The Reduced-Alpha-Width of the Lowest 1⁻ State of ¹⁶O Citation Dyer, Peggy Lynn (1973) The Reduced-Alpha-Width of the Lowest 1⁻ State of ¹⁶O. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/3PZ0-DY56. https://resolver.caltech.edu/CaltechTHESIS:10292015-105646231 Abstract Cross sections for the reaction 12 C(α,γ) 16 O have been measured for a range of center-of-mass alpha particle energies extending from 1.72 MeV to 2.94 MeV. Two 8"x5" NaI (Tℓ) crystals were used to detect gamma rays; time-of-flight technique was employed to suppress cosmic ray background and background due to neutrons arising mainly from the 13 C(α,n) 16 O reaction. Angular distributions were measured at center-of-mass alpha energies of 2.18, 2.42, 2.56 and 2.83 MeV. Upper limits were placed on the amount of radiation cascading through the 6.92 or 7.12-MeV states in 16 O. By means of theoretical fits to the measured electric dipole component of the total cross section, in which interference between the 1¯ states in 16 O at 7.12 MeV and at 9.60 MeV is taken into account, it is possible to extract the dimensionless, reduced-alpha-width of the 7.12-MeV state in 16 O. A three-level R-matrix parameterization of the data yields the width Θ α,F 2 = 0.14 +0.10 -0.08 . A "hybrid" R-matrix-optical-model parameterization yields Θ α,F 2 = 0.11 +0.11 -0.07 . This quantity is of crucial importance in determining the abundances of 12 C and 16 O at the end of helium burning in stars. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Physics) Degree Grantor: California Institute of Technology Division: Physics, Mathematics and Astronomy Major Option: Physics Thesis Availability: Public (worldwide access) Research Advisor(s): Barnes, Charles A. Thesis Committee: Unknown, Unknown Defense Date: 15 December 1972 Funders: Funding Agency Grant Number NASA Traineeship UNSPECIFIED NSF GP-28027 Record Number: CaltechTHESIS:10292015-105646231 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:10292015-105646231 DOI: 10.7907/3PZ0-DY56 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 9259 Collection: CaltechTHESIS Deposited By: Bianca Rios Deposited On: 29 Oct 2015 23:18 Last Modified: 16 Jul 2024 20:46 Thesis Files Preview PDF - Final Version See Usage Policy. 23MB Repository Staff Only: item control page

THE REDUCED-ALPHA-WIDTH OF THE LOWEST 1- STATE OF 16 0 Thesis by Peggy L. Dyer In Partial Fulfillment of the Requirements For the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1973 (Submitted December 15, 1972) -ii- ACKNOWLEDGMENTS I run especially grateful to Professor C. A. Barnes, who provided guidance and encouragement throughout this work. pleasure to work with him. It was a Appreciation goes also to Professor W. A. . Fowler, whose unfading interest in the 12 C(a,y ) 16 0 reaction rate motivated us to attempt these formidable meas urements. The technique adopted for these measurements was explored first by Dr. Barnes with Drs . A. Adams, M. H. Shapiro, and E. G. Adelberger, and later, in more detail, by Drs. D. C. Weisser and J. F. Morgan. Dr. H. B. Mak designed the amplifiers which made pos- sible the extraction of a time-reference pulse from the target. The chopping and bunching system on the 3 MV generator was constructed by Dr. M. R. Dwarakanath. Dr. Dwarakanath and Mr. J. G. Polchinski aided iu setting up the experimental apparatus on the 3 MV generator and in taking data. Dr. Eileen Hess of DHOM Products Ltd. carried out the conversion of amorphous carbon to methyl iodide require d for target prevaration. Two methods of extrapolating the 12 C(a,y) 16 tion to low energies are described in this thesis. 0 excitation funcThe 3-level R-matrix computer code was written by Drs. D. R. Thompson , D. C. Weisser and J. F. Morgan; the "hybrid" R-·matrix-optical-model fit was developed by Mr. S. E. Koonin and Professor T. A. Tombrello. A special thank-you goes t o the following members of the Kcllo~g Radiation Laboratory sLaff: Vlc Ehrgott, Barbara Zimmennan, -iiiLaurie Graham, Don Kinley, Bud Warrick, George Fastle, Don Woshnak, Will Schick, and Don McGrath. students and I am also indebted to the many graduate research fellows who helped during the long data- accumulation periods. I am grateful for financial assistance provided by a NASA Traineeship and by Graduate Research Assistantships from the California Institute of Technology. This research was supported in part by the National Science Foundation (GP-28027). -iv- ABSTRACT Cross sections for the reaction 12 C(a,y) 16 0 have been meas- ured for a range of center-of-mass alpha particle energies extending from 1. 72 MeV to 2. 94 MeV. Two 8"X5" Nal (T ~ ) crystals were used to detect ganuna rays; time-of-flight technique was employed to suppress cosmic ray background and background due to neutrons arising mainly from the 13 C(a,n) 16 0 reaction. Angular distributions were measured at center-of-mass alpha energies of 2.18, 2.42, 2.56 and 2.83 MeV. Upper limits were placed on the amount of radiation cascading through the 6.92 or 7.12-MeV states in 16 0. By means of theoretical fits to the measured electric dipole component of the total cross section, in which interference between the 1 - states in 16 0 at 7 . 12 MeV and at 9.60 MeV is taken into account, it is possible to extract the dimensionless, reduced-alpha-width of the 7.12-MeV state in 16 0. A three-level R-matrix parameterization of the data yields the width e2 a,F +0.10 0 • 14 -0.08 • zation yields e 2 a,F A "hybrid" R-matrix-optical-model parameteri+0.11 0 . 11 -0.07 This quantity is of crucial importance in determining the abundances of of helium burning in stars. 12 c and 160 at the end -v- TABLE OF CONTENTS I. II. III. GENERAL INTRODUCTION 1 A. Astrophysical Implications 1 B. Theoretical Description of the 160 Nucleus c. Previous Attempts to Determine 8 D. Scheme of the Present Experiment 2 a (7.12-Mev, 8 16 0) 9 12 EXPERIMENTAL METHOD 15 A. Introduction 15 B. Measurements of Yield at 8 = 90° 17 1. Targets: Preparation and Thickness Measurements 17 2. Target Chamber 19 3. NaI(Tl) Detection System; Efficiency 20 4. Time-of-Flight Technique 27 5. Electronic Configuration 30 6. Procedure for Collecting Data 32 7. Extraction of Yields 34 C. Measurements of Angular Distributions 35 D. Measurements of Cascade Radiation 38 RESULTS 41 A. Cascade Radiation 41 B. Conversion of Yield to Absolute Cross Section 43 C. Angular Distributions and Extraction of IA +1 2 44 D. Electric Dipole Contributions to the Total Cross Sections 48 E. Extrapolation to Lower Energies of the Electric Dipole Contributions 48 -vi- IV. DISCUSSION 51 A. Astrophysical Significance 51 B. The APPENDIX A. 12 C(a,y) 16 0 Experiment of the Future 52 Astrophysical Reaction Rate Fonnulae for the 12 16 C(a,y) 0 Reaction 57 APPENDIX B. Direct and Resonant Capture Processes in the 12 16 c(a,y) o Reaction APPENDIX C. Three-Level R-Matrix Fit to the APPENDIX D. "Hybrid" R-Matrix-Optical-Model Fit to the 12 16 c(a,y) o Data APPENDIX E. Measurement of the Yield of the . Reaction and of 19 12 c(a,y) 16 o Data 19 F(a,y) 23 Na F Target Content 62 70 72 74 -viiLIST OF TABLES Table No. 1 Page Yields of 7-MeV Single Gamma Rays and Yields 83 of Coincidences 2 12 C(a,y) 16 0 Yields . 0 from Measurements at 90 84 3 Quantities IA +1f IA _j Obtained from Angular 1 2 Distribution Measurements 85 4 El and E2 Contributions to the 12 C(a,y) 16 0 86 Total Cross Section 5 6 12 c(a,y) 16 o Capture Transitions Yield of 9-MeV Gamma Rays from . the in an Enriched 12 C Target 87 19 F Impurity 88 -viiiLIST OF FIGURES Figure No. Page 16 1 Energy Level Diagram of the 2 Schematic Diagram of Apparatus for Making Enriched 12 C Targets 3 Target Thickness Determination by the 0 Nucleus 89 13 . Reaction c(p,y) 14 N 4 Schematic Diagram of the Target and Detection System 5 9.17-MeV Standard Spectrum for a 20 .3-cm by 12.7-cm 91 93 95 97 NaI(Tl) Crystal 6 Electronic Configuration Used for Measurements of 12 16 0 C(a,y) 0 Yield at 90 7 Isometric Plot of a 12 c(a ,y) 16 o Two-Dimensional 99 101 Multichannel Analyzer Spectrum 8 Energy Spectra of Gamma Rays from the 12 C(a,y) 16 O 103 Reaction 9 Time Spectra of 9-MeV Events from the 12 C(a,y) 16 0 105 Reaction 10 12 c(a ,y) 16 o Angular Distributions 11 Variation of 12 Measured 1 IA +1 2 2 107 with Alpha Energy Contributions to the 12 c(a,y) 109 16 o Total 111 Cross Sections and 3-level R-Matrix Fits 13 Variation of the Ratio 113 Energy 14 Measured 1 - Contributions to the 12 C(a ,y) 16 0 115 S-factor and 3-level R-Matrix Fits 15 Measured 1 - Contributions to the 12 C(a,y) 16 0 Total Cross Sections and "Hybrid" R-Matrix-Optical-Model Fits 117 -ixFigure No. 16 Measured 1 - Contributions to the 12 C(a ,y) 16 O S-factor and "Hybrid" R-Matrix-Optical-Model Fit 17 12 C(a ,y) 16 0 Cross Sections of Jaszczak et al. 119 121 Compared with Fit to Caltech Data 18 Dependence of 12 c Mass Fraction on Core Mass and 0 2 a ,F 19 20 19 F Content of Enriched 12 125 C Targets The 13-MeV Gamma-Ray Yield of the 123 19 F(a , y ) 23 Na 127 Na 129 Reaction 21 The 9-MeV Gamma-Ray Yield of the Reaction 19 F(a ,y) 23 -1- I. The 12 GENERAL INTRODUCTION A. Astrop hysical Implications 16 o reaction follows the 3a-r12 c reaction in the c(a,y) chain of helium-burning reactions which can occur in the interior of a star which has exhausted the hydrogen fuel in its core. the rates of the 12 c(a ,y) 16 The ratio of o and the 3a-+12 c reactions (at the relevant stellar temperatures) effectively determines the mass fractions of 12 c and 16 0 at the end of helium burning in massive or intermediate- mass stars, since the succeeding reaction helium-burning temperatures. 16 o(a ,y) 20 Ne is very slow at 12 Whereas the 3et+ C rate is relatively well known at the present time (Barnes 1971), the 12 C(a,y) 16 0 rate was so highly uncertain prior to the present measurements, tha t the mass fraction of solved. 12 c at the end of helium burning was left completely unre- It was thus difficult for astrophysicists to calculate relative abundances of 12 c and 16 0 in the universe or to follow the evolution of a star past helium burning. As an example of the importance of the 12 C(a ,y) 16 0 reaction rate, we consider here 0.elium burning in intermediate mass (4 < M/M < 10) E> and massive (10 < M/M < 100) stars. E> Helium burning follows hydrogen burning. Following exhaustion of the hydrogen fuel by the conversion of hydrogen to helium, which takes place through the various chains of reactions characteristic of hydrogen burning, the central region of a star contracts and heats up. When this core becomes hot enough, helium burning begins and gravitational collapse is halted. At this point the central density is about -23 8 4 10 g/cm and the central temperature is of the order of 10 °K. reaction chain for nucleosynthesis of 12 C and 16 The 0 in helium burning is primarily concerned with the following three reactions: 12 3a.+ c ' 16 O(a.,y) 20 Ne • The relative rates of these three reactions at the appropriate effective interaction energies determine the abundances of elements left in the core at the end of helium burning. If the 12 C(a.,y) 16 . 0 rate is slow 12 12 compared with the 3a.+ c rate, then a large fraction of c will remain at the end of helium burning; if 12 c(a,y) 16 o is fast compared with 12 16 3a.+ c, then the end-product of helium burning will be 0, since the 16 o(a.,y) 20 Ne reaction rate is very small. rates there will be some mixture of 12 For intermediate c and The stellar reaction rate of the 12 12 c(a.,y) 16 o 16 0 remaining. C( a. ,y) 16 0 reaction is commonly parameterized in terms of a dimensionless, reduced•alpha-width of the state in 16 0 at 7.12 MeV, a quantity denoted 0 2 * a., F • The relation be- tween the rate at astrophysically important energies, which are of the order of 300 keV c.m., and 0 2 a.,F is given in Appendix A. The stellar re- action rate is directly proportional to the magnitude of mass fraction of 12 2 0a. , F • The C remaining at the end of helium burning, a quantity 16 0 *rn this work the symbol 0 2 will refer to the 7.12-MeV state in a. unless otherwise noted. The subscript "F" refers specifically to the quantity 0 2 as defined by Fowler et al . (1967). See Appendix a. A. -3denoted by Xe , may thus be expressed as a function of the mass of the star and of the quantity 0 2 a,F (See Section IV.A for a more quanti- tative discussion of the relation between Xe and 0 2F • ) a, A basic premise of current astrophysical theory is that most of the synthesis of elements heavier than helium has taken place in the interior of stars and that these elements have in some way been ejected into the interstellar medium (Fowler 1968). Recent calculations (Arnett 1972) suggest that massive stars (10 < M/M < 100) are the prim® ary source of 12 e and 16 0 Once 2 0a,F is known, it should be possible to calculate the relative abundances of 12 e and 160 at the end of helium burning, and from current astrophysical theory, to predict the observed "cosmol.ogical" abundance ratio fraction of 16 O.) Xe/X 0 . (X0 is the mass If the calculated and observed values do not agree, the astrophysical theory must be modified. Such an astrophysical theory must treat the following topics (Arnett 1971): (1) galactic evolution theory, in order to interpret present abundances in terms of continuous nucleosynthesis beginning billions of years ago, (2) the mass distribution of stars fo rmed from the interstellar medium, (3) the range of mass of stars contributing to nucleosynthesis of 12 e and 16 O, (4) the rates of nucleosynthesis durin g quiescent quasi-static helium burning in the core and in shells of the star, and during possible explosive stages, (5) the mechanisms for mass ejection, and (6) the fractions of mass ejected. can presently be treated unambiguously. None of these topics However, once the relevant nuclear reaction rates are determined empirically, severe constraints are placed on any viable astrophysical theory. -4Much effort has been spent recently in an attempt to follow the evolution of a star after core helium burning is completed. Because the helium fuel has now been used up, the core will contract, converting gravitational energy to heat, until a temperature is reached which is high enough for further nuclear reactions to take place. reactions will be depends upon what nuclei are present. What these Whether these reactions will ignite quiescently or explosively depends on many f actors, which include the amount and type of fuel available. One possible path at this point, for stars in the intermediate mass range (4 < M/M < 10), is explosive ignition of either 12c, by the El 12 12 c+ c reaction, or 160 ' by the 16o+l60 reaction. The resulting detonation could end wita a catastrophic mass loss, with or without a remnant. This stage of evolution has become of great interest in the last few years, especially because of the apparent concurrence of an analysis of pulsar observations made by Gunn and Ostriker (1970) and calculations of stellar models made by Paczynski (1970) and others. Gunn and Ostriker statistically analyzed data on 40 observed pulsars, using a rotating, highly magnetized neutron star as their model for a pulsar. The derived information such as the birth rate of pulsars and their scale height from the galactic plane indicates that pulsars may be the remnants of Type I I supernovae, and tha t all Population I stars in the mass range 2 < M/M < 10 E> could be progenitors of pulsars. On the other hand, evolutionary models of stars calculated by ,. Paczynski show that stars in the mass range a carbon-oxygen core of a bout 1.4 M El 4 < M/Mi) < 10 all develop and converge onto a single -5evolutionary track. After this, the core may become dynamically unstable and collapse, or may ignite carbon explosively, leading to the type of supernova explosio.n suggested by Arnett (1969). At this stage, however, the unknown 12 c(a ,y) 16 o rate allows only speculation, for the further evolution of the star is critically dependent on the amount of 12 C remaining at the end of helium burning. If there is a large fraction of 0 12 c (12 c(a,y ) 16o rate low, small 2 a, F), a carbon detonation could be initiated by the and the star could explode. 12 12 C+ C reaction, Arnett (1969) and Wheeler et al. (1970) agree that if such a carbon detonation takes place, there would be no remnant, and thus no neutron star. enough large 12 0 C to initiate a 12 12 C+ On the other hand, if there is not C detonation ( 12 C(a,y) 16 0 rate high, 2 16 ) the core will continue to contract until 0 detonates; a,F ' however, such an 16 would obtain for a 0 detonation would occur at higher densities than 12 c detonation. At these higher densities, electron capture processes are very rapid, and the core of the star would implode rather than explode. The 12 C(a,y) 16 There would in this case be a remnant. 0 reaction rate is thus a critical factor in predicting the relative abundances of theory and in specifying the amount of 12 c and 16 0 from astrophysical 12 c left in the interior of an intermediate-mass star at the end of helium burning, a quantity which is of decisive importance in determining the further evolution of the star. The di s cussion thus far has been primarily concerned with helium burning in the core of a star. An interesting phenomenon, which is perhaps related to helium burning in a shell outside the core, is -6the abnormally high carbon content of the atmospheres of certain very luminous, high ly-evolved stars, called carbon stars. Such carbon abundances are measured by observations of molecular bands of carboncontaining molecules such as CN. A c arbon sta r is defined as a star in which the number ratio of carbon to o xygen in the atmosphere is greater than unity. can form. When this is true, c arbon molecules other t h an CO In terms of the mass fractions, the criterion is that be greater than 1.33 Xe>· system give Xe Since the measured abundances for the solar Xe= 0.4 x0 (Cameron 1968), it is thought that these stars were not formed as carbon stars, but that they have evolved to that stage. Such high carbon abundances may reflect the abundance of carbon in a helium-burning shell inside the star. The temperature and density of a helium-burning shell are different from those o f a helium-burning core (for a star of the same ma ss); the relative rat e 12 16 of tl1e C(a,y) 0 reaction may thus be smaller in the shell. 12 ratio of c to 160 at the end of helium burning in a shell will then be higher than that 1971). The characterizing core helium burning (Paczynski At this stage of evolution, a star of a few solar masses is expected to have a carbon-oxygen core where helium burning has been completed, a helium-burning shell, a n intershell zone of helium whe re hydrogen burning has been completed but helium burning has not yet begun, a hydrogen-burning shell, and an envelope made up mo s tly of hydrogen. If the c a rbon content of the envelo p e is to b e des cribe d in terms of the carbon content of the helium-burning shell, there must be derived some mechanism for convective mixing between the two zones. -7A star in the red giant stage has a deep convective envelope; however, this convective zone will never reach into the hydrogen-burning shell. Schwarzschild and Harm (1967) and Weigert (1966) have found that during helium shell flashes, "convective tongues" may extend from the helium-burning shell to the intershell zone. After several flashes, the convective tongue can penetrate the hydrogen-burning shell. The intershell zone and the hydrogen-burning shell then contain carbon and oxygen. It now remains to find a mechanism for convective mixing of the hydrogen-burning shell and the convective region of the envelope. Smith and Sackmann (1972) have done so by considering the protons brought down from the hydrogen-burning shell to the carbon-enriched intershell zone. The energy release from the 12 C(p,y) 13N(e+ ,v) 13C reaction raises the temperature gradient to the extent that another convective tongue reaches from the hydrogen-burning shell to the convective region of the envelope. In order to calculate the amount of atmospheric carbon enrichment, it is necessary to know the ratio of 12c to 16 0 produced by the helium-burning shell. unknown rate of the 12 C(a,y) 16 Again, however, the 0 reaction limits one's ability to cal- culate the abundance ratio in the shell, and thus in the atmosphere. If the 12 C(a ,y) 160 rate were very small, so that 12 C would be the main product in the helium-burning shell, one helium flash in a 1 M would be more than adequate to produce a carbon star. ~ star Since there are probably several such flashes in a 1 M star, this theory predicts too e nfilch carbon enrichment if the 12 c(o.,y) 16o rate is very small. In the case of a 5 M star, it is more difficult to enrich the atmosphere Q with 12 c; the intershell mass is smaller, and the envelope is larger -8and thus contains a greater quantity of oxygen before mixing. theory will then predict too small an enrichment of 12 c(a,y) 16 o rate is very large. 12 The c if the There are, of course, many uncer- tainties in the astrophysical description of carbon stars. For example, the masses of observed carbon stars are, at best, very poorly known, and cannot be determined by simply observing the luminosities , since evolutionary tracks of stars of different masses tend to converge at this stage of evolution. 12 A knowledge of the C(a ,y) 16 0 rate will, therefore, impose a serious constraint on any theory of carbon star formation. B. Theoretical Description of the 16 0 Nucleus The dimensionless reduced-alpha-width a value b e tween 0 and 1. 0 2 a is expected to have Crudely speaking, it is a measure of the frac- tion of the time that the 7.12-MeV state of 16 0 looks like a 12 c nucleus plus an alpha particle. Because the 16 0 nucleus is one of the alpha-particle series nuclei, it might be expected that an alpha-particle, or c luster model, would describe the states of the nucleus well. However, such simple models have not been able to describe quantitatively even the low-lying state s in 16 0. A model which has had more success is one developed by Brown and Green (1965, 1966). They account for the low-lying odd-parity states by mixing a deformed odd-parity state, formed by excitation of three nucleons out of a deformed core, with a spherical shell-model state corresponding to a 1 particle - 1 hole excitation. In this picture the -97 .12-MeV state of 16 0 is predominantly 1 particle - 1 hole, whereas the 9.60-MeV state is predominantly 3 particle- 3 hole. Low-lying even- parity states are expressed as mixtures of a spherical shell-model ground state with deformed states formed by mixing 2 particle - 2 hole and 4 particle - 4 hole excitations out of a deformed core. Although it has had only moderate success at predicting transition probabilities, . 16 this model does well in predicting the energies of levels in 0 (with the proper choice of free parameters). Stephenson (1966) has used such a model to calculate He finds this quantity to be 0.08 ± 0.04, with the major uncertainty attributed to neglect of coupling to hi ghe r-energy configurations. c. Previous Attempts to Determine 0 ~~~~~~~~~~-~~~~~~~~~---.a 2 (7.12-Mev , 16 0) There have been many previous attempts to measure the alpha 16 width of the 7.12-MeV state of Loebenstein et al. 0; the results have varied widely. (1967) measured th e angular distributions 6 of deuterons from the reaction Li( 12 C,d) 16 0, hoping to measure by observing the transfer of an alpha particle from MeV state in 16 0. 6 0 2 a Li into the 7 . 12- However, it was found that the reaction proceeded not only by this direct process, but also through formation of a compound nucleus. The compound nuclear contribution was estimated theoretically and found to be, for the ener gies studied, two- thirds or more of the total cross section for the reaction leading to the 7.12-MeV state. Their result , 0.06 < 0 - 2 a ~ 0.14 , does not include any uncer- tainty in the theoretical estimate of the c ompound nuclear cont ribution -10to the cross section. Puhlhofer et al. (1970) attempted a similar measurement. measured triton angular distributions from the reaction 12 They c( 7Li,t) 16 o. This reaction was expected by the authors to proceed more strongly by . 6 12 16 direct reaction than the Li( C,d) 0 reaction studied by Loebenstein et al. The compound nuclear part of the cross section extracted for the case of the 7.12-MeV state was still high--about 50% of the total cross section. It was again necessary to subtract the compound contribution in order to find ea2 . ea 2 = O. 025, uncertain by a The result given is factor of 1.5 or 2, although this factor may well be mucll larger since the theoretical framework employed by Piihlhofer e t al. could not be applie d to the unbound states of 16 ea2 is already known. 0 for which ea 2 An attempt has been made to obtain fit to the p-wav e phase shifts for 12 by a multilevel R-matrix C+a. elastic scattering (Clark 1969). However, the present data are not accurate e nough at low energies to put useful limits on the value of ea2 , as our own analysis shows c learly . 16 16 . Tne alpha spectrum following the beta decay of N to 0 (Hattig 1969) has been fitted by Werntz (1971) and Barker (1971), in attempts to see interference between the tail of the 9.60-MeV state in 16 0 and the t a il of the 7.12-MeV state. Barker considered contribu- tions of 6 levels (three 1- and three 3-) to the spectrum. the p-wave and f-wave 12 He fitted C+a elastic scattering phase shifts, each with a 3-level R-matrix formula, in order to determine some of the parameters required for a description of the alpha spectrum . the 16 From a fit to N alpha spectrum, he determined that the interference in the case is destructive between levels and that e 2 a 16 N is in the range 0.06 -11to 0.24. Werntz considered only three 1 eters were constrained by the 1 tering and by known ft one of which is 0 2 a resulting range for levels. phase shifts of Some of the param12 values for the beta decay. c+o. elastic scatTwo parameters, , were varied to fit the alpha spectrum. 0 2 a is 0.013 to 0.105. The Barnes and Fowler (1970) have also investigated the implications of the measured a-spectrum from 16 N beta decay. They found that the interference between the 7.12-MeV and 9.60-MeV levels is destructive in the 0 2 (7.12) is not negligibly small. a 16 N case, and that This result is confirmed by the more detailed analyses of Werntz and Barker. The most direct way to obtain the astrophysical rate of the 12 c(a,y) 16 o reaction, is to measure the cross section for that reaction to as low an alpha energy as possible. 12 C(a ,y) 16 Early measurements of the 0 cross section did not extend low enough in energy that a reliable estimate of the rate at a few hundred keV could be made. Larson and Spear (Larson 1964, Larson 1965) measured the gamma-ray yield with a Nal(Tt) detector, and found the cross section at Ea.(c.m.)= 2.4 MeV (at the peak of the resonance corresponding to the 9.60-MeV state in 16 O) to be about 36 nb. Adams et al. (1968) introduced the time-of-flight technique to suppress the background of neutrons from the 13 c(a,n)l6o reaction; they found a"' 10 nb at Ea.(c.m.) = 2.0 MeV. Ewen (1970) used an NE226 non-hydrogenous liquid scintillator to suppre ss neutron background; he obtained 2.4 MeV. Jaszczak et al. a = 120 ± 80 nb at E (c.m.) a (1970, 1970a), by a method similar to the one described in this work, have measured the cross section down to a c.m. alpha energy of 1.4 MeV, but the statistical errors are so large -12that the extrapolated cross section for astrophysically interesting energies is still highly uncertain (Weisser 1970). In addition, the energy dependence of the cross sections measured by Jaszczak et al. is not in agreement with the work reported in this thesis. Since an extrapolation to stellar energies is involved, any error in the energy dependence is greatly amplified in the extrapolation. D. Since the Scheme of the Present Experiment 12 C(a,y) 16 0 cross section at c.m. alpha energies 8 near 300 keV is expected to be of the order of 10- nanobarns, it is not possible to measure the yield directly known method. in the laboratory by any The best that can be done is to measure the cross sec- tion over a wide range of energies which extends as low as possible, and to extrapolate to astrophysically important energies. Figure 1 shows an energy level diagram of the (Ajzenberg-Selove 1971). 16 0 nucleus The states which are of immediate interest in this work are the 7.12-MeV state and the 9.60-MeV state, both of which have 1 spin and parity. a broad resonance in the 9. 60 MeV in 16 Selove 1971). At a c.m. alpha energy of 2.4 MeV , the re is 12 C(a,y) 16 0 reaction due to the state at O, which has a c.m. width of 510 ± 60 keV (Aj zenberg- The 7.12-MeV state is 42 keV below the so that this state can affect the 12 C(a,y) 16 tail of the state, which extends above the 12 C+a threshold, 0 rate only through the 12 C+a threshold. The extent to which the t ail contributes to the cross section depends on the dimensionless reduced a lpha-width of the 7.12-MeV state: 0 2 a The strategy of the present experiment is to measure the yield -13of gamma rays for a range of alpha energies which extends above and below the resonance corresponding to the 9.60-MeV state in 16 O, and which reaches as far below this resonance as it is feasible to measure. Interference of the tail of the 7.12-MeV state in 16 0 with that of the 9.60-MeV state will cause the shape of the measured excitation function to depart from that due to a single resonance plus possible interference from the tails of higher energy states. If the interference between the 7.12- and 9.60-MeV states is constructive, the yield below the resonance due to the 9.60-MeV state will be larger than that which would be expected if 0 2 Cl were zero. If the interference is destruc- tive, the yield will be smaller, and it will be more difficult experimentally to obtain a value for the alpha width. Because the gamma-ray detection system does not cover the e ntire solid angle, it is necessary, in order to determine the total cross section, to know the angular distribution of the gamma rays at each energy. Furthermore, since most tneories which will be used to parameterize the data will consider only the 1 contributions to the cross sections, a knowledge of the angular distributions at various alpha energies will be required in order to determine the relative magnitudes of contributions from other angular momenta. It was originally expected that the angular distributions below c.m. alpha energies of ~3MeV would be of a pure 2 sin e form, charac- teristic of electric dipole radiation distributions with spinless nuclei in the incident channel. However, measurements made with one detector at 45° and one at 135° showed quite early in the experiment that the angular distribution at E (c.m.) = 2.4 MeV Cl is asymmetrical -14about 90°. This asymmetry indicates interference between states of different parity and has been attributed to the interference of the 2+ direct radiative capture process with the 1- resonant process. Another process which requires investigation is that of cascade radiative decay of the 9.60-MeV state in 16 0. This process is not expected to be important at astrophysically interesting energies (see Appendix B). However, the experimental configuration for measuring transitions to the ground state at higher alpha energies is such that cascades are not always separated from ground state transitions. Therefore a correction should be made to allow for them. There are many other resonant and direct capture processes which are allowed by conservation of angular momentum. transitions is believed to be competitive with 1 2 None of these resonant capture or + direct capture to the ground state of 160, but a few warrant fur- ther thought. Appendix B. A further discussion of this question is given in -15II. EXPERIMENTAL METHOD A. Introduction The basic components of the experimental configuration are: (1) a bunched and chopped beam of energetic alpha particles, (2) an enriched 12 C target, (3) two large NaI(T£) crystals for detection of outgoing gamma rays and (4) the electronic circuits for sorting pulses from the Na! detectors. The principal difficulties involved in measuring the 12 c(a,y) 16 o cross sections at c.m. alpha energies below 3 MeV are low yield (total cross sections of the order of nanobarns) and h i gh background. There are two types of background. The first type, called time-independent, consists of events which are not correlated in time witn the incidence of the beam on the target; these events may be caused by cosmic rays, by pile-up of low-energy gamma rays from radioactive elements in the target area, or by neutrons produced at various points along the path of the beam which have been scattered around tne target area one or more times. (These neutrons, many of which are produced in the target, will be termed "delayed" neutrons.) The second type of background, called time-dependent, consists of events which are correlated in time with the incidence of the beam on the target. These are events caused by the interaction of an incident alpha particle with some nucleus in the target (or very close to it) followed by immediate detection of a product particle. The primary source of this second type of background is the interaction of the alpha particles with the 13 c contaminant in the target, by the -1613 C(a,n) 16 . 0 reaction. This reaction produces neutrons (of about 4 MeV for the range of alpha energies considered here) which sometimes produce pulses in the detection system indistinguishable from those of 9-MeV gamma rays. (These neutrons will be termed "prompt" neutrons.) The experimental configuration described below is thus designed to allow separation of 12 C(a,y) 16 0 events from most background events, and to facilitate subtraction in the multichannel analyzer spectrum of that background which is not totally separated. The most important technique employed is the time-of-flight method for suppression of prompt-neutron and time-independent background. The first of the following sections will describe the experimental configuration for measuring the yield at 90 alpha energies. 0 for a range of Following this is a discussion of the modifications required for measurements of angular distributions and cascade radiation. Yields at 90° have been measured with beams from two different accelerators: the ONR-CIT tandem and the 3 MV generator. ferences in experimental configuration will be noted. Slight dif- Only data measured with the use of the tandem accelerator have been included in the analysis of this thesis, since the data needed for normalization of the yields obtained with the 3 MV generator have not yet been measured. The preliminary 3 MV generator data appear to be consistent with the tandem accelerator measurements; the statistical errors are not significantly smaller because of the large b a ckground from delayed neutrons which was encountered. Meas urements with the 3 MV g e nerator are continuing, and steps are being taken to reduce the neutron backg round. -17The derivation of the "thin-target" alpha energies quoted for the 12 C(a,y) 16 0 measurements is given in Section III.B. The range of energies considered extends up to the region where contributions to the cross s e ction from the resonance due to the 4 + , 10.34-MeV state in 16 0 become significant. The region of the narrow resonance at = 2.69 MeV corresponding to the 2+, 9.85-MeV state in 160, is E (c.m.) a excluded. B. 1. Targets: Measurements of Yield at 8 90° Preparation and Thickness Measurements It is clearly desirable to have as little the target. 13 Amorphous carbon, enriched to 99 . 945% from the Oak Ridge National Laboratory . C as possible in 12 c, was obtained This carbon was converted to carbon dioxide and then to methyl iodide by Dr. Eileen Hess of DHOM Products Ltd. A 3-mil thick, 1-cm by 8-cm tantalum strip was mounted inside a small pyrex tube, with stainless steel end caps sealed by Viton 0-rings, in such a way that an electric current could be passed through the strip (Figure 2) . The interior of the pyrex tube was evacuated and the methyl iodide was a dmitted to a pressure of 3 cm Hg. 0 When the strip was he a ted to a temperature of about 700 C, the methyl iodide decomposed; a layer of elemental c a rbon was deposited on the strip, and hydrogen and iodine remained as gas e s. was left on for about 2 minutes. Then the hydrogen and iodine were pumped out and the process was repeated. required to make a carbon layer 180 µg/cm strip. The he a ting current About 12 depositions were 2 thick at the center of the The e fficiency for conversion of methyl iodide to eleme ntal c a rbon on the targ et was about 10%. The final 13 c content of the -18targets was about 0.1%. From this 8-cm strip, several targets could be cut, each 1 cm square. These squares were mounted in the back of a rectangular Faraday cup of dimensions 1 cm by 1 cm by 2.5 cm long. In the case of the experimental arrangement on the tandem accelerator, this cup was made entirely of 5-mil tantalum. However, because of the greater amount of heat generated by the higher-intensity beam of the 3 MV generator, it was necessary in this case to clamp the target and Ta backing between two pieces of copper. bolted directly to the The copper pieces were then copper target rod, and cooling was applied to the other end of the target rod by means of air blowing across attached fins. Even with these added precautions, blistering of the carbon layer remains a serious problem. A strip of natural carbon, of approximately the same thickness 12 as the enriched C, was deposited on a Ta backing by the same process of methyl iodide cracking. This target was used for background meas- urements (see Section II.B.6). The thicknesses of these targets were determined by measuring tl1e width, due to proton energy loss in the target, of the very sharp resonance in the The enriched 12 13 C(p,y) 14 N reaction at Ep(lab) = 1.75 MeV (Figure 3). c targets used had thicknesses between 155 and 191 µg/cm 2; 2 the natural carbon targets, between 133 and 177 µg/cm . of alpha energies used in the 12 12 C(a,y) 16 For the range 0 measurements, the enriched C target thicknesses correspond to a loss in incident beam energy of approximately 200 keV. -19All targets used in the measurements reported here were cut from the same tantalum strip. It is important to investigate the effect of any target impurities. Thus far, this has been done experimentally only for 19 F (see Appendix E). 2. If the enriched 12 Target Chamber c target were placed in a typical target chamber using rubber 0-ring seals and oil diffusion pumps, and if the target were bombarded with a beam of high enough int e nsity to heat the target, tnen a layer of natural carbon (containing 1.1% build up on the target surface in a few hours. 13 c) would This natural carbon layer is produced when hydrocarbons in the vacuum system are cracked by the hot target. In order to prevent this, the target chamber was construc ted of stainless steel and was sealed by copper gaskets. ion pump near the target kept the pressure below 5 x 10 -7 torr. An The target chamber was isolated from the rubber 0-rings and diffusion pumps on the upstream por t ions of the beam pipe by a liquid-nitrogen cold trap. Thus, most hydrocarbon vapors were condensed before reach- ing the target chamber. With this system, the target could be bombarded by a beam of several hundred nanoamps for times accumulating to many weeks with no significant deposition of natural carbon on the target. (The long- term carbon deposition of higher-intensity beams has not yet b e en determined.) -20The target chamber for measurements at 90° consisted of a cross of 1.5" O.D. tubing of wall thickness 1/16" (Figure 4). Down- stream from the target position was placed a piece of quartz on which the beam could be viewed. (When a target was placed in the path of the beam, no beam was able to reach the quartz.) mounted in the transverse arms of the cross. Two targets were The copper rods support- ing the targets were mounted on bellows to avoid 0-rings. Compression of one or the other of the bellows placed the corresponding target in the path of the beam. Of the two targets, one was an enriched 12 C target, and the other was a natural carbon target used for background measurements (see Section II .B.6). It is necessary to avoid collimation or obstruction of the beam too near the targe t (see Section II.B.4). The collimation closest in position to the target was 75 cm away, at the entrance of the beam to the cold trap. At this point, a c ircular, 0.8-cm-diameter tantalum collimator was placed, in order to keep the beam from hitting the 1. 0-cm-diameter beam tube leading through the cold trap. The chamber was mounted on the south 20° b eam line in the t a ndem accelerator target area, and on the 0 0 beam line in the 3 MV generator target area. J. Nal(Tt) Detection System; Efficiency Gamma rays were detected by two 20.J-cm-diameter by 12.7-cmlong Nal(Tt) crystals. Scintillations in the crystals were monitored with 13.3-cm-diameter RCA type 4522 14-stage photomultiplier tubes, one mounted on each crystal . This type of tub e was chosen for its fast timing capabilities (see Section II.B.4) and good pulse height -21resolution. Sodium iodide was chosen because of its high efficiency for detection of high energy gamma rays. The energy resolution of this system, as measured by the 662-keV line of 137 cs, is 9.6% for one detector (serial no. ED98) and 10.8% for the other (serial no. ED97). The crystals were shielded with both lead and paraffin to reduce background yield. Approximately 5 cm of lead was placed around the crystals to suppress events caused by cosmic rays or natural radioactivity in the walls of the room. In the case of the measure- ments made at 90°, 8 or 9 cm of lithium carbonate suspended in paraffin wa.x was placed between the target and each crystal. shield reduced the prompt neutron background from the reaction by about 40%. This 13 C(a,n) 160 The attenuation of 9-MeV gamma rays (of the order of 20%) was taken into account. Because of the much higher delayed-neutron backgrounds encountered when using the beam from the 3 MV generator, the crystals were in this case surrounded by 10 cm of borated paraffin placed outside the lead shielding. These shields were constructed of 15% by weight anhydrous boric acid suspended in paraffin, and were surrounded on all sides with polyester plastic to add strength to the struct ure. The total efficiency for detection of gamma rays with this system is the product of the following factors: (1) the absorption of gamma rays in the Nal(Ti) crystals for the particular geometry involved (given the angular distribution of the gamma rays), (2) the spectrum fraction: that fraction of absorbed gamma rays which is recorded in the portion of the spectrum from which the yield is extr acted, and (3) the tram;mission of gamma rays through any material -22which lies between the target and crystals. Whereas the final value for the 12 0 2 Cl which is to be extracted from c(a,y) 16 o data is approximately linearly sensitive to the abso- lute scale of the cross sections (see Section III.E), it is much more sensitive to the variation with energy of the cross section, since an attempt is being made to see a small interference effect. It is there- fore very important to include, for all of the above factors, their variation with gannna-ray energy. The efficiency was calculated by the method of Lazar et al. (1956), which requires integration of the absorption over all gamma-ray paths through the crystal and through the absorbing material between the crystal and target. Measured standard spectra are then used to obtain the spectrum fraction. For a detector in the form of a right circular cylinder, the required integrals are of the form: -µ Q, ( 0 I ) J 11 =f P(cos0')e n crystal n -µ Q_ (0 I ) (1-e 22 )sinEJ'd0', where 0' P (cos 0') n angle of gamma ray with respect to axis of detector, Legendre polynomial, order n , linear attenuation coefficient for a gamma ray in the absorbing material between the crystal and target, Q,l (8') gamma-ray path length in the absorbing material between the crystal and target, linear attenuation coefficient for a gamma ray in Nal(T £ ), gamma-ray path length in Nal(TQ,) • These integrals were evaluated for each gamma-ray energy and for n ranging from 0 to 4, in order to take into account the interference of -231 - the + contributions in the angular distributions of gamma rays from and 2 12 C(a,y) 16 0 reaction (computer code RWKJL was used for the numeri- cal integration). The attenuation coefficients functions of the gamma-ray energy. by Grodstein (1957). µ 1 and The values for µ 2 are are tabulated Coefficients for intermedia te values of the tabulated energies were found by linear interpolation. (For the range of energies corresponding to ground state transitions in 16 0 for this experiment, this interpolation is between coefficients tabulated at 8 , 10, and 15 MeV.) The values of µ 1 for the paraffin shielding which contained lithium carbonate were calculated from the measured density of the shielding and of pure paraffin, and with the cross sections for Coillpton scattering and pair production for the elements H, Be, C and 0 (Grodstein 1957). An experimental check of this calculation of µ 1 was made by measuring the yield of 9.17-MeV gamma rays from the reac- . tion 13 C(p,y) 14 N at E (lab)= 1.75 MeV, with and without the paraffin p shielding between the crystal and target. transmissions agreed within 1%. The calculate d and measured There was a small amount of attenua- tion of gamma rays in the stainless steel wall of the target chamber and in the stainless steel housing of the Nal(TJI.) crystal. These attenuations were calculated using the linear attenuation coefficients for iron (Grodstein 1957). For an angular distribution of the form W(8) = L a n Pn (cos 8) , n where 0 is the polar angle, the efficiency for detection of events over the entire solid angle of the detector is given by the product of -24the spectrum fraction and the quantity J 8 where a o \ 2 L n J aon J no p n (cos 8 d) , is the polar angle of the detector axis with respect to the d beam direction. When the 12 c(a,y) 16 o yields were extracted from multichannel analyzer spectra, the counts were added over a region extending from 0.8E The actual pulse height spectrum for a 9-MeV gamma to y ray extends to zero pulse height, because of Compton scattering, but the shape at lower energies is obscured because of the large number of low-energy background counts. It is therefore necessary to find the fraction of the counts recorded in the interval 0.8E to y this For purpose standard spectra were measured for gamma rays of three different energies: (1) 6.13 MeV, from the E (lab) p 340 keV, E (lab) p 1.75 MeV, and at l.lE y E (lab) p (2) 9.17 MeV, from the = 163 keV. 19 13 F(p, ay) C(p,y) 16 0 reaction at 14 N reac·tion at 11B(p,y) 12 C reaction (3) 11.67 MeV, from the The 9.17-MeV gamma-ray spectrum is shown in Figure 5. In order to compute the spectrum fraction from these data, it is necessary to know the number of counts in the channel corresponding to zero pulse height. This quantity was calculated by the method of Zerby and Moran (1961), who note that only photons which scatter straight ahead once and then escape, contribute to counts in the zero pulse height channel . The cross section for such an interaction can be calculated from the differential Klein-Nishina formula. After s um- mation over the volume of the crystal, a formula is obtained for f 0 , -25the fraction of the spectrum in the channel corresponding to near-zero pulse height: f (2rrr 0 2 0 2 2 m c E - ) ni (8' )e 0 y 2 -µ Q, (8') 2 2 sin 8 'd8', crystal where LiE energy width of the zero pulse height channel, E y gamma-ray energy, r classical electron radius, ru c 0 2 0 D electron rest mass 1 electron density in Nal (TQ,) , and tne remaining quantities are defined as in the preceding formula for J n The computer code NTOT was then used to calculate the spectrum fraction. of f 0 The input was the spectrum, the ganuna-ray energy, the value , the energy calibration for the spectrum, and two points on the spectrum in the region just below 0.8E If there was cascade y radiation in the spectrum, these two points were obtained by drawing a smooth curve underneath the cascade radiation. The code fitted a parabola through these two points and through the measured point at 0.8E y Below this region, a straight line extrapolation was made. An iterative procedure was used to vary the number of counts in the zero pulse height channel until the fraction found in that channel. f 0 of the total spectrum was The spectrum fraction is the ratio of the number of measured counts in the region from 0.8E y to l.lE y to the total number of counts, obtained by adding counts in the linear, parabolic, and measured regions. The results obtained for the three -26spectra were as follows: Spectrum Fraction 6.13 MeV 66% 9.17 MeV 65% 11.67 MeV 63% S pee t rum f rac ti ons f or eac h gamma-ray energy for the 12c(~ ,y)16 0 reaction were calculated by linear interpolation between these three values. An experimental check of the calculated detection efficiencies was made by measuring the absolute efficiency for E y = 6.13 MeV, and the ratio of the efficiency at 11.67 MeV to that at 4.44 MeV. The measurement at E y = 6.13 MeV was made by comparing the 19 yield of 6.13-MeV gamma rays from the F(p,ay) 16 o reaction at E (lab) = 340 keV with the yield of the corresponding alpha particles. p The gamma-ray and alpha-particle yields were measured simultaneously. For this reaction at E (lab) p = 340 keV, the angular distributions of gamma rays and alpha particles are isotropic. The efficiency of the solid state counter used to detect alpha particles was therefore determined simply by the solid angle subtended by the collimator in front of the counter. The efficiency of the gamma-ray detection system is thus e: where Ny and Na y are counts and e: Y and e: a are efficiencies. The result of this efficiency measurement (accurate to about 3%) was within 6% of the calculated value. -27The ratio of 11.67 to 4.44 MeV efficiency was measured with the 11 B{p,y) 12 c reaction at pound nucleus state in E (lab) p 12 = 163 keV. At this energy, the com- c at 16.11 MeV is excited. This state decays primarily by cascading through the 4.44-MeV state, yielding simultaneously a 4.44- and a 11.67-MeV gamma ray. The efficiency ratio is thus The measured ratio (accurate to about 3%) was within 4% of the calculated value. 4. Time-of-Flight Technique The principal means of suppressing the background of prompt neutrons from the 13 C(a ,n) 16 0 reaction consisted of the recording, for each detected event, of the time between the incidence of the beam on the target and the detection of the event by a Nal (T,Q,) crystal. A gamma ray will take 0.3 nsec to travel 10 cm, while a 4-MeV neutron will take 3.7 nsec to go the same distance. Thus, e.g., for a dete c tor positioned 10 cm from the target, the difference in flight time from target to detector would be 3.4 nsec. and neutrons In order to separate ganuna rays with this configuration, the system mus t be capable of resolving times of less than 3 nsec. Two different accelerators were used for measurements of the 12 c(a,y) 16 o yield at 90°. Data in the c.m. alpha energy range of 1.72 to 2.94 MeV were taken with use of the ONR-CIT tandem accelerator. Chopping and bunc hing techniques were used to produce beam bursts approxima tely 1.5 n s ec wide a nd separated by 285 nsec (Dietrich 1964, McDonald 1970). The maximum beam intensity attainable was 300 nA. Preliminary -28data (the results of which are not reported in this thesis) for c.m. alpha energies from 1.64 MeV to 1.87 MeV, have been obtained with the 3 MV electrostatic generator, with a beam intensity of 2 µA. to 6 µA of beam was available.) (Up The beam from this machine was again bunched and chopped (the bunching was done inside the terminal rather than outside the tank as it was in the case of the tandem accelerator system); beam bursts were about 1.5 nsec wide and 93 nsec apart. The Nal(Ti) crystals were placed 10.76 to 13.30 cm from the target. In order to monitor the flight time of an outgoing neutron or gamma ray, it was necessary to have an electronic pulse representing the time that the beam pulse arrived at the target and another representing the time of detection of an event in one of the detectors. The time pulses from the detectors were obtained from the anodes of the photomultiplier tubes. These large negative pulses with rise- times of a few nanoseconds (about 2 volts in magnitude for a gamma-ray energy of 4 M.eV, with 2900 volts applied to the resistor chain of the photomultiplier tube) were fed through fast discriminators, and then into the start input of a time-to-amplitude converter. The time-reference pulses from the target were obtained by amplifying the signals of the beam bursts with a series of three fast, low-noise amplifiers, each having a gain of 8 and a rise-time of 1.2 nsec. These amplifiers were designed and built by Dr. H. B. Mak, on the basis of a circuit of Sherman et al. (1968). The output pulse of the third amplifier was passed through a fast discriminator; it was tt1en fed into the stop input of the time-to-amplitude converter. -29Use of a pulse coming directly from the target has distinct advantages compared to earlier experiments where the time-reference pulse was taken from the beam chopper. With the earlier system, it was not possible to change any of the high-energy focusing and steering, as this could change the beam flight-time from the chopper to the target. Furthermore, any drifts in these high-energy components would degrade the time resolution of the system. When the time-reference signal is derived directly from the target it is possible not only to refocus the beam during data accumulation periods (a quite necessary procedure for the long accumulation times required for 12 C(a ,y) 16 0 measurements), but also to change the energy of the beam, without changing the timing of the electronics. In order to take full advantage of this method of obtaining the time-reference pulses (i.e., from the target), it is necessary to have a reasonably large and steady beam. For time-averaged 4He+ beams of less than 100 nA, the output of the three fast amplifiers is not large enough to generate a reliable stop pulse. If the beam is unsteady, the time resolution will be degraded because pulses from a momentarily high beam will trigger the fast discriminator earlier than pulses from a momentarily low beam (a time-slewing effect). In order to check the operation of the target time-reference pulse, the output of the corresponding fast discriminator was scaled, and the number of counts was compared with the number of cycles of the chopping and bunching system oscillator, which determined the number of beam bursts in the same period. Whenever the time-averaged beam dropped below 100 nA, all elec- tronic circuits, including the current integration scaler, were -30automatically gated off. The two scalers counting stop pulses and oscillator cycles generally agreed within 0.2%. It is important to note that, since the crystals detect any gamma ray(s) arising from the beam burst on the target in a timewindow of only a few nanoseconds, much of the time-independent background is also suppressed by the time-of-flight technique. The overall time resolution which can be maintained over a period of many hours with this system is about 2.5 nsec, which is somewhat remarkable since Nal(Tt ) is usually considered to be a "slow" scintillator (l/e l ight-emission-time= 250 nsec). 5. Electronic Configuration The complete electronic configuration is shown in Figure 6. The linear signals, which indicate the energy deposited in the crystals, are taken from the ninth dynodes of tne p~otomultiplier tubes. The pulses from each detector are fed through a summing preamplifier and then into a linear amplifier. The summed outputs of the two fast discriminators receiving time pulses from the photomultiplier anodes and the output of the fast discriminator receiving time-reference pulses from the target, are fed into the start and stop inputs of the time-to-amplitude converter. The output of the time-to-amplitude converter is a linear signal, the magnitude of wnich indicates the difference in time between the arrival of the beam burst on target and the detection of an e vent by the crystals. Pile-up rejection is introduced to reduce background resulting from detection of two or more e vents of low energy which occur very -31closely in time. If two such events are separated by a time of a microsecond or less, the linear signals will sum to one larger signal. The resolving times for the fast discriminators, however, are much less, about 10 nanoseconds. Since the spectrum of events below 3 MeV is not of interest in this experiment, the lower levels on two fast discriminators are set to reject such events. Discriminator output pulses corresponding to energies greater than 3 MeV are stretched to form logic pulses which gate the linear pulses. Thus, for example, two 2-MeV pulses arriving 100 nsec apart would form a 4-MeV pulse in the linear network. However, this pulse would not pass through the linear gate, as there would be no logic pulse from the fast discriminator. The same logic pulses are used to reject coincidences between the two detectors, as a means of reducing cosmic-ray back ground. The amplified outputs of dynodes 10 are used only during setup time and between data-accumulation periods; these signals, kept separate for the two detectors, are converted into logic pulses which allow selection of pulses from one detector or the other for purposes of calibration of the energy scale. The output of the linear gate and the output of the time-toamplitude converter (properly delayed) are fed into a multichannel analy zer. A two-dimensional analyzer is used to store events in a 64 x 64-channel array. One axis corresponds to the energy of the event; the other, to the time of detection of an event, relative to the time that the beam burst arrives at the target. plot of such a spectrum. Figure 7 shows an isometric -326. Procedure for Collecting Data At the beginning of each set of measurements, the gains of the two detectors were matched, using an 241 Am/Be source (a compacted mix- ture of americium oxide with beryllium metal), which produces 4.44-MeV gamma rays from the reaction 9 Be(a,ny) 12 C occurring inside the source. In addition, it was necessary to adjust the lengths of the cables leading from the anodes of the two detectors, in order that the electronic pulse travel-time from the cathode of the photomultiplier tube to the input of the time-to-amplitude converter would be the same for both detectors. The 13 16 C(a,ny) 0 reaction, which produces 6.13-MeV gamma rays at lab alpha energies above 5.1 MeV, provided a convenient means of doing this when using the tandem accelerator. 3 MV generator, the 13 C(p,y) 14 . N reaction at (yielding 9.17-MeV gamma rays) was used. Ep (lab) When using the = 1.75 MeV This reaction was also used to calibrate the time scale, by moving the gamma-ray peak in the spectrum with a calibrated delay cable. The time resolution of the system was checked at this time. Before (and usually after) measuring the 12 C(a,y) 16 0 cross section at one or more energies, a data point was measured at E (c.m.) a = 2.42 MeV normalization. when using the tandem accelerator, for purposes of This procedure eliminated possible normalization errors between the measurements at different energies, which were made at different times and with slightly different experimental configurations. Thus, relative errors due to target thickness, beam current integration and positioning of the detectors were eliminated . -33The scheme for normalization of data measured with the use of the 3 MV generator is to measure the yield at each set of measurements . E (c.m.) = 2.18 MeV a for At the time that the measurements of four data points (at c.m. alpha energies of 1.87, 1.80, 1.72 and 1.64 MeV) were made, it was not possible to reach E (c.m.) = 2.18 MeV. a yield has been temporarily normalized to the yield of the reaction at E (lab)= 1.70 MeV. p can be normalized to the 12 C(a.,y ) At a later time this 16 0 yield at 12 12 The C(p,y) C(p,y) 13 N 13 N yield E (c.m.) = 2.18 MeV. a The results for these four measurements are not included in the analysis of this thesis. The check measurement at E (c.m.) = 2.42 MeV a also aided in identifying the region-of-interest of the two-dimensional spectrum (time vs. pulse height), a region otherwise not easily recognizable when making measurements at low alpha energies, because of the very small yield from 12 C(a.,y) 16 0. Since, in the two-dimensional spectrum, events due to prompt neutrons from the reaction 13 C(a,,n) 16 0 were not totally separated from events due to gamma rays from the reaction 12 C(a. ,y) 16 0, it was desirable to determine the time- and energy-dependence of the prompt-neutron background. A natural carbon target of approximately the same thickness as the enriched target used, and made by the same process, was placed in the target chamber. gies as the 12 C(a.,y) Measurements were made at the same incident ener16 0 measurements. In most cases, these backgrounds were measure d imme di ate 1 y b e f ore or a f ter t h e correspon di ng 12C(N,y)l6Q ~ measurement. -34Accumulated charge was measured with a BNI model 1000 current integrator. A +300V bias was placed in series with the current lead, to avoid loss of secondary electrons from the target. Checks made on the operation of the electronics included the following: (1) monitoring the gain of each detector periodically by noting the location of the 4.44-MeV gannna rays from an 241 Am/Be source, (2) monitoring scalers which recorded the number of logic pulses arising from four different modules of the pile-up and coincidence-rejection electronics, and (3) monitoring scalers which compared the number of stop pulses derived from the target with the number of cycles from the oscillator of the chopping and bunching system. 7. Extraction of Yields Analysis of the data consists of the following: (1) identifi- cation of a rectangular region of the two-dimensional spectrum corresponding to the time of arrival of gamma rays from the target and to the energy of the desired gamma rays (E y = 7.16+Ea (c.m.) in MeV), (2) addition of counts in that region and subtraction of those due to background, and (3) conversion of the yield to absolute cross section (see Section III .B). By means of radioactive sources, it was possible to calibrate the energy scale up to 4.44 MeV. Extrapolation of this calibration yielded a first estimate of the energy region of interest. By adding the counts in each time channel over this energy region, a time spectrum was produced, from which the time region corresponding to gamma rays could be identified. It was then possible to iterate: by adding -35counts in each energy channel over the identified time region, an energy spectrum of gamma rays was produced (Figure 8) from which a more accurate energy region of interest could be selected. (In the case of the lower a-energy data points, the 9-MeV gamma-ray peak could not be readily identified, and it was necessary to rely on the energy calibration from the normalizing run and from any other higher-energy runs taken at the same time.) Another summation over the proper energy range yielded the final time spectrum, from which the yield was extracted (Figure 9). The same sulIUilation was applied to the corresponding spec- trum obtained with a natural carbon target . The time-independent back- ground could be subtracted immediately from both time spectra. neutron background spectrum was then normalized to the matching the heights of the prompt neutron peaks. neutron background was subtracted from the represented gamma rays from the 12 12 12 The C spectrum by The resulting prompt C spectrum. c(a.,y) 16o reaction. The remainder It was necessary to iterate this subtraction procedure once, as there were, of course, some gamma rays from the trum from 12 12 C(a. ,y) 160 reaction in the background spec- C in the natural carbon target. The errors assigned to the yields were statistical, calculated from standard formulae for combining errors of quantities added and subtracted. An additional statisti- cal error was introduced when normalizing the yield to that at Ea. (c.m.) = 2.42 MeV. C. Measurements of Angular Distributions Angular distributions were measured on the north 10° beam line of the tandem accelerator. Gamma rays were detected with two 12.7-cm by 10.2-cm NaI(Ti ) crystals, placed 10.5 cm from the target, which were -36monitored with RCA type 4522 photomultiplier tubes. were surrounded with about 6 cm of lead. These crystals No paraffin shielding was used between the target and detectors. The target used was the same as that used for many of the 90° excitation function measurements. The target chamber was the same with the exception that the piece of beam tube surrounding the target (a cross in the case of the 90° measurements) was replaced by a tee, in order to provide a more symmetrical attenuation of the outgoing gamma rays. Also, the beam entrance to the tee was narrowed to allow 0 the detectors and shielding to reach backward angles up to 143 . With this tee, there was no longer a port at the downstream end by means of which to optically align the target with the beam. For this purpose of alignment there was constructed a copper-gasket-sealed flange, on which was mounted a piece of quartz to be placed in the path of the beam. This quartz could be viewed from the top by two prisms (forming a periscope). It was thus possible to line up the center of the chamber by viewing the beam on the quartz. removed and replaced by the target-holder. This flange was then The matching of positions of the target and quartz was done externally with the use of a telescope. The electronic configuration used for angular distribution measurements was basically the same as that used for the 90 function measurements. 0 excitation The pulses from the two detectors (which were generally at different angles with respect to the beam direction) were separated before being stored in the memory of the two-dimensional multichannel analyzer by means of a routing pulse originating at the -37tenth dynode of one of the photomultiplier tubes. The 4096 channels were used to store two separate 32(time) x 64(energy)-channe l twodimensional spectra. To insure that this system produced no artificial asymmetry between the two detectors, the = 6.5 MeV E (lab) a the 12 C(a ,y) 13 C(a ,ny ) 16 0 reactio n at was measured at 90° with each detector. In addition, 16 0 0 reaction at 90 was measured with each detector. The isotropic angular distribution of 8.06-MeV g amma rays from the reaction 13 C(p, y ) 14 Nat E p = 551 keV was measured with a natural carbon target to check the symmetry of the geometry and detector efficiencies. The yield was independent of angle, within the statistical accuracy of the data (about 3%); no correction to the 12 C(a ,y) 16 O data was warranted. As before, neutron background runs were taken wi t h a natural carbon target. With the exception of the measurement at Ea (c.m.) 2.83 MeV (in which case the yield of neutrons from the reaction 13 c(a,n) 16 o is small), these background measurements were made at all angles. Calibration of the energy scale was checked with the 4.44-MeV gamma rays from an 241 Am/Be source both before and after moving the detectors, since the presence of a magnet .on the ion pump created a non-uniform magnetic field, which caused a slight photomultiplier tube gain shift at backward angles (in spite of magnetic shielding around the magnet and around the photomultiplier tube). The procedure for extraction of yields from the two-dimensional spectra was identical to that used for the 90° excitation-function measurements. -38D. Measurements of Cascade Radiation Two different schemes were used in an attempt to measure the production of 16 0 through de-excitation of the 9.60-MeV state of 16 0 by gamma decay through a lower excited state. + In both schemes, only - cascades through the 6.92-MeV (2 ) or the 7.12-MeV (1 ) states were considered. In the first method the yield of 7-Me V gamma rays was extracted from the same were extracted. 12 C(a ,y) 16 0 spectra from which the 9-MeV yields The second method was a rearrangement of the experimen- tal configuration to look for coincidences in the detectors caused by cascading gamma rays. In all but the lower-energy 12 C(a,y) 16 0 spectra, a peak in the gamma-ray ener gy spectrum at 7 MeV could be observed (Figure 8), and the yields of the 7-MeV gamma rays were extracted in the same way as those of the 9-MeV gamma rays. The same energy calibration was used to determine the energy region-of-interest, and time spectra were computed by summing over this region. The corresponding spectra obtained with a natural carbon target were used to determine the shape of the prompt neutron background, as before. It was also necessary to subtract the yield of the lower-energy tail arising f roro the higher-energy groundstate transition. This was done by using the yields of the higher- energy gamma rays, the experimental 9.17-MeV line shape from the 13 C(p,y) 14 N reaction (see Section II.B.3), and a modification of the spectrum fraction code NTOT, in order to determine the fraction of total counts to be expected in the 7-MeV region. Only spectra obtained with the use of the tandem accelerator were analyzed for the 7-MeV gamma-ray yield. -39In order to look for coincidences in the detectors caused by two members of a cascade, a 1.6-cm-diameter glass target chamber and an enriched 12 C target were placed on the north 10 tandem accelerator. beam. 0 beam line of the The target was bombarded with about 1 µ A of D.C. The two 20.3-cm-diameter by 12.7-cm-long Nal(Tl) crystals were each placed 2.7 cm from the target. About 5 cm of lead shielding was placed around the crystals, and two cone-shaped lead shields were placed between the detectors to reduce background of genuine coincideuces from backscattering of photons from one crystal to the other. Two-dimensional spectra were accumulated with a multichannel analyzer. One axis represented the time between two detected events, one detected in each crystal. The second axis represented the energy of any pulse which occurred in coincidence with a pulse with an energy corresponding to the lower-energy gamma ray of the cascade (2.2 to 3.0 MeV, depending on the incident alpha energy). Yields were measured at c.m. alpha energies of 1.95, 2.18, 2.42, 2.56, and 2.80 MeV. Background measurements were made at the same energies with a natural carbon target. There was also a back- ground measurement made with the beam off. To check the proper operation of the coincidence configuration, a measurement was made at E (c.m.) a. in 16 = 3.18 MeV , on the resonance due to the 4 + state at 10.34 MeV 0, which cascades through the 6.92-MeV state. To extract yields from the two-dimensional spectra, the counts in each energy channel were added over the time region corresponding to real coincidences. A background from random coincidences was subtracte~ -40Such energy spectra were obtained for the enrichedand room-background measurements. 12 C, natural-C, The energy spectrum of the room- background measurement was subtracted from those of the enriched and natural-C targets according to accumulated time. 12 C The remaining energy spectra from the natural C target were normalized according to accumulated charge, reduced by a factor of 10 (the approximate ratio of 13 c in the natural C and enriched 12 c targets), and were then sub- tracted from the enriched- 12 C spectra. Unfortunately, because of the very poor counting statistics, no 7-MeV peaks could be observed in the resulting energy spectra. In order to extract an upper limit for the yield, counts were summed over a region corresponding to the expected 7-MeV peak. A background yield was extracted by summing over a region of equivalent size, half of the region being above and half below the 7-MeV region. The upper limit was taken as the greater of the follow- ing two quantities: this background. (1) the 7-MeV yield, and (2) the 7-MeV yield less -41- III. A. RESULTS Cascade Radiation The upper limits for the yield of coincidences, converted to absolute cross sections, are given in Table 1. The efficiency for detection of these coincidences was taken to be the product of the efficiencies for detecting each member of the cascade. J /2 o The factor was calculated as described in Section II.B.3 (the angular dis- tributions and the angular correlation were assumed to be isotropic for simplicity. This assumption is justified by the large solid angles subtended by the counters). The spectrum fraction for the 7-Me V gamma rays was taken from the measured spectrum of a 6.13-MeV ganuna ray (Section II.B.3), and the spectrum fraction for the lower-energy member of the cascade (for a 0.9E y to l.lEy region) was found by extrapolation of the 4.44-MeV spectrum fraction. The reduction in efficiency which occurs because cascades are not counted if both gamma rays go into the same detector was taken into account. The yields of 7-MeV gamma rays from the non-coincident measurements, converted to absolute cross sections (assuming an isotropic angular distribution), are also shown in Table 1. For the higher alpha energies, the cross section for production of 7-MeV gamma rays appears to be larger than the upper limit on the cross section for production of 7-MeV and ~2 -MeV gamma rays in coincidence. There are several factors which have not been taken into account in this analysis: the angular correlation, the angular distributions, the effect of possible cascades through the 6-MeV states in -4216 0. However, none of these factors can explain the large difference between the two sets of results at the higher alpha energie s. The d a ta seem to indicate that some of the 7-MeV gamma rays r e corded in the "singles" spectra are not in coincidence with a 'V2-MeV gamma ray, which suggests that some of the 7-MeV g amma rays c ome from impurities in the target. No attempt will be made to resolve this dilemma in the present work; more measurements of the cascade radiation are clearly needed . However, it is possible to obtain an upper limit to the yield of coincidences for the detector geometry used for the 90° measurements. If both memb e rs of the cascade are absorbed by the same detector, they may sum to form a pulse indistinguishable from that of a 9-MeV g amma ray. The analysis of the the ground state of 12 16 c(a ,y ) 16 o cross section for radiative capture to 0 is then affected. The detection of one member of the cascade in one dete ctor and the other member of the c a scade in the other detector may also produce a 9-MeV gamma ray pulse when the two pulses are added. (The 3-MeV discriminator leve l on the coincidence rejection circuit does not g ive rejection for coincidences which have a 2-MeV gamma ray as one member. It is only for the very highest alpha energies of the present work that cascade coincidence s will b e rejec t e d by this circuitry, since the lower-energy gamma ray of the cascade is then about 3 MeV . ) By taking into account the various efficiencies, it can be found that the efficiency for detection of coincidences for the 90° excitation-function geometry is about 6% of that for the geometry used -43for measuring coincidences. Thus the corrections to the 12 C(a,y) 16 0 cross sections for capture to the ground state are, at most, 6% of the cross sections given in Table 1. According to the coincidence measure- ments, the corrections would be less than 0.5 nb. If the 7-MeV yields from the singles spectra represent true cascade radiation yields, the corrections could be as large as 1.6 nb. Because of the small size of these corrections and because of the uncertainty in the interpretation of the cascade data, no attempt has been made to correct the 90° data at the present time. B. Conversion of Yield to Absolute Cross Section In Table 2 are listed the yields extracted from the spectra obtained at 90° and the absolute total cross sections obtained from these yields by assuming that the angular distributions are those of pure electric dipole tra nsitions . Corrections required by the electric quadrupole contributions will b e discussed in Sections III.C and III.D. The conversion from yield to absolute cross section requires a knowledge of the integrated charge, the target thickness (see Section II.B.l), and the efficiency of the detection system (see Section II.B.3). The product of these three factors cannot be specified with a precision better than 10%. However, because the yields are normalized to the yield at = 2.42 MeV, relative errors in the above factors are E (c.m.) a cancelled, and it is only the overall scale factor which is uncertain by 10%. The value of 8 2 a derived in the end is only (approximately) linearly dependent on such a scale factor (see Section III.E). -44The alpha energies at which the measurements are quoted were derived in the following way. As a first approximation for the effec- tive laboratory alpha energy, the incident laboratory energy minus half the energy loss in the target was calculated. The data were then fitted by the 3-level R-matrix code (see Appendix C). For each data point, the theoretical cross sections were averaged ove r an energy ranging from the incident laboratory energy to the incident energy minus the total energy loss in the target (using 10 keV steps). The laboratory alpha energy to be quoted for the data point was selected as the energy at which the theoretical cross section was equal to this average cross section. This effective energy was not in most cases different from the center-of-target energy by more than 10 keV. The derived laboratory alpha energy, when converted to c.m. energy, is the energy at which all 12 C(a ,y) 16 0 measurements are quoted in this thesis (unless specifically noted otherwise). c. Angular Distributions and Extraction of Figure 10 shows IA 2+_1_ the results of the yield analysis for the angu- lar distribution measurements. The quoted alpha energies were determined by the method described in Section 111.B. Differences between laboratory and c.m. angle were not considered; these differences are at most half of a degree in the present experiments. The angular distribution data are interpreted as arising from the interference of the 2+ direct capture process with the 1 capture process. resonant From the measured angular distributions it is desired -45to find the absolute magnitude of the ratio of the 2+ reaction amplitude (A +) to the 1 2 reaction amplitude (A _). 1 The angular distribu- tion which arises from the interference of these two contributions will have the shape, for spinless interacting nuclei, W( 8 ) where ¢ 12 is the phase difference between the two complex amplitudes and the functions Pn(cos 8) are Legendre polynomials. Each measured angular distribution was fitted with the above expression (corrected for the finite solid angle of the Nal(Tl) detec- IA2+1/IA1 _1, ¢12 , and a normalizing factor as free paramThe result was a value for IA2+1/IA1 _1 for each energy at tor), with eters. which an angular distribution was measure d. in Table 3. These values are displayed (Lack of sufficient statistical precision in the data pre- vented the determination of ¢12 .) Because the ratio of amplitudes was not always determined with high precision, and because angular distribution measurements were not possible at low ener gies, where the cross section is small, it is necessary to obtain a theoretical energy dependence for the 2+ intensity, in order to determine its contribution at those energies where angular distributions were not measured, and a t stellar energies . The measured energy dependence of IA2+/ A1 _I is consistent with that to be e xpected from direct E2 radiative capture, and this model h as -46been adopted for the 2+ amplitude. The theoretical cross section for direct radiative capture has been studied by Tombrello (1961). The differential cross section is given by Fermi's golden rule, where the matrix element for E2 capture is given by ~2 2 \' D (8 ) l KP y ,cpy x K where w , .k , and p y are the angular frequency, wave number, and state 2 of circular polarization of the gamma ray; D Kp element, and ey and gamma radiation. system. <Pi and and are the polar and azimuthal angles of the The charges and masses of the alpha particle and nucleus are tions ~y is a rotation matrix <Pf µ is the reduced mass. 12 C The func- are the initial and final wave functions of the Since the matrix element for direct capture is dominated by contributions from distances larger than the nuclear radius, the integral was evaluated by ignoring all contributions from the volume inside the nucleus. This approximation is valid as long as there are no nearby 2+ compound nucleus levels. (Measurements of the + 12 C(a,y) 16 section near the resonance due to the 2 , 9.85-MeV state in excluded here.) 0 cross 16 0 are The initial and final wave functions outside the nuclear volume can then be approximated as free and bound-state wave function!> of the Coulomb potential; no detailed knowledge of the internal wave functions is required. There remains one unknown parameter in the -47cross section: the amplitude of the final state wave function, i.e., 16 that of the ground state of O, at the nuclear surface. This magni- tude is related to the reduced-alpha-width of the ground state of 16 0. More detailed discussions of the derivation of the cross section and the numerical evaluation of the matrix element are given by Tombrello (1961) and Parker (1963). The quantity determined from Tombrello's formula is thus I A2 + 1 2 /ea 2 (g.s., 16O), where ea 2 (g.s., 160) the quantities urements. jA _j 1 2 2 2 IA2+1 /IA _1 1 is to be found by fitting obtained from angular distribution meas- This fitting was done by an iterative procedure, since was not known at the beginning. Its value was taken for the first iteration to be the total cross section obtained by neglecting 2+ contributions when deriving the total cross section from the yield at 90° (see Section III.B). jA +1 2 At the end of each iteration, the value of from that iteration and the value of IA _ 1 1 from the previous iteration could be used to calculate a better angular distribution, and thus a better total cross section. Subtraction of total cross section gave a new value for iterations, the value ea 2 (g. s., 16o) The final values of in Table 3. 2 2 from this • After several O. 043 ± O. 012 was obtained. jA +11IA _1 2 1 The calculated variation of jA _j 1 IA +1 2 obtained in this way are given IA +1 2 2 with alpha energy is shown in Figure 11; values for discrete energies are given in Table 4. The errors quoted for 0 2 a (g. s., 16 0). IA +1 2 2 arise entirely from the uncertainty in -48D. Electric Dipole Contributions to the Total Cross Sections The two me thods of parameterizing the data and extrapolating to lower energies which will be described (Appendices C and D) conside r only the El contributions to the total cross s e ction. The final numbers desired from the measurements are thus the quantities Once the yield at 90 0 (expressed in terms of an absolute quantity) and the magnitude of the E2 contribution to the total cross section are determined, it is possible to calculate ti ties jA _j 1 2 IA 1 are shown in Figure 12 and in Table 4. _!2 . The quan- The errors quoted come from the statistical errors in the yield (including that from normalization) and from the uncertainty in the quantity ea 2 (g.s., 16o) used in determining the value of Table 4 are the quantities (a= jA _1 1 2 2 + jA +i ). 2 2 jA2 +1 /IA1 -1 2 The quantities IA2+1 2 . Also given in and the total cross sections IA _1 1 2 and a are approxi- mately the same, except at the highest energ ies considered, since the E2 contribution becomes much smaller than the El contribution at low energies (Figure 13). E. Extrapolation to Lower Energies of the Electric Dipole Contributions The remaining problem is to determine the extent to which the El excitation function departs from that of a sing le resonance plus an interfering background from the tails of r e sonances corre sponding to higher states. One theoretical framework for carrying out the extrapolation is to make a 3-level ·R-matrix parameterization of the cross section (Weisser 1970). The three levels correspond to the 7.12-MeV state, -49- the 9.60-MeV state, and a fictitious state at 20 MeV, which represents the background from the tails of higher states. parameterization can be found in Appendix C. fits to the 12 c(a,y) 16 o data: eters are free to vary ( Ga 2 A description of this Figure 12 shows three (1) the best fit, in which three param- and the gamma widths of the 9.60-MeV and background states), (2) a fit in which Ga 2 is constrained to zero and the remaining two parameters are free to vary, and (3) a fit in which Ga 2 is constrained to 0.4 and the remaining two parameters are free to vary. Figure 14 shows the same data and the same fits to the data, expressed in terms of the S-factor instead of the total cross section. (S = aEe 2m1 • See Appendix A.) The S-factor gives t!le intrinsically "nuclear" dependence of the cross section, as distinct from the kinematic and barrier penetration factors. for the best fit is 1.4. The The S-factor at 2 Ga , F 2 X per degree of freedom E (c.m.) = 300 keV is found a lO is 0 • 14 +O. -0.08 , with stat is- 14 to be o . 20 +o. -0.12 . The result for ti cal errors only. The interference between the levels at 7.12 and 9.60 MeV is constructive. The value derived for G2 a lute value of the cross section. is not very sensitive to the absoIf all of the experimental data points are increased by 20% and fitted again by the 3-level R-matrix theory, G 2 a, F is increased by 24%. Another method of parameterizing the data for extrapolating to lower energies has been developed by Koonin and Tombrello (1972). Contributions from the bound state at 7.12 MeV in single-l~vel 16 0 are described by a pole; a potential is used to describe the contributions from the 9.60-MeV state, high-lying states and direct capture. A -50- description of this "hybrid" R-matrix-optical-model parameterization is given in Appendix D. requires In this case the fit to the the variation of only two parameters. 12 C(a ,y) 16 0 data Figure 15 shows two fits to the data: the best fit and a fit in which contributions from the bound state are omitted. in terms of the S-factor. Figure 16 shows the best fit expressed For the best fit, the X2 per degree of E (c.m.) 300 keV was found to be a +0.15 0.16_ . , which gives a value for 8 2 a,F of 0.11 ~:~~ , and the 0 10 freedom is 1. 3. The S-factor at interference was again found to be constructive between the levels. For comparison only, the data of Jaszczak et al. (1970,1970a) are shown in Figure 17, along with the 3-level R-matrix fit of the Caltech data. The two sets of measurements do not agree, for reasons which are not apparent. The 3-level R-matrix parameterization does not fit the Jaszczak data well; the Jaszczak data give a freedom of 8 and a range for The value for 8 2 a, F 12 C(a,y) 8 2 a,F 2 X per degree of extending from 0 to above 1. obtained from the present Caltech 16 . 0 data is in qualitative agreement with those values obtained by previous, less direct methods (see Sections I.Band I.C.) However, not enough data have been acquired yet at the lower alpha e nergies to determine the value of 8 2 a,F with high precision. It can be seen from Figure 14 that measurements with about 30% accuracy are required at E (c.m.) = 1.4 MeV (where the total cross section is expected to be a 2 approximately 0.3 nb) in order to obtain 8 with an uncertainty of a,F about 30%. -51IV. A. DISCUSSION Astrophysical Significance Although this experiment has not yet succeeded in placing very 2 narrow limits on the value of ea F • • it is o f interest to investigate 1 2c, a t the end of helium burnXC ' the mass fraction of 2 ing as determined by the presently achieved measurements of e a ,F the range of Arnett (1972), by considering the evolution of stars c omposed initially of pure helium in the mass range 2 < M /M < 100 , found a E> at the end of helium burning to decrease approximately linearly with increasing log M a. and log 2 Xe= 0.31- 0.667 log (M /M) - 0.267 log e a ~ a ,F Deinzer and Salpeter (1964) performed simila r calculations, and consiIn Figure 18, the mass fraction of dered lower masses as well. 12 c at the end of helium burning is shown as a function of the mass of the helium star for three different values of represents the 12 C(a , y ) 16 e 2 a ,F : the value which best 0 experimental data and the two values which are one standard deviation above and below the best value. of Xe for 2 < M /M a e < 100 are taken from the above formula of Arnett. The shape of the function for M /M e2 0.1 Deinzer and Salpeter for those of Arnett at M /M a a ,F e The values a 0 < 2 is obtained from the values of Their values are normalized to 2 (a 10% correction), and scaled with in the same way as those of Arnett--according to e2 a ,F 2 log e a F • ' The helium s tars of these calculations are thought to b e good representations of the helium cores of real stars, since the temperature -52and pressure at the hydrogen burning shell are small compared with those inside the core. masses M/M Arnett (1972) gives the following equivalent total corresponding to the core masses 0 M /M : a. 0 M/M Ma./M0 El 2 about 7 to 10 4 about 15 8 20 to 24 16 34 to 40 32 70 to 80 64 llO to 125 These values can be used to scale the abscissa of the plot of Figure 18 in terms of the total mass of the star. These values of 12 e(a.,y) 16o Xe emphasize the need to acquire better data in order to obtain a more precise value of For example, at M /M a. " = 2 , the range of Xe standard deviation of the best current value of e2 a., F which is within one e 2 a. , F extends from 0.2 to 0.7. B. 12 16 . The C (a.,y) 0 Expen.ment of the Future The improvement in the experimental configuration which would apparently produce the most rapid gain at the present stage of development, is the reduction of the amount of 13 c in the enriched 12 c target. This would reduce the number of prompt neutrons coming from the target, and thus allow the detectors to be get. placed a little closer to the tar- The solid angle would be increased and the error arising from background subtraction would then be decreased. Since the primary source of tirue-independent background with the 3-MV accelerator seems -53to be delayed neutrons due to the 13 c in the target, a considerable reduction of time-independent background would also result from reducing the target 13 C content. With the present method of making targets, it is found that a factor of two in isotopic purity is lost when converting the ORNL amorphous carbon to the final carbon target. 13 target with much lower following: (1) obtain 12 Thus in order to make a C content, it is necessary to do both of the C of higher isotopic purity, and (2) improve the target-making procedure in order to eliminate as far as possible the introduction of natural carbon. It is not clear where and when the natural carbon is being introduced during the present target-making procedure. It has been suggested by Dr. George Rossman that use of the reducing agent, lithium aluminum hydride, to convert co 2 to CH 3 0H in the chemical processing could introduce natural carbon, since the best commercially available LiAlH ates. 4 is known to be contaminated with carbon- The possibility of introducing natural carbon during the final stage of crackiu~ the methyl iodide could be largely eliminated by improving the methyl-iodide cracking chamber. Highly enriched 12 c, containing perhaps less than 1 part per 20,000 13 c, is shortly to be shipped to the Kellogg Radiation Laboratory from the Los Alamos National Laboratory. After some work devoted to improving the present target-making procedure, more data at lower alpha energies should be forthcoming. Use of only 2 µA out of the possible 6 µA or more of bunched and chopped beam available from the 3 MV generator was necessary to minimize blistering of the carbon on the target. With improvement of the -54target cooling, it might be possible to utilize more of the beam available from the 3 MV generator. If many targets were available, the bombarded target could be changed often, before damage from the beam became excessive. The large time-independent background due to delayed neutrons encountered on the 3 MV generator beam line is partly due to the proximity of the target and detectors to the accelerator and to the wall. With a major expenditure of effort, it might be possible to obtain a longer beam line in a different direction in the present target room. (With a still larger amount of effor t, it might be possible to move the wall!) With the introduction of a new high-intensity ion source currently being built by Dr. H. B. Mak for the tandem accelerator, it may be possible t o obtain large enough chopped and bunched beams from that generator. Because of the more spacious target area, there is less of a problem arising from the delayed return of neutrons originally produced at the target or along the beam line. When the limits of beam intensity and reduction of neutron background are reached, it might be possible to gain a small amount more by introducing anti-coincidence shielding in order to reduce cosmic-ray background. A worthwhile investigation would be an attempt to measure the 12 C(a,y) 16 0 yield by using a 12 C beam and a eliminate the n eutron background from the 13 4 He gas target. C(a,n) 16 tors could then be placed very close to the target. This would 0 reaction. Detec- Time-independent background could be a problem, but this could possibly be dealt with -55if a high-intensity chopped and bunched beam of 12 C could be obtained, and if the detectors could be shielded sufficiently. The main object of future measurements should obviously be to obtain measurements of the yield at lower alpha energies. It might also be possible to obtain the El contributions to the total cross section at slightly higher energies than those reported here. However, this would have to be done by making careful angular distribution measurements, since the 2+ direct capture process increases with increasing energy, and since the low-energy tail of the resonance at 3.18 MeV, due to the 4+ state at 10.34 MeV in dominant contribution to the cross section. 16 E (c.m.) a. 0, soon becomes the Measurement of the El con- tribution above this resonance, in addition to being rather difficult, may not be as useful as one might imagine because of the increasing contributions from the tails of resonances corresponding to the many higher 1- states in 16 0. For the sake of refinement of the understanding of the reaction mechanisms of the 12 C(a.,y) 16 . 0 reaction, it would be d esirable to have measurements of angular distributions at lower alpha energies. Further measurements of cascade radiation should be made, wi th a consideration of the 6-MeV states as well as the 7-MeV states. In order to obtain absolute confidence in measured cross sections in the range of tenths of nanobarns, it is necessary to know the content of any target impurity (in the carbon or in the tantalum backing) and to know the alpha-particle capture cross sections for all stable isotopes of the impurity element. nuclei need be considered. Because of Coulomb barrier effects, only light There are many light nuclei which are -56energetically capable of capturing an alpha particle and emitting gamma rays of 9 MeV energy or more. Thus far,_only the effect of 19 F has been investigated (Appendix E). Perhaps by the time all of these investigations are complete, large, high-efficiency, high-resolution germanium crystals will become available, and measurements of very small capture cross sections will become trivial. -57APPENDIX A Astrophysical Reaction Rate Formulae for the 12 C(a,y) 16 0 Reaction In this section we derive the formula for the rate of the 12 c(a,y) 0 2 a,F 16 o reaction in the interior of a star in terms of the quantity The derivation follows that of Fowler (1967) and Clayton (1968). The 12 C(a,y) 16 0 reaction rate per unit volume can be expressed in terms of the cross section, the flux of alpha particles, and the 12 number density of c nuclei given relative velocity alpha particles n a v nl2 c is the product of the number density of and the velocity of relative velocities The flux of alpha particles for a ¢(v) , where v • Since there is a spectrum J ¢(v)dv = 1 , it is necessary to integrate over all possible relative velocities. The reaction rate per unit volume is 00 P nan12 C J vcr(v) ¢(v)dv = nan12 C<crv> 0 The quantities na and n mass fractions Xa and Xe , the matter density number 12 c can be expressed in terms of the atomic p , and Avogadro's NA : n a pNAX /A a a (Superscripts "12" have been dropped.) Aa and AC are atomic masses. The reaction rate is now p Tue function ¢(v) , giving the distribution of relative velocities, is -58assumed to be the Maxwell-Boltzmann distribution, cf>(v)dv = where µ ( 2 ~kT) 3/2 is the reduced mass, k 2 2 expf-~~T) 4TTv dv is Boltzmann's constant, and T is the absolute temperature of the matter. For temperatures characteristic of helium burning, the average kinetic energies are orders of magnitude smaller than the Coulomb barrier between the particles. The particles with the best chance of penetrating the Coulomb barrier are those having the largest energy; however, because of the velocity distribution particles decreases with increasing energy. cf>(v), the number of such There is some effective interaction energy for which there is a maximum probability of interaction. This will be shown mathematically below. In order to evaluate the integral in the rate formula, it is necessary to know the cross section for the reaction. This cross sec- tion can be expressed as a product of three energy-dependent factors: (1) an exponential factor e -2nn which gives the probability of pene- tration through the Coulomb barrier, (2) a factor l/E which is characteristic of any quantum-mechanical interaction between two particles, and (3) a factor S(E) which depends on nuclear properties and is (hopefully) only weakly dependent on energy. o (E) We thus have = lli2.. E exp(-2nn) where and the quantities Z are atomic numbers. Since there are no -59resonances closer to the range of effective interaction energies for the 12 c(a,y) 16o reaction than the 7.12-MeV state, S(E) is approxi- mately constant within this range. Expressed in terms of center-of-mass energy, the integral becomes 00 8 1/2 <crv> -1/2) E S(E) exp ( - kT - bE dE (µTI) where 31.28 Z Z b a C 1 2 A / kev 112 , A The integrand is small for large values of E , because of the factor exp(-E/kT) , and is small for small values of tor 2 exp(-bE-l/ ). E , because of the fac- For intermediate values of E , the integrand has a maximum value, as noted above. An approximate value for the integral can be obtained by replacing S (E) with Seff , the value of the S-f actor at the energy E 0 for which the exponential factor has a maximum, and by replacing the exponential factor by a Gaussian function (the method of steepest descent). The effective interaction energy is given by E where T 9 0 (bkT /2) 213 0. 9226 T~/ 3 MeV is the temperature expressed in units of 10 peratures typical of helium burning (T ""2 x 10 The resulting rate is 8 0 K) , E 0 9 °K. For tem- is about 300 keV. -60- p = ·[ p 2 NA2 Since the major contribution to bound, 7.12-MeV state in 16 Seff comes from the tail of the O, the value o f Seff can be obtained approximately by extrapo lating a Briet-Wigner resonance shape into the positive-energy region (Fowler 1967): 2.67 x 10 r 6 (E + o where IE r 1)2 MeV-barns a.,F is the measured radiation width in MeV of the 7.12-MeV state and e 2 binding energy of the same state in MeV, 0 2 a ,F is the dimensionless reduced-alpha-width of that state. Inserting the values f 9 y = 62 x l0- MeV (Swann 1970) and JErl = 0.042 MeV (Ajzenberg-Selove 1971) gives 0.166 2 2 (E (MeV) + 0.042) ea,F MeV-barns 0 2 2 2 0.166 (0.9226T / 3 + 0.042) 0 MeV-barns . a ,F 9 Because there is some confusion in the definition of the dimensionless reduced-alpha-width of the 7.12-MeV state when the 12 C(a.,y) 16 0 measured cross sections are parameterized by multilevel formulae, the quantity 8 2 a. ,F is obtained by calculating the S-factor with the chosen parameterization at Ea (c.m.) = 300. keV, and then determining what -61value of 0a 2 would give that value of the 8-factor with the single- level formula given above. 0 2 a,F where 8 (0.342) _ 0 166 The quantity 0 2 a ,F 8(300 keV) 0.705 8(300 keV) is thus defined as 2 is expressed in units of MeV-barns . With this definition, the stellar reaction rate can be calculated in terms of the above simple formula for 8eff The final formula for the r e action r a t e per unit volume becomes where p has units of reactions cm -3 sec -1 -3 p , of g cm -62APPENDIX B Direct and Resonant Capture Processes in the 12 C(a,y) 16 O Reaction In the text of this thesis, it has been assumed that the primary contribution to the 12 C(a,y) 16 0 cross section at c.m. alpha energies of the order of 300 keV comes from the tail of the bound state at 7.12-MeV . in 160 , and that ground state transitions are the most important. Fur- thermore, when interpreting the cross sections measured in the region of the resonance corresponding to the 9.60-MeV state in 16 0, it has been assumed that the primary contribution to the cross section in this energy 16 range comes from the El resonant capture to the ground state of O. The interpretation of the data in this range has taken into consideration the resonant capture of alpha particles through the 1 9.60 MeV, the tails of higher 1 state at states and the tail of the 1 state at 7.12 MeV, and the E2 direct capture of alpha particles, all transitions being to the ground state of 16 O. In the case of the analysis by Koonin and Tombrello (1972; see Appendix D), the El extranuclear contribution is included. In the case of the R-matrix fit, El direct capture is partially included, since it would affect the empirically-determined parameters of the (fictitious) distant background state. There are many more processes, both resonant and direct, which are allowed by conservation of angular momentum and parity. momenta are listed in Table 5. Those of lowest angular The cross section for radiative capture is generally calculated from first order perturbation theory. This calculation requires integration over all of configuration space of the product of the final wave function (that of a bound state), the interaction Hamiltonian, and an initial wave function (that -63of a scattering state). That part of the interaction matrix element which comes from integration over the nuclear volume will be r eferred to as the resonant amplitude, whereas that part which comes from integration over the space outside the nuclear volume will be called the direct capture amplitude. The resonant and direct capture amplitudes for a given transition are, of course, coherent, since they are parts of the same matrix element. The division of the capture process into resonant and direct capture processes is somewhat arbitrary; however, such a division is useful, because the dependence on alpha energy i s quite different for the two parts, and it is sometimes possible to ignore one or the other in certain energy ranges . For a consideration of the relative magnitudes of the v arious direct and resonant capture processes, it is essential to consider both the astrophysical range of energies and the range of energ i es covered by the experimental measurements. It is first of al l neces- sary to determine the dominant mechanism at astrophysical energies; then, if the value of the cross section at these energies is to be detennined by extrapolation, that extrapolation must come from measurements of the same mechanism. If other processes contribute to the cross sections measured at higher energies, these must either be subtracted or taken into account in the parameterization. For a consideration of the magnitudes of the contributions of the various resonant and direct captures, it will be useful to compare the S-factors to the S-factor of the process believed to be dominant: the El capture to the ground state of 16 0. The S-factor for the astrophysical region, according to the analysis of this work, is -64S(300 keV,c.m.) ~ 0.06 to 0.3 MeV-barns. measured energy region range from S(3.0 MeV,c.m.) ~ 0.003 to The S-factors for the ~ S(l.8 MeV,c.m .) 0 .02 S(2.4 MeV,c.m.) ~ 0.07 MeV-barns. E 21+1 Resonant capture cross sections contain the factor where Ey and is the energy of the emitted gamma ray, and order of the multipole radiation. y 1 , is the For a given multipole order 1 the cross section for resonant capture leading to an excited state in 16 0 is smaller than that for resonant capture to the ground state by the factor Ees 21+1 [~) , where E gs is the gamma-ray energy of the con- es tinuum to excited state transition, and E gs is the gamma -ray energy of the continuum to ground state transition. (There are, of course, other energy dependent factors still to be considered.) For the astro- physically interes ting alpha energy of 300 keV (c.m.), and for the energy of the resonance corresponding to the 9.60-MeV state in E (c.m.) a 1 1 1 1 1 16 0, = 2.4 MeV, these factors are as fo llows: 21 1 excitation (E /E ) + (300 keV) energ;y (MeV) es gs 7 x 10- 3 6.05 6 x 10- 3 6 .13 4 x 10- 4 6 .92 1 x 10-4 7.12 2 6.05 2 6 .13 2 6.92 2 7.12 (E es /E gs ) 21 1 + ( 2 .4 MeV) 5 x 10- 2 2 5 x 102 x 10-2 4 2 x 102 x 10- 4 2 2 x 103 7 x 106 x 10- 3 6 2 x 107 2 x 10- 2 x 10-3 1 x 10-3 The smallness of the r at ios for Ea(c .m.) = 300 keV indica tes that cross sections for resonant captures to excited states are likely to be much smaller than those for captures to the ground state. The -65experimental configuration used for measuring the 12 C(a,y) 16 O cross section is not highly sensitive to the cascade radiation yield. Since the transition yields were extracted from the region of the full-energy peak in the pulse height spectrum (~9 MeV), cascade radiation contri- butes to the measured yield only when both members of the cascade are absorbed by the NaI(Tl) crystals and the energy deposited is sununed . The efficiency for detecting both members of the cascade is only 6% of that for detecting a single 9 - MeV ganuna ray (see Section III.A). effective ratios for E (c.m.) a = 2.4 MeV The are thus the product of the above listed ratios and the efficiency ratio 0.06. In the case of the direct capture process (Tombrello 1961), the factor E 2L+l also appears in the formula for the cross section, but y its effect is partially cancelled by the energy dependence of the radial integral. However, it is to be expected that the cross section for direct capture to an excited state is not much larger than that for direct capture to the ground state in the case of the 16 0 nucleus , since the reduced-alpha-widths of the excited states a r e not expected to be as much as 10 times larger than the reduced-alpha-width of the ground state. These widths have been measured by Loebenstein et al. (1967) and by Piihlhofer et al. (1970). width of the ground state of A value for the reduced- alpha- 16 0 has also been derived indirectly in the present work (see Section III.C). It is thus first of all important to consider the cross sections for capture 1 ea ding to t h e groun d state o f 16 0 ; i'f t h ese are f oun d to be small, then it is unlikely that the captures to excited states will be large. -66The EO transition from the s, p, or d plane-wave states is not expected to make a significant contribution to the cross section; it is believed that these transitions proceed primarily by pair emission. Neglect of pair emission is supported by the measurement of the lifetime of the 16 o+, 6.05-MeV s tate in 0 , which is found to be four orders of magnitude larger than the lifetimes of the 6.92- and 7.12MeV gannna-ray-emitting states (Ajzenberg-S e love 1971). Calculations have been performed for contributions to the groundstate gamma cross section from the tails of the following n a turalparity states in 16 0: 6.13 Me V 6 . 92 MeV 3 2+ 9.85 MeV 2+ 10.34 MeV 4+ 11.52 Me V 2+ 12.44 MeV 1- 13.09 MeV 1 - These cross sections were calculated with the use of a single-level formula which included the energy dependence of the gamma-ray and alpha widths and the level shift. The energy and width parame ters were taken from the compilation of Ajzenberg-Selove (1971). The S- factor for the tail of the 6.13-MeV state at 300 keV (c.m.) is MeV-barns, for gible. E ( c.m. ) a 1 2 8a (6.13-Mev, 6o) = 1; 10~ 7 this contribution is negli- The contribution for the 6 . 92-MeV state is 0.09 MeV-barns for = 300 kV e an d 8 2 a (6.92-Me v, 16 0) =1 . The reduce d-alpha- width of the 6.92-MeV state is expected to be somewha t smalle r than 1, although its value is highly uncertain. It is important to note that -67if the reduced-alpha-width of the 6.92-MeV state were 10 times larg e r than that of the 7.12-MeV state, then the contributions of the two states would be roughly equivalent at Ea(c.m.) = 300 keV. This is not very far outside the range of errors in the determination of the two reduced widths. Significant contributions to the cross section from the 9.85-MeV state are restricted to a very narrow range of alpha energies; this range has been omitted in the analysis of the 12 C(a,y) 16 0 cross section. Contributions from higher states consid- ered are not significant as long as the two higher 1 resonances interfere destructively in the region outside the two resonances. A separation of direct and resonant capture contributions of the p plane-wave initial state is not physically meaningful, since contributions to the inteLaction matrix element from the nuclear volume are significant at all energies under consideration, and the direct and resonant amplitudes are coherent. Werntz (1970) calculated the two El amplitudes for transition to the ground state and found the square of the magnitude of the extranuclear amplitude to be three orders of magnitude smaller than the square of the amplitude arising from the nuclear volume. Tombrello (1971) and Werntz (1970) have both considered the E2 capture to the ground state from the £ = 2 plane-wave state. This capture has been taken into account in extracting the El contribution to the cross section for the 2.4 MeV (c.m.) region (see Section III.C), and has been shown to be negligible in the 300 keV (c.m.) region (see Section III.D and Figure 13). Werntz considered in addition the inter- ference of this E2 direct capture with the resonant capture through the -682+, 9.85-MeV state in 16 0. Such an interference effect can extend well beyond the width of the resonance, and may be significant in the cases of the angular distributions measured at 2.83 MeV. = 2.56 and E (c.m.) a However, because the sign of the interfe rence is uncertain, this interference has not been taken into a c count in th e analysis of the experimental data. If more precise angula r distributions can be measured, it may be possible to determine the s ign of this interference; a more accurate analysis could then be made. From the analysis of Section III.D, the ratio of the E2 direct capture to t h e ground state, to the El resonant capture t o the ground state at Ea (c.m.) 2 300 keV is about 1 x 10- , which justifies the neglect of the E2 direct capture at astrophysical energies. 16 Of the direct captures to excited states in 0 fr om s and d plane-wave initial states, the one which i s mos t likely t o contribute significantly is that of the El capture to the 7.12-MeV state , from the s plane-wave initial state. Both Tombrello (1970) and We rntz (1970) considered this capture- Werntz found this cross section to be negligible. Tombrello finds the values MeV-barns and where p S(300 keV,c.m . ) S(2 • 4 MeV , cm) < 60p • • rv 2 ~ 200p 2 16 2 8a (7.12-MeV, o) 2 16 8 a (7.12-Mev, 0) MeV-barns, is the effective dipole moment of the system. The remaining problem is to determine the value of Devia tions from integral masses give a lowe r limit for 4 x10- 7 . Estimates of iso s pin mixing o f a into tne 7.12-MeV state give p 2 'V 4 10- . T = 1 p p 2 2 • of isospin c ompone nt Such an estimate is consis- tent with the dipole strength of the 7.12-MeV s t a te obtained from measurement of the radiative width (Swann 1970). This value for p 2 -69- would give the above S-factors negligible values. A consideration of typical dipole moments in other self-conjugate nuclei compared to typical dipole moments in non-self-conjugate nuclei suggests that might be between 10as high as 10 MeV state of -2 16 3 2 and 10- . In the unlikely event that p 2 p 2 were , then the S-factor for El direct capture to the 7.120 would be roughly equivalent to that for El capture to the ground state. It is more likely that the contribution is at least a few times smaller . Another direct capture cross section considered by Tombrello (1971) is that of E2 capture to the 6.92-MeV state, from the plane-wave state. s This S-f actor is expected to be three orders of magnitude smaller than that of El capture to the ground state. -70- APPENDIX C Three-Level R-Matrix Fit to the 12 C(a,y) 16 0 Data Weisser, Morgan and Thompson (1970) have parameterized the 12 c ( 16 . . f unction . (El co~tri. b utions . a,y ) 0 measure d excitation on 1 y ) wit h a 3-level R-matrix formula (Lane 1958). at 16 The three levels are located 0 excitation energies of 7 . 12 MeV, 9.60 MeV, and 20 MeV (the lat- ter is a fictitious level added to account for background strength from the tails of high-energy, broad 1 levels). The expr e ssion for the cross section is a where k wave number of the relative motion of the 12 c nucleus and alpha particle, rAa alpha width of level i rAY = 1 A , which is twice the product of the penetration function and the reduced-alpha-width, gamma width of level A , which contains the cubic energy dependence for electric dipole radiation, EA eigen-energy of level A , level-shift matrix, a function of the reduced-alpha-widths, a boundary condition number and an i =1 shift function. There are, in this formula, nine parameters to be determined; three for each level: a reduced-alpha-width, a gamma width, and a position of the level. Two of the parameters describing the 7.12-MeV level are determined from other experimental measurements: the gamma -71width, measured by resonance fluorescence techniques to be 62± 5 meV (Swann 1970), and the energy of the state--42 keV below the threshold (Ajzenberg-Selove 1971). 12 c+a A third parameter, the position of the background level, was taken to be 20 MeV excitation in 16 0; variation of this position over a broad range about 20 MeV showed that the results of the fit were insensitive to the exact position. Three more parameters, the position and the reduced-alpha-wid th of the 9.60-MeV level and the reduced-alpha-width of the background level, were obtained by fitting the p-wave phase shifts obtained from the 12 12 C(a,a) C elastic scattering data (Jones 1962, Clark 1968), with the 3-level R-matrix formula for 1- phase shifts. parameters to be determined by fitting the 12 This leaves three c(a,y) 16 o data: the gamma widths of the 9.60-MeV and background levels and the desired reducedalpha- width of the 7.12-MeV level . The final result was found to be insensitive to the exact values of the boundary condition number and the interaction radius. The fitting proce dure was iterative: with a set of initial values for the parameters, the p-wave elastic scattering phase shifts were fitted; with the new values for three of the parameters, the measured fitted. 12 C(a,y) 16 0 cross sections (1- contributions only) were This process was repeated, with the inclusion each time of the best parameter values from the previous fit . The final parameters were used to calculate the S-factor at 300 keV c.m . alpha energy. as described in Appendix A. From this, the value of 0 2 was d erive d, a ,F -72APPENDIX D "Hybrid" R..:.Matrix - Optical-Model Fit to the 12 16 C (a,y) 0 Data Koonin and Tombrello (1972) have developed a "hybrid" R-matrixoptical-model parameterization of the 12 c(a, y ) parameters are varied in fitting the data. 12 C(a,y) 16 16 o cross section. Two The formula for the . 0 cross section is frrr 2 p k a I1- (S+iP) Ray 12 R aa where wave number of the relative motion of the k 12 C nucleus and alpha particle, p penetration function for = S shift function for ~ ~ 1 ' =1 R cry capture R-function of R-matrix theory, R elastic scattering R-function of R-matrix theory. aa The R-functions are split into two parts: R R(O) + R(7 .12) aa aa aa R R(O) + R(7 .12) ay ay ay The superscript "7.12" refers to the 7.12-MeV state in 16 O; the super- script "O" includes the 9.60-MeV level, high-lying levels, and direct capture (extra-nuclear) processes. The R (7•12 ) and aa R< 7 • 12 ) bound state contributions to the R- ay functions are treated in the manner of R-matrix theory (Lane 1958). These quantities are described in terms of a pole associated with the -737.12-MeV level, where the gamma width and position are determined from experimental data (Swann 1970, Ajzenberg-Selove 1971) and the reduced. 12 16 alpha-width is to be determined by fitting the C(a,y) 0 data. functions and The R(O) which represent contributions to the Ray ' functions from the 9.60-MeV level, high-lying levels and direct capture, are treated in the manner of optical-model theory. generated by a potential acting between the ticle, with R (O) ay 12 These functions are C nucleus and alpha par- being scaled by an effective dipole strength, which . 12 16 is the second parameter varied in the fit to the C(a,y) 0 data. The potential consists of a Coulomb potential (that of a uniformly charged sphere) and a truncated real Woods-Saxon potential. The point of truncation gives the channel radius used in the R-matrix expression; fits were performed for a range of these radii, and that value was chosen which gave the best fit. The parameters describing the poten- tial were adjusted to give a best fit to the p-wave phase shifts of the 12 C(a,a) 12 C elastic scattering data (Jones 1962). -74APPENDIX E Measurement of the Yield of the and of When an enriched 12 19 19 F(a,y) 23 Na Reaction F Target Content C target from one particular tantalum strip was bombarded with alpha particles of c.m. energy 2.4 MeV, it was found that the yield of 9-MeV gamma rays was about 40% too high, and that there were events in the spectrum corresponding to gamma rays of ene rgies higher than 9 MeV. not used in measuring the 12 Targets from this strip were consequently c(a,y) 16 o cross sections. However, since an impurity was evidently present, it was desirable to investigate its identity and to check the other targets which were used for 12 C(a,y) 16 0 measurements for the same impurity. The isotope the reaction 19 19 F(a,y) F, which can produce high-energy gamma rays by 23 . Na, was suspected because of the possible presence of a fluorine compound in the chemical apparatus used to convert amorphous carbon to methyl iodide, just prior to its use for 12 c. Also, it was noted that the yield of 6~MeV gamma rays was abnormally high in the spectra obtained when bombarding the target with protons in order to measure the target thickness; this 6-MeV gamma-ray yield was attributed to the well-known nucleus 23 Na of the 19 F(a,y) 23 19 F(p,ay) 16 0 reaction. The compound Na reaction is excited to energies of 12.4 to 13.8 MeV for the range of alpha energies in which the 12 C(a,y) 16 0 measurements were made, so that ground state transitions produce gamma rays of about 13 MeV. The low-energy tail of a 13-MeV gawma-ray energy spectrum (arising mainly from Compton scattering) can -75produce pulses in the 9-MeV gamma-ray region. several states in 23 In addition, there are Na at excitation energies of a few MeV; cascades through these states can result in a yield of 9-MeV gamma rays. Two quantities are required in order to calculate the effect of a 19 F impurity in the target: (1) the amount of 19 F in the target, and (2) the cross section for production of 9-MeV gamma rays from the capture of alpha particles by 19 Measurements of 19 F. F content were made for two enriched 12 c tar- gets: the target which was used for most of the measurements considered in the present work (henceforth referred to as target A) and the target for which the 9-MeV gamma-ray yield from alpha particle bombardment was found to be too high (henceforth referred to as target B). 19 The F contents of these targets were determined by measuring the yield of 6.13-MeV gamma rays from the 19 F(p,ay) 16 O reaction at at which energy there is a strong, narrow resonance (Ajzenberg-Selove 1972). E (lab) = 872 keV, p ( f lab= 4. 7 keV), isolated The yields were measured for a range of incident energies extending from just below 872 keV to that energy plus the proton energy loss in the target. to obtain the magnitude of the the target. target. 19 It was thus possible F content as a function of depth in This measurement was also performed for a 20 µg/cm 2 CaF 2 All measurements were made with the same experimental con- figuration. The results are shown in Figure 19. there is a minimum in the 19 2 12 c targets, F content halfway through the target. Target B has roughly 60 times the of that of a thick CaF For both target. 19 F content of target A, and 'V0.5% -76The yields for the 19 F(a,y) 23 same technique as that by which the Na reaction were measured by the 12 C(a,y) 16 0 yields were measured. Gamma rays were detected with two 20.3-cm-diameter by 12.7-cm-long Nal(Tl) crystals, and time-of-flight techniqu e was employed to suppress prompt-neutron and time-independent background. A 20 µg/cm 2 CaF 2 target evaporated onto a tantalum backing (the same target that was used to make the 19 F content measurement) was supported in the target chamber used for the 12 C(a,y) 16 0 angular distribution measurements, on the north 10° beam line of the tandem accelerator. The target thick- ness is uncertain by ~20%; its value was obtained from the thickness monitor in the evaporation chamber. Events were stored in a two- dimensional multichannel analyzer. Data were accumulated for lab alpha energies ranging from 2.7 to 4.0 MeV. In Figure 20 the yields of gamma rays of energy corresponding to the ground state transition in shown. Na are For the alpha energies studied, these gamma-ray energies range from 12.7 to 13.8 MeV. 12 23 c(a,y) 16 The yields which are of interest for the o study are the yields from the 19 F(a,y) 23 Na reaction of gamma rays of energy corresponding to the ground state transition in 16 0 for the particular lab alpha energy. These yields are displayed in Figure 21. By combination of the 19 F content data and the 19 F(a,y) 23 Na data, it was possible to obtain for each of the targets A and B the yield of 9-MeV gamma rays from the 19 F impurity content of the target. 19 F(a,y) Na reaction due to the This yield for 1 µC of integrated charge and for an incident lab alpha energy the formula 23 Ea (inc) was estimated by -77- 12c [a,y]E (inc) a CaF 12c [p,ay]E (i) 2 Ii [a,y]Ea (i) p CaF 2 [p,ay]872 keV where tne target thickness is divided into about 15 intervals in depth and a sum is carried out over these intervals, and where yield of 9-MeV gamma rays from a CaF target from 2 23 19 the F(a,y) Na reaction for 1 µC of integrated charge, evaluated at an alpha energy of Ea(inc) less the loss of alpha particle energy in penetrating to the depth of interval is scaled to a CaF interval 12c [p,ay]E (i) p i 2 i ; the yield target thickness of that of , 12 yield of 6.13-MeV gamma rays from a C target 19 16 from the F(p,ay) o reaction for 1 µC of integrated charge, evaluated at a proton energy of 872 keV plus the loss of proton energy in penetrating to the depth of interval CaF 2 [p,ay]872 keV i , yield of 6.13-MeV gamma rays from a thick CaF 2 target from the 19 F(p,ay) 16o reaction for 1 µC of integrated charge, evaluated at the energy corresponding to maximum yield. (All energies are lab energies in this formula.) It is assumed that CaF 12c 2 [a,y] and [a,y] the efficiency for detection of the yields CaF 12c 2 and [p,ay] and of the yields [p,ay] tion is to be made if this is not true. yield measured with the 20 µg/cm 2 CaF are the same; a correc- Because the 19 F(p,ay) 16 0 target was not a thick-target CaF 2 yield, as required for determination of the quantity [p,o.y] , it 2 was necessary to correct the measured peak yield. Fowler et al. (1948) -78derive the following relationship between the maximum yield of a thin Y (~), where max target ~ is the target thickness in energy units, and Y (oo) max the maximum yield of a thick target 2 n where ~ ~ r -1 2~ tan r is the width of the resonance. 4 keV For this measurement, I'= 4.7 keV , so that and ~ ymax (oo) 2.2 y max (~) The results of this evaluation for target Table 6. For comparison, the measured yields of 9-MeV gamma rays from the 12 C(a,y) 160 reaction are given. The effect of the 19 F impurity is seen to be small, but not completely negligible. the 19 A are given in F(a,y) 23 Since the yield of Na reaction has not been measured over the full range of 12 alpha energies for which the C(a,y) 16 0 yield has been measured, it is not possible at present to obtain corrections at all energies. this reason, the correction has not been applied to the results given in Section III. than the statistical error 12 For C(a,y) 16 0 Although the correction would be smaller assigned to the 12 c(a,y) 16 o yield, the effect cannot be neglected in the final analysi.s, because there is an energy dependence. effect of the 19 F(a,y) 23 19 In order to obtain a preliminary evaluation of the F impurity yield on the derived parameter 8 2 a, F , the Na yields of Table 6 were subtracted from those for the I 12 C(a,y) 160 reaction (no corrections being attempted for the lower-energy points), and the data were fitted again with the 3-level R-matrix -79formula (Appendix C); the value of 2 0a,F decreased by only 5%. A completely reliable correction, however, can only be presented when the 19 F(a,y) 23 Na yields have been measured at lower alpha energies. It can be seen from the yields given in Table 6 that the much higher (about 60 times higher) 19 F content of target B would have a disastrous effect on the shape of the 9-MeV gamma-ray excitation function. The 19 F(a,y) 23 Na yield for target B is of the right order of magnitude to account for the 40% increase in the 9-MeV gamma-ray yield which was originally observed for this target. -80REFERENCES Adams, A., M. H. Shapiro, C. A. Barnes, E.G. Adelberger and w. M. Denny 1968, Bull. Am. Phys. Soc. 13, 698. Ajzenberg-Selove, F. 1971, Nuc. Phys. Al66, 1. Ajzenberg-Selove, F. 1972, Nuc. Phys. Al90, 1. Arnett, w. David 1969, Ap. and Space Sci. -2._, 180. Arnett, W. David 1971, private communication. Arnett, w. David 1972, Ap. J. 176, 681. Barker, F. C. 1971, Aust. J. Phys. 24, 777. Barnes, C. A. and William A. Fowler 1970, unpublished work. Barnes, C. A. 1971, Advances in Nuclear Physics _i, 133. Brown, G. E. and A. M. Green 1965, Phys. Letters 15, 168. Brown, G. E. and A. M. Green 1966, Nuc. Phys. ]2_, 401. Cameron, A.G.W. 1968, Origin and Distribution of the Elements, edited by L. H. Ahrens, Pergamon Press (New York), page 125. Clark, G. J., D. J. Sullivan and P. B. Treacy 1968, Nuc. Phys. AllO, 481. Clark, G. J., 1969, Aust. J. Phys. 11_, 289. Clayton, Donald D. 1968, Principles of Stellar Evolution and Nucleosynthesis, McGraw-Hill, Inc. (New York). Deinzer, W. and E. E. Salpeter 1964, Ap. J. 140, 499. Dietrich, F. S. 1964, Ph.D. Thesis, California Institute of Technology . Ewen, Klaus 1970, Ph.D. Thesis, Universitat zu Koln. Fowler, William A., c. C. Lauritsen and T. Lauritsen 1948, Rev. Mod Phys . 20, 236. Fowler, William A., Georgeanne R. Caughlan and Barbara A. Zimmerman 1967, Ann. Rev. Astron. and Astrophys. -2._, 525. Fowler, William A. 1968, Origin and Distribution of the Elements, edited by L. H. Ahrens, Pergamon Press (New York), page 3. Grodstein, G. W. 1957, NBS Circular 583. Gunn, J. E. and J. P. Ostriker 1970, Ap. J. 160, 979. Hattig, H., K. Hiinchen, P. Roth and H. Waffler 1969, Nuc. Phys. Al37, 144. Jaszczak, Ronald J., John H. Gibbons and R. L. Macklin 1970, Phys. Rev. C2, 63. Jaszczak, Ronald J. and R. L. Macklin 1970a, Phys. Rev . C2, 2452. Jones, c. Miller, G. C. Phillips, R. w. Harris and E. H. Beckner 1962, Nuc. Phys. 11._, 1. Koonin, S. E. and T. A. Tombrello 1972, to be published. Lane, A. M. and R. G. Thomas 1958, Rev. Mod. Phys. 30, 257. Larson, J. D. and R. H. Spear 1964, Nuc. Phys. 2-§_, 497. Larson, J. D. 1965, Ph.D. Thesis, California Institute of Technology . Lazar, N. H., R. C. Davis and P.R. Bell 1956, Nucleonics 14(#4), 52. Loebenstein, H. M., D. W. Mingay, H. Winkler and C. S. Zaidins, 1967 Nuc. Phys. A91, 481 McDonald, A. B. 1970, Ph.D. Thesis, California Institute of Technology . Paczynski, B. 1970, Acta Astr. 20, 47. Paczynski, B. 1971, Acta Astr. 21, 271. Parker, P.D.M. 1963, Ph.D. Thesis, California Institute of Technology Puhlhofer, F., H. G. Ritter and R. Bock 1970, Nuc. Phys. A147, 258. Schwarzschild, M. and R. Harm 1967, Ap. J. 150, 961. Sherman, I. S., R. G. Roddick and A. J. Metz 1968, IEEE Trans. Nucl. Sci. NS-15, 500. Smith, R. L. and I.-J Sackmann 1972, preprint. Stephenson, G. J., Jr. 1966, Ap. J. 146, 950. -82- Swann 9 C. P. 1970, Nuc. Phys. Al50, 300. Tombrello, T. A. and G. C. Phillips 1961, Phys. Rev. 122, 224. Tombrello, T. A. 1970, private communication . Tombrello, T. A. 1971, private communication . Weigert, A. 1966, Zeitschrift fur Astrophysik 64, 395. Weisser, D. C., J. F. Morgan and D. R. Thompson 1970, internal report. Werntz, Carl 1970, private communication. Werntz, Carl 1971, Phys. Rev. C4, 1591. Wheeler, J. Craig, Zalman Barket and Jean-Robert Buchler 1970, Ap. J. 162, Ll29. Zerby, C. D. and H. S . Moran 1961, Nuc. Instr. and Meth. 14, 115. -83TABLE 1 Yields of 7-MeV Single Gamma Rays and Yields of Coincidences The quantities in Column 2 were extracted from the two-dimensional spectra; i t is possible that some of this yield is produced by impurities in the target. The upper limits listed in Column 3 were obtained by observing coincidences between 7-MeV and ~2-MeV gamma rays. E For additional details, see pages 41 to 43. (lab) °Mev 7-MeV Gamma-Ray Yield nb 2.31 < 4 2.39 < 1 2 .49 1 ± 1 2.61 2.1 ± 1.2 2. 71 3.7 ± 1.2 2. 77 3.4 ± 1.2 2 .82 4.4 ± 1.4 2.87 4.6 ± 1.4 2.91 8.0 ± 1.3 3.01 12.4 ± 1.8 3.09 17.6 ± 2.5 3.23 15.2 ± 3.0 3.32 17.4 ± 2.8 3.42 14.0 ± 2.2 3. 71 16.8 ± 1.0 Yield of Coincidences nb < 3 < 1 < 5 < 2 < 8 3. 77 3.82 18.9 ± 0.9 3.92 25.9 ± 0.9 ·-84TABLE 2 12 c(a,y) 16 o Yields from Measurements at 90° Column 3 gives the number of counts, per mC of integrated charge, extracted from the spectra measured a t 90°. In order to relate these yields to absolute quantities, there is given in Column 4 the total cross section which would result if the angular distributions of gamma rays were those of pure electric dipole transitions. For additional details, see pages 43 and 44. E (c.m.) ~ev Ea (lab) MeV Yield counts/me o(l-) nb 1. 73 2.31 9.1 ± 2.8 1.8 ± 0.6 1. 79 2.39 10 .8 ± 2.1 2.2 ± 0.4 1.87 2.49 16.9 ± 2.7 3.4 ± 0.5 1.96 2.61 20.3 ± 2.8 4.1 ± 0.6 2 .03 2. 71 36.3 ± 2.8 7.3 ± 0.6 2.08 2.77 46.9 ± 3.0 9.4 ± 0.6 2.11 2.82 72 .6 ± 3.4 14.5 ± 0.7 2.15 2.87 82.5 ± 6.6 16.5 ± 1.3 2.18 2.91 99.8 ± 3.8 19.9 ± 0.8 2.26 3.01 147.1 ± 5.1 29.4 ± 1.0 2.32 3.09 201.4 ± 6.6 40.1 ± 1.3 2.42 3.23 190.0 ± 8.0 37.8 ± 1.6 2.49 3.32 161.1 ± 5.9 32.1 ± 1.2 2.56 3.42 110 .8 ± 6.6 22.0 ± 1.3 2.78 3. 71 50.2 ± 2.8 10.0 ± 0.6 2. 86 3.82 42.6 ± 2.5 8.5 ± 0.5 2.94 3.92 39.1 ± 2.3 7.8 ± 0.5 -85- TABLE 3 Obtained from Angular Distribution Measurements The quantities in Column 2 are obtained by fitting the measured angular distributions. The quantities in Column 3 are obtained from Tombrello's (1961) formula for the direct capture cross section, using ea.2 (g.s., 160) = 0.043± 0.012 to achieve consistency with these measured values and with the yields measured at 0 = 90°. For addi - tional details, see pages 44 to 47. E (c.m.) in MeV IA2+ II IA1-I measured IA2+ II IA1 -1 calculated 2.18 0.10 ± 0.10 0.19 2.42 0.14 ± 0.05 0.19 2 . 56 0.36 ± 0.06 0.29 2.83 0.58 ± 0.05 0.56 a. -86TABLE 4 El and E2 Contributions to the 12C(a.,y )l60 Total Cross Section The quantities in Column 2 are obtained from Tombrello's (1961) + 2 16 formula for the 2 direct capture cross section, using e (g.s., 0) = a 0 .043 ± 0 .012 . The values I Al-12 are obtained f r om the yield at 90°, 2 the detection efficiency, and the values IA + 1 The quantity a is 2 2 the total cross section, the sum of jA _j and IA2+ 12 For addi1 tional details, see pages 46 to 48. . 2 2 jA2+1 calc/jA _i 1 Ea (c.m.) MeV IA2+l2 calc nb 1. 73 0.15 1.8 ± 0.6 0.08 1.9 1. 79 0.18 2 .1 ± 0.4 0.09 2.3 1.87 0.24 3.3 ± 0.5 0.07 3.5 1.96 0.33 3.9 ± 0.6 0.08 4.2 2.03 0.42 7.1 ± 0.6 0.06 7.5 2.08 0.49 9.2 ± 0.6 0.05 9.7 2.11 0.54 14.3 ± 0.7 0.04 14.8 2.15 0.61 16.2 ± 1.3 0.04 16.8 2.18 0.66 19.6 ± 0.8 0.03 20.3 2.26 0.80 29.0 ± 1.0 0.03 29.8 2.32 0.94 39.7 ± 1.3 0.02 40.6 2.42 1.22 37.3 ± 1.6 0.03 38.5 2 . 49 1.43 31.5 ± 1.2 0.05 32.9 2.56 1.68 21.3 ± 1.3 0.08 23.0 2.78 2.61 9.2 ± 0.6 0.28 11. 8 2.86 3.03 7.7 ± 0.5 0.39 10.7 2.94 3.46 7 . 1 ± 0.4 0.49 10.6 IA1_,2 nb a nb -87TABLE 5 12 C(a,y) 16 0 Capture Transitions The various capture processes by which the 12 C(a,y) 16 O reaction may proceed are listed for the plane-wave states of lowest angular momenta. For additional details, see pages 62 to 69. Initial plane-wave state Order of multipole radiation s EO El E2 p EO El E2 d EO El E2 Final bound state in ground state 6.05-MeV 7.12-MeV 6.92-MeV 7.12-MeV ground state 6.05-MeV 6.92-MeV 6.13-MeV 7.12-MeV 6.92-MeV 6.13-MeV 7.12-MeV ground state 6.05-MeV 6.92-MeV 16 0 -88TABLE 6 19 Yield of 9-MeV Gamma Rays from the F Impurity 12 in an Enriched e Targ et The second column gives the yield of 9-MeV gamma rays from enriched 12 e target A which are produced by t he The values are obtained from me asurements of t he target and from measurements of the target. For comparison, the 12 e(a ,y) For additional details, see pages Lab incident energy MeV 19 19 F(a ,y) 16 23 19 F(a ,y) 19 23 Na reaction. F conte nt of the Na yield from a eaF 2 0 yields from Table 2 are given. 74 to 79. 23 F(a ,y) Na yield counts/me 12e(a,y)l60 yield counts/me 2.9 0.5 73 ± 3 2.95 0.3 82 ± 7 3.0 0.3 100 ± 4 3.1 0.1 147 ± 5 3.2 0.3 201 ± 7 3.3 0.6 190 ± 8 3.4 0.6 161 ± 6 3.5 0.6 111 ± 7 3,79 1.5 50 ± 3 3.9 0.7 43 ± 3 4.0 0.5 39 ± 2 -89- figure 1 Energy Level Diagram of the 1971). 16 0 Nucleus (Ajzenberg-Selove For details, see pages 8, 9, and 12. -90- ;; )' ~ ·~. ·' I'<•. :· ~. t. "( I -- --~­ 8.70 Figure 1 . ~ O • p-t -91- Figure 2 Schematic Diagram of Apparatus for Making Enriched 12 C Targets 12 This chamber is used to crack C-enriched methyl iodide. 12 Elemental c is deposited on the tantalum strip supported in the center of the pyrex tube. A weight, with flexible coupling to the bottom end cap, is suspended from this strip to take up length in the strip gained from heat expansion. cooled (not shown). The apparatus is water For additional details, see pages 17 and 18. --92·· TO LN2 TRAP TO MERCURY PRESSURE GAUGE ,.--~~~~~~~-r-~~ 0-RING TA TARGET STRIP PYREX TUBING WEIGHT COPPER BRA ID TO VACUUM PUMP ANO GAS INLET Figure 2 . -93- Figure 3 Target Thickness Determination by the 13 C(p,y) 14 N Reaction Both plots show the yield, as a function of incident laboratory 13 14 proton energy, of 9.17-MeV ganmia rays from the C(p,y) N reaction. E (lab) = 1.75 MeV is p primarily due to proton energy loss in the target and is a measure The width of the resonance which rises at of the target thickness which can be determined with the use of energy loss tables. enriched The top plot shows a measurement made with an 12 C target. The structure in the region of maximum yield 13 indicates that c is not uniformly distributed in the target. The bottom plot shows a measurement made with a natural carbon t a rget. In this case, such structure does not exist. see page 18. For additional details 0 g.--~~~~~~~~~~~~~~~~~----. If) 13ccp ,y)ll!N NATURAL CARB~N TARGET Do _Jo,_. w If) t-1 C'J >- (!) (!) 0 ~ (!) (!) (!) (!) o.__~~__.l~~~_.._l~~~-..__I~~~',__~~~ 1. 71.J 1 • 75 1 . 76 1 . 77 1 • 78 LAB PR~T~N ENERGY CMEV) 1. 79 -95- Figure 4 Schematic Diagram of the Target and Detection System The top diagram shows a vertical section of the target chamber and vacuum system (not to scale). natural carbon on the enriched 12 In order to minimize deposit of c target, copper gasket vacuum seals are used at all points downstream from the cold trap. For additional details see pages 19 and 20. The bottom diagram shows the detector geometry and the lead shielding (not to scale). For additional details see pages 20 and 21. \ -96- FioN ----- TARGET SUPPORT ROD PUMP COLLIM __ -- L ~ 1-D- ~I TROGEN --- --- COLD TRAP · -- - - - - - -- BERM DIRECTION ) -- - - - -- STA INLESS STEEL BEAM TUBE ~BELLOW S '-......_ ELECTRICAL INSULATION TARGET ____r--1---c_ c=~ E-~~ PHOTOMUL T!PL IER TUBE WEL L NRIC TL) CRYSTAL ~==n-~ L _ _ =_J 1 n E TL) STRL PHOTOMULTI PL IER TUBE WELL t:'===1. - u, ------------, r -- C~~-1 ~ L__~_,----J - ---.__ __ - T BEAM DIRECT ION Figure 4. ___J - _j "' LEAD SHI ELD I NG 14 fraction. For additional details, see pages 24 to 26. lation to the zero pulse height channel required for calculation of the spectrum This energy spectrum was measured with the reaction C(p,y) N at E (lab) = 13 p 1.75 MeV. An enriched C target was used. The solid curve represents the extrapo- 13 9.17-MeV Standard Spectrum for a 20.3-cm by 12.7-cm Nal(Tl) Crystal Figure 5 "I I \0 - 98-0 0 ;;1' 0 lf) tE>t '%. 1Ell tEll IEJI~ a El El El El eiEl en 0 0 ' (T) 0 lf) N :::E ::::> a: Lr) f-- u w <lJ C• CL (f) ::J tlO D a: -M a: r.-r.. 0 z a: f-- (f) > w :L rm 0 lf) El OOOB 0009 00011 l ::JNNt:lHJ ; SlNnrJJ 000<'. 12 C(a , y ) For details, see pages 28, 30, and 31. Electronic Configuration Used for Measurements of Figure 6 16 0 Yield at 90 0 I I \0 \0 PULSE STRETCHER LINEAR GATE r· I 17 J, 17 OYNOOE 9 ~ 17 er z 0 IJ.J 0 ~ OELAY ~ PULSE STRETCHER SLOW COINCIDENCE y AOC OE LAY x AOC ~ PULSE STRETCHER & ~r .. ,., SLOW COINCIDENCE ~ L b PULSE STRETCHER ~ PULSE STRETCHER l ~ I LINEAR DELAY TIME-TOAMPLITUDE CONVERTER ~ I I 17 I I I I I I I PULSE STRETCHER 17 SINGLE CHANNEL ANALYZER 17 AMPLIFIER 17 I PREAMPLIFIER OYNOOE 10 FAST FAST ~ FAST I FAST blSCRlMlNATOR blSCRJMJNATOR lSCRJMJNATOR I JSCRJHJNATOR J ~ ~NnnF EJ B 1-: '--- RCA 11522 Figur e 6. ~ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - _J I - SINGLE CHANNEL ANALYZER I I I I I I AMPLIFIER 17. 1'7 •'! AMPLIFIER --- LINEAR OELAY 17 •7 1'7 17 PREAMPLIFIER 17 CJ >- z IJ.J CJ 0 m ~RCA 11522 SUMMING PREAMPLIFIER •'] OYNOOE 10 I I I b 0 -101- Figure 7 Isometric Plot of a 12 c(a ,y) 16o Two-Dimensional Multichannel Analyz e r Spectrum This spectrum was measured at E (c.m.) a = 2.42 MeV, at the peak of the resonance due to the 9.60-MeV state in 16 0. The 9.60- MeV region in the spectrum is about three quarters of the distance from left to right. The gamma-ray region is roughly in the center of the vertical scale; the prompt-neutron region is at the bottom. For additional details, see page 31. .. 102 ' 12C(a ,y )18 0 Figure 7 . SPECTRUM -103- Figure 8 Energy Spectra of Gamma Rays from the 12 C(a ,y) 16 0 Reaction These spectra are obtained from the two-dimensional spectra by sunnning counts over the time channels corresponding to the arrival of gamma rays from the target, and subtracting the energy spectrum of the time-independent background obtained from the same twodimensional spectrum. Channel zero corresponds to zero gamma-ray energy; channel 64 to about 12 MeV. displayed on the plots. The c.m. alpha energies are Gamma rays of about 7 MeV are visible in the spectra measured at the higher alpha energies . details see pag es 34, 35 and 38. For additional -104-- t> CC a , v) 16 Cl i> C( a, v ) 16 Cl ENERGY SPECTRUM CH ALPHA ENERGY= I . 73 HEV RUN Gll4 _J _J UJ UJ z z a: z z a: ,u "'.... u J: c '"' (f') 1- 1- z z :::> :::> u D D u c c~ O ~6--· 16 Z4 32 40 48 56 64 0 16 CHANNEL NUMBER ~,---,---,--- il I ~~ <n I- z f CH ALPHA ENERGY=2 . l 5 MEV I I • I 8 16 ' u II cl 56 64 ·- - r--- - - , -, - - - ,----, - - ·r- ---,- ... t> C< a . v ) 1• Cl ENERGY SPECTRUM CH ALPHA ENERGY=2 .42 HEV RUN GllS l I RUN G32 J 24 32 40 46 56 64 CHANNEL NUMBER c ----,--,..--- I! "C< a , v ) 1• Cl ·-,---,---,---.. N ~ 12 C< a. v) 16 Cl ENERGY SPECTRUM "·~~ ~~·~,.~ ~· ~ ~ _J UJ z z ENERGY SPECTRUM l a: ,~ I 48 j 111,lmlilHP~ ~ lcl :::> D 40 n\ 1 N _J a iil ENERGY SPECTRUM II I :::> D u 0 32 iHi i cl c" 24 CHANNEL NUMBER ,.---r -- ,--- "C< a· v) 16 Cl 1 z RUN Gll2 J: (f') ~ ENERGY SPECTRUM CM ALPHA ENERGY= I . 96 HE V 11 lH ..... ~ <n I- !, ~ 1l1 1¥iN \. ~~--,-1':6 0 24 1 J: Uc 1 32 40 46 z :::> D u y 56 64 CHANNEL NUMBER Figure 8. 16 24 R ® CHANNEL NUMBER ~ ~ ~ -105- Figure 9 Time Spectra of 9-MeV Events from the 12 C(a ,y) 16 0 Reaction These spectra were obtained from the two-dimensional spectra by summing counts over the energy channels corresponding to the gamma16 ray energy of the ground state transition in O (9.60 MeV at the 16 peak of the resonance corresponding to the 9.60-MeV state in 0). The region of summation is taken from O. 8 * Ey to 1.1 * E y Time increases to the left. The circles with error bars correspond to 12 data taken with an enriched C target; the crosses, to data taken with a natural carbon target which havebeen normalized to match the prompt-neutron peak and the time-independent background. Some 12 16 C(a,y) 0 events are present in this background. These a re taken into account in the yield analysis. The narrow peak in the center of each spectrum corresponds to the gamma rays; the broad peak at 13 16 the left end, to prompt neutrons from the C(a,n) 0 reaction. The difference in flight times for neutrons and gamma rays is about 3 nsec, but the peaks are separated by about 6 nsec. The reason is that most neutrons lose their energy in the Nal(Tl) crystals in a series of several collisions, so that the risetime of the pulse produced at the anode of the photomultiplier tube is greater than that of a gamma-ray pulse. gered at a later time. The discriminator will thus be trig- For additional details, see page 35. - 106- 12 C< a, y) 16 0 12 C( a. v)" 0 TI HE SPEC TRUH CH ALPHA ENERGY= I . 73 HEY RUN G!l4 TI HE SPECTRUM CH ALPHA ENERGY= I .96 HEY AUN G42 I _J w z z a: :x: I NRNOSECONO ~~ I :°SFCONO J ,_ Cf) z ::J D u O~-~--~ 0 16 L __ 24 _ _L_ _ J __ ___J_ _ __ L_ - 32 40 CHANNEL NUMBER 0 ~ --··r --···-r-- --- , ·- ·- -, - -,- 12 C< a • v l 16 0 40 56 64 .,......... , . ,. -· ,-- , . .. . . 12 C< a . v l 16 0 1 I HE SPEC 1RUH CH ALPHA ENERGY=2 .15 HEY RUN Gll!i I I ME SPE.C !RUM CH ALPHA ENERGY=2. 42 HE V RUN G32 --- -r·- - r-·- - , -.. - r ....... I - ..... ·1 .. - --1 -- l _J w z z a: :x: u g I NANOSECOND ,_ ,_ Cf) z ::J D u O~-~---~ 0 16 24 32 40 64 40 CHANNEL NUMBER --···r - -...,--.. ··· 1-- - - r - ~ -T - --, - - --· 11 HE SPEC1RUH l II M~ Sf'EC1RIJM " ( (a• v >•• 0 _J w z z a: I NANOSECOND J:: w~ ,_ ,_ Cf) z ::J D w O~-~--~-~--~-~--~-~-~ 0 16 24 32 40 CHANNEL NUMBER 56 64 0~-~--~-~--~-~--~-~- 0 16 2tl 32 I.IC CHANNEL NUMBER Figure 9. 40 56 64 -107- Figure 10 12 c(a ,y) 16 o Angular Distributions The yields, expressed in arbitrary units, are plotted versus the angle 8 , measured with respect to the direction of the inci- dent beam of alpha particles. for four alpha energies. Angular distributions were measured The dashed curves are fits to the data obtained by assuming interference between 1 - and 2+ contributions to the cross section, taking into account the finite size of the detectors. The solid curves indicate the angular distributions which would be measured by a point detector . details see pages 44 to 47. For additional - 1 U8- ~-----,----,----,---,-----,----,----.---~.~ i :f: ~I 12 [ ( 0 , Y) 16 (j ~ !Z [ ( a ,y) 16 (j = 2 .16 HEY PQ(Nl OETECTOfl CM ALPHA ENERGY FJN ITE DETECTOR IA2·'l'IR1 - I= CO. IOtO .I Ol 1 ,; r PO HH O£TECTOl1 CM ALPHA ENF RGY FIN ITE OETECTOA IA2• /A1 - I x2 I DEG . FREEDOM = I .0 x2 I DEG. FREEDOM = D .8 I 2 .42 MEV : = C0 . 14!0 . 0 Sl ~ I -! ill i ~+ I I ' ' ' j d~ I I ~ ' "' - ~_l_. _ _ __l_____ ..L___.l.__ _ l_. ~ "O M tlO 100 L 20 120 . . THETA - ~- -· -,---·-r----·· · ' 1' \ I ' I r -·-r· -----, ~. 140 I I '- \ - ' - -L .• · -" - 60 tlO 100 " 120 HiE.TR ~ >J P.10 I GO 12 (( 0: , y ) IG CJ 12 [(a , ") 16 (j 2 . 56 HEV PO IN T OE TECTOA CH ALPHA FNERGY f INITE DETECTOR I A2•/A1 - I = C0 . 36>0.06l x 2 I DEG. FREEDOM = 2.2 1 PO INT OfTECTOA CH ALPHA ENERGY = 2 .83 HE'I , f INITE r£ TECTOf\ I R2 ... 1R1 - I = C0 .58!.0 . OS ) x2 I DEG . FREEDOM= 0.9 ~ l f/ I I _j I 1 ~ I I I I "" 180 2r- ---r---r- ·------r--r ·---r- - ··1· ·- - --r---, ·-·-----, 60 "'THETA 100 120 ... l ___ 160 100 20 ___.1,_ __,__ •• 60 '--"-· .\I 80 THE TA Fi g u re 1 0 . I 100 !20 1"0 lf;O 100 -109- Figure 11 Variation of IA 2 +1 2 with Alpha Energy This figure shows the results of calculations of the 2+ direct capture cross section from the formulation of Tombrello (1961). The scale is 30% uncertain, because of the error in the quantity Ga (g. s. , 2 16 0) = 0. 043 ± 0. 012 , which is determined by fitting amplitude ratios from the measured angular distributions. These values were used to extract the electric dipole contributions to the total cross sections. pages 44 to 48. For additional details see -110- E2 DIRECT CAPTURE CONTRIBUTION TO TOTRL CROSS SECTION CTOMBRELLO) ,,...... en 100 z a: <I CD 0 z z <I '-J z 0 ...... 1- u w en en en 0 a: u ('\j 10-1 w s~2cG.s .. t6o) - co.043±0.012) 10- 2 ~~~~~...__~~~~~~~~~~~~~~~~~~~~ 1 .o 1 .5 2.0 CM RLPHA ENERGY Figure 1-1. 2.5 CMEV) 3.0 3.5 -111- Figure 12 12 Measured 1- Contributions to the c(a ,y) 16 o Total Cross Sections and 3-level R-Matrix Fits The quantity IAl-1 2 i s p 1 otte d versus The solid curve is the best 3-level R-matrix fit to the data (Weisser 1970). Three parameters are free to vary. is 1.4. The X2 per degree of freedom The dashed curve represents a fit in which strained to 0 8 a 2 is con- and the remaining two parameters are free to vary 2 (X per degree of freedom= 2.8); the dotted curve is also a fit with two parameters free to vary, but with 2 (X per degree of freedom= 1.5). 48 and 49. Ga 2 constrained to 0.4 For further details see pages - 112- CR055 SECTION 12 cc Q'. ' y ) 16 0 C.I.T. DATA AND A-MATRIX FITS so ,..... en z @f 20 al 0 z a: z \.../ z 810 Iu w en en en 0 0:: u _J 5 a: I- 0 I- I I 2 1.__~~~~~~-'-~~~~~~~~~~~~~~~~~~~ 1.0 1.5 2 .0 CM ALPHA ENERGY Figure 12. 2.5 <MEV) 3.0 3.5 -113- Figure 13 The points with error bars are values derived directly from the angular distribution measurements; the solid curve represents cal2 culated ratios. The calculated values for are taken from 2 + the 2 direct capture formulation of Tombrello (1961), using 2 16 8 (g. s., 0) = O. 043 ± O. 012 . The calculated values for IA +1 IA1_12 a are taken from tne 3-level R-matrix fit to the El contributions to the total cross sections (Weisser 1970). The ratio becomes very + direct cap- small at low alpha energies; it can be seen that the 2 ture process is not significant at astrophysically interesting energies. For additional details see pages 44 to 49, 67 and 68. -114- q N > w L >- IJ')~ . a: - w z w a: I: 0.... _J a: L u q 0 N ~ ,,...... I >- a: ........ + N a: ~ "'? '.J u 0 ~ q L-~~~+-~~~-1-~~~~~~~_._~~~--+~~~-'~~~--J'--~~~L-~~~""-~~~~D os· o sti·o oti·o SE"O OE"O sz·o 0 Utll:l oz·o F:igure 13. s1·0 01·0 so·o o·o -115- Figure 14 Measured 1- Contributions to the 12 c(a ,y) 16 o S-factor and 3-Level R-Matrix Fits The data and fits shown here are the same as those of Figure 12, but the ordinate corresponds to the S-factor rather than the cross section. (S = crEe 2 n~. See Appendix A.) The solid curve is the best fit; three parameters are free to vary. made with 0a The other two fits are 2 constrained and two parameters free to vary. The 2 2 dashed curve corresponds to = O ; the dotted, to = 0. 4. It ea ea can be seen that more data at lower alpha energies is desperately needed in order to obtain a reliable extrapolation of the data to E (c.m.) = 300 keV. a For additional details see pages 48 and 49. -ll6- .5 5-FRCTOR 12 cc O'.. y) 16 0 C.I.T. ORTA ANO A-MATRIX FITS .2 .1 (/') ~ .05 a: OJ I > w L '-/ . 02 .01 .005 ----.002 0.0 0.5 1.0 1.5 2.0 CM ALPHA ENERGY Figure 11~. CMEV) 2.5 3.0 -117- Figure 15 Measured 1 Contributions to the 12 C(a,y) 16 0 .Total Cross Sections and "Hybrid" R-Matrix-Optical-Model Fits The quantity is plotted versus E (c.m.). a The solid curve is the best fit to the data (Koonin 1972). Two parameters are 2 free to vary. The X per degree of freedom is 1. 3. The dashed 16 curve represents a fit in which the bound state at 7.12-MeV in 0 2 For additional details is omitted ( X per degree of freedom= 7). see pages 48 to 50. ·- 118 - CRCISS SECT I CIN 12 CC a , y) 1s CJ KQQNIN ANO TQMBRELLQ FIT so ,...... Cf) z gf20 CD D z z a: '-/ z ~10 u w Cf) 1- Cf) Cf) D er: us _J a: I- D I- 2 1.__~~~~....._~....._~~-'-~~~~_._~~~~---<>--~~~---' 1.0 1.5 2.0 CM _8LPHA ENERGY Figure 15 . 2.5 <MEV) 3.0 3.5 -119- Figure 16 Measured 1- Contributions to the 12 C(a ,y) 16 0 S-factor and "Hybrid" R-Matrix-Optical-Model Fit The data and best fit shown here are the same as those of Figure 15, but the ordinate corresponds to the S-factor rather than the cross section. (S = crEe 2rrn. details see pages 49 and 50. See Appendix A.) For additional -120- .5 S- FACTDR K~~NIN 12 CC a , Y ) 1s () AND T~MBRELL~ FIT .2 .I "(/) ~ .05 a: CD I > lJJ :::E '-/ .02 (/) .01 .005 .002 .001 '--~~~'--~~~'--~~~'--~~~'--~~~..._~~~..._~~~ o.o 0.5 1 .0 1 .5 2.0 CM ALPHA ENERGY <MEV) Figure 16. 2.5 3.0 3.5 -121- Figure 17 12 C(a,y) 16 0 Cross Sections of Jaszczak et al. Compared with Fit to Caltech Data The data of Jaszczak et al. (1970,1970a) is shown with the 3-level R-matrix fit to the Caltech data (1- contributions only). The cross sections of Jaszczak et al. were obtained by assuming the transitions to be pure electric dipole. (This does not account for the discrepancy between the two sets of data.) additional details see pages 11, 12 and 50. For CROSS SECTION 12 cc Ci , y ) 16 0 O.R.N.L. DRTR RNO so FIT TO C.I .T. DRTR I f "en :z f£2o CD 0 :z a: :z '-" z 810 Iu w en en en 0 a: u _J 5 er: I- 0 I I- I 2 1 1.0 1.5 2.0 CM 2.5 ALPHA ENERGY Fig ure 17 . CMEV) 3.0 3.5 12 C Mass Fraction on Core Mass and Ga 2, F 52. ard deviation above and below the best value. For additional details see pages 51 and a, lations of Deinzer and Salpeter (1964) and Arnett (1972). The three curves represent 12 16 different rates of the C(a,y) 0 reaction; they are labeled by the corresponding 2 2 values of Ga , F . The solid curve corresponds to the best value for Ga , F obtained from the experimental data; the dashed curves correspond to values of G F2 one stand- The values are obtained by a combination of the calcu- C at the end of core helium burning is plotted as a function 12 of the mass of the helium core. The mass fraction of Dependence of Figure 18 I w I I-' N - 12hI I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I (f) I I f- I I I z I I ::J I I I I I I (/) I (f) a: I I I I I I I I I (/) I I I I I I I I 0 0 (f) (f) I I a: I I :E I I I I w a: I ' I I ' El u ' 0 CJ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ' \ \ o· r s·o r-i El I ::1' 0 Cl) a: a: _J I I __j__ -·· --- -- - 9· o h" O NOl lJ~8~ ss ~w N098~J \ • :E -125- Figure 19 19 F Content of Enriched 12 c Targets The yieldsof 6.13-MeV gamma rays from the 19 F(p, a y) 16 O reac- 2 tion are given for three targets: (1) a 20 µg/cm CaF target, 2 2 12 (2) a 158 µg/cm enriched C target, referred to as target A in 2 12 the text, and (3) a 185 µg/cm enriched C target, referred to as target B in the text. All targets were mounted on tantalum back- Target A and other targets from the same tantalum strip 12 16 were used for all of the c(a ,y) o measurements discussed in ings. this thesis. The width of the 872-keV resonance for the two carbon targets is due to the energy loss of the protons in the targets. The measurements for these two targets extend over the thicknesses of 19 the targets; the yield thus represents the F content as a function of depth in the target. It appears that in both cases there 19 is a relatively large amount of F near the surf ace of the target and near the tantalum backing, whereas there is a minimum in the content halfway through the target. pages 75 to 78. For additional details see C? D g ~---~---~---~---~---~---~----~---~---- 0 "' 19f(p.cxv)16o D a:J 0 :>:a :3~ 0 ::::> TH IN CRLCIUM FLUORIDE TRRGET 0 El u El a:D Uo 0 -a :.:g 0 a:"' w a.. 0 ,_ . J (f")D 0 z§ 0 ::::lD 8~ 0 0 0 0 0 (!)<!>(!)(!)o ~ <!> (!)(!) 0 (!) 0 0 a~----<>~---~---~---~---- 840 850 860 870 880 LooC>ooo<!>C>o "o~opoo 890 900 910 920 I I 930 LRB PROTON ENERGY ( KEV) C? a ~---~---~---~---~---~---~~---~---~---- "' l9fcp.cxv)16o a:J"' r · THICK 12 C TRRGET R El gj ....J ::::> "' El u El a: u o 0 ~~ 0 a: w a.. 0 0 0 "' "' z. ::::>r- ;":'"'LI u 0 o.,, (!) C? - 0 840 (!) (!) "' "' ~ _J ...... ______J_ _____ _J_ _______ __ J _ 850 860 "'"'"' "' "' "' "' 870 __J__ _ _ J_ ____ __J____________L_ -- --- 880 890 900 910 920 930 LRB PRO TON ENERGY CKEV) ~ 8 ~---~---~---~---~---~---·~----~---~---- "' 19f(p . av) 16o a:J 0 . ~~ ....J- TH ICK 12 C TRRGET B " ::::> El " u El 5 C? -o " " 0 :.:g a: w a.. "' o"' "' "'o ,_o (/") Zo ::::l O El =r u "" ~ n -- HIIO 070 I . l. BRO 890 900 l RH Ptilil ON f Nf f~G Y < Kf V) Fig ure 19. 910 !l20 -127- Figure 20 The 13-MeV Gamma-Ray Yield of the 19 F(a, y) 23 Na Reaction The yield of the g amma-rays of energ y corresponding to the grounds ta te transition in 23 Na is given as a function of the lab alpha energy (displayed here as the incident energy minus half the energy loss in the target) . CaF 2 These yields were obtained with a 20 µg/cm target, a singly-cha rged 4 2 He beam, and two 20.3-cm-diameter by 12.7-cm-long Nal(Ti) detectors placed 10.5 cm from the targe t and at angles of 90° with respect to the incident beam. details ,. see page 7 6. For additional --1 28 . 0 rn11--r-r--r----.~~,.rr-11-r---r-------irl!N"~-.-T"1-.-..~.....-.....-~~~.:::f. El w .......... >>- ~~ a: €) a: €) €) _J ~ EJ ti ff' 0 EJ a: El EJ z: (Y) l€>i N ~ 1€)1 E) >-.. l.[) ,,....._, D (I'") a: \d' 0: L: L: l€ll ~ :L > w '-./ (Y) >D ~ a: fl EJ 1€)! ('; IE>! '-../ LL m €) €) €) w er: €) EJ ~ w z ~ IE)! 1€)1 I CL ~ ~:tta ~ 1-e-1 f-Oi E> 1€)1 IE7et ~ w L: t€>l l€>i 1€)1 .> 1-e-1 1-€>-1 S8WQlnQJQ8JIW 09E 83d SlNnQJ t-E>---\ _J ocr: . (I'") (I) er: _J 0 . N QJ H ;:l 'lO •rl µ.. -129- Figure 21 The 9-MeV Gamma-Ray Yield of the 19 F(a,y) 23 Na Reaction These yields were extracted from the same spectra as those of Figure 20. In this case, the region of summation was that of gamma rays of energy corresponding to the 12 C(a,y) tion for the particular lab alpha energy. to determine the effect of the yields. 19 16 0 ground-state transi- These yields were used F impurity on the For additional details see pages 76 to 79. 12 C(a ,y) 16 0 - 1300 r'T'"T--.--i-.--.--.---,.--~_,.,....-.---.---.~~---~~~~~~~~~~ €) • 0 €) _J €) €) €) w t--f >>- a: a: a: ~ ~ a: C) a: z .> w CY) 2: > w (Y) (\J >-.. lJ) ,,........ ~ E> €) e >- CJ) El E> E> C) 0:: E> W z E> €) rl N Q) w '""' a: ..'lO1 ~ LL m E> ::r:: µ., €) (L _J . en a IT CY) a: _J E> €) E> €) €) E> S8W~ln~J~8JIW 09E 83d SlNn~J