peak widths. The next significant advance was made by H. Winkler who 0 noticed that the H /H- peak has maximum intensity at much highe r settings of the exchange gas and Einzel l ens than the other hydrogen beams. 0 He concluded that the H /H- beam was produced in the exchange canal by bombardment of the exchange gas. Thus, an obvious-thing to try was to put other gases in the exchange canal. We first tried o in the exchange canal and H in the source. The 2 2 predominant beam produced was o / 0 - ( ~ 10 µa at the LET). 2 2 This was not very satisfactory because the o - ion will not strip to 2 6 high charge states such as 0 + even assuming that the molecule is ° broken apart by the first collision in the stripper canal and that the 88 terminal voltage is 6 Me V. The reason is that the individual atoms in the molecule each have only 3 MeV energy on the average and it is the atomic velocity which determines the de gre e of stripping. We next tried H 0 in the exchange canal and H in the 2 2 0 source and found three peaks at the LET corresponding to H 0 /H 0 2 2 0 0 (5 - 10 µa), H o /OH- (5 - 10 µa) and H o / 0- (much weaker). 2 2 6 With 6 MeV on the terminal, it was possible to get 1/2 µa of 0 + on target - a significant improvement from the old method, not only because the beam was larger but because the ion- source filament now lasted much longer. Next, attempts were made to produce a negative neon beam. Neither neon in the e xchange canal and hydrogen in the source nor vice versa produced a measureable neon beam. With helium in the source and hydrogen in the exchange canal, peaks due to He+ /He 0 and He /He - were observed, but with very low intensity (less than O. 1 µa at the LET for He+ /He-, the stronger of the two). Attempts to make a negative sulfur beam were more successful. With H S in the exchange canal and H in the source, a · 2 2 current of 7 µa was obtained at the LET. The beam consisted of 0 H s / (H S- + HS- + S-), the different negative ions being too similar 2 2 in rigidity to separate with the 20° magnet. Satisfactory regulation 10 of the tandem was obtained on beams up to s +. For this last beam, an image current of 5 na was obtained at a terminal voltage of 6 MeV. The beam energy was 66 MeV, the highest ever obtained with the ONR-CIT tandem. Positive beam identification was made by observing the beam scattered from a gold foil with a semiconductor detector located at 30° with respect to the beam axis. Figure 41 shows the spectrum obtained with the tandem regulating on a 42. 4 7 MeV s + beam. At this time, argon was being used as the exchange gas. Also, the pumping on the high energy portion of the vacuum 89 system was not very satisfactory. These two facts explain the very large number of subsiduary peaks seen in figure 41. Due to the poor vacuum, large numbers of charge- exchange collisions could take place between the sulfur beam and argon gas the whole length of the high energy acceleration column. Thus, a small fraction of the sulfur and argon produced with charge states lower than that of the sulfur beam being regulated on will have the correct energy to get around the magnet. Under similar running conditions, an oxygen beam does not have the same large number of satellite beams although such beams were observed when oxygen was used as the stripper gas. Perhaps the sulfur satellite beams are enhanced because the similar masses of sulfur and argon maximize the momentum transfer per collision. Unfortunately, the above method for producing a sulfur beam has a serious drawback. The H S or something derived from 2 it forms a deposit on the ceramic balls which provide insulation for the parts of the ion source at 40 keV. After less than a day of running, arcing in the source is so bad that further operation is impossible and the insulating balls must either be cleaned or replaced. With H2S in the source and H in the exchange canal, 2 . breakdown occurs even faster. Clearly, another s ource of sulfur would be desirable but a suitable one does not seem to exist. A gas such as so 2 , if used in the exchange canal, would probably form beams such as so - and SO-. Molecules such as these would not 2 have enough velocity to be stripped to high charge states i. e. , they would behave like the o - ions discussed previously. 2 One further difficulty remains. It was discovered that the interval diameter of the exchange canal had been r e duced twofold by the formation of a metallic deposit. After this had been reamed out,·· 90 l.t was no longer possible to produce large beams from the gas in the exchange canal, probably because much higher exchange gas pressures are required for this method to work effectively (this was 0 confirmed directly for the H /H- beam -- see above). A twofold increase in the exchange canal diameter increases the conductance between 8 and 32 times, depending on the pressure. After the exchange canal has been cleaned out, there was some evidence that the ion source produced a larger hydrogen beam. Therefore, the idea of reducing the exchange canal diameter was not very popular. At this point, Dr. Kavanagh suggested that the reaction 56 3 Fe (I-Ie , n)Ni would be superior to heavy ion beam reactions for 56 the study of Ni . It was, and further work on heavy ion beams was 54 discontinued. 91 REFERENCES J . H. Aitken and W. R. Dixon, 1965, Nuclear Physics 67, 395. F. Ajzenberg-Selove and K. L. Dunning, 1960, Phys. Rev. 119, 1681. F. Ajzenberg-Selove and T. Lauritsen, 1959, Nuclear Phys ics_!_!, 1. J . D. Anderson, C. Wong and J. McClure, 1962, Nuclear Physics 36, 161. R. C. Axtma.nn and D. Kedem, 1965, Nucl. Instr. and Meth. 32, 70. J. N. Bahcall, 1965, to be published in Nuclear Physics. W. H. Barkas, 1963, " Nuclear Research Emulsions" , Vol. 1, Academic Press, New York. R. W. Bauer, A. M. Bernstein, C. Heymann, E. P. Lippincott and N. S. Vi all, 1965, Physics Letters 14, 129. M. Birk, G. Goldring and P. Hillman, 1963, Nucl. Instr. and Meth. 21, 197. J. H. Bjerregaard, P. F. Dahl, 0. Hansen and G. Sidenius, 1964, Nuclear Physics ~' 641. J. Borysowicz and R. 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B. Seaborn, G. E. Mitchell, N. R. Fletcher and R. H. Davis, 1963, Phys. Rev. 129, 2217. R. K. Sheline and R. W. Stoughton, 1952, Phys. Rev. 87, 1. R. K. Sheline and J. R. Wilkinson, 1955, Phys. Rev. 99, 165. A. Springer, 1965, PhD Thesis, Berkeley (unpublished). C. D. Swartz and G. E. Owen, 1960, "Fast Neutron Physics", Vol. 1, ed. by J. B. Marion and J. L. Fowler, Interscience, New York, p. 211. T: Tohei, 1960, J. Phys. Soc. Japan~' 372. H. Tyren and P. A. Tove, 1954, Phys. Rev. 96, 773. A. H. Wapstra, 1965, private communication. 95 D. 0. Wells, S. L. Blatt and W. E. Meyerhof, 1963, . Phys. Rev. 1:30, 1961. D. · 0. Wells, 1965, Nuclear Physics 66, 562. W. Whaling, 1958, Handbuch der Physik 34, 193; and also D. Demirlioglu and W. Whaling, private communication. 96 Table 1 . 9 Resonances in Be (a., n)C 12 for Ea. above 4. 0 MeV Ea. at r esonance (MeV) Excitation energy in c 13 (MeV) Gibbons and Macklina) Seaborn et al. b) 4.50 4.45 13. 8 5.00 5. 00 14. 1 . 5. 3 14.3 Present workc) 5. 40 ± o. 10 5. 75 7. 8 . 5. 7 ( 7. 1) 7.7 14.39 Approximate level width (keV) present work 240 14.64 6. 20 ± o. 05 14.95 400 7. 10 ± o. 05 210 7.95±0.05 15. 57 16. 1 16. 16 9. 10 ± o. 05 16.96 380 9. 7 ± o. 10 17.37 140 10. 2 ± o. 05 17.72 280 11. 1 ± o. 05 18.34 400 11. 70 ± o. 03 18. 76 80 240 a) Resonances in the total neutron cross section s ummed over all angles, measured up to E = 8. 2 MeV. See Gibbons and Macklin {1959). . a. . b) Resonances in the y4 • 43 yield at o0 measured up to Ea.= 10. 0 MeV. See Seaborn et al. (1963). 0 c) Resonances ill the n 0 yield at o • . See page 22. 97 Table 2 Important Ne utron-Induced Reactions in Silicon* Isotope Natural Abundance (%) Reaction Q value (keV)a) 92.21 *S.28( 1 n, a)M g 25 -2652. 6 ± 3. 2 . *Si28(n, p)Al28 -3852. 1 ± 4. 2 *S.29( 1 n, a)M g 26 32. 7 ± 3. 9 Si28 Si29 4.70 Si Si30 3. 09 29 (n, p)A1 -2893 ±7 8 1.30(n, a )Mg 27 -4201 + 5 Si30 (n, p)Al 30 -6510 ± 250 * See page 26. a) 29 Q values taken from Mattauch et al. (1965). 98 Table 3 Resonances .in Si 28 (n, a 0 )Mg 25 below 11. 3 MeV . All table entries are in MeV and have a standard deviation of 13 keV. Mainsbridge et al. (1963) investigated this same reaction for neutron energies up to8-:-5 MeV (see pa ge 36) but with poorer energy resolution. They identified resonances at 7. 300 ± O. 025 MeV, 7. 66 ± O. 02 MeV and 7. 94 ± O. 02 MeV. 7. 285 8.380 9. 840 7.430 8.510 10.000 7. 510 8.670 10. 150 7.635 8.800 10.460 7.780 8. 930 10.650 7.890 9.050 10.780 8.000 9. 290 10.990 8. 120 9.410 11. 230 8.240 9. 550 Table 4 t 3 Results of (He , n) Measurements Final Nucleus Si26 8 30 Our 3 (He , n) Q value (keV) 85± 18 - 573 ± 15 Mas~ Excess (keV)a) Excited States (ke V) This Experiment Other Work Best Value This Experiment Other Work - 7158 ± 18 - 7153 ± 80b) - 7131 ± 13c) - 7141±11 1787 ± 27 1780 ± 60b) 2803 ± 28 2790 ± 80b) -14270 ± 150d) -14065 ± 13 -14057 ± 15 2190 ± 40 -14190 + 150e) -14090 ~ 27c) tO tO Ar34. - 759 ± 15· -18394 ± 15 Ti42 -2865 ± 6 -25123 ± 7 -25090 ± 60cf' g) -25123 ± 7 Cr48 5550 ± 18 -42813 ± 19 '.'"43023 ± 2od1' j) -42813 ± 19 (720 ± 30)* -42743 ± 2od-' j) (2370 ± 50)* Ni56 4513 ± 14 -53899 ± 15 - -53902 ± 18k) -18394 ± 15 -53900 ± 12 2058 ± 35 2686 + 24 2710 ± 50k) 3950 ± 25 3940 ± 50k) (4980 + 50)* 4970 ± 50k) Table 4 Cont'd. Zn60 818 ± 18 -54186 ± 19 -54186 ± 19 (5350 ± 50)* 5350 ± 50k) 6600 ± 30 6620 + 50k) 1019 ± 25 * Assignment uncertain 12 a) C = 9. All numbers calculated from the experimentally measured quantities using the mass · table of Mattauch, Thiele and Wapstra (1965). b) Ajzenberg-Selove and Dunnmg (1960). ..... 0 0 c) Frick et al. (1963). d) Johnson, Chase and Imhof (1960). e) Robinson, Rhode and Johnson (1961). f) Oberholtzer (1962). 42 g) The mass excess quoted for Ti in Mattauch et al. is of unknown or.i gin and probably erroneous according to Wapstra (1965). - . h) Lieshout et al. (1955), i) Sheline and Wilkinson (1955). j) Mass estimate based on beta decay systematics. k) Hoot, Kondo and Rickey (1965). -t See Chapter V. 101 Table 5 . The 0 0 3 (He , n) Cross Section Measurements The quantities Eb' 9 and s are, respectively, the bombarding energy (in MeV), the half angle subtended by the detector and the ratio of the bombarding energy in the center-of-mass system to the Coulomb barrier, estimated using V = (Z Z 3e2)/(R + R 3). c x He x He Values of R were taken from Hofstadter (1956); R 3 was taken as x He 2. O x 10-1 3 cm. The data used for determining these cross sections are displayed in figures 22 to 29. See page 52 for further discussion. Final Nucleus Eb e Si26 11. 60 15 E: 1. 75 Ground- state Excited state Ratio of excitedcross section (Me V) rr to ground- state [probable J J cross section (mb/sr) 4. 3 ± 1. 7 1. 79 [2+ J a) 2. 80 [2+] a) o. 22 ± o. 07 o. 29 ± o. 12 830 11. 60 14 1. 60 3. 7 ± 1.1 2.19 [2+] a) o. 19 ± o. 05 Ar34 10. 81 16 1. 32 1. 4 + o. 5 2.06 [2+Ja) o. 10 ± o. 03 Ti42 11. 60 14 1. 23 o. 23 + 0. 09 Cr48 11. 00 17 1. 09 o. 15 ± o. 09 0.72 Ni56 Zn60 11. 51 18 11. 60 19 0.99 0.94 o. 12 ± o. 06 2. 37 o. 42 ± o. 23 o. 34 ± o. 15 2. 69 [2+] b) 1. 32 ± o. 35 3. 95 [O+] 1. 02 ± o. 26 5. 35 [0+,2+,4+] o. 36 ± o. 24 6.60 [2+] 2. 50 ± 1. 00 o. 12 + o. 04 1. 02 1. 45 ± o. 36 a) Spin and parit y are those of the corre sponding level in the chargeconjugat ed nucleu s . b) See discussion of Chapter VII, s ection 4 (pag·e 78 ). 102 Table.6 Charge- Symmetry Predictions Comparison of the measurements on Si Ti 42 with the predictions of charge symmetry. in MeV. Isobaric triplet M(Z = A/2+1)-M(Z = A/2) Calculateda) Measuredb) 26 34 30 , s , Ar and All numbers are Excited states Z = A/2-lc) Z = A/2+1 Mg26 Al26 Si26 4 •.88 5. 051 ± o. 019 . 1. 81, 2. 94 8 i30 P30 8 30 6.02 6. 140 t 0. 01 7 2. 23, 3.51 2. 19 8 34 Cl34 Ar34 5.88 6. 057 ± 0. 015 2. 13, 3.30 2.06 Ca42 Sc42 Ti42 6.76 7. 018 ± o. 014 1. 52, 1. 84 1. 79, 2. 80 a) Calculated using the mass table of Mattauch et al. (1965) and the formula on page 63. The locations of the first T = 1 states in 26 30 34 . Al , P and Cl were obtamed from Endt and Van der Leun 42 (1962) and that of Sc from Oberholtzer (1962). 3 . b) Calculated from our (He , n) Q value using the mass table of Mattauch et al. c) Taken from Endt and Van der Leun. 103 Table 7 Beta-Decay Energy of Alpha Nuclei t Mass difference (MeV)* Nuclear pair Estimated a) Zn 60 - c u 60 N1.56 - c 0 56 Cr 48 - V 48b) Measured 4. 170 ± o. 022 2. 19 ± 0. 05 2. 115 + o. 017 1. 70 ± 0. 10 1. 657 ± o. 019 * These mass differences, particularly Ni 56 - Co 56 , are of interest in the e- process. See Chapter IT. a) Taken from Everling (1963b). b) V48 mass taken from Mattauch et al. . ( 1965). t Based on the measurements of Chapt ers V and VI. 104 Table 8 Levels of V 48 t (energies in keV) Nelson. et al. a) Bjerregaardb) et al. Present workc) 306 ± 14 310 ± 12 316 ± 15 416 ± 14 420 ± 12 408 ± 10 514 ± 14 523 ± 12 616 ± 12 615 ± 20 751 ± 12 752 .± 14 771 ± 12 1049 ± 12 a) Nelson~t~. (1960}. b} Bjerregaard, Dahl, Hansen and Sidenius (1964). . 48 c) Computed using V mass from Mattauch et al. (1965). t See page 70._ 105 Table 9 56 Levels of Co (energies in ke V) ldent. B Nelson et al. a) Anderson et al. b) Wells et al. c) Bjerregaard et al. d) 159 ± 4 165 ± 15 164± 3 158 ± 12 166 ± 9 Present work 186 + 6 225 ± 6 280 ± 6 D 560 ± 15 578 ± 12 576 ± 9 F 825 ± 15 829 ± 12 832 ± 9 G 980 .± 15 965 ± 12 978 ± 9 1111 ± 9 984 + 4 1008 ± 12 H 1105 ± 15 1111 ± 12 I 1246 ± 13 J 1335(?) ± 13 K 1470 ± 6 1445 ± 12 1445 ± 13 1592 ± 18 L 1714 ± 12 1723 ± 13 N 1925 ± 12 1934 ± 13 0 p 2056 ± 12 2087+ 13 2222 ± 12 2225 ± 18 Q 2291 ± 12 2312 ± 18 R 2358 ± 12 2381 ± 18 M l'"i40 ± 5 a) Nelson, Plendl . and Davis (1962) . . b} Anderson, Wong and McClure (1962). c) Wells, Blatt and Meyerhof (1963). The similar experiment of Ohnuma and Hashimoto (1D65) gives results in agreement with these. d) Bjerregaard, Dahl, Hansen and Sidenius (1964). 106 Table 10 .. 60 * Levels of Cu (energies in ke V) B 72 ± 7 I 940± 9 s 2762 ± 13 c 298 ± 7 K 1428 ± 9 T 3000 ± D 375 ± 7 L 1673 + 9 u ., 3078 ± 13 . E ' 465 ± 7 M 1783 ± 9 v ' 3157 ± F 568± 9 N 1917 ± 25 w 3361 ± 25 F' 606 ± 9 0 2007 ± 9 x . 3477 ± 9 G 681 ± 7 p 2196 ± 9 y 3602 + 9 H 796 ± 7 R 2547 ± 9 * See page 70 and figure 32. 9 9 107 Table 11 . 3 The (He' , p) Q Values* (energies in keV) Previous Measurementsa) This work 3 56 (He , p)Co 7427.8±8.5 7410 ± 10 60 3 (He , p)Cu 5760. 3 ± 9. 5 5770 ± 12 Reaction Fe Ni 54 58 a) Calculated from mass table of Mattauch et al. (1965). * See Chapter VI. 108 Table 12 Decay of Cl 34m 34 The relative intensities of s y rays in the 13+ decay of c1 34m are listed. The 2. 13-MeV transition was arbitrarily assigned an intensity of 100. See page 75. . s 34 T rans 1T 10n m (energies in MeV) ) Relative intensity Toheia Present work 3.92 --> 3.30 weak < 0. 5b) 4.07 --> 3.30 weak < 0. 5b) 3.30 --> 2. 13 32 47 ± 8 2. 13 --> 0 100 100 ± 5 3. 30 --> 0 32 34± 5 4.11 --> 0 1 1. 2 ± o. 5 a) Tohei (1960). b) Not seen. 109 .Figure 1 Neutron and gamma- ray spectrum from the reaction 9 12 Be (a, n)c at a bombarding energy of 6. 00 MeV as seen in 0 a stilbene crystal loca ted at o • Neutron groups lea ding to 12 the first three states of C and the 4. 43- Me V gamma ray of C 12 are visible. The neutron energies are 11. 52, 6. 84 and 3. 25 MeV. See pages 15-16. The abs olute cross section for the n 0 group was found The sum, N , (equal 1 to 3430 ± 150) of all counts above channel 105, which corre- from this spectrum_in the following way. sponds to a proton energy, Ee' of 10. 23 ± 0. 03 MeV, was obtained. The total number of n neutrons detected in the 0 crystal is then 4 N 2 = NlEn/ (En - Ec) = (3. 07 ± 0. 15) x 10 . 18 . . The target was measured to have (5. 90 ± 0. 94) x 10 beryllium 2 atoms/cm (see text, page 50). Therefore the number of neutrons detected per incident a. particle per target atom is N = N / (Q/ 2e x 5. 90 x 10 3 2 18 ) = 1. 11± 0. 19x 10 18 From the graph of figure 2, 4m: = 0. 0256 ± 0. 0015. +2 cm Therefore the differential cross section is 0 . d<J / dO(O ) = N3/ 4TTE: = 4. 36 ± o. 74 mb/ sr . The final value for the cross section at this point was obtained by averaging the value from this spectrum and another spectrum 18 2 obtained with a thinner target (2. 68 ± 0. 54 x 10 atom/ cm ). It is 4. 88 ± 0. 98 mb/ sr (see figure 3) and includes 15% error to allow for the effects of multiple scatter and edge losses. -110- Figure 1 I05 r--~~--,..---~~--.~~~--.~~~---.-~~~-,...~~~--.-~~~--. 4 10 ~ z ::::> 0 (.) Cl ·Cl • 10 •• • •• 0 40 80 CHANNEL NUMBER 120 111 Figure.2 Single- scatter detection efficiency vs neutron energy for 9 the stilbene crystal used for the Be (a, n)C 12 neutron yield measurements of Chapter III. The dimensions of the crystal and the geometry used are given in the figure. The quantity e: is that fraction of the total number of neutrons emitted by an isotropic neutron source that is removed from the primary beam by scattering from hydrogen. The solid curve, which was used in our analysis, allows for attenuation of the primary beam by scattering from carbon (which does not produce an . observable pulse) as well as from hydrogen; the dashed curve was calculated assuming hydrogen scatter only and is about 10% higher. See text (page 19) for a discussion of the possible usefulness of this curve. The form of the efficiency integrals for the two curves is given on the figure; nHCJH and llcac are the linear attenuation coefficients for scattering from hydrogen and carbon respectively, and x is the path length of the neutron beam in the crystal. Values of nHcrH and 1Ccrc were taken from table I of Swartz and Owen (1960). The figure displays 4ne: for convenience in finding differential cross . . cm 2- s t erad'ians -1 . sect ions m -112~ Figure 2 NEUTRON DETECTION EFFICIENCY OF STILBENE . ___ 5.71-[] ! cm 0.030 cm _L ~ 3.a1-...J cm over crystal "'t:: 0.025 ~ ----HYDROGEN SCATTER ONLY A=I 0 ;020 B=nH o-H ---BOTH HYDROGEN AND CARBON SCATTER 10 12 14 En (MeV) 16 Figure 3 9 0 12 Cross section at o for the reaction Be (a,.n )c as a function of bombarding 0 energy. The resonances, indicated by arrows,may correspond to levels in the 13 compound nucleus c . See page 21 and table 1. The standard deviation on the absolute value of the cross section is 20%; the statistical error on each point is 2% or less for the points above 5. 5 MeV. ,..... ,..... "" !Q ~ v ~ 0 c: w 0 -0 - - 0 --_......._~---~ -114- - --e> v (JS/qW)UP/.OP N Figure 3 0 ·~ 0 co >Cl> C1 ~ w Figure 4 9 9 0 12 . Cross sections at o for the reactions Be (a., n )c and Be (cx.,n )c 12 as a 2 1 function of bombarding energy. The arrows indicate the position of resonances seen in the ground-state neutron yield (see figure 3). See pages 21 and 22. I-' I-' OI Q.l c: ~ -> -w- N 0 co <D lO 0 r0 --------- ----- ----- --- -- -116- Q 0 N (Js/qw) UP/..op 0 / I I I I I (\J c: t Figure 4 I ~ Q Q) Q.l -> l:j ~ w Figure 5 Upper portion of the pulse-height spectrum resulting from neutron- induced reactions in a silicon semiconductor detector. The peaks observed are identified with the different states of the final nuclei produced. See pages 38-39 for the 9 meaning of t.E. The incident neutrons, produced in the reaction Be (a., n)C 12 , had an energy of 9. 83 MeV. ..... ..... -J co N <i a. Q) > ~ I'<) co IO N O> :::;;; ve c;·o 9L6·o 119· 1 0 Cj O> :::;;; "' N c ti" (/) CL - <D - I'- - CXl 1e·1 ~- -a:.- ~=t; a.. ~- - Gl~ cri c t j_ N O> 6 6 £'£ 80 t>£ £08'2 9£L' 2 c;sc;·2 c 296' 1 (/) CD N Cj :::;;; II w <I IO N w <I co N 21rn·o ££~)'! <;L£ · 1 LIO' I c vL6·o CD N (/) Lvr2 602· 2~ 1e2·2 0 0 0 6 -118- -Cj- - Figure 5 >< I() (\J - 0 0 r<> 0 I() (\J CD ~ a:: w z ::> w ....J Cj-- :r: <( z z 0 0 (\J I() 0 u in 0 0 0 CjN- ci"'civ- 13NN'l1HJ C:l3d SlNnOJ . 119 Figure 6 Spectrum produced by a Cs 137 . gamma- ray source (EY = 0. 662 MeV) in a chilled lithium-drifted semiconductor detector. The m ost prominent feature is the Compton shoulder whose edge appears at Ee= 0. 468 MeV. Also visible are a small full-energy peak (I'= 20 keV) and a secondary Compton edge at E = 0. 468 + 0. 074 = 0. 542 MeV. e Using the known Compton scattering cross section, and the theoretical shape of the Compton profile {dashed curve), the active volume of the detector was deduced to be 0. 271 ± 0.035 3 2 cm . The detector area was 80 mm ; therefore the depth was 3. 39 + 0. 44 mm. This detector was the one used for the 28 3 D(d, n)He measurements of the Si + n yield curve. See pages 28 and 81. ~120~ · Figure 6 Ee ( MeV) 0.5 1.0 csl37 (230 µ.c.) 0 I I (/) ~6.2cm-~ I I w. ..,_ ~ 103 I ~ 0 LO 0:: w a... (/) ..,_ z => 0 (.) 10 2 .. 20 40 60 80 CHANNEL NUMBER 121 Figure 7 Mounting arrangement used for the Li-drifted semiconductor detector. A-detector; B-stainless steel front (0. 015 11 thick); C-stainless steel tubing (0. 010" wall thickness); D-copper bar; E-clamping bar; F-vacuum electrical feed-through. See page 29. Cross hatched material is brass. -122- Figure 7 TO FORE PUMP 1 F NEUTRONS< A B C----11 D LIQUID . NITROGEN 123 Figure 8 Two useful geometries for using a semiconductor detector as a neutron spectrometer: a) Head-on (see page 31), b) Side-on (see page 33). The cylinder represents the active volume of the detector. -124- Figure 8 a /\ I \ I \ N I \ I I \ I \ I \ ~t -4 r b N RADIATION · SOURCE h ~ Tr Figure 9 Spectrum produced in a silicon detector by neutrons from the reaction D(d, n)He 3 at a bombarding energy of 5. 15 MeV. After correction for the gas cell entrance foil, deuterium gas target thickness and kinematic energy spread of the outgoing neutrons, the average neutron energy at the detector was 8. 33 MeV. This is a typical spectrum 28 from the data used to obtain the Si + n yield curves of figures 12 and 14. The regions summed for the differe?t integral cross sections are indicated. A calculation of the a cross section obtained from this spectrum is given on page 82. 0 28 28 28 28 Low energy peaks due to Si (n, n)Si and Si (n, n')Si * (1. 77) are identified. 28 The arrows indicate the expected positions of the maximum energy Si -recoil calculated 28 from the position of the Si (n, a ) peak. A correction of 17%, taken from the data of 0 Sattler (196 5), has been applied to allow for the pulse- height defect of the recoil silicon atoms. See page 41. 1-l l"" 01 (\J I"> I 0. 0 ti (\J t I ti 0 ti Ul 0 0 J_ ti t 00 v 0 0 0 0 x Q S.LNnOJ -126- 0 v 'JTl·Lc, ~3d o~ o 00 _i_ 0 ( u 'u) - - (,u'u) - - - 0 0 0 Ul C\.I 0 o· 0 C\.I 0 0 Figure 9 0 l() 0 0::: (J :r: <l: z z w _J z :J ~ Q) Qw IC) 0 0 127 Figure 10 Spectrum produced in a silicon detector by neutrons from 9 12 the reaction Be (a.,n)c at a bombarding energy of 8.00 MeV. 9 After correction for the Be target thickness (5. 90 x 10 18 2 atoms/cm , equivalent to 49 keV) and kinematic energy spread of the outgoing neutrons, the average neutron energy at the detector was 13. 29 MeV. This is a typical spectrum 28 from the data used to obtain the Si + n yield curves of figures 13 and 15 to 18. The regions summed for the different integral cross sections are indicated. A calculation of the a cross section obtained from this figure is given on page 83. 0 -128- ~. Figure 10 a o-P 2 3 - - - - - - --&>n; ~ao-a2--"""I 150 u · ::t.. 0 tO a:: w 100 a... 0 (/) ~ z ~ 0 u 50 0 260 300 340 CHANNEL NUMBER 129 Figure 11 Experimental set-ups used for the measurement of the Si 28 + n yield curves (see figures 12-18). 3 Top: D(d, n)He as neutron s ource. 9 Bottom: Be (a., n) as neutron source. The data given on this figure, in conjunction with the spectra of figures 9 and 10 are used to calculate the absolut e 28 cross section for Si (n; a. )Mg25 in appendix 1 (page 81). 0 -130- ~ F i gure 11 h=6.29cm--- o+- -> BEAM .l+-C:= - INTEGRATOR Q= 27µ.C :> . P= 4 3.2mm Hg DETECTOR A =0.80cm2 V=0.275 ± 0 .020cm3 h= __., 2 .0±0. 1 ~ cm 4++ He BEAM INTEGRATOR Q= 150µ.C DETECTOR A=0.80cm2 V=0.40 ±0.06cm3 Figure 12 Total cross section for the reaction Si 28 25 (n, a.0 )Mg for 7. 2 :5 En :5 12. 0 MeV. Table 3 is a listing of the clearly- resolvable resonances on this curve. The reaction 3 D(d, n)He was used to provide neutrons and a Li-drifted silicon detector served as both target and detector. For details on how this curve was obtained and why it is useful, see Chapter IV, section 4 (starting on page 33). ,_. ~ r..>. I- I I I I I I I I I I I I I I I I I- -, -132- - - I I I I ~ I I I I I I I I I 1!"7 - - - 0 N Figure 12 I I I I - I I I I I - I r~ l· I - I - I I I() 0 - I 0 Q >- I I() 0 (qW)..0 c: w Figure 13 28 25 Total cross section for the reaction Si (n, a.0 )Mg for 11. 44 :5 En 5: 16. 40 MeV. 9 12 The reaction Be (a., n )c was used to provide neutrons and a Li-drifted silicon detector 0 served as both target and detector. For details on how this curve was obtained and why it is useful, see Chapter IV, section 4 (starting on page 33). ..... "" "" -134- 0 (qw) .D (\J 0 Figure 13 0 w c ~ L-~~.l--~~.l--~~-l--~~+-~~f-o---=fL~~t-~~t-~----t~ ~ 0 r<"> Figure 14 Total cross sections for peaks a. -a. (lower curve) and a. -p (upper curve) for 2 8 23 28 25 28 · the reactions Si (n, a.) Mg and Si (~, p)Af 2 for neutron ene~gies of 7. 2 to 12. 0 MeV. 3 The reaction D(d, n)He was used to provide neutrons and a Li-drifted silicon detector served as both target and detector. Figure 9 shows a typical spectrum from the data used to obtain these curves and indicates the regions summed for the different integral cross sections. The analysis, experimental techniques and possible applications of these curves are discussed in Chapter IV, section 4 (starting on page 33). ...... c,., 01 0 0 v 8 r<> . -136- (qW)..0 N 0 0 0 Q Figure 14 0 Q) > c ~ w Figure 15 Total cross sections for peaks a. -a. (lower curve) and a. -p (upper curve) for 0 0 23 2 28 28 25 28 the reactions Si (n, a.)Mg and Si (n, p)Al for neutron energies of 11. 44 to 16. 40 9 12 . MeV. The reaction Be (a., n )c was used to provide neutrons and a Li-drift silicon 0 detector served as both target and detector. Figure 10 shows a typical spectrum from the data used to obtain these curves and indicates the regions summed for the different integral cross sections. The analysis, experimental techniques and possible applications of these curves are discussed in Chapter IV, section 4 (starting on page 33). 1-l "" -J -138 - Cl) 0 Figure 15 0 1---+-~~~~----t----'-~~~-~~~~~---j~~..~l--~+-~~~~-h-'"'-~~~~y (qi.u) ..D ~ ~ c w Figure 16 Total cross sections for peaks a (lower curve) and a. (upper curve) for the 1 3 28 25 reaction Si (n, a.)Mg for neutron energies of 11. 44 to 16. 22 MeV. These curves were evaluated from the same data as the curves of figures 13 and 15. The reaction 9 12 Be (a., n )C was used to provide neutrons and a Li-drifted silicon detector served 0 as both target and detector. The analysis, experimental techniques and possible applications of these curves are discussed in Chapter IV, section 4 (starting on page 33). ...... (...:> co r<') 0 -140- 0 (\J (qW)..0 0 Figure 16 0 Figure 17 Total cross sections for peaks a. (lower curve) and a. {upper curve) for the reaction 2 4 28 25 Si (n, a.)Mg for neutron energies of 11. 44 to 16. 22 MeV. For details, see the caption of figure 16. ,_.. H:>. ,_.. r<'l 0 C\J 0 -142- (qW)_Q 0 Figure 17 0 Figure 18 Total cross sections for peaks p (upper· curve) and p (lower curve) for 01 23 28 28 the reaction Si (n, p)A1 for neutron energies of 11. 44 to 16. 22 MeV. For details, ·see the caption of figure 16. ...... ~ c.:> r<') 0 -144- C'J 0 (qW)..0 0 Figure 18 0 Figure 19 9 12 Cross section at 0° for the reaction Be (a., n )c as a function of bombarding 0 energy. This curve was measured with a silicon semiconductor detector (see page 36) . . It agrees well, both in absolute cross section and shape, with the curve of figure 2 in the ·region of overlap (Ea. = 5-6 MeV) and with the data of Risser, Price and Class (1957) who measured this cross section for 1. 7 ~ Ea. ~ 4. 8 MeV. ...,. ~ 01 > Q) ~ c: w Q co 0 C\I -146- (JS/QW} 7jp;.op Q Figure 19 IO '¢ N >© ~ Cj w 147 Figure 20 28 Pulse-height defect of the Si (n, p ) peak as determined 01 28 from a calibration based on Si (n, a.) peaks. See page 39. -148- Fi ure 20 0 140 0 120 - 0 >100 Q) - ~ JLL :r: 80 0 Cf) 0 >a::: w 60 z <.9 w 40 20 0 4 8 12 NEUTRON ENE RGY(MeV) 16 149 Figure 21 9 54 Thickness measurements of a Be target (top) and Fe target {bottom) performed by scattering 1-MeV protons from the tungsten backing with and without penetration through the target material evaporated on one side. The two graphs show the number of scattered protons per unit incident charge vs energy of the scattered proton, the latter being given by 2 2 E (MeV) ::: 0. 3841(1 - E /(2m c ))/ F p p p where F is the magnet fluxmeter reading. The square points delineate the profile of the back side i. e. , protons scattered without penetration through the evaporated material. The scattering geometry for both measurements is indicated. Note 54 that two measurements of the Fe thickness are obtained: the shift of the W profile and the width of the peak due to 54 protons scattered by Fe itself. These measurements were performed on the 26. 7-cm-magnetic-spectrometer station of the #1 ESG. See page 50 for further discussion of this figure. -150- Figure 21 Be9 ON W BACKING nt=4.02 x1018atoms/cm2 Cl> 0 (.) (/) . .ri '0 C f) r- z ::::> 0 (.) Fe 54 ON W BACKING nt=6.90xlo 17 atoms/cm2 LL 0 0::: w CD ~ ::::> z .660 .64o · FLUX METER READING I .620 151 Figure 22 The reaction Mg 24 3 26 (He , n)Si at a bombarding energy of 11. 60 MeV as seen in a silicon semiconductor detector at o0 with respect to the beam axis. The top spectrum is the sum of several runs directly as recorded in a 400- channel analyzer. Reactions induced in the detector by the ground- state neutron are indicated by arrows. See figure 5 for the spectrum of a single monoenergetic neutron in which the peaks are correlated more clearly with the corresponding nuclear reactions in the silicon which produce them. The bottom spectrum shows the top spectrum with the best calibration obtained for the ground- state neutron normalized to it and subtracted out. Families of pe.a ks associated with contaminants and excited states are explicitly identified. The ordinates are true numbers of counts before and after subtraction. obtained. See page 53 for a discussion of the results -152- Figure 22 1000 500 ...J w z z <{ :c u a: . ol--~~---1~~~-l-~~~-l-~~~-l-~~__Jl--~~-l-~::_~-l-~~~ ~1000 Cf) ..... ois(He3,noJ -ia1 lao Mg24(He3 ,n) Si26 no SUBTRACTED z :::> 0 u 500 noao I I t . 175 200 225 250 275 CHANNEL NUMBER 300 325 153 Figure 23 . a s n·icon . The reac t ion 8 1.2s(He 3, n )s30 as seen m 0 detector at o at a bombarding energy of 11. 60 MeV. In the subtraction spectrum, the large dip just in front of 26 the n -a. peak arises in the same way as the dip in the Si 1 0 spectrum (see figure 22 and the discussion of artificial dips on page 53). 0 This spectrum, which was taken at o , does not show n very clearly, particularly when artifically1 produced dips and rises of comparable magnitude are present. However, in spectra taken at other angles, n shows up clearly even before subtraction. the n 1 In fact, at 30°, cross section is about three times that of n • (See the 0 1 n and n angular distributions of figure 30.) For notation 0 1 see figure 22 and for a discussion of the results see page 55. -154- Figure 23 500 __J w z z<( ::r: 0 et: w a.. CJ) I- z ~ 0 0 500 5;28(He3,n) 530 no SUBTRACTED ·OO ao 0 Cl2 (He3,nol Po1 a2 01 ao @:)') 0 0 0 0c:B> 0c£ . 0 0 noao I I J0 8 t 0 0:;)~ 0 -~ 0 0 00Y 0 0 0 0 0 ~ 150 175 200 225 • 250 CHANNEL NUMBER 275 300 325 155 Figure 24 The reaction s 0 32 3 34 (He ,n)Ar as seen in a silicon detector at o at a bombarding energy of 10. 81 MeV. For notation, see figure 22 and, for a discussion of the results, see page 55. -156- Figure 24 s 32 (He 3 ,n)Ar 34 0 532(He3 ,nol 0 400 200 _J w z z <! I (..) 0:: w a.. en ..._ 400 532 (He 3 ,n) Ar 34 z 0 16 lHe 3 ,nol :J 0 ·la (..) 1 no SUBTRACTED la 0 200 C12 lHe 3 ,nol 125 150 175 CHANN~L 200 NU MBER 225 250 157 Figure 25 The reaction Ca 40 42 3 (He , n)Ti at a bombarding energy of 11. 60 MeV as seen in a silicon detector. The upper spectrum shows the peaks produced by neutrons leading 14 42 18 to the ground states of 0 , Ti and Ne with the detector at 0°. The lower spectrum shows the same peaks with the center of the detector at 45°, its face subtending an angle 28 of 10°. The kinematic shift of the Si (n, a. ) peaks is 0 · indicated by ~Ek'. There was about four times more carbon · on the target when the lower spectrum was taken. See page 56 for a discussion of the results obtained and figure 22 for notation. -158 - Figure 25 Ca 40(He 3 ,n) T i 4 2 6=0° 600 ca 40 (He 3 , n 0 l 400 _J w z z <( 0 200 er w Q_ (/) 1- z :::> 0 0 Ca40(He3,n )Tj42 9=45° 100 cl2(He3 n0 l 0 . 00 0 _JP01 ' la2 {a1 ao}--- . 6Ek ---J .00000~·· 0%_ .· . . . . ____._____...____ .. · . · .... 0 . . ·.· ~- . .. .__ 200 250 CHANNEL NUMBER 300 350 159' Figure 26 The reaction Ti of 11. 00 MeV. 46 (He~, n)C r 48 at a bombarding energy Note that the ground-state neutron subtraction cannot be extended below channel 255 because of the presence 9 of groups from Be (a., n ) in the calibration reaction. For 1 notation s ee figure 22 and for a discussion of the results see page 57. -160 - F i i r e 26 200 100 10 0 50 0 0 0 0 0 0(,) ~ 0if'. ...J w 6> z z<( :c (.) 0 0 0 n 0 SU BTRACTED 0 00 0 0 0 Ti 46 0 3 (He , n1l 0 a:: 50 w 0 0 0 0 Q_ (/) I- z :::i 0 (.) 0 0 n 1 SUBTRACT ED 0 0 0 ® ~ 0 0 0 50 0 0 0 T1.4 6 (H e 3, n 2 ) 0 0 ct? 0 2 50 275 300 325 CHANN EL NUMBER 3 50 375 161 Figure 27 The reaction Fe of 11. 51 MeV. 54 3 56 (He , n)Ni at a bombarding energy The middle spectrum was obtained after two subtractions and the bottom after three more. Three excited 56 states of Ni are definitely seen and there is weak evidence for two more. The a. peaks of these latter two are indicated 0 in the top spectrum between channels 200 and 225. The subtractions and the results obtained are discussed starting on page 59. For notation, see figure 22. Ffo:ure 27 1000 - 200 :14 Fe 3 (He ,n0 1Ni 500 56 100 0 500 I N.56• I I 'ao 250 300 CHAN NEL NUM BER 3 50 Figure 28 . 60 3 (He ,n)zn Q value. See 3 58 60 the next figure for the subtraction spectra. Left: The reaction Ni (He , n) Zn at All the data used for one determination of the Ni 58 a bombarding energy of 11. 60 MeV. Top right: Spectrum obtained by bombarding 28 24 28 the target backing. The Si (n, a.) peaks of (He 3 ,n) reactions on Mg , Si and 0 60 C 12 are identified both here and on the Zn spectrum. The magnesium and silicon 9 accumulated on the target during the run. Bottom right: One of the Be (a., n ) spectra used to calibrate the neutron group leading to the ground state of ZnBU See page 63 for a discussion of the results obtained. >-4 O') ~ c ~ Ni 58 (He~ n) Zn TARGET BACKING 3 EHe = 11.600 MeV EHe3 = 11.600 MeV 60 B ~ 400 75 A c ~ ~ 58 3 Ni (He, nol • ••• _J w z 300 z • II ~ c Si (He~n)s,, 24 3 .26 (He,n)S1 28 30 A Mg B (.) e I Cl:'. w 50 C12(He3,n)O Al,J. Al,·~~~~. •• •• <! I A ~• • ao B .25 - ,_. I a.. CALIBRATION SPECTRUM Cf) En = 12.300 MeV 0) 1- z P23 !a4 ::> 200 1°3 !Poi 1°2 1°1 200 ~ I 0 (.) x 1/5 100 100 ":rj ....... °2 1-"j (!) ~ ():) • 225 250 275 300 325 225 CHANNEL NUMBER 250 275 300 325 Figure 29 60 The first excited state of zn . See the preceding figure for the raw data. Left: Peaks remaining after subtracting the ground-state calibration spectrum. Right: Peaks remaining after subtracting the target- backing spectrum attributed 28 to Mg and Si contaminants. The first three peaks of the Si (n, a.) spectrum 60 produced by the neutron group to the first excited state of Zn are clearly revealed. See page 63 for a discussion of the results obtained. .en CJ! \; a2 J,Oo !a1 400 I- 1l fa2 1 tao tal 1 n0 AND BACKGROUND n0 SUBTRACT.ED SUBTRACTED EHe3 = 11.600 MeV 300 B A ll li --' w z z A <{ I 0 5 200 A Mg 24cHe~ n) Si 26 B Si 28 (He~n)S 3 0 ~ EHe3 = 11 .600 MeV t PU j 1 a.. (f) I- z ::> JOO \-- I I I • f. I • l "oao • ..,........ • 275 f. ~ I I• 300 f . . r.. I· t 1 • •• •' • . ,_ ... , • • 250 I Q) • • •-' • • • ••• • 225 fQ I ....... I I • 0 I- l t ~ 0 0 z 60 1 n N.58(H 1 e,3 n ) N.58(H 1 e,3 n )Z n60 325 225 250 CHANNEL NUMBER 275 • • • • • • • • • • 300 325 ~ ....... ~ >i CD 1:1.? c:.o 167 Figure 30 28 3 30 Angular distribution of neutrons from Si (He , n)s 30 to the ground and first- excited states of s measured in a semiconductor detector at a bombarding energy of 11. 60 Me V. The vertical error bars are largely from uncertainty in the 28 relative variation of the Si (n, a. ) cross section but also 0 include statistical uncertainty. The horizontal lines on each point indicate the total angle subtended by the detector face. The error on the absolute cross section is 30% and the error on the relative magnitude of the ground and first-excitedstate neutron yields is 20%. The solid lines are theoretical fits which assume a stripping process and use the plane-wave Born approximation with R ::: 5. 0 fermis. See page 65. -168- -------,,---- r-- . 4 3 Figure 30 169 Figure 31 ~ The proton spectrum from the reaction Fe 54 3 56 (He , p)Co at a bombarding energy of 11. 50 MeV and laboratory angle of 15°. Peaks C and E and the small peak at about 41. 5 Mc did not appear at other angles. They are probably spurious peaks produced by bursts of noise in the array detectors. 56 The remaining peaks correspond to levels in Co , except perhaps J which was not seen with certainty at other angles. See page 70 and table 9. -170- Figure 31 . 2500 . 250 Fc 54 ( Hc 3 , p) Co 56 e • 1s 0 ~000 200 u ::t. 0 ~ 1 ~00 5C a: w a. "'>-z R Q :> 0 u 1000 P 0 N M J H G l I I j j I j j j I I +. 500 c B A I I I 100 171 Figure 32 The proton spectrum from the reaction Ni 58 (He 3 , p)Cu60 at a bombarding energy of 11. 50 MeV and laboratory angle of 15°. Peaks J and Z are proton groups from the reaction 14 12 3 c (He , p)N ; peak Q is a proton group from a light target contaminant with A > 16. The remaining peaks correspond · 60 to levels in cu . Peaks FF' are a closely-spaced doublet and peaks Wmay be up to 4 levels. See page 70 and table 10. -172- Figure 32 Ni58 (He 3 , p) Cu60 e: 15• 800 ZYXW VUT S 11 I I II I R OP ON ML K J HGF'FEDC BA I I I l I I l l I I ll I I I Il (.) :::i..600 ~ a: . (\J w CL ~ 3 400 8 200 34.0 34.5 35.0 35.5 36.0 36.5 37.0 FREQUENCY (Mc) 37.5 38.0 39.0 39.5 173 Figure 33 Summary of Q-value measurements for the mass-56 56 56 system. See pages 59-62 (Ni ) and 70-71 (Co ). All numbers are in MeV. -174- Figure 33 6.60 -5.35 -----4.98 ------- 7.410± 0.010 Fe 54 +He3 -p 4.513 ± 0.014 Fe 3.95 2 .69 2 .381 2 3122.225 2.0871.934 I. 723 1. _ 592 1.445 1. 246 I. Il l 09780.832 . 0 .576 0 . 166 . Co56 54 3 +He -n 175 Figure 34 Summary of Q-value measur e ments for the mass-60 60 60 system. See pages 63 (Zn ) and 70-72 (Cu ). All numbers are in MeV. -176- Figure 34 5.770 ± 0.012 Ni 58 + He 3 -p . 1.02 0.818 ±0.018 Ni58 + He 3 -n I I Zn 6 0 I I I I 3.60234773.361 . 3.157 307 8 ~3.000. I I 2.762 2 .547 2 .196 2.007 1.917I. 783 1.6731.428 0.9400796Q§§Jo.6060 568 I 0.465 0 375·- I 0 .298 . I 0.072 I cu60 I I I 4 .170 ±0.022 MeV I I I I I I . 177 Figure 35 Gamma rays seen in the first two seconds after the 3 bombardment of Sb S with 10-MeV He summed over 2 3 approximately 1000 bombardment cycles. The top curve is the total yield in the first two seconds; the bottom, the yield in the first minus the yield in the second. The following gamma rays (energies in MeV) are seen: 0. 51 annihilation 34 radiation; 1. 17, 2. 13, 3. 30 and 4. 11 all produced in 8 34 following the decay of c1 m; 1. 46 and 2. 62 from the decay 40 of K and RdTh in the concrete walls of the target room; and 1. 77 which may be due to the 1. 77-MeV gamma ray which 28 .28 follows the beta decay of Al (T_112 = 2. 28 m) to 81 . The 28 . Z7 28 Al is presumably made by Al (n, Y)Al . See Chapter VII, section 2 (page 74) for a discussion of the results obtained from this spectrum. -178- Figure 35 105 o.51c 134 534 tor 2.13-0:51 ~ Ar40 1.46 Si28(?) 2.13 l 2.13+0.51 lCOINC. 534 1 A 3.30-0.51 3.30 i l lBKGNDl r 3.30+0.51' l 104 COINC. ThC,.. 2.62 CJ) w _J X IOO ~ l BKGND. 0 0 Q 10 5 534 0:: w 4.11 ~ z l Cl.. ::> 0 (.) 103...._~~'--~--''---'---'~~--'-~~.-J..~~-L..~_.......__....~~......_..._·_~_·~~--'·~10 0 40 80 120 CHANNEL NUMBER 160 . 200 179 Figure 36 The mass- 34 system showing only those levels of interest to the work described here, which chiefly concerned 32 3 34 34 Ar made via s (He , n)Ar . See page 55 for a description of the Q-value measurements of the ground and first- excited 34 states of Ar , and pages 74-77 for the measurement of the 34 positron branch to the 0. 67-MeV level of c1 and the relative intensities of the gamma rays following the beta decay of c1 34 m(O. 143). -180- Figure 36 2.06 L----0--- - - 0 ..;..+ __, 6. 06 Ar34 l.2s (2+) (T=I) 2.16 0.67 32.40m 0.1 4 3 c134 c2+ 4.11 47 1.2 2.129 34 100 ..___.l,_ __.__..__-=-..J - 5 . 5 2 534 l.59s 13+>0.012 .e6 -0.76 s32+He 3 -n 181 Figure 37 Gamma- ray spectrum observed in coincidence with 54 3 56 neutrons from the reaction Fe (He , nY)Ni . Peaks are seen corresponding to gamma rays of energy 1. 28 ± 0. 06 MeV and 2. 66 ± 0. 10 MeV. The apparent peak in channel 46 (EY = 3. 47 ± 0. 13 MeV) is not statistically significant and, if it exists, does not correspond to a transition 56 between known levels of Ni . See page 77. . -182- Figure 37 80 _J w z 60 z <[ I u ! i 0::: w Q... 40 (/) I- z :::::> 0 u 20 0 25 50 CHANNEL NUMBER 75 100 183 Figure 38 Known levels of Ni 56 separated into a vibrational band built on the ground state and a vibrational or rotational band built on the state at 3. 95 MeV. Evidence in favor of this interpretation is given on pages 78 and 79. -184- Figure 38 ~16.3 Ni55 + n 8.015 Fe52 +a 7.193_ c 0 55+ P 1 6.60 + 0 . 03 {2+) 3.950±0.025 {O+) 5.35 ± 0.05 4 .97 ± 0.05 4.513 ± 0.014 Fe54 + He3-n L _______ 0+ l Nj56 j 185 Figure 39 Left: Energy levels of Ca 40 below 8. 6 MeV. Center: Levels in the proposed rotational band with their energies redefined with respect to the o+, 3. 38 MeV level (see page 79). Experimental errors are given. The error on the 7. 12-MeV state is an estimate of the error in the data of Bauer et al. (1 965) ; the remaining errors are those quoted by Braams (1956). Right: The rotational spectrum calculated from E(J) = 0. 092 J(J + 1) MeV. -1868 .59 8.38 8.11 7 92 Figure 39 (4+,5 ) 2+ 4+ 7.5 -------7.12 6.94 >6+ 2+,3 6.58 3- 3.77 ±0.02 ~6+ 3 .864 s+ 1.840 4+ 0.552 2+ 36.28 6 029 · 5.901 35.606 5.621 4+ 5.202 5.2415.272 4.483 5- 3 .900 3.730 2+ 3 3.348 o+ o+ ca4o 1.854 ±0.009 0.552 ±0.006 2+ o+ o+ Figure 40 Negative ion current at the LET vs 20° magnet current measured with a mixture of 93% H2 and 7% o 2 in the source, and H in the exchange canal. The ion .source 2 controls were adjusted to maximize the beam labelled 0 +;0-. Useful oxygen beams · have been obtained from the three broad peaks explicitly identified as being oxygen. Each peak is seen to have considerable fine structure, probably due to different combinations of oxygen and hydrogen. ,_,. The maximum probable range for such CX> -.:i structure is indicated for o0 /o- and o+/0- peaks. See page 86. The energies indicated on the graph were measured with an electrostatic analyzer. The dotted curves are helium peaks found with a 00- 50 mixture of He and 0 source and H2 in the exchange canal. 2 in the H0/H- (40 keV) 80 keV o+;o-n H3+/H- (53.3 keV) 10-1 H20°?'H20- 67.7keV H2+/H- (60 keV) (?) 40keV io3++;0- i H+/H- (80 keV) !0°;0- H20/H20- 0 - 10-2 ::l iHe+/He- I- z w (\ 0:: 0:: II I (.) 11 I-A I I I I I :::> 00 00 II 1- w _J 10- 3 I \ iHe°/He- I \ I I I I I \ ,, I I I I I I I\ I \ 10-4 10-~ '' I I ., ,J I, I 1 100 I I ti \ \ I I I I I I I I \ I I ,; I '' I ·- 150 I I I I 1 I I • ,, "Ij ...... I (]~ 1-i I I I I (t) \ I I I\ ~ 0 I I I I I I I I 200 250 MAGNET CURRENT (ma) I I 300 I I I I I 350 '. I I I I 400 I I I I 189 Figure 41 Energy spectrum of particles scattered through 30° from a gold foil as seen in a semiconductor detector. The 7 tandem was regulating on the S + beam and the terminal voltage was 5. 30 MeV. of the remaining peaks. See text (page 88) for explanation -190- Figure 41 SCATTERED BEAM ENERGY(MeV) 10 20 40 30 i Ar3+ l Ar4+ (/) l 55+ 3 I- 10 i z Ar6+ ::::> 8 LL 0 a: w m ~ 2 ~10 IO 0- 0 50 00 100 CHANNEL NUMBER ooo 150 0 200