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UBC Theses and Dissertations

The direct capture reactions t([alpha, gamma]) Li7 and O16 (p, [gamma])F17. Riley, Peter Julian 1958

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THE DIRECT CAPTURE REACTIONS T( «K, ¥ )L i ' AND 0 (p,V by PETER JULIAN RILEY B.A.Sc., University of British Columbia, 1956 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in the Department of PHYSICS We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September 1958 ABSTRACT The d i f fe rent ia l cross section for the capture of t r i t ium by alpha part ic les to form L i? has been measured using a tritium-zirconium target and 1.64 mev. alpha par t i c les . The d i f fe rent ia l cross section for the gamma-ray transi t ion to the ground state of L i ? was found to be 2.54+: .46 x l O " ^ 1 cm. 2 per steradian at 90° to the incident alpha beam di rect ion. At the same energy, the rat io of the d i f fe rent ia l cross section at 90° for transit ions to the f i r s t excited state to that for transit ions to the ground state of L i ? was found to be approximately 0.40. The Tfatf )L i? 90° d i f ferent ia l cross section has been measured relat ive to the d i f fe rent ia l cross section at 1.64 mev. using alpha part ic les of energies 0.515, 0.72, 0.98, 1.23, and 1„94 mev. From the smooth change of the reaction cross section with energy i t can be concluded that the reaction proceeds by direct radiative capture. At a l l energies, the rat io of the d i f -fe rent ia l cross section at 90° for transit ions to the f i r s t excited state to that for t ransi t ion to the ground state was approximately 0.4. Preliminary angular d istr ibut ion measurements at 0 ° and at 90° to the incident alpha beam direction indicate that the angular distr ibut ion i s not isot rop ic . The rat io of the y i e l d at 0 ° to the y ie ld at 90° was found to be 1.40 t 0.37 at an alpha part ic le energy of 1.64 mev. Di f ferent ia l cross section measurements for direct radiative capture of protons by 0 ^ have been made relat ive to the cross section at 800 kev. , using a so l id tungsten-dioxide target and protons of energies 0.618, 0 9823, 1.13, 1.536, and 2.04 mev. Absolute 90° d i f ferent ia l cross section values were based on the measurement of the 90° d i f ferent ia l cross section for t ran-si t ions to the f i r s t excited state i n F 1 ? at 800 kev. of 10.4 £ 1 . 3 x 10~32 cm. 2 per steradian made by Robertson. The d i f ferent ia l cross section for the gamma ray transitions to the f irst excited state of at 90° to the inc i -dent proton beam direction, was found to vary smoothly from 0.41 x 10"^! cm.2 per steradian at 0.618 mev. to 11.9 x 10"-^ cm. 2 per steradian at 2.04 mev. At a l l energies the ratio of the differential cross section at 90° for tran-sitions to the ground state to that for transitions to'the f irst excited state was approximately 0.20. In presenting th i s thes i s i n p a r t i a l fu l f i lment of the requirements for an advanced degree at the Univer s i ty of B r i t i s h Columbia, I agree that-the L ibrary s h a l l make i t f ree ly ava i lab le for reference and study. I further agree that permission for extensive copying of t h i s thes i s for s cho la r ly purposes may be granted by the Head of my Department or by h i s representat ive . It i s understood that copying or pub l i ca t ion of t h i s thes i s for f i n a n c i a l gain s h a l l not be allowed without my wr i t ten permiss ion. Department The Univer s i ty of B r i t i s h Columbia, Vancouver 8, Canada. Date Stp{ , % V^ti TABLE OF CONTENTS CHAPTER PAGE I INTRODUCTION 1 II THE T(oC,y)Li7 REACTION 6 1. Apparatus: 6 (a) Target arrangement 6 (b) Gamma ray detector 6 (c) Electronics 8 2. Target: 9 (a) Target tritium content . • . . . . . • . • . . • o . . . . . e » . « e . . . » . . e 9 (b) Target thickness 13 3. Experimental: 14 (a) Background 14 (b) Procedure 13 4. Variation in gamma ray energy with alpha particle energy.. 19 5. Cross section determination: 21 (a) Background • 21 (b) Determination of the absolute cross section 22 (c) Errors 23 (d) Determination of the excitation function 24 6. Angular distribution measurements 25 7. Summary of experimental results 26 I H DISCUSSION 1. Comparison of T(«/, X)lA' with the mirror reaction He%.J0Be7 28 2. Comparison of T(pC;^)Li? with the inverse reaction u7(y,ocjT 29 3. The ground state of Li? 31 IV THE 0 l 6 (p , ^ )FX7 REACTION 38 1. Previous measurements 38 2. Apparatus: • • 38 (a) Target and target arrangement 38 (b) Gamma ray detector 40 (c) Electronics 42 3. Experimental: 42 (a) Background • 42 (b) Procedure 43 4. Target thickness 43 5. Determination of the excitation function 45 APPENDIX I. Gamma ray efficiencies for the 1.75 x 2.00 inch crystal . . 49 II. The Biased Distorter 54 BIBLIOGRAPHY 64 LIST OF ILLUSTRATIONS  NUMBER SUBJECT FACING PAGE FIGURES: 1. Low energy levels of L i 7 1 2. Low energy levels of F^ 7 4 3 . Target arrangement and beam tube 6 4. RdTh spectrum, showing calculation of full-energy peak efficiency for T&.jOLi 7 radiation 7 5. 20 mev. gamma ray spectrum from T(p,y )He^ 12 6. Stopping cross section for alpha particles in zirconium and in tritium 14 7. on T spectra, showing rise in target dependent back-ground at low energy 16 8. Gamma ray spectrum from tritium target 19 9. Variation in gamma ray energy with alpha energy 20 10. 3j09 mev. calibration gamma ray spectrum from C l 2 (d,P, J )013 22 11. Variation in T(©v\)f)Li7 90° differential cross section with Van de Graaff energy 24 12. Penetrability v s . - p a r t i c l e energy for reactions T(«< t }pLi 7 and for He3(*^)Be7 28 13. Gamma ray spectrum from a tungsten oxide target 43 14. Variation in 0 l 6 ( p , ^ ) F 1 7 90° differential cross section with energy 47 15. Gamma ray efficiencies for the medium counter 53 16. Percent f a l l in distorter output pulse height with input pulse repetition rate 56 17. Block diagram of biased distorter circuit 57 18. Biased distorter circuit diagram 64 PLATES: I. The Biased Distorter 54 ACKNOWLEDGEMENTS The author wishes to thank Dr. J . B. Warren, who suggested and supervised this research, and Dr. G. M. Griffiths, for his many suggestions and discussions of the thesis topic. The author is grateful to Mr. P. Singh, whose assistance was most helpful, and to Mr. G. Jones, for the design of the biased distorter and for suggestions concerning a l l electronic problems. Thanks are due also to Mr. D. Lindquist for help in operating the Van de Graaff generator. The author would like to thank Mrs. W.C. Olsen for assistance in the preparation of this thesis. The author gratefully acknowledges receipt of a Bursary and of a Studentship granted by the National Research Council. 2 4 6 5 + 3 / 7 E q 2 4 6 5 H e 4 + H 3 M 7 3 i r i Li .7 Li C y,t) J = 1/2" J = 3 / 2 " FIGURE I LOW ENERGY L E V E L S OF CHAPTER I INTRODUCTION: This thesis concerns the study of two reactions, both of the direct capture type but otherwise unrelated, (a) THE REACTION T ( ^ , y ) L i 7 Nuclear she l l model theory considers the L i nucleus as comprising three nucleons (one proton and two neutrons) i n the l p shel l outside a closed Is s h e l l . To f i r s t order, the ground state properties of L i 7 should be deter-mined by the odd proton i n the l p she l l , the angular moments of the two neutrons being coupled to zero. With the added concept of spin-orbit coupling, the ground state of L i 7 should be a P3/2" l e v e l , with the proton spin aligned paral-l e l to i t s orb i ta l angular momentum, and the f i r s t excited l eve l should be a Pl/2" l e v e l . There also should be a one-to-one correspondence between the energy 7 7 leve l s , spins, and parity values of L i and those of i t s mirror nucleus, Be , after correction for neutron and proton mass differences and coulomb binding effects. 7 The spin and parity of L i i n the ground state have been measured and found to be 3/2, of negative pari ty ( J .E . Mack, 1950), i n agreement with the above predictions. The f i r s t excited l eve l of L i 7 i s now believed to be a J - 1/2" l e v e l . Evidence such as the superallowed nature of the beta-decays B e 7 ( 6 ) L i 7 , 7 7* 7 and Be ( t ) L i , indicate that the ground state and f i r s t excited states of Be' are 3/2" and l/2~ states, confirming the one-to-one correspondence between low-ly ing states of L i 7 and Be 7 . L i 7 i s more stable than Be 7 by 0.863 mev., i n reasonable agreement with the calculated charge effect between the two nuc le i . However, the one-particle, or "Schmidt" description of the L i 7 nucleus above predicts a magnetic moment of 3.79 nuclear magnetons, compared with the experimental value of 3.26 nuclear magnetons ( J .E . Mack). To predict a magnetic moment closer to the experimental value, i t i s necessary to consider the vec--2-torial addition of the angular moments of the three p-nucleons. In the three-particle description J - 3/2 can be obtained either with the angular moments of the neutrons coupled to zero, as in the one-particle description, or with the orbital part of the angular momentum of the two neutrons aligned parallel. This second state gives a magnetic moment of -0.77 nuclear magnetons (Mayer and Jensen, 1955)j a suitable mixture of the two states could give the experimen-tally observed magnetic moment. Both the one-particle and the three-particle nuclear shell-model 7 descriptions of the L i ' nucleus predict a negative nuclear quadrupole moment, there has been considerable disagreement concerning the sign of the nuclear quadrupole moment of Li? , which now appears to be positive (see Chapter II) in direct disagreement with simple shell model predictions. Thus, the single particle shell model predicts the angular momentum, parity, and approximate magnetic moment of the ground state of Li? while a more accurate description of the ground state may be obtained in terms of three particles. Further refinements are required in order to explain the apparently positive sign of the nuclear quadrupole moment. The present work is a study of the T(»K . )y /)Li? reaction, which has not been previously reported. If an alpha-particle of energy less than (7/3 x 4.78) or approximately 11 mev. is used to bombard a tritium target, the T ^ ^ j L i reaction is the only reaction energetically possible apart from scattering. Above 11 mev. the particle reaction T(»< ;Li^)n becomes possible. The T(pC,|^)Li? radiative transitions might occur either through direct radiative capture, similar to the D(p, f )He^ and the 0^(p, j ^ F 1 7 reactions, or through compound nucleus formation through the tails of resonances at L i ' excited levels at 0.477 mev. and above 4.6 mev*; 'The energy deperidenceVand-cr^ thus be sensitive to the type of capture process. Since the levels at 0.477 mev. and at 4.61 mev. are not broad levels, the probability of radiative - 3 -capture with compound nucleus formation at an energy midway between these two l e v e l s i s low. I f we consider the d i r e c t r a d i a t i v e capture process, a t r i t o n with s p i n 1/2, and an alpha-particle with spin 0 can form i n i t i a l 2S, 2P, etc. states, depending on the o r b i t a l angular momentum of the alpha p a r t i c l e . S wave cap-ture, with e l e c t r i c dipole emission to the J = 3/2 - ground state of L i 7 , would be expected to be the most probable capture process; the angular d i s t r i b u t i o n , due to the S-wave capture, would be i s o t r o p i c . Hence, the study of the T ^ j O L i 7 reaction should y i e l d information concerning the type of capture process, and i n p a r t i c u l a r i t should show whether the above d i r e c t radiative S-wave capture, with subsequent e l e c t r i c dipole emission, occurs. A detailed study of the reaction may also y i e l d information concerning the structure of the ground state of L i 7 , about which there has been much interest and considerable d i s a -greement . The reaction T t V ^ j L i 7 i s also of i n t e r e s t f o r comparison with the inverse reaction L i 7 ( j ' J o i )T on the basis of r e c i p r o c i t y . (See Chapter H.) An accurate comparison of the cross sections '0r to fZ y cannot be made, however, since values of (T* have not been reported below 4«7 mev., and because of disagreement between the reported cross section values f* f o r higher energies. From a very approximate comparison, the cross section f o r T («c (y ) l d 7 should l i e i n the region from 3 microbarns to 0.1 microbarns at an alpha p a r t i c l e energy of 1.5 mev. With the r e l a t i v e l y t h i n t r i t i u m target available and the l i m i t a t i o n on beam current due to target heating, the counter used i n the present investigation was sensitive enough to detect r a d i a t i o n with cross sections as small as 0.1 microbams. This s e n s i t i v i t y proved to be adequate f o r an investigation of the T(p<,f ) L i reaction. ( 3 / 2 ) ( 7 / 2 " ) ( I / 2 - ) 1/2 + J = 5 / 2 1 4 - 3 5 4 9 9 • 5 9 9 + 16/17 O 5 9 9 0 ' 6 + •17 FIGURE 2 LOW E N E R G Y L E V E L S OF F 17 (b) THE REACTION O l 6 (p . frO*17 Shell model theory treats the pl? nucleus as a single proton moving in the potential of the closed 0"^ core. The ground states cf both F 1 7 and i t s mirror nucleus 0* 7 are predicted to be D5/2 levels with the odd nucleon aligned with its spin parallel to i ts orbital angular momentum. Experimental measurements are consistent with D5/2 for the ground states of both nuclei. The f irst excited levels of 0 1 7 and of F 1 7 appear to be levels, again consistent with present shell model predictions. Theoretical calculations for the cross section and angular distribu-tion of the reaction 0^(p, y)F*" 7 are being made by a California Institute of Technology group (private communication from N. Tanner). Similar calculations based on shell model predictions and on a direct radiative capture process, are being performed by Dr. G.M. Griffiths of this laboratory. Comparisons between theoretical predictions and experimental measurements should provide a check on the assumed theoretical models. The 0l6(p, v/)Fl7 cross section at stellar energies is of interest in astrophysics. The conversion of protons into alpha particles via the carbon-nitrogen cycle occurs as follows: C 1 2 ( p , ^ ) N 1 3 —> C 1 3 t / 3 f N 1 4(p, ^ )0 1 5 — N 1 * ^ ^ *, Nl5(p,^)C12 J lost from the cycle by the competing reaction , J^O 1^, i s replaced by the reactions 0 l 6 (p , p F 1 7 >6L1+ff, and 0 1 7 ( p , « ) N 1 4 . For stars whose main source of energy is the carbon-nitrogen cycle, the O ^ p , ^ )E^7 cross section ultimately determines the carbon-oxygen ratio in the star as a function of the stellar temperature (Cameron, 57). It i s not possible to measure the 0^(p, ^ c r o s s section at stellar energies; however, infor-mation obtained at the energies available is essential for theoretical extra-polations of the reaction cross section to the stellar energies. In order to check the theoretical calculations of cross section for the 0^(p, reaction, and because of the interest of this reaction in astro-physics, i t was felt that more accurate cross section and angular distribution data would be of value. The 90° differential cross section has been recently measured at 800 kev. by Robertson (57) of this laboratory. The present work was undertaken to provide a measurement of the 90° relative differential cross section in the energy range from 0.6 to 2.0 mev. - T A R G E T P O T I S O L A T I N G V A L V E W A T E R C O O L I N G A L P H A B E A M — F R O M V A N D E G R A A F F FIGURE 3 TARGET A R R A N G E M E N T AND B E A M TUBE -6-CHAPTER II THE T f o . p L i 7 REACTION; 1. Apparatus -(a) Target arrangement A schematic diagram of the target arrangement i s shorn in Figure 3, A tritium-zirconium target, with tungsten backing material, was used. The tar-get chamber, similar to one described by Alexander (1955), was that used by Robertson (1957) with tungsten oxide targets. Water cooling was applied to the target assembly in order to reduce target deterioration due to overheating. The target and support were insulated with a lucite ring to enable beam current measurements to be made; a positive potential of 90 volts was applied to the target system to reduce secondary electron error in the beam measurement. The beam current was measured with a current integrator, (Edwards, 1950). One integrator count corresponded to a charge of 107 microcoulombs to an accuracy of 1$. Since i t was found that charge leaked from the target on the water cooling hoses at a rate of from lk% to 20$ of the observed rate of charging, the true number of integrator counts was 1.17 - .04 the observed number of counts. (b) Gamma ray detector The detector used for this experiment was a 2.5 inch diameter by 3.5 inch long cylindrical sodium iodide, thallium activated, (Harshaw) crystal mounted as described by Robertson (1957) on a Dumont 6363 photomultiplier. The efficiency of the counter for gamma r a y s , £ ( E , E/2) is defined as the ratio of the number of counts of a gamma ray of energy, E, above a bias energy of E/2, to the number of gamma rays incident on the crystal. An efficiency of 0.612 .009 has been measured by Larson (57) for 6.14 mev. radiation, using FIGURE 4 RdTh SPECTRUM (2-5 in-DIAM- X 30 in-LONG XTAL) , SHOWING CALC-OF FULL- ENERGY PEAK EFFICIENCY FOR T ( a , r ) RADIATION w Z O o 8 0 0 0 -6 0 0 0 4 0 0 0 -2 0 0 0 F U L L - E N E R G Y P E A K E F F I C I E N C Y F O R T ( a , y ) R A D I A T I O N = c ( E , E / 2 ) X N , / N , + N 2 = ( - 5 6 ) X t 2 5 ) = I 14 ) % I -31 M E V ( E / 2 ) 10 15 C H A N N E L N U M B E R 2 0 2 5 gamma rays from the reaction F (p J^fO© . The efficiency, €. (E> E/2) at 1.17 and 1.33 mev. has been measured by P. Singh and H. Dosso (1957) of this Labo-ratory, using a Co source calibrated by the National Research Council of Canada. In order to extrapolate crystal efficiencies to other energies, the theoretical crystal efficiency has been calculated by P. Singh. Because the agreement between theoretical and experimental efficiencies at both 1.25 mev. and 6.14 mev. is within 5%, theoretical estimates of crystal efficiency are considered accurate to within 10% in the energy range 3 mev* to 6 mev. Since the detailed shapes of the separate gamma rays were not ob-served in this experiment due to overlapping of the spectra from two gamma rays and the presence of a high "target dependent" background, the efficiency was defined only for the number of counts under the fu l l energy peak of the T(e<^)Li7 gamma ray spectrum. Comparison spectra from Rdth and from G^(d,p,0C^ were used to compute fu l l energy peak efficiencies for the crystal at 2.62 and 3.09 mev. The efficiency calculation for 2.62 mev. radiation i s indicated by Figure 4 . The fu l l energy peaks of the T(©v(]f)Li spectra were broader than those from the mono-energetic calibration gamma ray spectra because of the spread in T(<<.,f ) L i 7 reaction gamma ray energy from the finite target thickness. The crystal efficiencies €(E, Eb) were consequently defined to a bias energy Eb slightly below the base of the fu l l energy peak for the calibration spectra. At 2.62 mev., '£ (E,E/2) = (56 ± 5) % and at 3.09 mev., e(E,E/2) « (56.4 15)% where the efficiences are theoeretical estimates of efficiency. At 2.62 and 3.09 mev., the f u l l energy peak efficiencies for T ^ y jLi? spectra were (14.1 ± 2.1) % and (13 t 2) % respectively. A l l runs were made at a counter distance of 1.91 inches from the front of the crystal face to the centre of the target, the counter being pushed -8-as close to the target pot as the shielding would allow in order to obtain a large solid angle. The solid angle was determined using the experimental measurement of the effective centre of Robertson (1957). The distances from the crystal face to the effective centre for 0.51, 1.28, and 6.14 mev. radia-tion are respectively 1.43 1 .08,in., 1.47 ± .10 i n . , and 1.60 £ .10 i n . A l l measurements are in agreement to within the experimental error. The effective centre distance used for a l l runs in the present experiment, extrapolated from the above data, was 1.52 i n . , again with a probable error of approximately 0.10 inches. The counter therefore subtended a solid angle of 0.418 steradians at the target, to a probable error of approximately &%. Slight photomultiplier gain shifts were observed, the maximum gain shift being approximately 1%. The photomultiplier gain shifts, a function of the photomultiplier counting rate, appeared less serious in the present work than in work where protons were used to bombard tungsten oxide targets (Robert-son, 1957)• A possible explanation is that high intensity radiation from the zirconium is much lower in energy (K X-ray from zirconium of 18 kev.) than radiation from tungsten (K X-ray of 66 kev.j 112 kev. Coulomb excitation line) and therefore causes less photomultiplier gain shift. However, the photomul-t ipl ier gain shift produced by alpha-particles on a tungsten target has not been investigated with the present counter, (c) Electronics The high voltage supply for the photomultiplier dynode chain was 1100 volts, supplied by an Isotopes Development Limited Stabilized power supply. The preamplifier after the photomultiplier was a 6J6 (parallel) cathode follower. The negative output pulses drove a Northern Electric wide band amplifier type 1444, which fed a "biased distorter" amplifier (see Appendix III). The "biased distorter" output was fed into a 30 channel Marconi kicksorter. The kicksorter -9-channei edges were set up by feeding pulses from an accurately linear mercury pulse generator (Robertson, 1957) onto the grid of the 6J6 cathode follower. The mercury pulse generator pulses were also used to check the stability of the electronics except for the photomultiplier, which was then checked by means of sources. 2. Target -(a) Target Tritium Content The tritium-zirconium target kindly supplied by Oak Ridge National Laboratories consisted of 429 mcs. of tritium taken up in a very thin film of zirconium (1.33 mgms., 1 -1 atomic ratio of tritium to zirconium) evaporated onto tungsten backing material. The target was circular, of diameter ( i t 1/128) inches, and of uniform thickness of (.0239 1 1 .0001) inches. The target tritium content has been measured on June 20, 1956, 1.58 years before this experiment was carried out. The tritium content at the time of this experiment, therefore, was estimated from N = No e ~ t / T where T = mean l i fe where T^ = £ l i f e = 12.26 years, so that T mean = 17.69 years t = 1.58 years, and No = 429 millicuries Therefore N = 429 (.914) = 392 millicuries Then from dN/dt = N/T mean, where dN/dt = 392 x 37 x 10^  dis./sec. N • 8.09 x I O 1 8 atoms of tritium The target area was 5.07 cm. ; therefore, on the assumption that the tritium was distributed uniformly over the target, the target tritium content was -10-1.60 x 10^ atoms of tritium per cm.2 After the T ( o » , y ) L i 7 work had been completed, the tritium content of the tritium target used was checked approximately, assuming the 90° differen-t i a l cross section for T(p, JO He4 reaction as measured by Perry and Bame (1955). The target was bombarded with 830 kev. protons, and the gamma ray flux was measured, n^, the number of tritium atoms per square centimeter of target, was then computed from J I Nv. H = 7 3 F \ ' ~ ' ~~ ' -r- ' x where € i s the efficiency of the counter r i s the target to effective centre distance A is the area of the face of the counter is the transmission coefficient for 20 mev. radiation through the 1/16 i n . brass walls, =o.S£T8 'Wp i s the number of protons incident on the target ^ £ i s the 90° differential cross section for T(p,]f/)He4 The target arrangement and gamma ray detector for the T(p,y)He 4 runs were the 7 same as those used in the T(c<,y )L i ' work. However, no target water cooling was used in the T(p( jOHe4 work. The following changes in the electronics were made; f i rs t , the voltage for the photomultiplier dynode chain was 880 volts, as this voltage gave a convenient gain with no apparent loss in resolution; second, a 100 channel Computing Devices of Canada kicksorter was used instead of the 30 channel Marconi kicksorter. It was therefore possible to count the whole 20 mev. wide spectrum at one time with reasonable dispersion. The crystal efficiency for 20 mev. radiation was computed from ab-sorption coefficients given in Siegbahn (1955) for Na and Iodine, J A . was calculated to be 0.1613 per centimeter for 20 mev. radiation for sodium iodide. -/iJL Then 6 = (i - e ) = 0.74. d^>x efficiency was then obtained from^tx x A -11-where A = area of the face of the crysta l , and r = distance from the target to the effective centre of the crys ta l . The distance from the crysta l face to the effective centre, x , has been measured by Robertson (1957), and has been found to disagree with the theoretical value predicted from x = - I n Co.5 (1 H-cyp -^1)1 However, theoret ical ly , X g p m e y < - Q . 8 g *6.1U mev. And i f we use the experimental value of 1.60 l i n . f o r XQ.i^mey. t h e x 20 mev. = 1.41 i n . * .10 i n . However, since x for a part icular crystal varies only with JH, then for the crystal used X 2 0 mev. should « x for 1.7 mev. radiat ion. From Robertson's measurements, x - ^ 7 2^^^= 1.48 t .1 inches. Within the probable error , the two values for x are the same; the value of x = 1.48 - .10 inch was used for this experiment. The above estimation of d ^ x eff iciency i s an approximation of the calculation of du>x e f f . = j e x o I Cos. <f>) c ^ v J r 2 v as performed by Perry and Bame, and i s jus t i f i ed because the inverse square relationship between the counting rate and distance does hold for distances measured to the effective centre. Currents of 5 microamperes were used at a bombarding energy of 830 kev. Time dependent background was negl igible over most of the energy range studied. The count rate between 10 and 20 mev. being 20 counts per minute, the bombarding energy was chosen below 1 mev. to avoid neutron pulses from the T(p,n)He 3 reaction. FIGURE 5- 20 MEV GAMMA RAY S P E C T R U M F R O M T ( p y ) H e O 2 0 4 0 6 0 8 0 CHANNEL NUMBER -12-Since the ef f ic iency calculat ion was based on the to ta l absorption coef f ic ient , i t was necessary to count the to ta l number of pulses produced by the gamma rays in the crysta l * Fluorine was found to be present i n the ta r -get; consequently, the low energy pulse spectrum from T(p,y)He^ was obscured by the 6*14 mev. f luorine gamma rays. However, the pulse distr ibut ion from T( p^)He^ was extrapolated smoothly to zero pulse height from above 6 mev. The pulse spectra, Figure 5, i s similar to that observed by Perry and Bame. n^, the number of t r i t ium atoms per cm.2, was calculated from the following data: r = 3.48 i n . A = 4.91 in? Nr= 35,300 counts. n_ s 50 integrator counts^ x 107 microcoulombs 1.602 x l O " ^ = 0.74 o'ys 0.958 for 20 mev. rad ia t ion through 1/16 i n . brass U1- - 2.96 x 10"*3 0 cm 2/steradian for ^> = 812 kev. d M > 9 0 ° " The target thickness, A, has been computed from Whaling (1954) to be 36 kev. , computed so that E f = 830 - A/2 s 812 kev. 1ft o n^ i s therefore computed to be 1.25 x 10 atoms/cm. which compares with the value of 2.03 x l O 1 ^ atoms/cm. 2 calculated on the basis of a 429 mi l l i cur ie target t r i t ium content. Errors are as follows: r 2 = 8% dr- = 1% H = 5# e = 10$ The standard error i s therefore 15$. -13-F o r the T ( ^ , j ^ ) L i ' c r o s s s e c t i o n c a l c u l a t i o n s , a t a r g e t t r i t i u m c o n -t e n t o f 2.03 x 1 0 1 8 a t o m s / c m . 2 r a t h e r t h a n 1.60 x 10^ a t o m s / c m . 2 , was assumed, s i n c e t h e T ( f (y ) H e 4 check was r u n on o n l y one p o r t i o n o f t h e t a r g e t . F u r t h e r , t h e T(f,)OHe4 check was done a f t e r the T f o r " )Li7 work and t h e r e may have been 7 some t a r g e t d e t e r i o r a t i o n d u r i n g t h e TC*,^  ) L i ^ r u n s . (b) Target T h i c k n e s s The t h e o r e t i c a l t a r g e t t h i c k n e s s was computed f rom t a b l e s c o l l e c t e d by W h a l i n g (1957), w h i c h d e f i n e t h e s t o p p i n g c r o s s s e c t i o n € K ( E^) i n terms o f ev-cm. /atom. From t h e mass o f 0.00133 grams o f z i r c o n i u m i n the t a r g e t , 18 2 the number, n ^ , = 1.734(10 ) atoms p e r cm. o f t a r g e t ; a u n i f o r m l a y e r o f z i r c o n i u m m e t a l over the t a r g e t s u r f a c e was assumed. Then t h e Z r t a r g e t t h i c k -n e s s , £ , i n k e v . a t an - p a r t i c l e energy ? i s g i v e n by A - ^ ( E j * n Z r x ( I O " 3 ) k e v . V a l u e s o f € ( E ) f o r a l p h a p a r t i c l e s i n z i r c o n i u m (Z o f 40) were e x t r a p o l a t e d f r o m v a l u e s g i v e n f o r Ge (Z o f 32) and f o r Ag (Z o f 47). 6^ ( w a s assumed t o v a r y l i n e a r l y w i t h Z , i . e . The p r o b a b l e e r r o r s quoted f o r ( € ^ ) A and (fe^  )Qe were 10%, t h e e r r o r t h e r e -f o r e expected f o r ( 6 ^ ) ^ r i s expected t o be a p p r o x i m a t e l y 15$. ( ) Z r c o u l d not be e s t i m a t e d f o r e n e r g i e s below 1 mev. by t h i s method owing t o l a c k o f d a t a . A second, l e s s a c c u r a t e e s t i m a t e o f {^^Zr w a s u s e c * ^ o r e n e r g i e s below 1 mev. Tables o f * « / £ p ( W h a l i n g , 1957) were used t o g i v e f r o m t h e r e l a t i o n s h i p < k ( £ * ) - ( € * / € „ ) X € r ( * r = ) where = t h e s t o p p i n g c r o s s s e c t i o n f o r p r o t o n s i n z i r c o n i u m a t an energy FIGURE 6 x 10 4 0 -a o 2 0 STOPPING CROSS SECTION €a{Ea) , FOR ZIRCONIUM AND, IN TRITIUM ALPHA PARTICLES IN 0 - 4 0 8 € a ( Z r ) = € _ ( G e ) + 0 - 5 3 [ « a U g ) - € a ( G e ) ] e ( Z r ) = U a / € p ) X € p ( E p = E a / 3 9 7 ) « a t T ) = ( € a / « p ) X « p < E p = E a / 3 - 9 7 ) W H E R E € p = € p ( H 2 ) 12 1-6 E a C M E V ) -14-Ep, where Ep i s evaluated for Eoc . 3.97 To obtain € p (Ep) i t was necessary to extrapolate from £p for Cu (Z of 29) to €p for Au (Z of 79). A l inear dependence of €p(Ep) on Z was assumed. The probable error in was given as 20$. If the probable error i n the ep extrapolation error i s approximately 20$, then the standard error in as computed by th is method should be approximately 30$. The approximate stopping power of the t r i t ium i n the target was simi lar ly computed from 6 = £ ~ x € p r / E p = _E^\ \ 3.97 / where 6^ E ) was the stopping cross section for alpha part ic les i n hydrogen gas. The standard error in €, /<£. i s again 20$; there i s presumably also some error i n assuming that i ^ ) ^ - (%)f The computed stopping cross sections are shown plotted i n Figure 6. To within the probable error, there i s no change i n the tota l stopping cross section for the target i n the energy range 0.5 to 2 mev. At 1.64 mev., A = L ( € »< ) Zr X n Zr ( ^ t x n t ] * 1 , 2 7 x 1 0 ~ 3 k e v * where the factor 1.27 i s introduced because the target i s oriented at 52° to the ^-bearn. Then A - [(1.734) (97) x 10 3 + (9.24) (1.60) x IO 3 ] * 1.27 x 10" 3 = 232 kev. 3. Experimental -(a) Background Since a low reaction y ie ld was expected, considerable care was taken to reduce interfer ing radiat ion. The walls of the target chamber i n the v i c i -n i ty of the target, and the stops i n the side arm were gold plated to reduce coulomb excited gamma radiat ion. A l i q u i d nitrogen trap was used i n front of -15-the target chamber to reduce the formation of carbon deposits on the target from cracked dif fusion pump o i l vapors. Before the experiment was performed, the target chamber, stops, and other side arm components were thoroughly cleaned to remove carbon deposits. The magnet box of the 90° deflection mag-net was also removed and thoroughly cleaned with steel wool and hot dilute n i t r i c a c i d . The target, target chamber, and gamma ray detector were surrounded on a l l sides by approximately four inches of lead i n order to reduce background from secondary cosmic radiat ion, radiation from radioactive sal ts i n the con-crete, and machine X-ray background. With th is shielding, the time dependent counting rate in the energy range from 2.G to 3.5 mev. was $ counts per minute. Lead and paraff in blocks were placed between the magnet box and the counter to reduce background from any (d,n) and (rX,n) reactions i n the magnet box. To estimate the to ta l background from sources other than from contami-nants i n the target i t s e l f , a sheet of zirconium metal was placed on the reverse side of the target holder to the target, and the target holder r e -versed to run the "beam dependent" background. The beam dependent background was approximately 12 counts per minute in the energy region 2.0 to 3*5 mev. for energies below 1.6 mev.; that i s , 50% higher than the time dependent back-ground. I f i t i s assumed that radiation i s readi ly detectable i f i t i s twice as intense as background, with the above background and a beam current of 10 -31 2 microamperes, i t would be possible to detect a cross section of 10 ^ cm. with the target thickness used i n the present work of 1.60 x 10 1 * atoms per cm. 2 The beam dependent background increased above 1.6 mev., and by 1.9 mev. had increased to 68 counts per minute i n the energy range from 2.0 to 2 0 0 IOO 2 - 6 2 M E V E a = 7 2 0 K E V 2 0 0 IOO 2 - 6 2 M E V E a = 5 1 5 K E V o o C——o-2-62 M E V 2 0 0 r -1 0 0 E a = 4 1 5 K E V ~o—rj—°—a—°-y— a o n Z r - " B E A M D E P - " B A C K G R O U N D * * * * * » * • f * - • . * * - ^  * T « I 2 0 0 I O O 2 6 2 M E V 2 0 M E V 3 5 M E V I 10 15 2 0 2 5 C H A N N E L N U M B E R 3 0 FIGURE 7 a ON T S P E C T R A , SHOWING RISE IN TGT -DEP - BACKGROUND AT LOW ENERGY C A L L R U N S A R E O F 30 X 107 / I C O U L O M B S ) -16-3.5 mev. The increase in background is believed to be caused largely by (d,n) reactions from the base of the Van de Graaff accelerator tube. Any molecular deuterium in the alpha beam would be a prolific source of neutrons from C^ 2 (d,n) and C 1 3(d,n) reactions. The Gp(tl/n)Q^ reaction cross section should also increase with energy. Considerable radiation from the zirconium backing is also possible for energies above 1.6 mev. However, at a l l energies the beam dependent background was small compared with "background" from the target i t se l f ; that i s , a large number of counts remained below the characteristic gamma ray spectrum counts attributed to T(fC,|^) reaction gamma rays after subtraction of beam dependent background. The spectrum shape of the "target dependent" background indicated that i t was caused by neutrons; apart from the small irregularities the background de-creased monotonically with increasing pulse energy. In the alpha particle energy range from 0.7 to 1.6 mev., this "target dependent" background yield was from.4 to 7 times the beam dependent background yield. The target;, depen-dent background increased markedly at E « 1.9 mev., and also at energies below 0.7 mev. At 0.5 mev., the background was higher by a factor of 2 than at 0.7 mev,, and at 0.4 mev., was higher by another factor of 2. Figure 7 shows this increase in target dependent background at low Van de Graaff ener-gies. Neutrons were observed with a neutron counter at 1.9 mev., but not at 300 kev., although i t i s possible that the bias of the neutron counter was incorrect. The Nal crystal radiation at 300 kev, did not have significant 1/2 hour half-life of the (I 1 2^, n) reaction characteristic of the absorption of neutrons in a Nal(TA) crystal; counting stopped when the beam was removed. No characteristic gamma ray spectrum was observed in the background spectrum -17-in the energy interval from 0,7 mev. to 6.2 mev. Further, since the number of target-dependent background counts above 6.2 mev. was approximately equal to the number of time-dependent counts, the high target dependent background was not caused by gamma rays of energy "greater than 6.2 mev. Neutrons were expected through H (t,o< )2n and H (t,n)He reactions from "knock-on" tritons in the target. The neutron yield, however, should increase monotonically (Ajzenberg and Lauritsen, 1955). The reaction T(d,n)He^ has a maximum near Ed = 107 kev., with a cross section of 4.95 barns (Argo et a l . , 1952), and therefore should be a prolific source of neutrons at low energy i f molecular deuterium were present in the alpha beam. Cross sections for higher deuterium energies are as follows: Ed (kev.) cross section (bams) 107 4.93 109 4.44 190 2.78 243 1.85 270 1.50 384 0.77 653 0.38 Since the target used in the present T ^ j O l d ? work was reasonably thick (appro-ximately 50 kev. for protons), the high target dependent background at low bombarding energies could be caused by the T(d,n)He^ reaction. However, the present work was done with no deuterium source bottle present in the Van de Graaff accelerator; deuterium contamination of the alpha beam was therefore not expected. Further measurements are s t i l l required to determine the source of the target dependent background. At a l l energies the target dependent background introduced uncertainty in the yield measurement from T(o<, )Li7. Because the yield from the reaction gamma rays decreased with decreasing energy, i t was not possible to estimate -18-the reaction cross section at alpha particle energies below 0.50 mev. (b) Procedure The target was bombarded with singly charged alpha particle beams of from 3 to 5 microamperes supplied by the University of British Columbia electrostatic generator. The target was positioned at 38 ° to the beam tube to avoid attenuation of the radiation by the target holder. The 38° orien-tation was chosen, rather than the more usual 45° position, because of a con-venient mark for target alignment at 38°» To check for target uniformity, spectra were recorded on four different portions of the target. No signifi-cant differences in yield were so obtained, indicating reasonable target uniformity. It was also hoped to reduce target dependent background by changing the target position. Prolonged bombardment changed the target sur-face from a light mottled-grey to a dark smudged-grey colour, indicating the presence of contaminants such as carbon, probably from the break-down of pump oils and vacuum grease. 1.6 mev. was chosen as the energy for an absolute determination of 7 yield because of a relatively high ratio of T(^,^ )Li reaction yield to back-ground at this energy. Buns at other energies were preceded and followed by runs at 1.6 mev. in order to check more easily for target deterioration. Runs were kept short (30 integrator counts of 107 microcoulombs each), also in order to check more easily for target deterioration. Deterioration was ob-served only once, following a run at 1.2 mev. The beam current of 5 micro-amperes, is believed to have been too high or else the beam was not sufficiently defocussed, thereby heating a small section of the target too intensely. Spectra were recorded of transition directly to the ground state of L i 7 , indicated by jf , and of transitions to the first excited level of L i 7 , CHANNEL NUMBER - 1 9 -indicated b y j ^ . Transitions from the f i r s t excited l eve l of Id? to the ground state,K^, were observed. However, no cross section measurements were made using if 2 transit ions. Figure 8 i s a pulse distr ibution spectrum for TCy^) radiation showing J , ^ 3 * Measurements were made on ^ , and ^ a t bombarding energies of .515, .720, .980, 1.64, and 1.94 mev. The l inear i ty and cal ibration of the Van de Graaff energy scale measured by the generating voltmeter were determined by measuring the positions of the .340, .8735, and 1.372 mev. reso-nances of F^(p,c< ,y ) 0 ^ . A l l runs were made with the same energy dispersion, and because the change of gamma ray energy i s only 3/7 of the change of alpha part ic le energy, most of the spectra were recorded over the same energy range also. The energies of the gamma ray spectra i n the 3 mev. region were measured by using RdTh as a cal ibrat ion point for the mercury pulse generator amplitude scale. The l inear i ty of the pulse height versus gamma ray energy scale was approximately 1%. Frequent checks were made on the kicksorter channel positions. 4. Variation i n gamma ray energy with alpha part icle energy -In order to check that the observed radiation rea l ly originated from 1(0^^)1^7, careful measurements were made on the variation i n gamma ray energy with alpha part icle energy. The gamma ray energy for the transit ion to the ground state from the capturing state i n the reaction T(«t\f)Li i s given by E f + (  kft) - 2 . 4 6 5 + Mf 5" where E^j i s the gamma ray energy i n mev., and E i s the average energy of the alpha part ic le i n the target. The effect of doppler shift i s neglected. Since measurements were made with the counter at 9 0 ° to the incident alpha beam, doppler shift was eliminated, and the above expression i s correct. Neglecting the small effect of r e c o i l , FIGURE 9 - VARIATION IN GAMMA RAY E N E R G Y WITH A L P H A E N E R G Y 2 4 0 O 0 - 4 0 E a , 0 - 8 0 1 -20 1 -60 I N C I D E N T A L P H A E N E R G Y ( .MEV ) -20-E f x = 2.465 +3/7 The observed values of are shown plotted i n Figure 9. Changes i n E follow closely A E n = 3 / 7 A E ^ where A^E = change i n energy of the incident alpha beam, which are the changes we expect i n E ^ ^ since the target thickness remains approximately constant at a l l energies used. This seems excellent evidence that this reaction i s being observed. However, E j ^ i s 105 kev. less than 2.465 + 3/7 E^ where E ^ i s the energy of the incident alpha beam. The theoretical estimate of the target thickness was 232 kev. We therefore expect from E^ = E ^ - A/2, where A i s the target thickness, that the average alpha-particle energy i n the target i s 116 kev. less than the i n c i -dent alpha part ic le energy. Since A E f = 3/7 A E , E should be 50 kev. less than 2.465 -v 3/7 E ^ The observed value of E ^ i s therefore 55 kev. too low. However, this 55 kev. energy discrepancy could be caused either by a concentration of t r i t ium near the back of the target, or by the presence of more zirconium i n the target than i s indicated. An approximate check on the target thickness was made by measuring the width of the full-energy peak of 1 # I f the f u l l width at 1/2 maximum height of the full-energy peak for a l i n e source i sPj jkev. , and the target thickness i s A kev., then the resultant width P of the f u l l energy peak is r— 1 given approximately by P s/2 -*Tg2 kev. I f we approximate the f u l l energy peak by a Gaussian, at any energy i n the target the f u l l energy peak for reaction gamma rays can be represented by a Gaussian. The observed f u l l energy peak of the spectrum represents an in f in i t e sum of small -21-Gaussians spread over the target thickness. For target thicknesses A less than or approximately equal to the resolution width TR the observed f u l l energy peak i s approximately Gaussian i n shape and of width as given above. The mean value of & computed from A = Jy2 _ p^ 2 i s 100 kev. , i n agree-ment with the estimated target thickness of 232 kev. for alpha par t ic les . The above calculat ion i s not an accurate calculation of target thickness be-cause of f luctuations of counter resolut ion; the probable error i s estimated to be 20 kev. A concentration of t r i t ium near the back of the target should cause the target to appear thinner; the presence of extra zirconium would cause the target to appear thicker. The above measurement of the gamma ray peak width therefore does not explain the discrepancy in gamma ray energy. Because the f u l l energy peak of Yz. coincided with the (full-energy -m Q c 2 ) peak of ^ >, the energy w a s n o * accurately determined. jf^ was also observed of energy approximately 0.5 mev.; however, precise energy and y i e l d measurements were not attempted. 5. Cross section determination -(a) Background Because of the high target dependent background, the beam and time-dependent background measurements were of l i t t l e use i n determining the true background l e v e l . The background level was estimated from the appearance of the spectra; counts recorded below the base of the ful l -energy peaks were con-sidered as background. The numbBr of counts i n the ful l -energy peak of Y 2 w a s determined by subtracting from the ful l -energy peak of t n e contribution from the (full-energy - mrjC 2) peak of Jfj . This (full-energy - mgc2) contribution was determined by assuming the spectrum shape for / to be the same as the spectrum 6 0 0 0 FIGURE 10 3 0 9 M E V CALIBRATION GAMMA RAY S P E C T R U M FROM C l 2 ( d p , r ) C 1 3 4 0 0 0 2 0 0 0 1-5 4 2 0 /I 2-5 /I O 10 2 0 C H A N N E L N U M B E R shape for the Cx ,< J(d,p, 3.09 mev. gamma ray, shown in Figure 10. Again, counts below the full-energy peak were considered to be background, (b) Determination of the absolute cross section The counts attributed to y, transitions during five runs over four different sections of the target were summed. The differential cross section for transitions at a bombarding energy of 1*64 mev. was calculated as follows: *^Vt ^per steradian ~ (du3 ^ * ^ from which, ( d r ) = 1 Hy. r 2 1 1 ( d « , ) « ^ ( e A n ^ nr where 6 = 0.13 is the fu l l energy peak efficiency of the counter, r = 3.43 inches is the target to effective centre distance, 2 A r 4*91 inches , is the area of the face of the counter, ~ 0,956 is the transmission coefficient for 3.06 mev. radiation through 1 the 1/16 inch brass walls, n^ r 140 integrator counts x 107 micro coulombs x 1.17 is the number of l t 6 0 2 x 1 0_!3 alpha particles incident on the target, nj = 1.60 x 10 1 8 x 1.27 * 2.03 x 10 1 8 atoms per cm.2, where 1.27 was intro-duced because the target was at 52° to the alpha beam, 2956 counts, after background subtraction. Then (d<r) 2956 x (3.43)2 x 1 x 1. (du.) .956 0.13 x 4.91 1.095 x 1017 2.03 x 10l 8 90° - 2,54 x 10"31 cm. per steradian. The ratio of the differential cross section for ^ 2 transitions compared with the value computed above for y transitions was calculated from (der) r2 N ^ 2 9tr Using 0.14 as the fu l l energy peak efficiency for 2.62 mev. radiation, (d£) Id^ Tj T2 £H3 - 1260 x A£ x 0.956 = 0.40 2956 .14 0.954 90^  Adding the contributions from both transitions, the 90 differential cross —31 2 section at a bombarding energy of 1.64 mev. is 3.54 x 10 cm. per steradian. Assuming an isotropic angular distribution, the total reaction cross section -30 2 is therefore 4.4 x 10 -^cm. If the tritium is distributed uniformly throughout the zirconium layer, the average energy of the alpha particles in the target at a bombarding energy of 1.64 mev. is (1.74 - .116) mev. However, i f the tritium is concen-trated near the back of the zirconium layer, as the observed gamma ray energies indicate, the average energy of the alpha particle beam in the target is (1.64 - .23) mev. (c) Errors Sources of error in the differential cross section measurement for transitions at a bombarding energy of 1.14 mev. are as follows: Source Probable Error r , effective centre and beam position 8% € , counter efficiency 15% n ^ , number of incident alpha particles 3.4$ 0 - 5 » 0 V A N D E G R A A F F E N E R G Y ( M E V ) FIGURE II VARIATION IN T ( a , r ) L i DIFFERENTIAL CROSS SECTION WITH VAN DE GRAAFF ENERGY -24-N yt , from counting s ta t is t ics - 5$ ) from background error - 7 $ ) 7.7$ ( Z : ( e r r o r ) 2 j l / 2 ) = 1 9 $ For y 2 t ransi t ions, the probable error i n the estimation of N ^ 2 was 2 2 $ , caused by counting s t a t i s t i c s (5$), background error ( 1 5 $ ) , and subtraction error (15$). The standard error i n the estimation of (d<r )/(d<*))f2 i s therefore 23$. No attempt has been made to allow for possible error i n the t r i t ium con-tent of the target; th is could introduce a considerably larger error into the 1 cross section measurements. (d) Determination of the Excitation Function Di f ferent ia l cross section measurements re lat ive to the measurement at 1 . 6 4 mev. were made at bombarding energies of 1 . 9 4 , 1 * 2 3 , 0 . 9 3 , 0 .72, and 0.515 mev. For }ft t ransi t ions, whose energy varied from 3 .13 to 2 . 5 9 mev., the counter ef f ic iency was assumed to vary l inear ly between £ 3 ^ 0 9 mev. s and € 2 . 6 2 mev, = .14. For ^ t r a n s i t i o n s , whose energy varied from 2 . 1 to 2 . 7 mev., the ef f ic iency was assumed to be constant a t € 2 # 6 2 mev. s ^ n e probable error i n a l l cases was considered to be 15$. The s l ight changes i n transmission coeff icient for the brass target pot walls were neglected. Relative cross sections were computed from ( d r ) = (d<r ) X N J L x JL^LL 1 . 6 4 mev. ( d - ) ( d - ^ ( , 1 . 6 4 mev. (N/ t ^ 1 . 6 4 mev. e The result ing d i f ferent ia l cross sections, a l l measured at 9 P ° to the incident alpha par t ic le beam, are tabulated below, and are shown plotted i n Figure 1 1 . E^mev. N ti -31 2 w f 2 Ufi x 1 0 " 3 1 cm 2 / Counts/30 i n t . ( d T ) x 1 0 cmf/ Counts/30 i n t . (d«>)y0 s ter . UMTi ster . _ 1 . 9 4 7 1 4 9 6 2 , 8 6 . 6 3 260 200 . 9 7 .74 1 . 6 4 6 3 3 50 2 . 5 4 .41 260 70 . 9 7 . 2 6 -25-1.23 517 38 2.08 .39 200 70 .74 .26 0.98 344 28 1.31 .25 140 50 .52 .19 0.72 240 40 0.89 .21 140 50 .52 .19 0.515 173 41 0.64 .19 60 40 .22 .15 The probable error in cross section values for transitions is larger than the probable error for transitions because of the added uncertainty in N ^2 caused by the subtraction of the contribution of the (full energy - n^c2) peak of Yi from the full energy peak for ^ 2 transitions. 6. Angular Distribution Measurements -Angular distribution measurements were made at 0° and at 90° at 1.64 mev. onj^ transitions. The same counter, a 2,5 x 3.0 inch sodium iodide crys-tal mounted on a 6363 Dumont photomultiplier, was used as in the cross section measurements. A 1.75 in. diameter by 2.0 in. long sodium iodide (thallium activated) crystal, mounted on an R.C.A. 6342 photomultiplier, was set at 90° to the incident alpha beam and used as a monitor counter. All pulses from the monitor counter greater than 2. mev. triggered a discriminator and were subse-quently recorded by a scaler. The target was oriented at 45° to the incident alpha beam so that the gamma rays were attenuated by the target equally in the 0° position and in the 90° position. The counter was moved farther from the target than in the cross sec-tion measurements in order to reduce the solid angle subtended by the counter. The yield was reduced by a factor of approximately 5 to the yield in the cross section measurements; at this reduced yield the time dependent background was comparable with the target dependent background. The yields at 0 and at 90 were compared by assuming a constant flux per unit solid angle. Integrating a sin 2 yield over the counter at the effec-tive centre for the distance used (r s 6.66 inches) gives a result differing -26-by approximately 1% from that of an isotropic dis tr ibut ion; integrating a s i n " y i e l d over the counter at the effective centre for the distance used i n the cross section measurements (r • 3.43 inches) gives a result di f fer ing by appro-ximately 3% from that of an isotropic dis tr ibut ion. At both distances the error i n assuming a constant flux per unit sol id angle i s small. The angular distr ibution could therefore be more accurately measured with the counter closer to the target, that i s , with an effective centre distance of approximately 3.5 rather than 6.6 inches, because of the lower background to y i e l d rat io at the larger so l id angle. From the above measurements, (1 ± .37) 1.39 o 0 The yields at 0 ° and at 90° di f fer only by a l i t t l e more than the probable error of the measurement, but i t would appear that the angular d i s t r i -bution i s def ini te ly not i sotropic . 7. Summary of Experimental Results -7 From the smooth change of the ?(*>Y)IA cross section with energy i t can be concluded that the reaction proceeds by direct radiative capture. The 90° d i f ferent ia l cross section for transitions d irect ly to the ground state of L i 7 i s 2.54 x 10""31 cm. 2 per steradian at a bombarding energy of 1.64 mev. Adding the contributions from the ground state transit ions, ^ t > and from transitions through the f i r s t excited l eve l of L i 7 , ^ , gives a 90° differen-t i a l cross section at 1.64 mev. of 3.54 x 10"^ cm. 2 per steradian, which corresponds to a tota l reaction cross section of 4.4 x l C T ^ c m . 2 i f we assume -27-an isotropic angular dis tr ibut ion. The mean alpha-particle energy i n the tar-get i s believed to be between 116 and 230 kev. less than the bombarding energy as measured by the Van de Graaff generating voltmeter. Relative cross section measurements have been made at bombarding energies from 0.5 to 1.9 mev. At a l l energies the rat io i s approximately 0.4. Assuming an isotropic angular dis tr ibut ion, the tota l T(«<y)Li7 reaction cross section i n the energy range studied can be expressed approximately by <T~ = 3E where 1 = (bombarding energy - .116) mev. Cr*-Preliminary measurements indicate that the angular distr ibution i s not i sotropic , as would be expected from a purely s-wave capture process, the y i e l d at 0° to the incident alpha beam being larger than the y i e l d at 90°. A L P H A P A R T I C L E E N E R G Y ( M E V ) 0-5 10 1-5 2-0 2-5 3 CHAPTER III DISCUSSION; 7 3 7 1, Comparision of T(oc!.f)Li with the mirror reaction He (p<, y )Be -After the present T(e<»)f ) L i 7 work had been performed, i t was learned that similar work had been done on the mirror reaction He3(o<( Jf)Be7 at the U.S. Naval Research Laboratory. Cross section values obtained for the He^Co^y )Be7 reaction are given below. (Private communication from R. L. Johnson for H.D. Holmgren) The third column gives comparable cross section n values for the T(cAv|f )Li reaction, where to allow for target thickness, E i s taken as ( E ^ d e G r a a f f - 116 kev.) Average U. -particle energy_in target Eo< He3(cA^)Be7 microbarns T ( * , r ) L i 7 microbarns Ratio tf^He3,c* 1.3 mev. 1.30 t .08 3.9 3.0 1.1 mev. 0.76 ± .06 3.4 4.5 0.9 0.40 *.02 2.7 6.7 0.7 0.19 4..02 2.0 10.5 0.5 0.04 ± . 0 2 1.6 40 To compare the H e 3 ^ f )Be7 cross sections with the T{d,y ) L i 7 cross sections, the penetrabilities (l/Ao) 2 , for s-wave capture, and ( l / A l ) 2 , for p-wave capture, were plotted for the two reactions, as shown in Figure 12. 2 2 2 2 Values of (l/A) , where A s F G, where F ^ j and G^ ^ are the regular and irregular Coulomb fractions, were taken from "Graphs of Coulomb Functions", (Sharp, Gove, and Paul, 1953). In these graphs, (A) 2 is plotted versus p for specific values of log^Q^, Z Z ' / R where^ = 29.05 - \ and = 0.1574 Z Z' ( ^ ) ^ Z and Z1 are the atomic numbers of the colliding particles, -29-y t * i s the reduced mass i n atomic mass uni ts , l/3 l/3 R i s the nuclear radius, which was taken to be 1.45(3 + 4 ) Fermis *^is the kinetic energy of the re lat ive motion of the two par t ic les . From the known values of alpha part ic le bombarding energy, values of ^ and then values of ^ were obtained. From Figure 12, the values of the rat io of ( l / A o ) 2 for o«. on I to ( l / A o ) 2 for<*. on Hte3 are respectively 2.8, 3.8, 5.8, U , and 30 for the alpha part ic le energies 1.3, 1.1, 0.9, 0.7, and 0.5 mev. The rat ios of the observed cross sections for the two reactions are approxi-mately equal to the rat ios of the penetrabi l i t ies for the two reactions over the whole energy range. The agreement between the two sets of cross section data i s therefore considered to be good. 2. Comparison of T ( * . ^ ) L i 7 with the inverse reaction L J ^ C X A M T -The expected cross section for the photodisintegration reaction L i ^ ^ c O T can be calculated from the measured cross section for Ti* ^ jf using the pr inciple of rec iproci ty . From rec iproc i ty , ( 2 I A + 1 ) ( 2 I a + l ) P a l o ; b = (2 I B - t - l ) (2I b -+ D P b V b a where (2I A + l ) = (2 Lp +• l) ' = 2 (2 I a + 1) = ( 2 ^ + l ) = 1 ( 2 I B + 1 ) = (2 1^+1) =4 (2I b +1) = (2 1^ + 1) = 2 Pa = £ -firn+t^ EL, = centre of mass J<-par t ic le energy « 9/49 E_, L ab. = h Y c Then 1JL£- - 4 ( P f ) 2 <TY<K " ( P ^ ) 2 -30-For E , = 1.6 mev.. rr~ - 56 The cross section (T~ measured i n the present work i s approximately 4 micro-X barns at 1.6 mev. Thus, (7^ = 240 microbarns for E ^ = 3.2 mev. An excitation function for L i (J.ok )T was f i r s t measured by T i t t e r -ton and Brinkley (1953) for energies up to 24 mev. using bremsstrahlung radiation from a synchrotron. Ti t terton and Brinkley (1953) also carried out absolute cross section measurements for L i 7 ( y , ° < ) T at 6.14 mev. using f luorine radiat ion, and at 14.3 and 17.6 mev. using radiation from the 440 kev. reso-nance i n L i 7 ( p ,]{')Be8. The observed cross section at 6.14 mev. was 15 micro-barns was found at 6.14 mev. by S t o l l and Wachter (1953), also using f luorine radiat ion. Erdos, S t o l l , Wachter, and Wateghin (1954) investigated the reac-t ion Li7(](,ck )T using radiation from a 31 mev. betatron. Excited levels i n L i ? were found at 4*7, 5.5, 6.8, 8.3, and 9 mev. The f i r s t three levels (4.7, 5.5, and 6.8 mev.) had a relat ive intensi ty of 1 : 0.75 : 0.75. The absolute cross section for Li7(^, <*. )T obtained from known C-^Of. }<*) cross sections was approximately 190 microbarns at 4»7 mev. The cross section for Li7(y > 0^)T calculated from the cross section for T( o<, f )L i? observed i n the present work i s apparently i n reasonable agreement with the measurements of Erdos, S t o l l , Wachter and Wateghin, but i n marked disagreement with the cross section values observed by Tit terton and Brinkley, and by S t o l l and Wachter. It would be interesting to investigate the photodisintegration of IdTat lower energies than has been done, where the reaction cross section could be expected to depend more on the ground state wave function, and less on the characterist ics of higher excited l e v e l s . I t has been shown by Peaslee and Telegdi (1953) that comparison of -31-the y ie lds from L i 7 ( ) f ,cOT and Li 7 (^, /v^)Li^ provides a way of ident i fy ing the T = 3/2 levels of L i 7 . When L i ' ' i s bombarded with gamma rays, excited states of T = 3/2 and T = 1/2 result from the selection rule A T = 1 , 0 . L i 6 has both T = 0 and T = 1 low-lying levels j He^ has only T = 0 low-lying l e v e l s . Neutron and t r i ton emission i s therefore allowed from T a \ states. From T = 3/2 excited states, neutron emission i s allowed to the T = 1 state, but t r i ton emission i s forbidden from the selection ru les . More levels i n the neutron y i e l d curve from L i f y , / ^ ) L i ° above 9 mev. (Katz and Goldenberg, 1954) than i n the t r i ton y i e l d curve from L i 7 ( tf.cOT i n the same energy region, support the above argument. However, the argument i s of no concern i n the present work, since the very low levels of L i are T s \ states. Presumably, at high energies, the T ( « r \ , ^ ) L i 7 reaction cross section would not show reso-nances at T = 3/2 levels of L i 7 . 3 . The Ground State of L i 7 -7 There has been much interest i n , and speculation on, the L i nucleus. From Shel l Model considerations the ground state wave function of L i 7 i s uniquely defined i n a JJ configuration as having J s 3/2, T s £ (Mayer and Jensen, 1955)• The ground state configuration i s (*i s ) 2 ( ^ i p 3 / 2 ) 2 (TT i s ) 2 (trip3/2) where V indicates a neutron state, and IT indicates a proton state . The configuration, (v-jp3/2) (TJ i/»3/2) which makes up the wave function, contains levels with J s 7/2, 5/2, 3/2, and 1/2, i . e . the two neutrons and one proton combine in JJ coupling as i s indicated below, where negative values of Mj are not indicated. 6r;/»3/2) (* <p3/2) (*;/>3/2) %_ _ J _ 3/2 3/2 1/2 7/2,5/2,3/2,1/2 7/2 1/2 -1/2 5/2,3/2,1/2 5/2 -32--1/2 / -3/2 3/2,1/2 3/2 -3/2 1/2 -1/2 3/2,1/2 3/2 -3/2 1/2 1/2 The desired wave function i s therefore of the form // 3 / 2 I 3/2 ^ 3/2 -3/2 1 , 3/2 1/2 -1/21 r3 /2 = a [ f > p ) C ^ )|+b|(7r ^ ) ( V ^ ) (S> )| * o|<* f V 2 ) (IT J ^ ) ^/2)|+ d|(f p ? / 2 ) ( ( ^ 2 ) j where the bars indicate that the term is a totally anti-symmetrized Slater determinant. The desired eigenfunction with J = 3/2, T = 1/2, fu l f i l l s the two conditions that 3/2 3 (i) T ^ 3 / 2 = g V / = ° and 7 3/2 /"-"/ which follow from the relationships M M U J + ^ L =yj (J + 1) - M (M-r-1)' L , and Tz + 1 T 4 ^ T 3 = / T (T+ 1) - Tz (Tz + 1) ^ T The two conditions , 3/2 + r 3 / 2 J <L 3/2 - Q * r 3/2 are sufficient to determine the three ratios of the coefficients. The nor-malized eigenfunction obtained i s t A / 2 3 / 2 ( T = 1/2) r / L m<» j ? / 2 ) W ^ / 2 ) ( 1 ^ 3 / 2 ) | -21«^ /2) ( ^ 2 ) U ^ Mayer and Jensen compute the magnetic moment of this eigenfunction to be 3*03 -33-nuclear magnetons, in reasonable agreement with the observed value of 3.257. The nuclear quadrupole moment is calculated to be negative, equal to -11/15 x 2/5 <r 2>cm. 2 There has been much disagreement concerning the sign of the nuclear quadrupole moment of Li? Q. largely because of the difficulty in calculating the magnitude of the electric f ie ld gradient, q, at the nucleus in the Id-2 moleculej the product eqQ has been measured accurately for Li? by the nuclear resonance method. After measurement of the product eqQ, Kusch (1949) reported the nuclear quadrupole moment of L i ' to be positive, in direct disagreement with simple shell model predictions as discussed above. The electric f ield gradient, q, was subsequently recalculated by Harris and Melanoff (1952) using both a Heitler London function and a 12 term variational (James) func-tion,, for the molecular wave functions for L i 2 . The results of the two calculations of q differed in sign; however, the James function, which was considered the more accurate, gave a negative q, and so a negative Q. Recent calculations by Ishiguro et a l . (1957) lead to a positive Q for L i , of mag-nitude 9.6 x 10 cm. , neglecting Sternheimer correction, (Sternheimer, 1950) or of magnitude 10.8 x 10 cm. (including Sternheimer correction). It therefore appears l ikely that the nuclear quadrupole moment of Li? i s 7 positive; the charge distribution for L i is then apparently prolate. A negative nuclear quadrupole moment for Li? is also predicted in the f irst approximation of Wigner's coupling scheme (Present, 1950). In this coupling scheme, the orbital wave function is characterized by a definite symmetry with respect to permutations of the nucleons. Instead of the 2-valued spins T and S, Wigner introduces the 4-valued spin "j ; the repre-sentations of the 4-dimensional unitary group than characterize the multiplet -34-system (Wigner, 1937). In terms of the partition numbers £ ^ i + /I2 + ^3 J the partitions for L i 7 are £.3], £2 + l j , and Cl * 1 +lj , in the order of decreasing symmetry of the orbital wave function. For symmetry f 3J, the orbital part of the wave function is completely symmetric under permutations of the three nucleons; for symmetry [. 1 4 1 + l\ , completely antisymmetric. The ground state configuration is (15^2P ^ ^3/2)> ° ^ symmetry [ 3 j • Present (195°) explains the positive nuclear quadrupole moment of 7 L i by configuration interaction. The ground state configuration consists of %> functions of symmetry [33 from the low odd parity excited configurations (154 2P2 3P) and (154 2P24f) mixed with the (154 2P3) configuration. Present finds that a l l data are adequately explained without the breakdown of L-S coupling or a large departure from partition symmetry. The argument appears reasonable, since the configuration interaction need not be large to produce a positive nuclear quadrupole moment. Avery and Blanchard (1950) have attempted to explain the positive nuclear quadrupole moment of L i 7 on the basis of a combination of spin-orbit interaction (breakdown of L-S coupling), and the breakdown of partition sym-metry. A (s p ) configuration ia assumed. The angular momenta of the 3 p-nucleons can be combined to give 10 linearly independent eigenfunctions, 8 of which have J :3 / 2 . L-S coupling is assumed; i . e . the two neutrons can combine to form ^S, 3 P , and "^D states. These can combine with the p-proton in L-S coupling as is indicated by the table below: 1 2 1 0 - 1 - 2 1 0 - 1 S 0 0 0 0 0 t £ i £ t J Mj^  3 2 1 2 1 0 1 0 - 1 0 - 1 - 2 - 2 - 1 - 3 - 3 5 -1 2 2 1 2 2 1 2 2 The states ( D p) D, ( D p) P, and ( D p) F, where the notation i s "(neutron state, proton state) combined state", can therefore be formed. In addition, the three p-nucleons can form the following states: ( ^ 2p) ^P (3 P 2pj 2p (3p 2p) *P (3p 2p) 2 D {h 2p) <3p 2p) 3^ (3p 2p) 2s The (3p 2p) % and the (h 2p) 2 F states are rejected since they do not have J = 3/2. The above eight states are expressed i n terms of their symmetry pro-perties as follows: V 1 = 22 P [ 3 ] ^ 5 = 22 ,-D [2 22p L2 • l ] ^ £2 * l l V 3 = 24p [ 2 * 1 ] . V 7 = 42D [ 2 - 1 ] [ 2 . 1 ] = [ l -t-1 + where the functions l|/ are l inear combinations of the f i r s t set of eight eigen-f unctions, such that the symmetry properties given b y | A ^ + ^ 2 + ^ 3] a r e sat i s f ied . The set (j/ was obtained by Avery and Blanchard by the usual rules for combining angular momenta. The notation for the functions i s (2S+ 1) (2T+ 1) Lp 1 + \ 2+ \ 3] 7 In the f i r s t approximation of Wigner's the ground state of L i consists of the function y = 2 2 P [ 3 3 where \f 1 s </£ (I s 2 p) z P + 2 / 3 ( X D2p)2 P -36-8 However, Avery and Blanchard, under the assumption that s ^ y * f ind a positive quadrupole moment for L i 7 , as well as reasonable agreement with magnetic moment and Be7 K-capture data, i f the ground state wave function i s almost a l l of symmetry [2 + l\ , with the largest contribution from the not D states. L and S are therefore/good quantum numbers; the data suggest that y may be a good quantum number. The above ground state configuration, since i t involves large depar-tures from she l l model theory, does not seem as reasonable as the configura-7. tions deduced by Present to explain the positive quadrupole moment of L i . 7 Most recent work concerns the intermediate coupling models for L i , for which the nuclear quadrupole moment i s negative, i n agreement with simple shel l model predictions (Ingl is , 1953). In pure L-S coupling, the lowest states of L i 7 are the multiplets ^P, V, e t c . , i n order of increasing ener-gy. Inglis takes the multiplet separations from interaction energies computed from the direct and exchange integrals L and K, as evaluated by Feenberg and Wigner (1937). Inglis specializes the interaction for the operator ° i j V ( r j _ j ) , where 0^ s 0.3 P4 0.2 Q P i s the Majorana operator and Q i s the spin exchange operator. The multiplet sp l i t t ings , defined b y H ' = £ a l . s s A L . S , are obtained from 3 trace invariance. In J-J coupling the ground configuration i s (P3/2) . The spin-orbit energy i s 3a/2, and the separations between states of different J have been calculated. Inglis finds the best f i t between experimental energy levels and theory at a/K = 0.7, where a i s a measure of the L-S multiplet sp l i t t ings , and K i s the multiplet separations. The coupling a/K = 0.7 i s very close to pure L-S coupling. -37-Aeurback and French (1955) have determined the intermediate coupling parameter, f = a/K c 1.4 from consideration of the reaction L i 7 ( p , d ) L i ^ , L i ° * i n reasonable agreement with the predictions of Ing l is . They obtain f - approxi-mately 2.5 from the reaction L i ^ ( d , p ) L i 7 , L i 7 . * D. Kurath (1956) finds the intermediate coupling parameter a/K approxi-mately = 2. Since the T ( « * , y ) L i 7 reaction, i n the low energy region studied here, occurs through direct radiative t ransi t ions, and therefore i s sensitive to the 7 properties of the ground state and of the f i r s t excited state of L i , i t i s hoped that the reaction cross section and angular distr ibut ion w i l l be of use in determining five ground state and f i r s t excited state wave functions. -38-CHAPTER IV THE O l6(p.t JF 1 7 REACTION; 1. Previous Measurements -The O l 6(p,H ) F 1 7 reaction was first observed by Dubridge et al (1938) by measuring the annihilation quanta from the decay of Laubenstein et a l (1951) measured the relative cross section from 1.4 to 4.1 mev. by measuring the yield of annihilation radiation. Warren et al (1954), in this laboratory, observed the gamma radiation directly and attributed the non-resonant character of the cross section for gamma emission in the region 0,8 to 2.1 mev. to a direct radiative capture process. The 0^(p ,Y )F^7 cross section was found to .be 6 i 3 x 10 cm. at 1.90 mev. The angular distribution for the 2 transitions, which go via the f i rs t excited level of F^ 7 , was approximately 1 + (5 i l ) s in 2 © at 1.9 mev. The angular distribution for theY^ transitions, which go directly to the ground state of was believed to be isotropic. Recently, the differential cross section has been measured at 800 kev. by Robertson (1957) in this laboratory. The differential cross section at 90° to the incident proton beam for V 2 transitions was found to be 10.4 2 1.30 x 10~ 3 2 cm.2 per steradian, and the ratio, at 90° of the yield for f ^ transitions to the yield for ^ 2 transitions was found to be 1.4 3" .03. Using the angular distribution of the gamma rays found by Warren et a l at 1.9 mev. for the angular distribution at 800 kev., Robertson estimated the 0^(p, X cross section to be 9«3 x 10 J cm. at 800 kev. for transitions to the f irst excited state of F 1? and 1.8 x 10~^ cm.2 for transitions to the ground state. 2. Apparatus -(a) Target and Target Arrangement For reasons as described by Robertson (1957), solid oxidized tungsten targets, approximately 0.02 x 1 x 0.75 inches, were used for this work. The -39-tungsten was oxidized by suspending i t i n a heater c o i l of nickel wire inside a b e l l j a r . Heating was continued i n the presence of commercial grade oxygen for approximately 10 minutes u n t i l a dark blue grey tungsten oxide layer was formed over the surface of the tungsten. The target chamber and target arrangement were as described i n Chapter I I . A 3heet of clean tungsten was placed on the reverse side of the target holder for beam-dependent background measurements. No heating was applied to the target assembly; after prolonged bombardment the target changed to a deeper blue colour, presumably due to the formation of cracked o i l depo-s i t s . The f i r s t tungsten plates used were cleaned i n potassium hydroxide solution, etched, and rinsed i n d i s t i l l e d water before oxidation. Since Robertson had found traces of N a 2 3 i n tungsten oxide targets, the targets were checked for N a 2 3 . Gamma rays from N a 2 3 are a 0.45 mev. gamma ray from Na23(p,p' / j N a 2 3 and a 1.60 mev. gamma ray from Na 2 3 (p , <<V)Ne2 .^ The checks for N a 2 3 contamination were made by running an excitation curve over the resonance at 1287.5 kev., which decays by proton emission giving the 0.45 mev. gamma ray. A significant increase of 0.45 mev. radiation at the reso-nance energy confirmed the presence of N a 2 3 i n the target. N a 2 3 was also found i n significant quantities on clean, unoxidized tungsten, indicating the poss ib i l i ty of N a 2 3 contamination through the cleaning i n potassium hydroxide, which contains traces of sodium. The tungsten plates were therefore only heavily etched (approximately 4 amperes for 5 minutes), and then boiled i n d i s t i l l e d water for l/2 hour before oxidation. At no time were the plates touched by hand. This procedure reduced the sodium content such that the N a 2 3 gamma ray y i e l d was estimated to be 60 counts per 100 microcoulombs of -40-beam above a 300 kev. bias at the resonance energy of 1287.5 kev. proton energy for the counter-target arrangement used in this work. Excitation functions are given for gamma rays from the proton bombardment of Na 2 3 by Stelson and Preston (1954) and by Burling (1941), The yield of gamma rays from the sodium contamination of the target in the energy region of the f u l l -energy peaks of the O ^ p ^ Y )F 1 7 ^ and ^ 2 transitions was estimated to be negligibly small for a l l energies used in the present work, (b) Gamma Ray Detector Preliminary runs were made at 830 kev. and 1.64 mev. with the large 2.5 x 3.5 inch crystal described in Chapter II. A positive photomultiplier gain shift of k% was observed at 1.64 mev. after bombardment of 70 integrator counts at a beam current of 5 microamperes. Because gain shifts distorted the ful l energy peaks of t and Y 2 , i t was decided to use a 1.75 x 2.0 inch sodium iodide (thallium activated) crystal mounted on a Dumont two-inch photomultiplier tube. With this smaller counter, a positive gain shift of 6% was observed at 1.64 mev. after bombardment of 100 integrator counts at a beam current of 6 microamperes. This gain shift was reproduced by flooding the counter with radiation from a Eu^^^ source (strong lines at 87 kev. and at 330 kev.) for 1/2 hour. The Dumont photomultiplier tube was therefore replaced with an R.C.A. 6342 two-inch photomultiplier tube, code number 8-4-246. The above counter arrangement, consisting of an R.C.A. 6342 photo-multiplier mounted on a 1.75 x 2.00 inch crystal, was used for a l l 0^(p,lf )F^7 155 measurements reported in the present work. Flooding the counter with a Eu source (count rate of 30,000 per second) produced no apparent gain shift when calibration runs were made before and immediately after flooding. It was necessary to remove the Eu before calibration because of interfering high -41-energy radiation from Eu. When was used to flood the counter, and a calibration made simultaneously with RdTh, a negative gain shift of 6% was observed, similar to the negative gain shift observed by Robertson with the large counter. The gain shift disappeared immediately the Cs source was removed. During the oxide runs, a positive gain shift of 4$ with a decay time of a few hours was observed after bombardment at 2.0 mev. for 20 minutes with a beam current of 3 microamperes. Calibrations were made with the beam off; the negative gain shift was therefore not observed. However, the reac-tion spectrum from the oxide target was displaced upwards on the kicksorters, indicating a net positive gain shift. It is not understood why flooding the counter with a Eu source did not produce a similar positive gain shift. Pos-sibly the oxide runs produced a higher intensity of very low energy radiation (112 and 66 kev.) than came from the Eu source. For accurate energy determination, i t i s necessary to avoid intense low energy radiation, as from tungsten irradiated with protons of energy above 2 mev., and to calibrate with the beam on the target. The calibration radia-tion must then, of course, be much less intense than normal radiation to avoid extra gain shifts. When intense low energy background radiation cannot be avoided, as in the present work, a thin absorber could be placed in front of the counter. This was not done during the present 01^(p,y )F-^7 runs. The average of five determinations of resolution gave a counter resolution of 8.9 £ 1% for 0.662 radiation from a Cs-^ -37 source, where the resolution is defined as the f u l l width at one-half maximum amplitude of the full-energy peak. Between 960 and 1200 volts, the resolution was independent of the voltage supplied to the dynode chain; 1200 volts was used for the -42-present work. The energies of the 0^(p,Y)F^" 7 gamma rays, and y ,^ are 0.66 mev. and 1.16 mev. at a proton energy of 600 kev., and 2.48 mev. and 1.98 mev. at a proton energy of 2.00 mev. The efficiency of the crystal for gamma rays, £ (E, E/2), where E/2 is a bias energy of 1/2 the incident gamma ray energy, has been obtained for the energy region 0,60 to 2.5 mev. (Appendix I.) Since the detailed shapes of the Y ^ and Jfg spectra below the full-energy peaks were not accurately observed in this experiment, comparisons were made with /37 6S tZ the spectra from Cs , Zn , Na , and RdTh sources, and the efficiency £ (E, E - .20) defined to a bias of 200 kev. below the incident gamma ray energy. (c) Electronics -The electronics were set up as described in Chapter II. The stabi-l i t y of the electronics during the runs was better than 0,1%, The kicksorter was set to cover a 1 mev. energy region in the vicinity of the f u l l energy peaks of V-^ and Y 2 transitions; most runs were made without altering the kicksorter dispersion. 3. Experimental -(a) Background The target and target chamber were surrounded by approximately 4 inches of lead to reduce background radiation. The time dependent background was approximately 50 per minute in the energy region 1/2 to 3 mev. At proton energies below 1.1 mev., the beam dependent background, on clean tungsten, was approximately the same as the time dependent background. Above 1.1 mev., the beam dependent background rose steadily. At 2 mev. the beam dependent background in th e energy region 1.8 to 3 mev. was 110 counts per minute, compared with the time dependent counting rate of 8 counts per minute in this C H A N N E L N U M B E R -43-energy range. Part of the rise in background with energy can be attributed to (d,n) reactions in the magnet box. 2.37 mev. gamma rays could be expected from carbon contamination of the target and beam stops; however, the back-ground spectrum showed no significant gamma ray peak, but decreased uniformly over the energy range studied. The walls of the target chamber had been gold plated to reduce fluorine contamination; i t i s possible that the plating is insufficiently thick, or impure. Background radiation could also come from impurities in the tungsten backing; some radiation could come from the tungsten i tsel f . (b) Procedure Protons of 0.618, 0.823, 1.13, 1.54, and 2.04 mev., supplied by the university electrostatic generator, were used to bombard a tungsten oxide. The beam energy, governed by the sniffer separation, was known to approxi-mately 1%, The counter face was positioned as close as possible to the tar-get chamber in order to obtain a maximum counting rate, the distance from the counter face to the target being 1.63 inches for a l l the runs. Since prel i-minary runs showed target deterioration for beams of 6 to 7 microamperes, beam currents were from 3 to 4 microamperes. The target was checked for deterioration by frequent checks of the yield at 1.54 mev. No target deterio-ration was observed during the experiment. Spectra were recorded of the fu l l -energy peaks of ^ ^ and ^ 2 « A typical spectrum, at a bombarding energy of 1.13 mev., is shown in Figure 13. 4. Target Thickness -The target thickness was necessary in order to obtain the mean proton energy in the target. The target thickness was calculated from Robert-19 son's ice target results. For an ice target containing 1.118 x 10 7 molecules -44-of water / cm. , Robertson observed 92 counts per integrator in the 2 fu l l 2 energy peak. The number of oxygen atoms /cm. in the oxide target used in the present work is then given by N A C n o ™ V oxide x -" • ice x t jpe x n^ 0 JJ _Q_ oxide £ oxide 2 X ice where Ny are the number of full-energy peak counts per integrator, JX are the solid angles, and £ are the efficiencies of the two counters used. Then n = ^ x 0.377 x 0.31 x 1.118 x 19 1 0 ° 92 0.753 0.27 From Robertson's calculations, the stopping cross section, , of tungsten dioxide for 800 kev. protons i s °~ s 35 x lO""-^ e.v. - cm. / molecule, W02 and since ( A E ) ^ Q * c X N G X V 2 > where ( A E ) ^ i s the target thickness, Then ( A E ) ^ • 59 kev. at a proton energy of 800 kev. The target thickness at other energies is then given by (A E ) = (A E l „ A x *"™2 2 W 0 2 8 0 0 (<rW02) goo Where ^.was computed from atomic stopping power data diven by Whaling (1957). The following values of target thickness were obtained: Ep (mev.) °"(W02) (A E ) K E V > 0.600 40.5 x 1 0 - 1 5 68 0.800 35 " 59 1.10 29 " 49 1.50 25 " 42 2.00 21 " 35 The target thickness was also computed directly from the observed -45-o energy. Since the counter was at 90 to the incident proton beam, E y 2 • 0.10 -»- 16/17 Ep* , and Ep - Ep" = 4 / 2 , where Ep is the bombarding proton energy, Ep is the mean proton energy in the target, and A i s the target thickness. At a bombarding energy of 0.823 mev., E y ^ = 0.840 mev., consistent with a target thickness of 62 kev., in good agreement with the above computation of 59 kev. However, at 1.53 mev., and also at 2.04 mev., E y 2 was consistent with a target thickness of 100 kev. An explanation for the apparent discre-pancy is the presence of a negative gain shift with a short decay time constant, as was observed by flooding the counter with a Csl37 source. Calibrations were made with the beam offj consequently, the apparent energy £ y 2 v & 3 decreased. The approximate target thicknesses were also estimated from the ob-served with the fu l l energy peaks for ^ 2 transitions. The mean value of the target thickness, A , was computed from A = \/r2 - rR2 where p and f , as defined previously, are respectively the width of the R full-energy peak for V 2 transitions, and the width of the full-energy peak for a mono-energetic gamma ray source. Target thicknesses were found to be 66 kev. for Ep = 0.84 mev., and 46 kev. for Ep • 1.13 mev., in reasonable agreement with above estimates. Values of target thickness computed from the widths of the full-energy peaks are not, however, considered accurate because of fluctuations in counter resolution between runs. 5. Determination of the Excitation Function -Relative cross sections were computed from the following data: -46-Ep mev. A kev. Ep mev. Xta l effy. Xta l effy. eY2 No. of integrator counts Gamma % ray counts per NIT2 i n t . 0.618 69 0.583 - 0.345 ' 100 - 20.2 2 0.823 60 0.793 0.17 0.30 30 5.50 .4 45.2 2 1.13 49 1.11 0.13 0.21 50 12.2 .2 90.9 5.5. 1.536 41 1.52 0.10 0.145 50 20.4 .9 135.5 8 2.04 35 2.02 0.078 0.10 50 22.9 2.8 175 9 Cross sections were estimated relat ive to the cross section for Y2 transitions at 800 kev., by means of {d r^} (dO N, N y2,800 x ^2 .800 x ^ Y 2.800 e » 90 where N ^ 2 ggo I s the observed number of gamma ray counts per integrator for ) 2 transitions at a proton energy of 800 kev. , 6 y 2 800 ^ s t n e c o u n t e r eff iciency for Jf2 transitions at a proton energy of 800 kev. , and i s the transmission coefficient through the 1/16 inch brass target pot walls . The values of absolute cross section were based on the measurement of the 9 0 ° d i f ferent ia l cross section f o r ^ 2 transitions at 800 kev. of 10.4 ± 1.3 x 10~ 3 2 cm. 2 per steradian by Robertson. The following values of 9 0 ° d i f ferent ia l 2 cross section, i n units of cm. per steradian, were obtained: <r Ep mev. (dH 7JM (do 0.583 0.793 0.214 x 10-31 0.412 x 10~ 3 1 1.04 x 10-31 0.205 14 MEAN PROTON ENERGY IN TARGET, Ep FIGURE 14 VARIATION IN o ' 6 ( P / ) F 1 7 9 0 ° DIFFERENTIAL CROSS . SECTION WITH PROTON ENERGY 1.11 0.642 x 10~^x 2.96 x 10~ J X 0.217 1.52 1.39 x 10~ 3 1 6.38 x 10~31 0 # 2 1 7 2.02 2.23 x 10-31 n . Q x 1 0-31 0.188 The crystal efficiencies are believed accurate to within 12$, giving a probable error of 17$ in the ratio of the two efficiencies. The probable error in the number of reaction counts per integrator is approximately % . The probable error in the ratio of the differential cross sections i s there-fore approximately 18$. Yields were estimated on the basis of a constant solid angle, since the distance from the crystal face to the effective centre has been shown not to vary significantly with energy in the energy region studied (Appendix I) . The ratio of (&«r) to (d <r) of .205 ± .037 at 0.793 mev. is higher than <.d/Al Cd^)y 2 the ratio found by Robertson of 0.14 £ .03 at 800 kev., although to within the probable error the results are in agreement. The effect of angular dis tr i-bution was not considered in estimating the yields. In the present work the counter subtended a solid angle of 0.669 steradians at the effective centre. A sin 6 distribution over this solid angle yields approximately k% less than o an isotropic distribution with the same 90 differential cross section. Since the angular distribution for ^ transitions is nearly s in 2 ©, the ratio of ( d y ) to (d ( r j found above may therefore be consistently high by nearly 4$. (dT'Vi ^ ¥ 2 To summarize, the 0x^(p,}f JF 1 7 90° differential cross section for -31 2 2 transitions varies smoothly from 0.41 x 10 ' cm. per steradian at a -31 2 proton energy of 0.58 mev. to 11.9 x 10 J cm. per steradian at a proton energy of 2.02 mev. The ratio of the 90° differential cross sections for transitions to Y 2 "transitions is approximately 0#20 in this energy region Using the angular distribution for if transitions found by Warren et al (1955) as being proportional to 1 +• 5 sin2©", the total cross section for ^2 transi-tions is given by <r' - 4V (1+ 2/3 x 5) x ( d O - 8.98 x (d f) * 2 6 tdZTT^o (dZO 9 0 ° On this basis, °y2= 0.37 microbarns at 0.583 mev., and 10.7 microbarns at 2.02 mev. Adding the contribution from ^ transitions, assumed to have an isotropic angular distribution, gives an 0"^(p,2f total reaction cross section of 0.44 microbarns at 0.583 mev., and 13.5 microbarns at 2.02 mev. If we assume the above angular distributions, the ratio of the cross sections, °Vl =0.28. However, in order to establish this ratio, more accurate angu-•V2 lar distributions need to be measured. -49-APPENDIX I GAMMA RAY EFFICIENCIES FOR THE 1.75 x 2.00 INCH CRYSTAL The efficiency of the 1.75 by 2 inch crystal has been measured for the 6.14 mev. gamma rays from the 340 kev. resonance of F^^(p,<»^V)0^ by Larson. The efficiency for gamma rays,t (E, E/2), where the bias energy was chosen as l/2 the incident gamma ray energy was found to be 0.388 i .019. The effective centre distance used was 2.18 i .71 cm., as determined by an inverse square plot. For the 0 l 6 (p,lf )F17 measurements described in Chapter IV, i t was necessary to determine the efficiency of this counter for gamma rays in the energy region from 0.6 mev. to 2.5 mev. The efficiency for radiation from Co°^ has been determined with a Co°^ source whose strength was measured by the National Research Council to be 0.134 millicuries to an accuracy of 5$. The present crystal efficiency measurements were made 1 year, 7 1/2 months after the source calibration, so that taking T^ for Co° ° to be 5.24 years, the strength at the time of the efficiency measurements was 0.1094 millicuries. Measurements were made with the source 80 cm. from the face of the crystal, with the source holder axis perpendicular to the counter axis. From kicksorter spectra, the number of counts were recorded to a bias of 0.625 mev.j i . e . i t was assumed that the mean efficiency for the 1.17 mev. and 1.33 mev. radiation was equal to the efficiency for 1.25 mev. radiation. The efficiency to \ - energy bias, WAS given by a. 6 (2.25, 0.625) = N * L_ , n 2 No A With N v "the number of observed counts above background, 2 No the number of gamma rays emitted per second by the source, and' 2 A/r i s the solid angle subtended by the area of the counter face -50-positioned at the effective centre of the crystal. The value of 2 . 1 8 ± .72 cm. was used for the effective centre distance. Since a large source to counter distance (80 cm.) was used, any error in the effec-tive centre distance is negligible. An efficiency for the total number of counts recorded in the pulse spectra to zero energy, € (1.25, 0) was also computed. A low energy peak at approximately 220 kev., believed due to back-scattered radiation from the mu-metal shield, aluminum and brass casings, and the lead counter shielding, was neglected. From the formula for Compton scattering of photons, h v a hvQ / [ l + (1 - cos ©)] where brQ = energy of i n i t i a l photon in units of mc2, hv = 220 kev., for hvQ = 1.25 mev., corresponds to a scattering angle & of 155 ° , approximately the angle expected for back-scattered radiation. The flat Compton spectrum t a i l was extrapolated horizontally down to zero pulse energy to obtain the total spectrum counts. Runs were made both with the sides of the counter shielded with a lead castle and unshielded. The flat Compton t a i l of the pulse spectrum was 12% higher with the lead castle than without i t ; the efficiency was consequently higher when using the castle. The calculated efficiencies are as follows: £ (1.25, 0.662) = (40.5 ± 2) % with the lead castle shielding, and * (1.25, 0.662) • (37.9 ± 2) % without the lead castle shielding. The two efficiencies differ significantly because most of the probable error comes from uncertainty in the source strength. The total crystal efficiencies were (r. (1.25, 0) - (72.0 t 7) %t with the lead castle shielding, and t (1.25, 0) - (63.8 £ 7) %, with the counter unshielded. - 5 1 -A g a i n t h e two e f f i c i e n c i e s d i f f e r s i g n i f i c a n t l y . £ ( l : . 2 5 , 0 ) = 6 1 . 5 $ , computed f r o m ( l - exp - / * • / ) , i n r e a s o n a b l e a g r e e m e n t w i t h t h e m e a s u r e d v a l u e when n o t u s i n g t h e s h i e l d i n g . B e c a u s e o f t h e s m a l l e r dependence o f £ ( l . 2 5 > 0 . 6 6 2 ) t h a n € ( 1 . 2 5 , 0 ) o n t h e s h i e l d i n g u s e d , a n d t h e n e c e s s i t y o f e x t r a p o l a t i n g b e l o w t h e b a c k - s c a t t e r e d gamma r a y p e a k i n e s t i m a t i n g C ( 1 . 2 5 , 0 ) , b o t h t h e o r e t i c a l a n d e x p e r i m e n t a l e f f i c i e n c i e s w e r e c a l c u l a t e d t o a b i a s e n e r g y o f o n e - h a l f t h e i n c i d e n t gamma r a y e n e r g y . T h e o r e t i c a l e f f i c i e n c i e s were e s t i m a t e d b y means o f a method d e v e -l o p e d b y P . S i n g h o f t h i s l a b o r a t o r y . The e f f i c i e n c y i s d e f i n e d b y A, B , a n d C a r e t h e r e l a t i v e p r o b a b i l i t i e s f o r t h e r e s p e c t i v e a b s o r p t i o n p r o c e s s e s t o p r o d u c e s p e c t r u m c o u n t s a b o v e t h e 1 / 2 e n e r g y b i a s ; t h a t i s , f o r more t h a n 1 / 2 o f t h e gamma r a y e n e r g y t o be a b s o r b e d b y t h e c r y s t a l . I n t h e e n e r g y r e g i o n f r o m 0 . 6 t o 3 m e v . , w h e r e t h e m o s t i m p o r t a n t a b s o r p t i o n p r o c e s s i s Compton S c a t t e r i n g , m o s t u n c e r t a i n t y i s i n t h e e s t i m a t i o n o f t h e p r o b a b i l i t y o f f u r t h e r a b s o r p t i o n b y t h e c r y s t a l o f s e c o n d a r y p h o t o n s whose e n e r g y i s s t i l l g r e a t e r t h a n E / 2 f o l l o w i n g a s i n g l e Compton e v e n t . I f s u c h a s e c o n d a r y a b s o r p t i o n p r o c e s s o c c u r s , i t i s assumed t h a t t h e r e s u l t i n g s p e c t r u m p u l s e f r o m b o t h e v e n t s l i e s a b o v e t h e 1 / 2 e n e r g y b i a s . A where fx i s t h e t o t a l a b s o r p t i o n c o e f f i c i e n t , f t tT a n d fl a r e t h e t h e o r e t i c a l p h o t o - e l e c t r i c , C o m p t o n , a n d p a i r - p r o d u c t i o n c o e f f i c i e n t s r e s p e c t i v e l y , i i s t h e l e n g t h o f t h e c r y s t a l , s o t h a t ( 1 - e x p . - / * / ) i s t h e t o t a l f r a c t i o n o f t h e gamma r a y s a b -s o r b e d i n t h e c r y s t a l . T h e o r e t i c a l e f f i c i e n c i e s w e r e c a l c u l a t e d f o r 1 . 2 5 mev . a n d 6 . 1 4 FIGURE 15 GAMMA RAY EFFICIENCIES FOR THE MEDIUM COUNTER 1 0 2 0 3 0 4 0 5 0 6 0 G A M M A R A Y E N E R G Y i M E V ) -52-mev., and compared with the experimental efficiencies. Efficiencies were also calculated energies of 0.6, 2.0, and 3.0 mev. The results are as follows: E € (E. E/2) Theoretical 6 (E/E/2) Expt. 0.6 0.58 0.392 t .03 1.25 0.43 2.0 0.384 3.0 0.378 6.14 0.42 0.388 t .019 Since only the upper part of the spectra of Y ^ and y g were observed in the Ol6(p,>r)F17 work, the efficiencies were estimated to a bias of 200 kev., which f e l l slightly below the bottom of the f u l l energy peak. Spectra from C s 1 3 7 , Z n ^ , Na 2 2 , and RdTh were used to estimate {. (E, E-200 kev.). Efficiencies are shown plotted in Figure 15. Effective Centre Measurement: The distance from the crystal face to the effective centre was deter-mined experimentally for gamma ray energies of 1.25 with a Co°^ source, and for 0.51 mev. with a Na 2 2 source. The distances, obtained from a distance vs. 1/ ^ counting rate plot, were 2.40 + .20 and 2.50 i .20 cm. for the 0.51 and 1.25 mev. radiation respectively. The distance measured by Larson at 6.14 mev. for the effective centre was 2.18 t .72 cm. The effective centre dis-tances for the three energies are equal to within the probable errors, as was observed by Robertson for the 3.0 x 2.5 inch crystal. The simple theoretical calculation of the effective centre distance of x « -1" (0.5 (1 exp. - J ) ) gives a distance of 2.12 cm. for 6.14 mev., 1.95 cm. for 1.25 Riey., and 1.55 cm. for 0.51 mev. radiation. As in the case of the large crystal, the theore-t ica l ly predicted distances are significantly different from the observed effective centre distances. PLATE I THE BIASED DISTORTER APPENDIX II  THE BIASED DISTORTER The biased distorter, which replaced an older biased amplifier, ac-cepts negative pulses from a high gain Northern Electric Linear Amplifier and provides variable gain and cut before driving the Marconi Kicksorter. A block diagram of the distorter circuit is shown in Figure 17 and a detailed circuit diagram in Figure 18. The chief advantage of the present biased distorter over the older biased amplifier is that the output pulses of the distorter are shaped to have a constant rate of rise, rate of fall , and a constant width from the beginning of the pulse to the back edge of the pulse, independent of the shape of the input pulse. Dependence of kicksorter channel edges on pulse shapes (especially rate of rise of the pulses), are therefore minimized by means of the biased distorter. The distorter has the following characteristics: 1. Accepts negative input pulses from 0 to 50 volts. It will tolerate appreciable positive overshoot without overloading. The input pulse length should be between 0.2 microseconds and 6 microseconds, from the beginning of pulse rise to the start of the fall of the pulse. The pulse should have recovered completely in 10 microseconds, since otherwise extreme lengthening of the distorter output pulse results. (See amplifier and pulse shaper.) 2. The output pulse size is from 0 to 50 volts, and is linear from 1 to 50 volts* The rate of rise, when driving 200 pf. of cable capacity, is 14 volts per microsecond. The rate of fal l is 9 volts per microsecond, and the width from the beginning of the rise of the pulse to the beginning of the fal l of the pulse is 6 microseconds. 3. A fixed dead time of 15 microseconds, beginning 1 to 2 micro--55-seconds after the input pulse, is available during anti-coincidence operation by means of a switch located at the back of the biased distorter chassis. 4* The distorter has possible gains of 1, 1.5, 2, 3, 4, and 5, and a continuously variable bias level from approximately 1/2 to 50 volts. 5. The distorter can be gated either by coincidence pulses, or by anti-coincidence pulses. 5 volt coincidence gate pulses of from 1 to 2 micro-seconds in width are supplied by a coincidence gate pulse generator, or they may be fed directly into the gate from external equipment. The gate pulses may be of either positive or negative polarity, since two coincidence inputs, connecting to the primary of a step-up pulse transformer, are provided. A shorted input connector is used to ground the unused side of the primary trans-former coil. These gating pulses should not be longer than 3 microseconds, since the pulse transformer differentiates longer pulses. To drive coincidence gate pulses into the 100 ohm input impedance of the pulse transformer, the pulse source should be approximately 15 volts, into a step-down pulse trans-former. 12 volt, 15 microsecond anti-coincidence gate pulses are fed directly into the gate by an anti-coincidence gate-pulse generator, which also supplies dead-time pulses. The generator is driven by 6 volt positive pulses, fed into a step-up pulse transformer. To drive the 100 ohm input impedance of the pulse transformer, the 6 volt input pulses should come from a 20 volt source, fed into a step-down transformer. A slight change in the circuit would enable anti-coincidence pulses to be fed directly into the gate from external equipment i f so desired. 6. Curves A to F in Figure 16 show the dependence of the distorter output pulse height on pulse repetition rate. Two pulse generators were used FIGURE 16 PERCENT FALL IN DISTORTER OUTPUT PULSE HEIGHT WITH INPUT PULSE REPETITION R A T E i o UJ I UJ (0 _) D Q. d O O z _J < o 4 O 4 8 12 O 4 8 12 16 2 0 A C O I N C I D E N C E B G A I N I C U T 7 C G A I N 5 C U T 7 I D G A I N I C U T O E G A I N I C U T O F G A I N 5 C U T O G G A I N 5 C U T O 5 10 2 0 INPUT P U L S E R E P E T I T I O N 1 0 0 ( X 1 0 0 0 p p s ) R A T E -56-simultaneously; "calibration" pulses were provided by a 60-cycle mercury relay pulse generator (Robertson), and pulses of a high repetition rate were supplied by a General Radio Co. "Unit pulser", type number 1217-A. The curves show the percentage fa l l in distorter output pulse heights, for constant amplitude input "calibration" pulses, with increasing pulse repetition rates from the unit pul-ser. For all tests, the distorter output pulse height, for input"calibration" pulses, was approximately 30 volts. For curve A, the distorter was operated on coincidence. The coinci-dence gate pulse generator was synchronized with the "calibration" pulses; pul-ses from the unit pulser were rejected by the distorter gate. Up to a pulse repetition rate of 20,000 per second of amplitude 14 volts, the output amplitude was constant. For curves 6 to F, the gate was operated, on anti-coincidence. Curves B and C show the gate response to a high pulse repetition rate. Low-amplitude (10 volt) pulses from the unit pulser were removed after the gate by a high cut setting; only "calibration" pulses reached the distorter amplifier. For curves D to F, since zero cut setting was used, all input pulses reached the amplifier. For curves D and F, low amplitude pulses (10 volts for gain 1, and 2 volts for gain 5) were used from the unit pulser together with high amplitude "calibra-tion" pulses from the mercury relay pulse generator. For curves E and G, high amplitude pulses from the unit pulser only were fed into the distorter. The curves show that for accurate pulse-height measurements, a high pulse repetition rate should be avoided during anti-coincidence operation of the distorter. If the low-amplitude pulse rate is high, a high cut setting should be used to reduce the pulse rate into the amplifier. The amplifier i t -self should be used in a low gain position when accepting a high pulse rate. FIGURE 17 BLOCK DIAGRAM OF BIASED DISTORTER CIRCUIT C O I N - I N P U T C O I N -P U L S E G E N -I N P U T G A T E A N T I - C O I N -I N P U T A N T I - C O I N -a D E A D T I M E P U L S E G E N -C U T A M P L I F I E R D I O D E S T R E T C H E R 71 H C A P - C O M P -P U L S E K A N D I A H D I SC -R E S T O R I N G C U R R E N T C C T -L I N E A R R I S E C C T -O U T P U T Large input pulses produce a s l ight ly larger f a l l i n the distorter output at high repeti t ion rates than do small ones; however, a l l pulses larger than a few volts into the amplif ier produce signif icant decreases i n the distorter output pulse height for repetit ion rates greater than 5000 per second. For most accurate pulse height measurements, the f a l l of the distorter output pulse height at high pulse repeti t ion rates can be avoided by running the d i s -torter on coincidence operation, and using pulses only i n the required energy range to tr igger the gate. Descriptions of sections of the biased distorter as shown by the block diagram of Figure 1*7 are given below. Linear Gate; Input pulses are fed into a gate c i rcu i t (VI and V2). A constant d . c . current i s produced i n VI anode by d . c . anode fol lowing, (Farley, page 7) which holds the anode of VI at (390/470) x 150 volts = 120 v o l t s . The 56 k. plate resistor sets the plate current at 3 milliamperes. V2 i s normally held off by a 7 volt grid-cathode b ias . When suitably gated, th is section acts as a White cathode follower (Farley, 1955, page 105) when driven by negative input pulses. V2 i s turned on hard by a posit ive gr id signal from the plate of V I . This unclamps the 1N100 diode, D2, from ground, allowing the negative input pulses to be transmitted to the bias c i r c u i t . For posit ive input pulses, or for posit ive overshoot after negative pulses, V2 remains o f f , and VI acts as a cathode follower with a "long t a i l " , carrying 5.5 milliamperes. The 1W100 diode, D l , i s biased o f f , and the cathode of VI follows the g r id , allowing VI to maintain a constant current (5.5 milliamperes) during the pulse. The output signal i s eliminated through strong attenuation by the diodes Dl and D2. When the gate i s closed V2 does not turn on in response to a negative -58-input pulse, since i t s gr id i s clamped at (-150 + 9) volts by the cathode of V3. VI i s turned off by the negative input pulse since i t s cathode i s clamped v ia diode 01 to approximately ground potent ia l . A small output pedestal (~* 1/4 volt) i s produced as a result of switching current i n the diodes DI and D2. To protect the diodes D4 and D5 at the gr id of V2, the anode of VI i s prevented from r i s i n g above 150 volts when VI i s turned off by the diode D3 to the 150 vol t l i n e . Coincidence and anti-coincidence pulses are fed onto the gr id of the cathode follower V3. During anti-coincidence operation the gr id of V3 i s held at (-150-+- 17) v o l t s , which biases off D5. The gr id of V2 thus follows the plate of VI , since D4 i s held i n conduction by the 1.5 milliamperes supplied through the 100 k. res is tor . The cathode of V2 i s always held at (-150+ 16) volts by the two Zeimer diodes. During coincidence operation, the cathode of V3 i s held at (-150 + 9) v o l t s ; the gr id of V2 i s therefore clamped to (-150 + 9) volts v ia D5 by the low impedance (~ 100 ohms) of the cathode follower. A posit ive signal from VI cannot raise the grid voltage of V2, since D4 cuts o f f , and therefore no output pulse i s obtained. The two diodes, D4 and D5, form a simple coincidence c i rcu i t (Farley, page 131, Figure d) , transmitting to V2 the minimum of the voltage pulses at the plate of VI and at the cathode of V3. Anti-coincidence gate pulses lower the cathode of V3 from (-150 +• 17) to (-150 + 9) v o l t s , thereby closing the gate. Coincidence pulses ra ise the cathode potential of V3 from (-150 -r 9) to (-150 + 17) v o l t s , opening the gate. A pulse transformer input i s used for the short coincidence pulses, allowing the use of either positive or negative input pulses. Cut C i rcu i t : The output of the gate i s fed into a 1/2 to 50 vo l t cut c i r c u i t , 59-similar in design to a diode discriminator circuit described by Moody (1950), and used in the Marconi kicksorter. Only that part of the input signal greater than the bias voltage is transmitted. The bias level is set by a 15 turn helipot. The total 50 volt drop across the helipot coil is set by a 20 k, trimpot mounted on the top of the distorter chassis, which regulates the cur-rent in the helipot coil. Amplifier; The amplifier is a cathode-coupled amplifier, with a boot-strap circuit (Farley, page 107) in the plate of V6 to provide a high effective load and so a high gain. Anode following (a.c. and d.c.) via V8 tends to maintain a constant current in V6 . A signal is therefore generated at the grid of V6 equal in magnitude to the input signal at the cathode of V6. This signal is an attenuated version of the signal appearing at the cathode of V8, the low impedance output point. V7 provides a high-impedance, high-current cathode load for V5 and V6j stray capacities in this cathode load limit the rise time of the amplifier to 0.2 microseconds. The input pulse width from the beginning of the pulse to the beginning of the fa l l of the pulse should consequently be greater than 0.2 microseconds. 2 series 1N100 diodes limit the amplitude of the output pulse to 50 volts. Pulse Shaper: (a) Diode stretcher -The output from the amplifier is fed into a White Cathode follower (V12 and V13), which drives a diode stretcher (Farley, page 18) consisting of Vii*. B and the 220 pf • capacitor. On the back edge of the input pulse to the diode stretcher, the anode of V14 B is held negative by the charge on the 220 -60-pf. capacitor. A 9 microampere current from the 300 volt line, fed into 220 pf., restores the grid of V15 to ground potential at the rate of dv/dt = 9/220 = .05 volts per microsecond. This leak is required to restore the grid of V15 to ground for pulses too small to trigger the d.c. restoring section of the circuit. (b) Linear Rise Circuit -The output pulse is taken from the cathode follower V15, whose cathode load is the constant current pentode Vl6 (Farley, page 32). Because of the capacity loading on the cathode of Vl$, V15 turns off during the rise of the pulse. The rate of rise of the output pulse is given approximately by dv/dt = i/c ~ 7(lO""3)/250 (10-6) = 28 volts per microsecond. Additional loa-ding by approximately 200 pf. of cable feeding the pulses to the kicksorter reduces this rate of rise to the observed rate of 14 volts per microsecond. 6 microseconds after the front edge of the input pulse, a restoring current of 3 milliamperes from the plate of V19 discharges the 220 pf. capa-citor in the diode stretcher. The back edge of the output pulse falls at the rate of 9 volts per microsecond, in reasonable agreement with dv/dt = i/c = 3(l0-3)/220(l0m6) = 14 volts per microsecond. V15 is being turned on during the back edge of the pulse, and so can provide sufficient current to cathode follow. The output pulse has a positive overshoot of approximately 1 volt since the anode of V14B rises to 1 volt above ground before V14B conducts the excess 3 milliampere discharge current away. The input pulse should be shorter (completely restored by some 10 microseconds) than the output distorter pulse since unless the back edge of the input pulse remains smaller than the output pulse, the 3 milliampere dis-charge current is short-circuited through V14B. If this occurs for a slowly -61-failing input pulse, the output pulse then falls with the input pulse for the duration of the discharge current (a few microseconds). After the discharge current, the output pulse falls at the .05 volt per microsecond rate governed by the 9 microampere current flow from the 300 volt line; i.e. extreme leng-thening of the t a i l of the output pulse results. Kandiah discriminator and Restoring-current pulse circuitry: The 6 microsecond delay of the restoring current is provided by a Kandiah discriminator (Journal of the Institute of Electrical Engineers, June 1954, page 239), VI? and V18, which is triggered by a positive pulse (appro-ximately 1/2 volt) from the plate of V8. A positive 40 volt, 6 microsecond, square output pulse is taken from the plate of V18, and differentiated. The positive edge of the pulse charges the 150 pf• capacitor through a 1N100 diode, which shorts the signal to ground; the negative edge unclamps the 1N100 diode so that the 150 pf• capacitor is discharged in approximately 10 microseconds by the 0.5 milliampere current from the 270 k. resistor. V19 is therefore held off for some 10 microseconds; during this time its plate current is switched through the 1N96 and V14A diodes into the 220 pf• of the diode stret-cher. Kandiah Triggering Pulse: Capacity Compensating Pulse: A positive pulse from the plate of V8 triggers the Kandiah discrimi-nator and provides a capacity compensating pulse for the diode stretcher. Negative overshoots in the coupling circuit are short-circuited to ground through the 1N96 diode. Positive pulses from the diode stretcher are strongly attenuated by the back resistance of the 1N100 diode; pulses from the grid of V17 are similarly attenuated. Since approximately a 1/2 volt signal is required to trigger the Kandiah discriminator, and th is corresponds to output pulses from the distorter of approximately 1«5 vo l ts , fo r output signals of less than 1 1/2 volts the Kandiah discriminator does not t r igger . The rate of f a l l for smaller output pulses i s therefore .05 volts per microsecond set by the 9 microampere current into the diode stretcher. Dead-Time and Anti-Coincidence Pulse Generator; A diode mixing c i rcu i t i s used to introduce either or both of the two tr igger pulses (anti-coincidence or dead-time) to the input of the u n i -vibrator (V20 gr id ) , enabling the generator to be used i n anti-coincidence and dead-time operation simultaneously. Dead-time input pulses are integrated before reaching the grid of 720. A variat ion i n the time of tr iggering of the generator i s provided by a trimmer capacitor i n the integrator, mounted on the back of the distorter chassis, which allows the generator to be triggered from approximately 1 to 2 microseconds after the input to the gate. Dead-time pulses, being ident ica l to anti-coincidence pulses, can only control the gate during anti-coincidence. The pulse generator i t s e l f (V20 and V2l) i s a cathode-coupled un i -v ibrator , with the f i r s t tube (V20) held off by a 15 vol t gr id bias i n the d . c . state . As described ear l ie r , the anti-coincidence tr igger pulses are 6 vol t posit ive pulses, fed i n through a step-up pulse transformer. Coincidence Gate Pulse Generator: The coincidence gate pulse generator, which i s mounted i n a separate chassis from the rest of the biased d istor ter , provides approximately 5 vo l t negative pulses of length from 0.5 to 2 microseconds. The pulse generator (V9 and V10) i s a modified Scarrott o s c i l l a t o r , (Farley, page 43) operating i n the fashion described by Kandiah, with a cathode follower output. The -63-generator input pulses are approximately 1/4 v o l t , fed i n through a step-up transformer. The input pulses should be shorter than the 1 to 2 microseconds length of the generator output pulses. As with the coincidence input to the gate, the coincidence generator input pulses may be of either po lar i ty , since two coincidence inputs, connecting to the primary of a step-up transformer, are used. A shorted input connector i s used to ground the unused side of the primary transformer c o i l . Power Supplies; The distorter 300 vol t power supply i s a Model 32, Lambda regulated power supply "300 MA" ser ies , rated at 200 to 325 volts d . c . at a current of from 0 to 300 milliamperes. The -150 vol t power supply i s a Model C-281 Lambda, "Com-Pak Series 200" power supply, rated at 125 to 325 volts d . c . at a current of from 0 to 200 milliamperes. The 150 vol t supply i s taken from the plate of a voltage reference 0A2 tube, V22 connected (with a series plate resistor) across the 300 vo l t l i n e . A l l co-axial cables, except for the two specif ied below, are Telcon KIG-M ( I C B ) (50 ohm characterist ic impedances). The output cable and the input cable to the anti-coincidence generator are Telcon AS48 (100 ohm characterist ic impedance, 12 1/2 p f . per foot capaci-tance) cables. 3 0 0 V LINEAR GATE I2AT7 BIAS AMPLIFIER COINCIDENCE GATE PULSE GENERATOR 85A2 6 C L 6 I 6AH6 6AH6 6AH6 IG IN GATE PULSE OUT 3 0 0 V BIASED DISTORTER A. POWER REQUIREMENTS 185 MA AT 300 VOLTS 135 MA^AT - ISO VOLTS H E A T E R S ' V' 1,5,6,9,12,14,15, 17,18 COMMON 6-3 V, 2*3 AMP-V' 2,3,7,13,16,19 COMMON 6-3 V, 1-7 AMP (-125 V DC) V- 8,10,11,20,21, COMMON 6-3 V, 1-9 AMP U 5 0 V D C ) (V3,I2AT7, HASHTRSIN PARALLEL) - I 5 0 V oov ^J50V " > 22ma t5|na G N D B. C O M P O N E N T D E S I G N A T I O N RESISTANCES ARE IN OHMS IK • I 0 3 OHMS IM = 10 6 OHMS UNSPECIFIED RESISTORS ARE l / 2 WATT CAPACITIES ARE GIVEN IN MICRO-FARADS I PF = I 0 " 6 | J F A L L TRANSFORMERS ARE VALOR PT-530D TURNS RATIO 3-3 TO I SUPPRESSOR GRIDS OF ALL PENTODES CATHODE CONNECTED COINCIDENCE GATE PULSE GENERATOR IS MOUNTED ON A SEPARATE CHASSIS THE SYMBOL * ABOVE A RESISTANCE MEANS A WELWYN HIGH STABILITY (l %) RESISTOR - I 5 0 V 403 B 6AH6 - I 5 0 V 403 B SI6 O U T o-5ov P U L S E SHAPER RATE OF RISE - 14 V PER | 4 S E C ^ RATE OF FALL * 9 V PER [iSEC A / C INPUT 1 - 5 V ) D E A D T I M E A N D A N T I - C O I N C I D E N C E G A T E P U L S E G E N E R A T O R VAN DE GRAAFF, PHYSICS, UNIVERSITY OF BRITISH COLUMBIA DESIGN5 G. JONES DRAWING1 P RILEY DATE* MAY 17, 1958 CONSTRUCTION' P. RILEY -64-BIBLIQGRAPHY Ajzenberg, F . , and Lauritsen, T . , 1955, Rev. Mod. Phy. 22, 77 Alexander, T . K . , 1955, M. Sc. Thesis, University of B r i t i s h Columbia Argo, H .V . , Taschek, R . F . , Agnew, H.M. , Hemmend irxger, A . , and Leland, W.T. , 1952, Phy. Rev. 82, 612 Auerback, T . , and French, J .B . , 1955, Phy. Rev. 9jS, 1276 Avery, R. and Blanchard, C . H . , 1950, Phy. Rev. 28, 704 Burling, R. , 1941, Phy. Rev. 60, 340 Cameron, A . , 1957, Atomic Energy of Canada, A . E . C . L . No. 494, Report No. CRL-41 Dosso, H.W., 1957, M.Sc. thesis , University of Br i t i sh Columbia Dubridge, S., Barnes, S., Buck, J . , and Strain, C. (1938), Phy. Rev. j>3_, 447 Edwards, M . , 1950, M.A. thesis , University of B r i t i s h Columbia Erdos, P . , S t o l l , P . , Wachter, M . , and Wateghin, V . , 1954, Nuovo Cimento, 12, 639 Farley, F . J . M . , 1955, "Elements of Pulse C i rcu i t s " Feenberg, E . , and Wigner, E . , 1937, Phy. Rev. j j l , 95 Feingold, A . M . , 1956, Phy. Rev. 101, 258 Harris, E . G . , and Melkanoff, M.A. , 1953, Phy. Rev. 20 (1953), 585 Ingl i s , D.R., 1953, Rev. Mod. Phy. 25_, 390 Ishiguro, E . , Kayama, K. , Kotani, M . , and Mizuno, Y . , 1957, Journal of the Physical Society of Japan, 12, 1355 Johnson, R . L . , 1958, Private communication for H.D. Holmgren Katz, L. and Goldemberg, J . , 1954, Phy. Rev. 9J>, 471 Kurath, D . , 1956, Phy. Rev. 101, 216 Kusch, P . , 1949, Phy. Rev. 26, 138 Larson, E . A . , 1957, M.A. thesis , University of B r i t i s h Columbia Laubenstein, R., and Laubenstein, M . , 1951, Phy. Rev. 8Jt, 18 -65-Mack, J . E . , 1950, Rev. Mod. Phy. 22 (64) Mayer, M.G. , and Jensen, J . H . D . , 1955, "Elementary Theory of Nuclear Shel l Struc-ture" Moody, N . F . , Howell, W.D., Ba t t e l l , W . J . , and Tapl in, R . H . , 1950, Atomic Energy of Canada Limited, CREL - 464, "A Comprehensive Counting System for Nuclear Physics Research" Peaslee, D . C . , and Telegdi, V . L . , 1953, Phy. Rev. 22, 126 Perry, J . E , , and Bame, S . J . , 1955, Phy. Rev. 22, 1368 Present, R .D. , 1950, Phy. Rev. 80, 43 Robertson, L . P . , 1957, M.A. Thesis, University of Br i t i sh Columbia Sharp, W.T . , Gove, H . E . , and Paul, E . B . , 1953, Chalk River Project, "Graphs of Coulomb Functions" Siegbahn, K. , 1955, "Beta and Gamma Ray Spectroscopy" Stelson, P . , and Preston, 1954, Phy. Rev. 9J>, 974 Sternheimer, R. (1950), Phy. Rev. 80, 102 S t o l l , P . , and Wachter, M . , 1953, Nuovo Cimento 10, 347 Ti t terton, E.W., and Brinkley, T . A . , 1953, Proc. Phy. Soc. 66A. 194 Ti t terton, E.W., and Brinkley, T . A . , 1953, Proc. Phy. Soc. 66A, 579 Warren, J . , Laurie, K. , James, D. , and Erdman, K. , 1954, Can. J . Phy. 3^, 563 Whaling, W., 1957, Kellogg Radiation Laboratory Preprint Wigner, E . , 1937, Phy. Rev. .51, 106 

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