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The reaction Li7 (OC,[gamma])B11 and states of Boron 11 Phillips, Gilbert James 1957

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THE REACTION" L i 7 (OC, )f) B " AND STATES OF BORON 11 GILBERT JAMES PHILLIPS B.Sc. University of Manitoba, 19^9 M.A. University of B r i t i s h Columbia, 1952 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the Department of PHYSICS We accept this thesis as conforming to the required .standard. THE UNIVERSITY OF BRITISH COLUMBIA October, 1957 Abstract Modifications to the University of B r i t i s h Columbia Van de Graaff Generator have provided for the production of beams of singly-charged alpha particles. Alterations have been made to the ion source, analysing magnet, and reverse electron beam energy stabilizing system. Well-focussed beams of 10 to 15 microamps resolved of singly-charged alpha particles were available, at energies up to above 1.2 Mev. The nuclear reaction L i 7 (ocs)f) b" was studied by bom-barding targets of lithium metal evaporated onto copper backings. The gamma rays from the decay of states of By/ were observed with Nal (Tl) s c i n t i l l a t i o n counters and associated electronic equip-ment, including a 30 channel Marconi Pulse Amplitude Analyser. In the range of alpha particle energies available, three resonances were known for the capture of alphas by L i , forming states of B " at 9.28, 9.19 and 8.92 Mev. The decay of these states included cascades through lower excited states, i n partic-ular one at h,k6 Mev. The widths of these resonances were measured respectively as 8, 1 and <1 kev, in laboratory co-ordinates. The second of these values is significantly lower than previously reported. Measure-ments were also made of the yields of gamma radiation, and the angular distributions of certain gamma rays from each resonance. Experimental results and calculations have been compared with ap-propriate theoretical values to obtain information on the angular momenta and parity of certain of the B states. The zero spin of the incoming alpha particles puts a useful limitation on the input channel spin. Assignments suggested by the data were as follows. For the ^.^6 Mev state, 5/2 ; for the 9.28 Mev state, 5 / 2 + . Data for the 9.19 Mev state cannot distinguish between 3/2~~and 5/2 , while for the 8.92 Mev state, the angular momentum would be re-stricted to 3/2 or 5/2 i f the state was formed by the capture of p-wave alphas, but the parity was not determined. These results indicate that the states of B" are cer-tainly more complex than the simple single-particle picture pro-posed by Jones and Wilkinson (1952), which i s inadequate to de-scribe the present results. Further investigation i s invited. tEJje ptttterstijj of ^§rtttglj Columbia Faculty of Graduate Studies P R O G R A M M E O F T H E F I N A L O R A L E X A M I N A T I O N FOR THE DEGREE OF D O C T O R O F P H I L O S O P H Y of G I L B E R T J A M E S P H I L L I P S B.Sc. University of Manitoba M. A. University of British Columbia W E D N E S D A Y , N O V E M B E R 6 t h , 1957 a t 3:30 p .m. I N R O O M 300, P H Y S I C S B U I L D I N G C O M M I T T E E I N C H A R G E D E A N G . M . SHRUM, Chairman G. M. GRIFFITHS A. EARLE BIRNEY J. B. WARREN S. W. NASH K. C. MANN F. K. BOWERS M. BLOOM -ABSTRACT Modifications to the University of-British Columbia Van de Graaff Gener-ator have provided for the production of beams of singly-charged alpha particles. Alterations have been made to the ion source, analysing magnet, and reverse electronbeam energy stabilizing system. Well-focused beams of 10 to 15 microamps resolved of singly- charged-alpha particles were available, at energies up to above 1.2 Mev. The nuclear reaction Li?(alpha, gammaJB11 was studied by bombarding targets of lithium''metal' evaporated onto copper backings.' The gamma rays from the decay of states of B 1 1 were observed with Nal (Tl) scintillation counters and associated electronic equipment, including a 30 channel Marconi Pulse Amplitude Analyser. In the range of alpha particle energies available, three resonances were known for the capture of alphas by Li 7 , forming states of B 1 1 at 9.28, 9.19 and 8.92 Mev. The decay of these states included cascades through lower excited states, in particular one at 4.46 Mev. The widths of these'resonances were1'measured'respectively as 8, 1 and <.l kev, in laboratory co-ordinates. The second of these values is significantly lower than previously reported. Measurements were also made of the yields of gamma radiation, and the angular distribution of certain gamma rays from each resonance. Experimental results and calculations have been compared with appropriate theoretical values to obtain information on the angular momenta and parity of certain of' the "'B11 states. The zero''spin of the incoming alpha particles puts a useful limitation on the input channel spin. Assignments suggested by the data were as follows. For the 4.46 Mev state, 5/2~; for the 9.25 Mev. state, 5/2?*Data'for the' 9.19 Mev state cannot distinguish' between 3/2'~ and 5/2 ~whiie for the 8.92 Mev state, the angular momentum would be restricted to 3/2 or 5/2 if the state was formed by the capture of p-wave alphas, but' the* parity was not determined. These results indicate that the states of B 1 1 are certainly more complex than the simple single-particle picture: proposed-by Jones and Wilkinson (1952), which is-inadequate to describe the present results. Further invest-igation is invited. G R A D U A T E S T U D I E S Field of Study: Physics Chemical Physics A. J. Dekker Dielectrics and Magnetism F. D. Stacey Electromagnetic Theory W.' Opechowski Electronics A. Van der Ziel Geophysics A. R. Clark Nuclear Physics K. C. Mann Physics of the Solid State . . . J. S. Blakemore andJ. B. Brown Quantum ' Mechanics -G. , ! M. Volkoff Quantum Theory of Radiation F. A. Kaempffer Special Theory of Relativity W. Opechowski Theory of Measurements A. M. Crooker X - Ray Crystallography J. B. Warren OTHER STUDIES Differential Equations T. E. Hull Mathematical Statistics S. W. Nash Network Theory A. D; Moore In presenting t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements, f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree th a t permission f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e . I t i s understood tha t copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission. The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, Canada. Department of Date ^3^-Acknowledgements The author i s pleased to make the following acknowl-edgements. Dr. J.B. Warren, of the Physics Department, University of B r i t i s h Columbia, Van de Graaff Group Supervisor, has pro-vided advice and direction during the course of this research. Dr. C.A. Barnes, of the Kellogg Radiation Laboratory, California Institute of Technology, directed the i n i t i a l stages of this research programme, initiated many of the modifications to the Van de Graaff Generator, and contributed many helpful discussions of alpha particle reactions. Dr. G.M. Griffiths, of the Physics Department, Univer-sity of Br i t i s h Columbia, in directing this research,has contri-buted his time and advice most generously during the performance of the experiments, analysis of the results, and preparation of this thesis. Many members of the Van de Graaff Group, both past and present, have participated i n the modification, maintenance, and operation of the Generator during the course of these experiments, and have provided valuable discussions of the problems which have arisen. Financial assistance has been received from the National Research Council i n the form of a Studentship held during 1955-1956. Table of Contents Page A Introduction 1 £ Apparatus 5 1. Production of Alpha Particles 5 (a) Ion Source 5 (t>) Helium Thermal Valve 7 (c) Operation of the Helium Valve 9 2. Van de Graaff Modifications 11 (a) Magnetic Fields for Deflecting Beams 11 (b) Electron Gun and Energy Stab i l i t y 11 3. Beam Path After Acceleration Ih (a) Stops and Beam Shutter Ik (b) Target Contamination; Background Radiations. 15 k. Targets 16 (a) Target Chambers 16 (b) Lithium Furnace 16 (c) Target Backings 17 (d) Target Preparation 17 5. Gamma Ray Detection 19 (a) S c i n t i l l a t i o n Counters 19 (b) Electronics for Angular Distribution Measurements 21 (c) Electronics for Angular Correlation Measurements 22 (d) Additional Electronic Apparatus 25 6. Experimental Procedures 26 (a) Targets and Counters • 26 (b) Electronics 27 C Experimental Results and Calculations 30 1. Resonance Widths and Gamma Ray Yields 30 (a) Measurement of Widths 30 (b) Calculation of Reduced Particle Widths 32 (c) Measurement of Gamma Ray Yields 3h (d) Calculation of Radiation Widths 38 2. Angular Distributions •.. (a) Measurement of Angular Distributions ........ (b) Corrections (c) Calculation of Angular Distributions 3 . Angular Correlations Table I Collected Results D Conclusions E Appendices T ' I Commercial Components • II (a) Magnetic Deflection of Charged Particles ... (b) Energy Resolution I l l Angular Distribution Calculations P Bibliography List of Illustrations Figure No. T i t l e Facing Page 1 . Energy Levels of Boron 11 . 3 2 . Ion Source Power Oscillator .. h 3 . Ion Source Components 5 k. Ion Source Extractor. Canal 6 5 . Helium Thermal Valve ' , . 8 6 . Electron Gun Mounting • • ,. 12 7 . Magnet Box and Extension Pole Pieces ....... 13 8 . Beam Tube and Target Mounting lh 9 . Lithium Furnace and Target Chamber ......... 17 1 0 . Cathode Follower Header 18 1 1 . Header with Delay Line Pulse Shaping 19 12. Spectra from Large Counter 20 1 3 . Biased Amplifier 21 1*+. Angular Distribution Electronics; Block Diagram 22 1 5 . Angular Correlation Electronics; Block Diagram • 23 1 6 . Phase Inverter 2h 1 7 . O.96O Mev Resonance; Thick Target 31 1 8 . 0 . 8 2 0 Mev Resonance; Thick Target 32 1 9 . O . 9 6 O Mev Resonance;. Excitation Function and Spectrum Mt 2 0 . Magnetization Curve for Analyzing Magnet ... 57 2 1 . Deflecting Fields for 20 cm Radius 58 2 2 . Deflecting Fields for 30 cm Radius 59 2 3 . Deflecting Fields for Singly-Charged Alphas. 60 2h, Diagram for Energy Resolution Calculation .. 6 l 2 5 . Calculated Energy Spread i n Beam 62 A.Introduction This thesis describes the modification of the U.B.C. Van de Graaff Generator for the acceleration of singly-charged alpha particles, and an investigation of certain excited states of boron 11 produced by the reaction L i 7 (ocjf )B/y . Alpha particles have certain advantages over other nuclear projectiles. They have zero spin, which limits the input channel spin for alpha-induced reactions to a single value, a simplifying restriction for .the analysis of nuclear decay schemes. Where a useful intensity of doubly-charged alphas can be obtained, the energy of the accelerator is effectively doubled, an attractive possibility for Van de Graaff experimenters. No detectable amount of doubly-charged alphas has been produced with the apparatus described below, and i t would appear that more complex ion-source arrangements are necessary to generate usable numbers of the doubly-charged ions , ( B i t t ne r , 1954; Temmer 1955). Beginning i n 1911 with Rutherford ' s determination of nuclear s ize by scatter ing experiments, nuclear react ions were studied fo r two decades w i th natura l alphas as the only p a r t i c l e source. Natural alphas produced the f i r s t recognized nuclear react ion N f ¥ ( * , p ) 0 / 7 (Rutherford, 1919) as w e l l as the Be («*»n) C react ion leading to the discovery of the neutron, (Chadwick, 1932). A r t i f i c i a l l y accelerated alphas became ava i l ab le wi th the development of p a r t i c l e accelerators i n the ear ly 1930*s, p a r t i c u l a r l y with the cyc lo t ron . Though t he i r production i n Van de Graaffs was reported as ear ly as 1933 (Tuve, Hafstad and Dahl, 1933)> i t i s only i n comparatively recent years that ex-tensive use has been made of Van de Graaff alphas. As pointed out by Bennett, Roys and Toppel (195D> alpha capture appears to be a " s imple" process, analogous to pro-ton capture, rather than to the more complex deuteron-induced processes, where the s t r ipp ing react ions may compete with or r e -place compound nuclear formation. This i s perhaps not surpr i s ing i n view of the t ightly-bound alpha s t ructure. The L i B react ion was f i r s t reported by Bennett, Roys and Toppel (1951)> and subsequently by Jones and Wilkinson (1952) and Heydenburg and Temmer (195^)• Figure 1 shows the known leve l s of B / y up to 16 Mev, (Ajzenberg and Laur i t sen, 1955). B e + d 15.818 B 1 0 + n 1 1 . 4 5 9 10.23 9.19 6.76 14.0// / / / / / / / / / >>»/////////// 13.2 / / / / / / / // //////WW / / / I 1.8 10.61 9 8 6 , 9 . 2 8 8.57  7 . 9 9 7 . 3 0 6.81 B e ° + p 1 1 2 3 3 L i 7 + a 8 . 6 6 7 5 0 3 4 . 4 6 F i g I E n e r g y L e v e l s o f B o r o n II - 3 -Jones and Wilkinson studied the angular distributions of the gamma rays, and made assignments for almost a l l levels up to 9.28 Mev on the basis of a s t r i c t single-particle shell model (M&yer and Jensen, 1955), i n which the ground state was assigned the configuration (1 p3/2), the f i r s t excited state (1 pl/ 2 ) , i.e. the upper level of the ground-state spin-orbit doublet, and higher states were assumed to be formed by excitation of the odd proton to higher levels i n the d,s and f shells. Considerable information on the B 1 1 levels, and those of i t s mirror nucleus C / ; has been obtained from stripping re-actions on B / < ?. Evans and Parkinson (195*0» from Butler theory analysis of data from B / 0 (dp) B / /, obtained results disagreeing with the assignments of Jones and Wilkinson, particularly for the f i r s t excited state. Their data was somewhat complicated by compound nucleus interference in the stripping reaction. How-ever, the results of Cerineo (1956) on the mirror reaction B / 0 (dn) C " support the conclusions of Evans and Parkinson with-out ambiguity. Recently Wilkinson (1957) has reported that measurement of the lifetime of this state by doppler-shift tech-nique supports his earlier assignment of 1/2 , and suggests that the apparent disagreement of the stripping data may result from a spin-flip of the outgoing particle in the stripping reaction. The mass 11 system appears in reasonable agreement with the charge-independent nuclear force picture of mirror nuclei up to the close doublet in B " at 6.80 Mev where no such doublet has been observed in C x /. This might be explained by a shift of the > o o > — a OQ_ a £ o oo 10 3 > c ^ x E a | 0 -o 3 ° - W N X i-t> o fcJ 0<3 •d P (?) CD #> Vcvl O o CM S I O o cp _ © o. i_ a (0 CO > o o o CM o CM o CM E E c o £ O c 3 s S — - X o to CM .0 V 3 » *• O F i g I o n S o u r c e P o w e r O s c i l l a t o r upper level of the doublet in C - raising the energy level from a position predicted by comparison with the mirror level i n B when the level l i e s near the separation energy for a particle. Levels of the mass 11 system above 6 Mev are of considerable interest for the mirror nucleus picture, and invite further study, (Lauritsen, 1952). A detailed investigation of the gamma rays from the three resonances i n L i (e*>^) B within the Van de Graaff energy range has been attempted. The system appears considerably more complex than at f i r s t imagined, and a complete interpre-tation of the level scheme up to 9 Mev w i l l require a good deal of further investigation. While this experiment was i n progress, an abstract of a similar study was published (Meyer-Schutzmeister and Hanna, 1957), but no further details have appeared up to the present time. E m ® o a ja O a 3 O a> > A a o a o •o noi > 9 o >-t> o (ft 93 CD o — 9 j T ) JUUiH u (D .2 o w O O CM > F i g 3 I on S o u r c e C o m p o n e n t s B. Apparatus 1. Production of Alpha P a r t i c l e s (a) Ion Source: P o s i t i v e ions were produced i n a conventional radio f r e -quency ion source. C i r c u i t of the 200 watt power o s c i l l a t o r i s shown i n figure 2, and the arrangement of the ion source and associated equipment i s shown schematically i n figure 3» Modi-f i c a t i o n s for the production of alpha p a r t i c l e s included the addition of the helium cylinder and helium valve, and an improved gas manifold. During the course of these experiments, a new gas mani-f o l d , with helium-leak tested toggle valves, (Appendix I contains data on c e r t a i n commercial components),and an attached P i r a n i gauge, was i n s t a l l e d . The toggle valves were supplied with 1/k inch pipe threads, which had to be vacuum-sealed to the manifold and to adaptors f o r 0-ring couplings. This was accomplished by tinning the threads i n the manifold and couplings with indium metal,(Appendix I ) . Palladium leaks i n the hydrogen and deuterium cylinders have been replaced with thermal valves, s i m i l a r i n operation, though considerably more compact than the helium valve, to be described below. These thermal valves have a small leakage rate even when nominally closed, thus allowing a small contamination of one gas by another i n the discharge. Because of the difference i n i o n i z a t i o n potentials of hydrogen, (or deuterium) and helium, H i O 0 . 2 5 I I I n c h e s F i g 4 I o n S o u r c e E x t r a c t o r C a n a l - 6 -a d d i t i o n of hydrogen or deuterium to a helium discharge produced a much greater contamination of the ion beam than i n the r e -verse s i t u a t i o n , i . e . the a d d i t i o n of helium to a hydrogen or deuterium discharge. The i o n i z a t i o n potentials are: (Kaye and Laby, 1956) v H 13.598 ev He 2**.58 " He* 5k.k « Background radiations due to contamination of helium discharges by deuterium were observed, and w i l l be discussed be-low. The solenoid-operated toggle valve i n the deuterium gas l i n e was i n s t a l l e d to eliminate t h i s contamination. Figure h shows the base of the discharge tube and the extractor canal, through which ions l e f t the discharge tube and entered the accelerator tube. Focussing of ions into and through the extractor canal was effected by the shape of the plasma i n the lower part of the discharge tube. S a t i s f a c t o r y extraction of ions depended on the shape of the extractor canal. Too r e -s t r i c t e d an opening at the top allowed erosion of the aluminum canal by the i o n beam, producing asymmetries i n the e x i t hole, and metal sputtering of the Vycor tube surrounding the canal en-trance. Both these e f f e c t s contributed to poor focussing by a l t e r i n g f i e l d gradients and the shape of the plasma, thus lower-ing the y i e l d of ions. Alpha p a r t i c l e beams were p a r t i c u l a r l y destructive to i n c o r r e c t l y shaped canals. The p r o f i l e shown i n figure h seemed to reduce the rate of serious erosion. A two l i t e r helium cylinder was constructed of l A inch brass. One end was removable, and sealed i n place on a neoprene O-ring. A 150 p s i . pressure gauge and a toggle valve were mounted on one end, a second toggle valve on the other. The helium valve was strapped to t h i s b o t t l e , and connected to one toggle valve with an O-ring coupling. (b) Helium Thermal Valve:. Singly-charged alpha p a r t i c l e s were obtained by i o n i z -ing helium gas i n the radio-frequency ion source. This required a controlled flow of reasonably pure helium i n t o the gas mani-f o l d . Since the d i f f u s i o n rate of helium through metals i s a l -most zero, the palladium leak, often used f o r hydrogen or deu-terium, could not be used, and some type of mechanical valve was required. For operation i n a Van de Graaff, the valve had to be rugged and dependable, capable of remote c o n t r o l , had to pro-vide positive shut-off, f i n e c o n t r o l of the gas flow, and have a reasonably short operating time-constant. Valves operating by the d i f f e r e n t i a l thermal expansion of d i s s i m i l a r metals, with e l e c t r i c a l heating, f u l f i l l a l l the above requirements. Examples are given by Green (1953)» and Shire (195^). Some designs had previously been tested i n t h i s laboratory, and the valve used was developed from these, (Heiberg, 195^ PP. 65-66). This differential-expansion needle valve i s shown i n figure 5. Body and end-plates of the valve were of brass; the F i g 5 H e l i u m T h e r m a l V a l v e needle of a " s t a i n l e s s " type s t e e l , of unknown composition. Copper-plated stainless s t e e l G-rings,(Appendix I ) , provided a positive seal at the ends to withstand the operating temperatures of several hundred degrees centigrade, and pressures up to 100 p s i g . S a t i s f a c t o r y operation of such a valve was dependent on the choice of taper f o r the needle. The 10 degree half-angle used appeared to provide reasonably slow opening, and hence f i n e control without s t i c k i n g i n the seat. Incorporation of the valve seat i n one end-plate rather than i n the valve body allowed a good match of the tapers on the needle and seat, as both could be cut on a lathe with the same setting of the compound-rest. The f l o a t i n g nut at the fixed end of the needle allowed the needle to be lapped onto the seat with the valve p a r t i a l l y as-sembled. F i n a l lapping was done^ with no. 1000-grit lapping com-pound . The heating element consisted of approximately h meters of 0.010 inch nichrome wire, t o t a l resistance about 90 ohms (0,222 ohms per cm), wound over a mica i n s u l a t i n g sheet, and lagged with about 6 mm of asbestos paper. ^00 cycle AC power was supplied v i a a variac and a 150 VA i s o l a t i n g transformer,(Appendix I ) . Tank helium was used, (Matheson welding grade, 99.99$ pure), the gas bottle being f i l l e d by passing the helium at 150 psig. through an activated charcoal trap at l i q u i d nitrogen - 9 -temperature, (77 degrees K). (c) Operation of the Helium Valve: The helium valve was i n s t a l l e d i n the Van de Graaff on October 25, 1955, and operated s a t i s f a c t o r i l y from that date, with no attention other than periodic f i l l i n g of the helium gas b o t t l e . Beam currents of up to 20 microamps resolved of s i n g l y -charged alpha p a r t i c l e s were observed; 10 to 15 microamps were t y p i c a l l y a v a i l a b l e during experiments. Suitable loading of the ion source o s c i l l a t o r , corresponding to o s c i l l a t o r plate currents of 200 to 250 ma were obtained at a power input of approximately 55 watts to the thermal valve. With the top terminal of the Van de Graaff open, these o s c i l l a t o r load currents were obtained with ion source manifold pressures of about 350 microns. When f i r s t turned on, the leak required frequent ad-justment f o r a period of about one-half hour. This presumably was the time required f o r the leak to reach thermal equilibrium with i t s surroundings. Ambient temperature inside the top t e r -minal of the Van de Graaff at 50 lbs nitrogen pressure, measured with a maximum thermometer over long periods, including uninter-rupted runs of 16 hours, reached 52 degrees C. The helium valve proved quite sensitive to the regu-l a t i o n of the 110 V, kOO cycle AC power i n the top terminal, and during periods when t h i s regulation was poor, the valve r e -quired continual adjustment to keep the loading of the ion source o s c i l l a t o r and the beam, constant. - 10 -The thermal, time constant of the helium valve appeared reasonably short; turning off the leak power extinguished a nor-mal discharge i n less than 5 seconds. Leakage rate through the closed helium valve into the manifold was observed to give a pressure rise of three microns i n one minute i n a volume estimated at 20 cc (manifold and Pirani gauge). This rate did not constitute a serious drain on the helium supply, and produced negligible pressure rise i n the ac-celerator tubes. Although the helium valve was at times observed to operate without adjustment for periods of up to two hours, more frequent attention was usually required. A finer adjustment on the heater power would have been convenient. Addition of a second heater winding to the leak, with the variac controlling one wind-ing, and the second connected to a constant \oltage source by a switch would give the desired degree of control. Before installation i n the Van de Graaff, the helium valve was tested on the ion source of a 50 kev accelerator. At this time the line spectrum of singly-ionized helium was observed, and a search made for lines indicating doubly-ionized helium, i n o e particular those at *f685.8 A and 6560.1 A, using a direct vision spectroscope (Canadian Arsenals Ltd. Type 55). These lines were not observed. - 11 -2. Van de Graaff Modifications (a) Magnetic Fields for Deflecting Beams: Magnetic deflection of singly-charged alpha particles required significantly higher fiel d s than for the deflection of protons or deuterons of_similar energies. For example, on the original 20.3 cm radius i n the deflecting magnet, 1 Mev protons, deuterons, and singly-charged alpha particles required fields of 7, 10 and Ik kilogauss respectively. Appendix II discusses the f i e l d requirements. Operation of the beam-deflecting magnet at these higher fields raised problems i n machine control which led to several modifications of the Van de Graaff Generator. (b) Electron Gun and Energy Stability: The accelerating potential of the Van de Graaff was stabilized by a beam of electrons injected at the earth end of the dif f e r e n t i a l pumping tube, and intensity-modulated by a signal derived from the position of the deflected beam relative to a pair of s l i t s or "sniffers", thus fixing the accelerating poten-t i a l with reference to the f i e l d of the deflecting magnet. When i n i t i a l l y attempting to deflect beams of 0.8 to 1.0 Mev alpha particles, i t was found that the electron beam ceased to stabilize the accelerating potential, apparently the result of the fringing f i e l d of the magnet affecting the elec-tron beam entering the di f f e r e n t i a l tube. The base-plates of the accelerator and di f f e r e n t i a l tube manifolds were relatively close F i g 6 E l e c t r o n G u n M o u n t i n g - 12 -to the yoke of the magnet ( v e r t i c a l separation $k cm) and t h i s distance was decreased by the l i f t i n g lug on the yoke on the d i f f e r e n t i a l side (height of lug 12 cm). With the magnet on, f l i p - c o i l measurements indicated appreciable magnetic f i e l d s even between the pumping manifolds. O r i g i n a l l y the electron gun was mounted external to the base-plate of the d i f f e r e n t i a l manifold, about 10 cm above the l i f t i n g - l u g on the magnet. Electrons were injected at about 2.5 kev energy, and d r i f t e d a distance of about 1.5 meters up through the s t e e l pumping manifold before entering the vacuum-tube proper. Magnetic f i e l d gradients i n t h i s d r i f t region, produced by the f r i n g i n g f i e l d , could apparently d e f l e c t or de-focus the electron beam s u f f i c i e n t l y that i t d i d not a r r i v e at the top terminal of the accelerator. Shielding the external gun structure with a mu^metal s h i e l d , (5 inch photomultiplier s h i e l d ) , with a 0.25 inch mild s t e e l housing, and with t h i s housing l i n e d with 0.25 inches of s i l i c o n s t e e l transformer laminations f a i l e d to produce any im-provement. This d i f f i c u l t y was f i n a l l y overcome by remounting the electron gun structure on a H-.5 cm diameter brass tube, project-ing up into the base of the pumping manifold f o r a distance of about 1 meter. This arrangement i s sketched i n figure 6. In t h i s p o s i t i o n the d r i f t distance for the electrons was greatly reduced, and the gun structure was well removed from the region F i g 7 M a g n e t B o x a n d E x t e n s i o n P o l e P i e c e s - 13 -of high fringing-fields. This arrangement has operated satis-factorily since February, 1956. Several improvements were made to the analysing magnet. Extensions on the pole faces increased the effective radius of curvature, from about 20.3 cm to about 30.5 cm, thus decreasing the f i e l d required to deflect particles of any given energy. As originally designed, the magnet had 11.5 inch radius circular pole faces with a 5 inch gap, supporting 16 inch square pole faces 2 inches thick, leaving a 1 inch gap. A strong fringing-f i e l d was produced by the segments of the circular faces extend-ing beyond the square faces, with maximum fringing fields at the position of entry and exit for a beam following an 8 inch radius. Shims were provided only at the entry position. The modified arrangement i s shown i n figure 7. Three pairs of pole-face extensions, 2 by 3 by4:3/8 inches were machined from soft iron, and bolted to the 16 inch square pole-faces. Each extension was fitted with a semi-cylindrical adjustable shim , of 3A- inch radius. Brass rocker-arms were attached to the shims. A new magnet box was constructed of 7 /8 inch diameter copper tubing. Two quarter-circles of this tubing were joined at the entrance position, and hard-soldered to a rectangular brass flange, one inch thick. This flange was bolted to the pole-piece extensions at the top of the gap. Similar flanges connected to the free ends of the copper tubes by O-ring seals, and bolted to the side extensions. Locking bars on these flanges held the shim rocker-arms i n position. F i g 8 B e a m T u b e a n d T a r g e t M o u n t i n g - Ik -This arrangement permitted relatively easy removal of the magnet box, and the interior of the copper tubes was conven-iently cleaned with steel wool or chemicals. For this modified arrangement, the radius of curvature, taken as the geometric radius plus half the gap width, was 30.5 cm. A 1 Mev singly-charged alpha particle required about 10 kilogauss deflecting f i e l d to follow this curvature, compared to about l^f kilogauss with the former arrangement. Deflecting fields for the particles up to 2 Mev energy are given i n figure 22 (Appendix I I ) . 3. Beam Path After Acceleration (a) Stops and Beam Shutter: Figure 8 i s a schematic diagram of the apparatus t r a -versed by the beam after leaving the accelerator tube. At the entrance to the magnet box was a molybdenum stop with a 2>/k inch aperture, and insulated quartz and molybdenum shutters which could be turned into the beam path to measure the total v e r t i c a l beam. After deflection, the vertical spread of the beam was limited by the gold sniffers, and the horizontal spread by an annular gold stop, with a 1 cm aperture, mounted i n front of the solenoid-operated beam shutter. A focussed beam was about 2 mm wide at the target,i.e. much narrower than this stop-opening. - 15 -The solenoid-operated beam shutter, which carried a quartz focussing plate, protected the targets from the beam ex-cept when making observations, thus prolonging target l i f e . A switch on the main control panel allowed remote operation of this shutter. (b) Target Contamination and Background Radiations: Carbon deposits were observed to accumulate on surfaces struck by the beam, particularly on the sniffers and target. These deposits were a serious source of background radiations, presumably from the reaction C (<*>n ) 0 (0.=2.201 Mev), a pro-l i f i c neutron source i n spite of the low isotopic abundance of C / 3 , ( l . l # ) . Carbon deposits were produced from hydrocarbon vapours i n the vacuum system, chiefly from pump oils and vacuum grease. To limit these deposits, dry neoprene gaskets were used on a l l static joints i n the beam tubes, and vacuum grease on moving seals, (target holder and gate valves), was kept to a minimum. The beam tube and magnet box were frequently dismantled for cleaning of exposed surfaces, stops and sniffers. Two liquid nitrogen cold traps were used on the beam tube: a pyrexside-arm at the exit of the magnet box, and a brass and stainless steel trap at the target chamber, which carried an annular stop with a 2.5 cm aperture, through which the beam passed. With these precautions, the targets acquired only a faint greyish coating during runs of up to twelve hours, although heavier deposits occurred on the sniffers. - 16 -Deuterium contamination i n the ion beam was another source of background radiation. With an alpha particle beam passing through the magnet box, the deuterium fraction was de-flected by the magnetic f i e l d to strike the inside of the magnet box a few inches above the axis of the horizontal beam. A con-siderable quantity of lead and paraffin was supported by a Dexion frame so as to surround the beam tube at the exit of the magnet box and attenuate radiations from this region. Addition of the solenoid-operated valve in the deuterium line to the ion source f i n a l l y eliminated this source of background radiation. h. Targets (a) Target Chambersi Several target chambers were tested during the early phases of this experiment. The f i n a l design i s shown i n figure 9. A 2 inch glass port gave a clear view of the interior when making or bombarding targets. Beam current measurements were fac i l i t a t e d by insulating the target stem on a lucite ring. Target backings were kept cool by an external blast of air on the heavy copper target stem. (b) Lithium Furnace: Thin lithium targets were prepared by evaporation of lithium metal onto copper backings i n vacuo. A lithium furnace of brass and stainless steel with an e l e c t r i c a l heater, which sealed into the target chamber, i s also shown i n figure 9. The copper c o i l was water-cooled while evaporating lithium to protect the neoprene O-rings. A one ohm nichrome heating element was Target Backing G l a s s 1 Furnace Tube Beam Tube Luc i te \ 7 Sliding Seal Brass Body O 2 I nches T a r g e t C h a m b e r B r a s s O - Ring Q r o o v e s Cool ing Coi l S t ee l O i_ I n c h e s L i t h i u m F u r n a c e F i g 9 L i t h i u m F u r n a c e a n d T a r g e t C h a m b e r - 17 -wound over a mica sheet around the stainless steel tube. Up to 125 watts were supplied to the heater by a variac and 10:1 step-down transformer. The melting and boiling points of lithium are, respectively, 186 and 1380 degrees C. (e) Target Backings: Evaporated lithium targets were laid down on copper backings 0.015 inches thick. It was observed that during some long runs with f a i r l y large beams (more than 10 mieroamps) the yield from a target decreased slowly with bombarding time, and the surface of the copper developed a blistered appearance over the region where the beam had struck. Silver backings were tested, but the yield seemed to decrease more markedly than with copper, although no blistering was observed. Cooling the target backings by blowing air on the stem of the target holder appeared to pre- • vent this deterioration of the lithium targets on copper backings. (d) Target Preparation: To make a lithium target, a lump of lithium with dimen-sions of 3 to 5 im was cut under benzol and quickly transferred to the furnace. The furnace was then mounted on the target cham-ber, and the latter evacuated. With the target chamber at d i f -fusion-pump pressures, the cold-traps operating, and cooling water on, the furnace was heated with about 50 watts input. Af-ter a few moments heating, the pressure gauges on the magnet box indicated a sudden, momentary rise to pressures of several microns. This probably marked the melting of the lithium and the l i b e r -ation of absorbed gases. Pressures quickly returned to the order of 10 " * mm, and the lithium started to appear on the target backing Fig 10 Ca thode Follower Heade r - 18 -a short time later. No pressure rise was observed during the evaporation process. However, the gauges were situated some dis -tance from the target chamber, with three cold-traps intervening, and so did not record small pressure changes i n the target chamber. Lithium f i r s t appeared on the copper backing as a dark, transparent layer, giving a "black mirror" appearance. As the layer built up, i t became less transparent, and took on" an ash-grey matte surface. This colour f i r s t appeared when targets were about 30 kev thick. Several hours of bombardment produced only slight blackening of the targets, indicating that very l i t t l e carbon was being deposited. No deposits thick enough to shift the measured position of the L i (*>« ) B resonances were observed, indicating that any deposits were less than a kilovolt thick. Thin evaporated targets were quite uniform i n thickness, as indicated by the shape of the excitation functions. A very thick target, made by depositing successive layers of lithium, was less uniform. For some tests and calibrations, B/y was used as a tar-get for the B " ( p f Y) Q/2 reaction. Targets of B " separated isotope on 0.002 inch gold f o i l backing were available. (Supplied by the Harwell Electromagnetic Separator Group). F i g u H e a d e r w i t h D e l a y L i n e P u l s e S h a p i n g - 1 9 -5« Gamma Ray Detection (a) S c i n t i l l a t i o n Counters: Two s c i n t i l l a t i o n counters were used for these experi-ments. The f i r s t consisted of a Nal(Tl) cylindrical crystal 2.5 - 0.005 inches diameter by 3.5 * .005 inches long (Earshaw Type 10 D Ih s e r i a l no. P 926) mounted on a Duraont 6363, 3 inch photo-multiplier. This w i l l be referred to as the "large" counter. A second, to be referred to as the "small" counter, was a c y l i n -d r i c a l crystal 1.75 inches diameter by 2 inches long (Harshaw Type 7 D 8, s e r i a l no. J 155) mounted on an R.C.A. 63^2, 2 inch photomultiplier. Optical connection from the windows of the crystal containers to the phototubes was made with Dow-Corning no. 200 silicone o i l , viscosity 10 * centistokes at 25 degrees C. Leakage of the silicone o i l was prevented by a rubber sleeve slipped over the phototube and the crystal container. For the large counter, a sleeve was made by vulcanizing a sheet of 1/32 inch rubber. For the small one, a sleeve was cut from a toy bal-loon. Neither counter has shown any loss of resolution over a period of a year. The large crystal, photomultiplier, potentiometer chain, and cathode follower were mounted i n a brass cylinder 9 cm diameter by 38.5 cm long. The cathode follower c i r c u i t i s shown i n figure 10. The small crystal was supported in an aluminum tube 5.6 cm diameter by 5.*+ cm long, attached to a brass cylinder 7.6 cm dia-meter by 28 cm long. Two circuits were used to match this detector to a pulse-cable. The f i r s t was a cathode follower similar to that of figure 10. The second, shown i n figure 11 was introduced Fig 1 2 S p e c t r a f rom L a r g e Counter - 20 -when measuring angular correlations. It i s discussed i n section 5 (c). On "both counters, the cathode follower valve and a l l cable connections were mounted on the ends of the brass cases, keeping the detectors cylindrical for ease i n handling and shielding. Typical gamma ray spectra for the large counter are shown i n figure 12 for C s / 3 7 , Ra Th, and C ' z gamma rays. Energy resolution was about 7% at 2.62 Mev. The efficiency of the large crystal, as a function of gamma ray energy, had recently been studied experimentally by E.A.G. Larson, and L.P. Robertson, and theoretically by P.P. Singh, a l l of this laboratory. Theoretical calculations agreed within % of measured values for Co*° gamma rays (1.17 and 1.33 Mev), and for the 6.1^ Mev gamma rays from the F (p>c*0 0 reaction. Mr. Singh supplied a calculation of the crystal ef-ficiency appropriate to this experiment, which w i l l be discussed below. The small counter, used chiefly as a monitor, was sup-ported by an X-ray tube stand, with no shielding on the crystal. The large counter was mounted inside a set of interlocking lead bricks, having a 9.5 cm hole, lined with l A inch steel tube. Ad-ditional lead shielding was used around the region of the crystal; the counter and shielding were carried on a Dexion trolley. - 21 -(b) Electronics for Angular Distribution Measurements: High voltage for both photomultipliers was supplied by an I.D.L. Type 532 EHT supply, and a potentiometer with separate adjustments for each counter. The photomultipliers were operated with about 1 kev on the large counter, and about 0.925 kev on the small one. A Lambda Model 28 regulated power supply fed both cathode followers. An adjustable diode limiter in the cathode follower c i r c u i t shown in figure 10 prevented severe over-loading of the pulse amplifier by cosmic ray pulses. Pulses from the large counter were fed to a Northern Electric Model 1W+ wide band amplifier, whose time constants were used for pulse-shaping. Generally a "top cut" (integration time constant) of 1 microsecond, and a "bottom cut" (differentiation time constant) of 5 microseconds were used. Pulses from the Northern Electric amplifier were fed to a biased amplifier, figure 13,and from the biased amplifier to a Marconi 30 Channel Pulse-Height Analyser ("kicksorter"). The biased amplifier incorporated a coincidence-anticoincidence c i r c u i t or "gate" which was used during the angular correlation experiments. A Dynatron model 1009A scaler was attached to the dis-criminator output of the Northern Electric amplifier to provide a monitor for the counts in the large detector. This discriminator was set to a bias level just above the 2.62 Mev gamma rays from Ra Th. For a number of the angular distribution experiments, the monitor consisted of the small counter feeding pulses to an F i g 1 4 A n g u l a r D i s t r i b u t i o n E l e c t r o n i c s ; B l o c k D i a g r a m - 22 -Atomic Model 20*fB linear amplifier, and a Dynatron model 1009A scaler. Gains of the amplifier and photomultiplier were adjusted to keep 10 Mev pulses below the saturation amplitude of the am-p l i f i e r , and the bias of the scaler was adjusted to just above 2 . 6 2 Mev. A block diagram of this general arrangement for angular distribution experiments i s shown i n figure lk. (c) Electronics for Angular Correlation Measurements: To observe the angular correlation between pairs of gamma rays, equipment was added to provide energy selection i n the monitor channel, arranged so that pulses of the selected energy in the monitor channel opened the gate on the biased am-p l i f i e r to admit the time-coincident pulses from the large counter to the kicksorter. A block diagram of the angular-coincidence apparatus is shown in figure 15. The channel from large crystal to kicksorter was as described above, with the addition of a delay-line at the input to the Northern Electric amplifier, with matching resistors, and operation of the biased amplifier gate in the coincidence position. For the monitor channel, negative pulses from the cathode follower of the small crystal were fed to an EKCo Type 10^ 9B linear amplifier. Positive pulses of up to 70 volts amplitude from the EKCo amplifier went to an Atomic model 510 Single Channel Analyser ("SCA") which provided the energy discrimination i n this P> o era CD N 03 F i g 15 A n g u l a r C o r r e l a t i o n E l e c t r o n i c s ; B l o c k D i a g r a m - 23 -channel. Output pulses from the SCA, 15 volts negative, were i n -verted by a phase inverter, figure 16, to provide positive pulses for operation of the biased amplifier gate. An output point was added to the SCA to provide a posi-tive pulse out for each pulse of amplitude greater than the SCA base li n e . Pulses from this output were coupled by an 80 ohm cable and pulse transformers (Appendix I) to a Dynatron 1009A scaler. This provided a monitor channel for angular coincidence measurements, and for some of the angular distribution runs, when this channel was used solely as a monitor. The SCA was not designed for use i n time^coincidence measurements, i t s operation being as follows: Input pulses met a discriminator which defined the "base line." A l l pulses of ampli-tude greater than this base line setting were amplified a factor of ten by an "expansion amplifier", and applied to a second dis-criminator. This second discriminator determined an amplitude above the base-line setting. Output of both discriminators was fed to an anti-coincidence c i r c u i t . An output pulse appeared only i f the lower discriminator and not the upper one was triggered, i.e. only for pulses which f e l l within the "window" amplitude. An output pulse appeared only after an input pulse had crossed the base line, and, without crossing the window discrimin-ator, had f a l l e n below the base line again, thus i t was the t r a i l -ing edge of the input pulse which determined the position in time of the output pulse. For pulses with an exponential decay, pulses F i g 16 Phase Inverter - 2h -of different amplitude f a l l i n g within the window width gave a variation of up to several microseconds delay in the appearance of an output pulse. The cathode follower header of figure 10 on the small counter was replaced with that of figure 11 i n an attempt to over-come this d i f f i c u l t y . This c i r c u i t provided delays-line shaping to produce "square1' pulses, 2 microseconds long, rather than ex-ponential pulses, so that there would be much less variation i n length for different pulse amplitudes. The improvement was not as great as had been hoped, as the shaped pulses were s t i l l some-what rounded on top, and this shape was exaggerated by the expan-sion amplifier i n the single-channel analyser, so that the out-put pulse was triggered by the sloping portion of the top of the "square" pulse. The variation in delays was,however, reduced to about one microsecond. Satisfactory coincidence operation was achieved by i n -serting a delay i n the spectrum channel sl i g h t l y greater than the maximum delay i n the monitor channel, and using a gate pulse of sufficient duration to ensure that a l l truly-coincident pulses entered the biased amplifier without clipping. This arrangement increased the resolving time of the coincidence system but the operation was found to be adequate. For the spectrum channel, 180 cm of 2500 ohm ferrite-loaded delay line (Appendix I) pro-vided a total delay of about 3*5 microseconds. The gate i n the biased amplifier was opened by pulses of greater than approximately 10 volts positive, the gate remaining - 25 -open for the duration of the pulse above this amplitude. The out-put pulse of the SCA had a rounded top, and the phase inverter incorporated a gain control, which allowed a variation of the amplitude, and hence the duration (because of the rounded shape) of the gate pulse. Gate pulses of about 6 microseconds duration were found to be satisfactory. Pulses fed to the EKCo amplifier were also fed i n par-a l l e l to a length of cable, with a resistive termination, during experiments. This cable was used when setting the window position of the SCA. Its use w i l l be discussed below. (d) Additional Electronic Apparatus: Beam currents to the target were measured with an elec-tronic current integrator, described in Edwards, (195D. A 300 volt battery biased the target positive to suppress secondary electron emission. A system of switching relays gave simultaneous starting and stopping of the current integrator, kicksorter, scalers, and an electric timer. This system was controlled by the integrator to give readings for a certain number of integrator counts. Pulse generators using Western El e c t r i c 276D mercury switching relays, and based on Chalk River designs, were used for the setting and calibration of the kicksorter (Robertson 1957). The pulses were shaped to have approximately the same rise-time as those from Nal crystals (0.25 microseconds), and were of suf-f i c i e n t l y low level that they could be fed directly to the photo-- 26 -multiplier headers, through the "test" connector (figures;, 10 and 11) thus providing a check on the whole electronic channel after the photomultiplier. For setting and checking the channel-spacing of the kicksorter, the amplitude of the relay pulses could be modulated with a sawtooth waveform. 6. Experimental Procedures (a) Targets and Counters: Variations of gamma ray intensities with angle, measured with respect to the beam direction were observed, using the large counter to examine the spectra and the small counter as a monitor. For this purpose the small counter was kept i n a fixed position near the target chamber, while the large counter, with i t s lead shielding, was rotated i n the horizontal plane about the target. Focussed beams were centered on the target by observing the fluorescence of the lithium when struck by the beam. A zi-muthal position of the large counter was set with the aid of a protractor placed on top of the target chamber, and spacing from target to the counter was determined by lucite spacing-blocks used to set the distance from the outer wall of the target cham-ber to the face of the crystal. Some of the gamma rays studied were of low intensity, and to obtain reasonable counting rates i t was necessary to use f a i r l y small spacings between target and detector, and hence to accept f a i r l y large solid-angles. High angular resolution was - 27 -therefore not available for these low-intensity transitions. However, since the angular distribution functions were not ex-pected to contain terms of higher than the second power i n cos ~6-measurements at 0 and 90 degrees with respect to the beam direc-tion were adequate to determine the angular distribution coef-fic i e n t s . Accordingly these two angles were used i n the dis-tribution measurements. Two 90 degree positions were available, one on either side of the target chamber. Repeated runs i n these and the 0 degree position were made i n measuring each distribution. The target was rotated so that the gamma radiation always passed through the copper target backing to the large counter, i.e. for the detector at 0 degrees to the beam direction, the plane of the target was at approximately h$ degrees to the beam, with the face of the detector "looking at" the back of the copper target plate. Background runs were made with the target reversed so that the alpha beam struck the copper backing. When used as a monitor, the small crystal was supported with i t s axis vertical,above the horizontal plane of the beam, allowing maximum clearance for the large counter around the tar-get chamber. For angular correlations, the small counter was placed with i t s axis i n the horizontal plane, at 135 degrees to the beam direction, at a distance chosen to make the effective solid angles of the two crystals approximately equal. (b) Electronics: Channels of the kicksorter were set with the mercury re-lay pulse generator, and calibrated using the pulse generator and - 28 -a test source, usually Ra Th. A Ra Th source was also used to set the base line of the SCA when the small counter was used as a monitor. Energy calibrations were occasionally checked with the h.h3 Mev gamma radiation from B ( p , f ) C , and the 6,1k Mev radiation from F '* (p,<xX) o'*,' To calibrate the SCA for energy selection and coincidence counting, pulses from the small counter were fed to the Northern Electric amplifier in parallel with the EKCo amplifier. A spec-trum from the small counter was thus displayed on the kicksorter. Using the mercury pulse-generator, pulses were fed into the small counter, with amplitudes corresponding to the desired positions on the kicksorter spectrum, and the SCA base line and window dis-criminators set to include this range of pulses. The cable to the Northern Electric amplifier was then disconnected and term-inated with an equivalent impedance, (about 9 0 ohms) during the experiments. Operating energy for the Van de Graaff was chosen by determining an excitation function over the resonance being studied for each new target, the gamma rays being counted at the output of the Northern Electric discriminator, and by the monitor counter. A typical excitation function over the O.96O Mev resonance i s shown in figure 19. The energy of the accelerator was measured by a generating voltmeter, and once an operating point was chosen, the electron gun stabilizing system kept the energy constant within narrow limits, and with only infrequent adjustments. - 29 -Energy resolution of the analysed particle beam reaching the target depended upon the angle subtended at the center of the magnetic f i e l d by the gap between the sniffers. The simplified analysis given i n Appendix II indicated that the range of ener-gies i n the beam for typical sniffer positions was several tenths of a percent, i.e. several kilovolts at 1 Mev. However, obser-vations made while measuring resonance widths indicated that the resolution was one kilovolt or better. A well-focussed beam formed,at the position of the snif-fers, a line focus about 2 mm wide by 25 mm high. It was expected that the alpha particle fraction of the beam was closely homogen-eous i n energy on leaving the accelerator, and that the rather wide vertical spread of the deflected beam represented a small range of particle energies, i.e. the analysing system was highly dispersive. In that case, the range of energies for particles passing between the sniffers would have been considerably less than that indicated by the simple geometric calculation. This energy range was also a measure of the sensitivity of the s t a b i l i z -ing system. - 30 -C Experimental Results and Calculations 1. Resonance Widths and Gamma Ray Yields (a) Measurement of Widths: Evaporated lithium targets several hundred kilovolts thick were used for width measurements. The shape of the thick-target excitation functions at the resonances was determined by-measuring the yield of gamma rays at closely-spaced energy i n -tervals across each resonance. Alpha particle energies as i n d i -cated by the generating voltmeter were held constant to about one kilovolt at each point. The total width P of the resonances,in laboratory co-ordinates, was determined by f i t t i n g theoretical curves to these experimental points. The Breit-Wigner single-level formula for the cross-section (f (E) i n the neighborhood of a narrow, isolated resonance of the (<*^) reaction i s (1) where: 2 r~i 2. (E - E ) - ( ' / 2 ) SI f1 i s the total width of the resonance \2. " " alpha particle width /y » total radiation width E^ " " resonance energy 10 *-c 3 O o T " o o © o o o o o o rO O O O CM o o o F i g 17 0 . 9 6 0 M e v . R e s o n a n c e ; T h i c k T a r g e t in 6 Hi O P o d 03 H 10 (0 -<J> d > o (0 d E *-o > o m CD O in CD c m m d 9 C 4) - 31 -= (2.1 + 1) i s t h e s t a t i s t i c a l (2s +1) (2 j , + 1) w e i g h t i n g f a c t o r f o r : s s p i n o f i n c i d e n t p a r t i c l e j ; " " i n i t i a l s t a t e j " " c o m p o u n d " I n t e g r a t i o n o f t h i s f o r m u l a g i v e s t h e f o l l o w i n g e x p r e s -s i o n f o r t h e y i e l d Y o f gamma r a y s a s a f u n c t i o n o f a l p h a p a r t i c l e e n e r g y E a n d t a r g e t t h i c k n e s s t Y = C \ t a n " ' t Y (2) t l + y ( y - t ) w h e r e : C i s a c o n s t a n t y = E - E a n d y a n d t a r e m e a s u r e d i n u n i t s o f ' /2. T h i s f u n c t i o n w a s f i t t e d t o t h e e x p e r i m e n t a l p o i n t s t o d e t e r m i n e t h e w i d t h s o f t h e r e s o n a n c e s . I n f i g u r e s 17 a n d 18 a r e s h o w n t h e e x p e r i m e n t a l p o i n t s a n d t h e " b e s t f i t " t h e o r e t i c a l c u r v e s f o r t h e 0.960 a n d 0.820 M e v r e s o n a n c e s . I n t h e c a s e o f t h e r e s o n a n c e a t O.MX) M e v , b e c a u s e o f t h e l o w y i e l d o f gamma r a y s a n d t h e s m a l l w i d t h o f t h e r e s o n a n c e , i t w a s o n l y p o s s i b l e t o s e t a l i m i t o f < 1 k e v o n t h e w i d t h . T h e s e w i d t h s i n l a b o r a t o r y c o - o r d i n a t e s w e r e r e d u c e d t o c e n t r e - o f - m a s s v a l u e s b y m u l t i p l y i n g b y t h e f a c t o r F i g 18 0 . 8 2 0 / l e v R e s o n a n c e •, T h i c k T a r g e t - 32 -M c / M/ = O.636 where: M Q i s the reduced mass = M / i s the mass of the incident particle Mj2 i s the mass of the target nucleus The resulting values of the particle widths f» were: Resonance Energy 0,kO0 Mev 0.820 Mev 0.960 Mev Lab. Co-ords. <• 1 kev 1. kev 8. kev Centre-of-mass <<-l »• 0,6k " 5.1 » (Experimental results and calculations are collected in Table I at the end of Section C.) The above values are i n somewhat better agreement with those of Bennett, Roys, and Toppel (195D than with those of Heydenburg and Temmer (195*+) > quoted in Ajzenberg and Lauritsen (1955), particularly for the 0.820 Mev resonance, for which the latter observed a laboratory width of about 6 kev. (b) Calculation of Reduced Particle Widths: The total width P of a resonance may be expressed as the sum of reduced particle and radiation widths: P = ^ [p (particles) + fy'(radiation) In the energy range of these experiments, no particle emission other than the re-emission of alpha particles was - 33 -energetically possible, thus: r • c + £17 a o) Reduced alpha particle widths }f«c were calculated from the relation, (Blatt and Weisskopf 1952, page 390) r ~ - — C — w 2 K V j R where: K i s the wave-number of the incident particles vt i s a factor depending on the height of the coulomb barrier and the angular momentum of the incident alpha particles, calculated from the tables of Bloch et a l (195D> and from the graphs of Sharp, Gove, and Paul (1953) R = r 0 (A, +A 2 )» the interaction radius , „ -/3 using r 0 = I .H-5 x 10 cm, the value R = 5*08 x 10 cm was obtained for the L i plus alpha reaction. The choice of a suitable value of r 0 for the calculation of the interaction radius i s a matter of some uncertainty. For light nuclei, consisting of assemblies of relatively few nucleons, the radius R i s not a well-defined quantity. Experimentally, i t s value seems to depend upon the method of observation; whether, for example mass-radius or charge-radius is being measured. The above value of r e seems to be commonly used for reactions of light nuclei (Moszkowski 1955)• Note however that Sharp, Gove and Paul - 3^ -(1953) used the expression „ ' / 3 - / 3 R = 1.5 A, x 10 cm The problem of nuclear r a d i i i s currently receiving much attention. For a survey of the f i e l d , see Chapter 2 of Evans (1955). Values of the reduced alpha particle widths were: 0.960 Mev resonance 560 kev 0.820 Mev resonance 175 kev In the case of the O.MDO Mev resonance, the reduced alpha particle width would have to be very large i f the total width were to be measurable, for, i f the reduced width is assumed to be of the same order as the two above, (say 350 kev), the total width of the resonance would be only about 5 ev, i.e. of the same order of magnitude as the radiation width, as pointed out by Ferguson et a l (1957). (c) Measurement of Gamma Ray Yields: Yields of gamma rays were determined from thick target spectra taken above each resonance. Spectra covering the range of gamma ray energies from 2.5 to 10.0 Mev were corrected for background, normalized, and divided into energy intervals of 2 Mev, each covering the photo-and pair-peaks of one of the gamma-rays, or cascades. The number of counts i n these intervals was then corrected for absorption and for counter efficiency. - 35 -Absorption occurred i n the copper target backing, the brass target chamber, the lithium target and the face of the aluminum crystal container. The latter two effects were small, and were therefore neglected. The copper target backings were 0.15 inches thick and their angle with respect.to the beam and counter varied from 90 to h5 degrees, so that the thickness of copper in line with the axis of the counter ranged from 0.015 to 0.021 inches (0.0381 to 0.0^37 cm). Since the variation i n absorption was small over this range, and since the counter subtended a large solid angle at the target (about 12 degrees half-angle), an average thickness of copper of 0.0*+ cm was assumed. Brass walls of the target chamber were 1/16 inch (0.159 cm) thick, symmetric about the target i n the horizontal plane. Absorption of gamma rays in copper and brass was calculated using total absorption coefficients from the tables of Davisson and Evans (1952). P.P. Singh has calculated the efficiency of the large counter as a function of gamma ray energy up to 10 Mev for the following definition of efficiency £ at gamma ray energy Ey : „ no. of counts i n 2 Mev interval below E y € (By ) = y total no. of gamma rays incident on the face of the crystal This calculated efficiency was approximately constant above 3 Mev, and an average value of 58$ was used. - 36 -A further correction was necessary i n the case of the weak ground-state transitions from the 9.19 and 9.28 Mev levels. The observed 9 Mev peaks included counts due to lower energy cas-cade gamma rays detected in coincidence. Corrections were c a l -culated for such coincidences from the intense radiation due to cascades through the level at h.k6 Mev. It was necessary to consider two processes: random and true coincidences. The random coincidence rate was N c f counts per second, where N c is the counting rate per second and T is the resolving time of the counting apparatus. T was taken to be 5 microseconds, the decay time-constant used in the Northern Electr i c amplifier. The counting rate for true coincidences was a function of N the number of disintegrations per second giving a cascade £ the efficiency of the counter (g) the solid angle of the counter and of the angular correlation between the com-ponent gamma rays of the cascades. The angular correlation ex-periments, discussed below, indicated that i n the plane of the beam the component gamma rays of the cascades through the h,h6 Mev level from both the 9.28 and 9.J9 Mev levels had very small correlations. For the purpose of these calculations the correla-tions were assumed to be zero. It was further assumed (a rather crude approximation in view of the angular distribution data) that the radiation was isotropic, and with these assumptions, the - 37 -coincidence counting rate for detecting both members of a pair of coincident gamma rays was: while the counting rate for detecting only one gamma ray from each disintegration was: 2 N (a> € and the ratio of true coinci-dences to random counts was therefore: 60 € For the 9.19 Mev level, the number of true coincidences was about 50 times the number of random coincidences, and the num-ber of coincidence counts was about k0% of the total number of observed 9 Mev counts. For the 9.28 Mev level, true coincidences were about 10 times as frequent as random coincidences, and the number of coincidences were about 10$ of the observed 9 Mev counts. With these corrections, the results gave the number of gamma rays i n the solid angle of the counter for a given number of incident alpha particles. Using the angular distribution co-efficients discussed below, the total number of gamma rays over V- was calculated, and the relative intensities determined. Relative Gamma Ray Intensities: Resonance Energy OAOO Mev 0.820 Mev 0.960 Mev 9 Mev Radiation (96$) 1$ 12$ 7 H " 8$ 13$ if.5 " " ( W 91$ 75$ - 38 -Values for the 0.^-00 Mev resonance are those observed by Ferguson et a l ( 1 9 5 7 ) . Calibration of the 1 .0 microfarad range of the current integrator was done by feeding i n current from a battery through a resistor chain. The battery voltage was 1 8 9 . 5 V, (Electronic Instrument Ltd. Model Mf Substandard Meter, no. M + 2 9 7 ) , and the resistor chain consisted of four 10 megohm Nobeloy 1% resistors. This gave a current of *+.738 microamps, comparable to the beam current during yield measurements. Integrator sensitivity was 109 .3 microcoulombs per count, k similar calibration, done one year earlier, was within 3% of this value. Values of the gamma-ray yields Y per incident alpha particle were: Resonance Energy O.hOO Mev 0 .820 Mev 0 . 960 Mev 9 Mev Radiation 0 . 5 x i d " " O.Oh x 1 6 " " 2 . 3 x 1 6 " " 7 " " G.32 x » 2 . 5 x " h.5 » " 3 . 6 x " 1 5 . x » (d) Calculation of Radiation Widths- r Radiation widths were extracted from the total widths as follows. The di f f e r e n t i a l yield dy of gamma rays from the (o*,V) reaction may be expressed as dy = Q* (E) dT where: - 39 -O* (E) is the cross-section per incident particle of energy E, per target nucleus Nj is the number of incident particles per second T is the number of target nuclei per cm The total yield of gamma rays per incident particle written as: may be Y = y/N; = N (dx / dE) where: CO CT (E) dE (5) where: N is the number-density of the target nuclei dx / dE i s the reciprocal of the energy-loss per cm, of the incident particles i n the target material, assumed to be constant over the «*» narrow resonances. 0" (E) dE i s the integrated cross-section for a thick target. These quantities were evaluated as follows: Y values have previously been calculated, and are listed above, N = n° = h.6h x 10 atoms per cm M 23 n 0 i s Avogadro's number, 6.025 x 10 atoms per gram-atom d is the density of lithium, 0.531*- gms per cm M i s the atomic weight of lithium, 6.9^0 - IfO -The energy-loss of charged particles moving through an absorbing medium is given by the expression: z where: dE / dx _ kTTe2 ~x N B (6) m 0 V e i s the electronic charge, M-.80 X 10 esu z i s the charge on the incident particle, 2, i f the alpha particle is assumed to be stripped — 2 9 m i s the rest-mass of the electron, 9.108 x 10 gm V i s the velocity of the incident alpha particles B i s the "stopping number" of the absorbing material 2 'm0 V * B = Z log where: Z is the atomic number of the absorber, 3 for lithium. I i s the average excitation potential of the absorb-ing atoms. Direct calculation of dE / dx, using the above expres-sions, was complicated by uncertainty i n the choice of values for Z and I to suitably describe the complicated charge-exchange pro-cesses occurring as low energy alphas come to rest in a thick lithium target. However, the relationship (Bethe, 1936) B = s B (air) may be used to determine dE / dx, where s is the "stopping power" relative to air for the target material -1+1 -dE / dx (lithium) = N ( l l t h l u m > s dE / dx (air) (7) N ( air) J9 3 N (air) = 5.276 x 10 atoms per cm (15 degrees C and 76 cm) dE / dx (air) values were taken from the range-energy-curves for low energy alphas given i n Bethe (1950) s = 0.53 for lithium; Geiger's value, quoted i n Bethe (1936, page 272). The resulting values of dE / dx (lithium) were: at O.hOO Mev l.Oh Bev /cm » 0.820 « 1.09 " " 0.960 » 1.11 « These values are in good agreement with those from the data i n Whaling (1957). The integral was evaluated by integrating the Breit-Wigner single-level formula, (1) above, giving: a y 2 / f ^ Fr (8) r r r We assume that /y i s much less than / «. , and so make the approx-imation j~i j » reducing (8) to OOa. Y 2 TT* X 17 (9) - h2 -It was then possible to calculate the values of the radiation widths from (9) above. These values were: Resonance Energy O.hOO Mev 0.820 Mev 0.960 Mev Total . radiation width 0.02 ev 0.32 ev 1.75 ev Partial radiation widths: to ground state (0.019 ev) 0.00^ ev 0.21 ev to ^.^6 Mev state (0.001 « ) 0.29 " 1.31 " to 6.8 (?)'» «« 0.026 " 0.23 " Ferguson et a l (1957) 96$ and h% Weisskopf•has calculated the lifetimes of states of light nuclei against decay by gamma radiation of various multi-polarities, assuming the radiation is produced by single-particle transitions. The..-radiation widths for dipole radiation obtained by Weisskopf are given by: \r (El) = 0.11 E y A ev n 3 - ( 1 0 ) ]y (Ml) = 0.019 Ey ev (Moszkowski 1955) Values of Ey.are i n Mev. Wilkinson (1955)» having surveyed about 100 transitions for which there i s strong evidence of dipole character, concluded that for E l transitions the experimental values are 0.032 times the Weisskopf values, within a spread factor of 7 either way, and that the Ml transitions are 0.15 times the Weisskopf values, within a spread factor of 20. Values calculated from the above expressions, - ^3 -and also after multiplication by Wilkinson's correction factors are listed below. These values may be compared with the observed values given on page k-2. Calculated radiation widths, in ev (a) Weisskopf values (b) Wilkinson values Resonance Energy 0A00 Mev 0.820 Mev 0.960 Mev ial Ibi Ial 1*1 Ial IbJ. to ground state: E l 351. 11.2 38h. 12.3 396. 12.7 Ml 13.5 2.0 lh.7 2.2 15.2 2.3 to h.h6 Mev state: E l 52.5 1.7 55A 1.8 Ml 1.7 0.26 2.0 0.3 2.1 0.32 to 6.8 (?) Mev state: E l 6.7 0.21 7.5 0.2*+ Ml 0.26 O.O^ r 0.29 0.0*f 2. Angular Distributions (a) Measurement of Angular Distributions: Por radiation between states of definite angular mo-menta and parity, the angular distribution function is of the form: W (-€•) = £ hi cos2i L where i takes on a l l integral values from zero to the smallest of 1/ , j or 1 2 where 1 / and 1^ are the angular momenta carried by the incoming particle and the outgoing radiation, and j is the spin of the i n -termediate state, (Deutsch, 1951). Non-isotropic angular d i s t r i -butions were observed for radiations from the three levels i n B formed by alpha particle capture. Therefore 1/ must be =T 1. It has been assumed that the states were formed by the capture of - Ulf -p-wave alpha particles (1, =1), and the angular distribution function was thus assumed to be: W ( ^ ) = A 0 + A J J cos* ^  (110 and since only relative intensities are described by this expression, we let A0 = 1 Values of the coefficient A z may be determined from measurements made at zero and 90 degrees to the direction of the incident beam, even with poor angular resolution. As some of the gamma rays were of low intensity, i t was necessary to make measure-ments with the counter close to the target, reducing angular resolution in favour of increased counting rate. Details of dis-tributions more complex than ( 1 1 ) above would not have been de-tected with this arrangement. Thin evaporated lithium targets were used for angular distribution measurements. Excitation functions were taken over the resonance being studied for each new target, and the alpha particle energy set at the peak of the resonance. Gamma ray spec-tra' and background counts were taken with the large counter at zero degrees and 90 degrees to the beam direction. A thin-target excitation function and gamma ray spectrum at the 0.960 Mev res-onance are shown i n figure 19. Repeated runs were made, using two 90 degree positions in the horizontal plane. Distance from the counter to the target, and hence the solid angle, was kept constant during each run. - h5 -(b) Corrections: The spectra were corrected for background, normalized to the monitor counter, and divided into energy regions covering the photo-and pair-peaks of the different gamma rays. Intensity of gamma rays i n the counter was proportional to the solid angle subtended by the counter at the target. This solid angle was determined i n terms of an "effective centre" of the large crystal. Inverse square measurements with this crystal on the 6.1*f Mev gamma rays from F / ^ ( p , oc V ) o ( L a r s o n , 1957) indicated that this "effective centre" was h.2 ± 0.2 cm from the front of the crystal. Distance from target to crystal used during the experiments ranged from 8.2 cm to 10.8 cm and so the half-angle subtended by this effective centre ranged from about 12 to 15 degrees. Calculations using the total absorption coefficient of Nal indicated that the position of the "effective centre" of the crystal would be expected to vary only slightly with gamma ray energy i n the range from 2 Mev to 10 Mev. In the case of the gamma rays from cascades through the h.k6 Mev level, the spectrum observed was due to a pair of gamma rays only slightly separated in energy, and so consisted of six overlapping peaks, which coalesced into a single large peak when displayed on the kicksorter with minimum expansion. To obtain the distributions of each of the pair of gamma rays, the distribution of the sum, i.e. of the large peak, was f i r s t obtained. Then the resolution of the kicksorter was increased to separate the photo-peak of the higher-energy component, and the angular distribution - if6 -of the higher energy gamma ray determined directly, as the dis-tribution of this photo-peak. Using a spectrum of the *+.*f3 Mev gamma ray from B *' ( p , 0 C / 2, the ratio of counts in the photo-peak to the to t a l number of counts in the photo- and pair-peaks for a gamma ray of this energy, was determined. Using this ratio, the contribution of the higher-energy radiation of the *f.5 Mev cascades was sub-tracted from the sum, and the distribution of the lower energy peak determined from the remainder. Estimates of errors arising from a number of sources were made. Geometrical errors included the f i n i t e size of the target area struck by the beam, errors in positioning of the coun-ter with respect to the target, and absorption of radiation by materials in and near the target chamber. Probably the greatest uncertainty was in the definition of the solid-angle of the crys-t a l in terms of i t s "effective centre" as described above. The absorption corrections were assumed to be constant over the an-gular region covered, and the geometrical errors were a l l lumped as a probable error i n the solid angle of the counter. S t a t i s t i c a l errors were calculated for the spectra, background, and monitor counts. The resulting values of the an-gular distribution coefficient kx in the expression W = 1 + A, c o s ^ were: - h7 -Resonance Energy O.U-OO Mev 0.820 Mev 0.960 Mev 9 Mev radiation - 0.33 1 0.06 - 0.h2 ± 0.0V 7 M n • * 0.30 ± 0.10 0.0 ± 0.03 *K5 " " - 0.17 1 0.02 + 0.1*6 ± O.Oh h.k6 » » - 0.15 ± 0.02 + 0.10 ± 0.0** (c) Calculation of Angular Distributions: Following the Racah coefficient method outlined by-Wilkinson (1955)> and using the tables of coefficients given by Biedenharn and Rose (1953)» values of the angular distribution coefficient kz were calculated for a number of possible tran-sitions, involving various spins and parities. The values of spins and angular momenta involved i n the reactions can be de-noted as follows: 7 H alpha + L i — > B > (B ) + gamma spin angular spin spin spin angular spin momentum momentum 0 . 3 / 2 1 and any transition may be represented by j/ (1,) j ( 1^) j ^ . As discussed i n section 2.(a) above, only p-wave alpha particles (1/ = 1) were considered, so that a l l calculated transitions were 3/2 (1) j (1 2 ) 2Zi (see Appendix III for details of these c a l -culations) . - ho -3» Angular Correlations Angular correlations'were measured between the pairs of gamma rays cascading through the level at h.k6 Mev from the 9.19 and 9.28 levels with both counters i n the plane of the beam. For both cascades, the observed correlation was close to zero. This observation has been used in calculating the gamma ray yields above. Correlations in a plane normal to the beam required modifications to the target chamber and the mounting of the detec-tors which had not been made at the time of these experiments. - if 9 -Table 1 Collected Results of Experiments and Calculations (a) Total Resonance Widths P Resonance Energy O.lfQO Mev 0.820 Mev 0.960 Mev Lab. Co-ords. 1 kev 1. kev 8. kev Centre-of-mass 1 " 0.6*f » 5.1 » (b) Relative Gamma Ray Intensities 9 Mev Radiation (96$) 1$ 12$ 7 " 11 8$ 13$ *f.5 11 " ( W 91$ 75$ (c) Gamma Ray Yields Y per Alpha Particle • y - • / / . -'I 9 Mev Radiation 0.5 x 10 0.0U, x 10 2.3 x 10 7 " 11 0.32 x «• 2 .5 x » ^.5 " " 3.6 x » 15. x " (d) Experimental Radiation Widths i n ev Total Width 0.02 0.32 1.75 Partial Widths: to ground state (0.019) 0.00*+ 0.21 " if.1+6" Mev " (0.001) 0.29 1.31 " 6.8 (?) " « 0.026 0.23 (e) Calculated Radiation Widths, in ev (a) Weisskopf Values (b) Wilkinson Values Resonance Energy O.hOO Mev ,0.820 Mev 0.960 Mev lal 1M 1*2 Ibl l a l Ibl to ground state: E l 351. 11.2 38*f. 12.3 396. 12.7 Ml 13.5 2.0 l^f.7 2.2 15.2 2.3 to *f.*f6 Mev state:El hh. l.h 52.5 1.7 55.^ 1.8 Ml 1.7 0.26 . 2.0 0.3 2.1 0.32 t 0 6 , 8 ( ? ) s t l t e : E 1 6 ' 7 ° - 2 1 7 ^ ° ' 2 h *M1 0.26 0.0k 0.29 O.Olf - 50 -(f) Experimental Angular Distribution Coefficients Resonance Energy 0.*f00 Mev 0.820 Mev 0.960 Mev 9 Mev Radiation - 0.33 1 ©.06 - O.U-2 ± O.O^ f 7 " 11 + 0.30 ± 0.10 0.0 ± 0.03 If.5 " " - 0.17 1 0.02 + 0.lf6 ± O.O^ f l+.lf6 " " - 0.15 - 0.02 + 0.10 ± 0.Oil-Calculated values of the theoretical angular d i s t r i -bution coefficients are given i n Appendix III. - 51 -D Conclusions We now consider what information regarding excited states of B " can be extracted from the above data. The alpha particle capture occurs i n sharp resonances, so i t i s appropriate to apply Breit-Wigner formalism. The capturing states are sharp and well-separated, and so are expected to have well-defined values of angular momentum and parity. The L i ground state i s taken to be 3/2 . Non-iso-tropic angular distributions of gamma rays were observed from the states at 9.28, 9.19 and 8.92 Mev i n B" produced by alpha par-t i c l e capture. Consequently the alpha particles must carry i n an angular momentum of at least 1, = 1 (p-wave). 7 Capture of p wave alphas by L i would produce states of 7 B with angular momenta of 1/2, 3/2, or 5/2. The value 1/2, indicating no orbital angular momentum,is ruled out by the ob-served non-isotropic distributions. We therefore consider 3/2 or 5/2 as possible angular momentum values for these B " states. // Por these three states of B , the principal modes of decay are either a transition directly to the ground state, or a cascade through the level at h.k6 Mev. For B , the ground state is 3/2~(Gordy, Ring and Burg, 19^8). Considerable information on the h.k-6 Mev level i s available from the stripping reactions on B / 0. Evans and Parkinson (1951*-) observed i n the reaction B/0 (d,p) B V that this state was formed by the capture of p-wave neutrons (l n= 1 '•)•• This observation has been confirmed by Cox - 52 -1 and Williamson (1957) , and further supported by the work of Cerineo (1956) on the mirror reaction B '° (d,n) C / /. This mode of formation limits the possible angular momenta of the k,h6 Mev level to the values 3/2, 5/2, 7/2, or 9 /2 , a l l of negative parity. The mean lifetime of this state has been measured by Swann, Metzger, and Rasmussen ( 1 9 5 7 ) hy the scattering of gamma rays on B * , (E^ = k.k3 Mev, from N / S (p*) Q/2)m The value quoted for the lifetime is T = 0 . 7 ° x 1 0 seconds, equivalent to a radiation width of 0.87 ev, whereas the Wilkinson-adjusted value for a magnetic dipole transition of this energy i s about 0.28 ev, calculated from equation ( 1 0 ) above. This seems sufficiently good agreement to conclude that the transition from the h.k6 Mev level to the ground state has a (magnetic) dipole character, i n which case the possible angular momenta for this state are r e s t r i c -ted to 3/2 or 5/2 • These values were also suggested by Meyer-Schutzmeister and Hanna ( 1 9 5 7 ) • The observed transitions from the 9.28 level to the ^.^6 level and to the ground state have respectively angular distribution coefficients of + 0,h6 and - 0 . ^ 2 , indicating d i f -ferent angular momenta for these two f i n a l states. As the ground 1 In connection with the problem of the angular momentum of the f i r s t excited state of B 7 / , at 2,lh Mev, discussed i n Section A, page 3> i t i s of interest that Cox and Williamson (1957) report that no stripping peaks were observed i n the proton groups of the B y o (d,p) B " reaction from either the 2.1*f or the 5.03 Mev levels, for deuterons of energies 2.5 to 3.9 Mev. Strip ping groups were observed with 7.7 Mev deuterons, but were less well defined than those from other levels. - 53 -state of B " is 3/2 , we conclude that the h,k6 Mev level should be assigned the value 5/2. Returning to the 9.28 Mev level, the relative inten-sities of the gamma rays indicated that the transition to h.h-6 Mev was favoured over that to the ground state. The observed radiation width of the favoured transition, 1.31 ev, is i n reasonable agreement with the Wilkinson-adjusted value of 1.8 ev for an E l transition, indicating that the 9.28 Mev level has positive parity. The observed angular distribution coefficient of + O.h-6 to the h,k6 Mev level agrees with a 5/2 to 5/2 tran-sition, but not with 3/2 to 5/2 (Appendix III). Therefore the 9.28 Mev level is concluded to be 5/2 +, and this assignment also gives agreement for the angular distribution coefficient of the ground state transition, 5/2 to 3/2. It might then be suggested that the 9.28 to h.h6 Mev transition has a single-particle character, while the 9.28 to ground state transition involves a single particle transition plus some re-arrangement of nucleons i n the p shell, thus pro-viding a possible explanation for the relatively low intensity of the latter. Meyer-Schutzmeister and Hanna (1957) have sug-gested 3/2 or 5/2 for this state, i n disagreement with this con-clusion. Since no details of their work have been published, i t is not possible to judge i t s r e l i a b i l i t y and consistency. For the 9.19 Mev level the transition to the ground state was highly unfavoured. Its transition probability was less than 2% of that to the Mev level, compared to about 17$ for - 5^ -the comparable ratio for transitions from .the 9.28 Mev level. The observed radiation width of 0.29 ev to the U-.h6 Mev level agrees with the Wilkinson-adjusted value of 0.3 ev for an Ml transition, and in this case the selection rules allow competi-tion from E2 radiation. The mixed Ml and E2 transitions allow the angular distribution coefficients to vary over a wide range of values, depending on the mixing ratio. The observed coeffic-ient of - 0.17 would f i t a 5/2 to 5/2~ transition, with a large admixture of E2 radiation; or a 3/2*" to 5/2~ transition with values of about - 0.2h or - 2.0 for o6, the mixing parameter, (see Appendix III). The present data i s then unable to d i s t i n -guish between 3/2 or 5/2 for the angular momentum of the 9.19 Mev level, though negative parity i s suggested. Meyer-Schutzmeister and Hanna (1957)» have suggested 3/2 or 5/2 + for this level. The latter value i s not consistent with the results of the present experiment. It should be noted that the angular distribution co-efficients to the ^ .^6 Mev level from both the 9.28 and 9.19 Mev levels disagree with those published by Meyer-Schutzmeister and Hanna. In the case of the 8.92 Mev level, decay directly to the ground state i s highly favoured over any other transition (96$, Ferguson et a l 1957). The observed angular distribution coeffic-ient of - 0.33 i s consistent with either 3/2 or 5/2 for the an-gular momentum, but the observed transition probability of 0.02 ev Is much smaller than those calculated for dipole transitions. It does not appear possible at present to further limit the possible - 55 -assignments for the 8.92 Mev level, and the data would suggest that the possibility of i t s formation by d-wave (1 = 2) alphas cannot be entirely discounted. It i s apparent that the system is far more complex than the simple single-particle picture suggested by Jones and Wilkinson (1952). Considerably more work must be done before a complete and consistent level scheme can be formulated. - 56 -E Appendices APPENDIX I Data on Certain Commercial Components Toggle Valves: Hoke Inc., Englewood, N.J. Model k$2 1/h inch NPT male fittin g s 200 psi. 1/8 inch seat; neoprene seat and packing Indium Metal: Supplied by Consolidated Mining and Smelting Co. Ltd, Latest Canadian production figures given i n The Canada Year Book 1956 are: 195^ **77 troy ounces: value $1278. A summary of the physical and chemical pro-perties of the element, i t s current and potential uses, and an annotated bibliography of the scien-t i f i c literature up to 19*+9 may be found in the book: Indium by Maria Thompson Ludwick: 1950 published by the Indium Corpor-ation of America United Aircraft Products Inc. Box 1035 Dayton Ohio and 5257 Queen Mary Road, Montreal P.Q.-for the helium valve: stainless steel, copper plated 3/32 inch tubing, l : l A inch OD part no. U 2310-01250 Isolating Transformer: Hammond Manufacturing Co. Ltd., Guelph, Ont. part no. H 38907; 115 V WO cps 3 kv DC continuous operation at 50 degrees C Delay Cable: Columbia Technical Corp. 61-02, 31st Ave. Woodside 77 N.Y. Type HH-2500 2800 ohms 20 pf. per foot 350 V rms 0.6 microseconds per foot Pulse Transformers: Valor Electronic Components Culver City, C a l i f . PT 530 D 1 k to 75 ohms PT 53^ D 1 k to 1 k ohms min. p r i . inductance 10 mH; 300 V DC max. r i s e , f u l l y loaded 0.06 microseconds max. pulse volts 100 Metal 0-Rings: M a g n e t C u r r e n t - A m p s F i g 2 0 M a g n e t i z a t i o n C u r v e f o r A n a l y s i n g M a g n e t APPENDIX II (a) Magnetic Deflection of Charged Particles The equation of motion for charged particles moving nor-mal to a uniform magnetic f i e l d i s : m v B q v = r (12) where: B i s magnetic induction, maxwells per cm. (gauss) q is charge on the particle, emu v i s particle velocity, cm per second m i s particle mass, gms r i s particle path radius of curvature, cm For particles accelerated through a potential V emu: V q = 1/2 m v ergs and equation (12) may be written: 1 0 7 / 2 m iV ' (13) B = r V V where the potential V is in Mv. Using the values: Particle Mass Charge -zv -zo p 1.672^8 x 10 gm 1.60199 x 10 emu d 3.3^35 " 1.60199 QC 6 . 6 ^ » 1.60199 6.6M*-2 » 3.20398 11 the constant 107^J~2 m i n equation (13) has the values! p l . ¥ i 5 x 10 5 d 2.0V3 it 0 6 2.880 » 2.036 " o an P 0>3 CD Ul CD 0 . 5 1.0 1.5 A c c e l e r a t i n g P o t e n t i a l - M v 2 . 0 F i g 21 D e f l e c t i n g F i e l d s f o r 2 0 c m R a d i u s - 58 -The above relation of magnetic f i e l d and accelerating potential has been evaluated for these particles i n the range 0 to 2 Mv, and plotted in figure 21 for 20 cm radius, and i n figure 22 for 30 cm radius. Figure 23 compares these r a d i i for singly-charged alphas. On the scale of these figures, the curves for d and are indistinguishable. The energy of the particles i s , of course, double that of singly-charged particles accelerated through the same potential. Figure 20 shows the magnetization curve of the deflect-ing magnet. The hysteresis loop is 0.2 amp wide at a current of 15 amp. (b) Energy Resolution The v e r t i c a l separation of the sniffers and their dis-tance from the centre of the magnetic f i e l d defines a range of energies for the particles passing between the sniffers. Neglect-ing fringing f i e l d effects, and assuming a well focussed beam of particles entering normal to the magnetic f i e l d , this range of energies may be calculated as follows: (see figure 2*f) r is the radius of the path of particles deflected through 90 degrees, and passing midway between the sniffers r ' i s the radius of the highest energy particles pass-ing the sniffers; deflected 90 -£degrees ra i s the radius of the lowest energy particles pass-ing the sniffers; deflected 90 +#degrees - 59 -*er i s the half-angle subtended at the centre of the magnetic f i e l d by the gap of the sniffers r < r < r from figure 2*+: r - r " = * r _ = sin ^ AT = r ^  sin ^ r - r " (1 + sin ve- ) Prom equation (13) above, for accelerating potential V: r = k (V) k i s a constant a r _ r " 2 V Then 4 V = 2/lr = 2 r * sin ^ - . V r r " ( 1 + sin^-) and similarly: ^ V = 2 r / sin V r ' (1 - sin*-) For small angles, both cases may be approximated by: 6 V = 2 = 200-0$ V Typical values of 4 V . the energy spread i n the beam, •V are plotted i n figure 25 for four spacings of the sniffers from the centre of the magnet. The spacing used i n these experiments was 100 cm. 0 0.5 1.0 1.5 2.0 A c c e l e r a t i n g P o t e n t i a l - M v . F i g 2 3 D e f l e c t i n g F i e l d s f o r S i n g l y - C h a r g e d A l p h a s - 6 0 -APPENDIX III Angular D i s t r i b u t i o n Calculations Values of the angular d i s t r i b u t i o n c o e f f i c i e n t Az i n the angular d i s t r i b u t i o n function: W ( # 0 = 1 + Az cos z & were calculated with the a i d of notes by Wilkinson (195*0 and tables of c o e f f i c i e n t s by Biedenharn and Rose (1953)• A nuclear re a c t i o n i s represented by the notation: J , (1,) J (I*) zz where J 7 , j , j 2 are the angular momenta of the i n i t i a l , intermediate, and f i n a l states, and for alpha p a r t i c l e capture reactions, 1 / i s the angular momentum carried by the incoming alpha p a r t i c l e , (spin zero), and 1 £ i s the m u l t i p o l a r i t y of the emitted gamma ray, (spin one). A "pure" t r a n s i t i o n involves the emission of gamma rays of a single m u l t i p o l a r i t y . I f more than one mu l t i p o l a r i t y of rad-i a t i o n competes i n the decay, the t r a n s i t i o n i s termed "mixed". For a ra d i a t i v e capture reaction with pure r a d i a t i o n , the angular d i s t r i b u t i o n function i s of the form: kyu. P ^ where K « = 2 1, (1/ + 1) t h e t i p a r t i c l e f a c t o r " 2 1/1, + 1) -A,*. = F * (1, j) F ( 1 2 % z j) values of the F's given i n the tables of Biedenharn and Rose P^ = the Legendre Polynomial of order yU. When the decaying state has d e f i n i t e angular momentum j , and d e f i n i t e p a r i t y , only even values of M. appear, the maximum I c E 9 a "0 9 c H) (ft •d (» (ft CD <y> H c U V 11 « w • o • o Q. P i g 2 4 D i a g r a m f o r E n e r g y R e s o l u t i o n C a l c u l a t i o n - 61 -v a l u e o f y ^ - b e i n g t h e s m a l l e s t o f 1, , l z o r j. I n t h e c a s e o f m i x e d t r a n s i t i o n s , w i t h r a d i a t i o n s c o n -1* 2 l ' s i s t i n g o f o n e p a r t o f 2 - p o l e r a d i a t i o n t o cc p a r t s o f 2 * -p o l e r a d i a t i o n , w h e r e 1 2 a n d l a d i f f e r b y o n e , t h e d i s t r i b u t i o n f u n c t i o n h a s t h e f o r m : ^ F ^ a r j - d ) + 2 ^ (-D J J * [ (2j + 1 ) ( 21 * + l ) ( 2 1 z + 1)] G ^ U ^ 1 2 2Z o) f T h e G ' s a r e g i v e n i n B i e d e n h a r n a n d R o s e . T h i s e x p r e s -s i o n i s n o r m a l i z e d t o 1 + a n d g i v e s t h e s u m o f t h e t w o p u r e r a d i a t i o n s , w e i g h t e d a c c o r d i n g t o t h e i r i n t e n s i t i e s , p l u s a m i x i n g t e r m t o d e s c r i b e t h e i n t e r f e r e n c e . C o e f f i c i e n t s c a l c u l a t e d f o r c e r t a i n v a l u e s o f oC a r e g i v e n b e l o w . V a l u e s o f k2 i n W = 1 + A 2 c o s ^ P u r e d i p o l e t r a n s i t i o n s : j = 3/2 t o : j = 5/2 t o : j = 7/2 t o : j^ A 2 j 2 A ^ A ^ 3/2 - O . i f l 3/2 - 0.38 5/2 + 0.125 5/2 + 0.57 5/2 - o A l 7/2 - O.lh 7/2 + 0.80 P u r e q u a d r u p o l e t r a n s i t i o n s : j = 3/2 t o : j = 5/2 t o : •5,2 ^ 2 ^ £ 3/2 0.0 3/2 + 0.23 5/2 + 0.5 5/2 - 0.2 7/2 - 0.32 1.6 0 . 0 0 . 2 0 . 4 0 . 6 0 . 8 I. S n i f f e r S e p a r a t i o n — C m s . F i g 2 5 C a l c u l a t e d E n e r g y S p r e a d i n B e a m - 62 -M i x e d t r a n s i t i o n s , m a g n e t i c d i p o l e a n d e l e c t r i c q u a d r u p o l e : J* 3 / 2 5/2 3 / 2 5/2 7/2 j = 3 / 2 t o : + 1 - 1 + 1 - 1 j * 5/2 t o : ©c + 1 - 1 + 1 - 1 + 1 A * - 0.8U, + 0 . 9 0 + 1 .^7 - O .38 + l.hl - 0 .8 l f + 0 . 1 6 + 0 . 0 9 - 0 . 7 7 + 0.6*r - 63 -F Bibliography Ajzenberg, F. : Lauritsen, T. 1955 Rev Mod Phys 2Z, 77 Energy Levels of Light Nuclei V Bennett, W.E. ; Roys, P.A. ; Toppel, B.J. 1951 Phys Rev 82, 20 Simple Capture of Alpha-Par t i d e s Bethe, H.A. ; Bacher, R.F. ; Livingston, M.S. 1936 Rev Mod Phys 8, 82; 2, 69 Nuclear Physics Bethe, H.A. 1950 Rev Mod Phys 22, 213 The Range-Energy Relation for Slow Alpha-Particles and Protons i n Air Biedenharn, L.C. ; Rose, M.E. 1953 Rev Mod Phys 2£, 729 Theory of Angular Correlation of Nuclear Radiations Bittner, J.W. 195^ Rev Sci Inst 2$, 1058 Production of Doubly Charged Helium Ions Blatt, J.M. ; Weisskopf, V.F. 1952 John Wiley and Sons, Inc., New York Theoretical Nuclear Physics Bloch, I.; Hull, M.H. Jr. ; Broyles, A.A. ; Bour.icius, W.G. ; Freeman, B..E. ; Breit, G. 1951 Rev Mod Phys 22, 1^7 Coulomb Functions for Reactions of Protons and Alpha-Particles with the Lighter Nuclei Cerineo, M. 1956 Nuclear Physics 2, 113 (North-Holland Pub-lishing Co.) Energy Levels of C and Angular Distributions of some Neutron Groups from the B / 0 (d,n) Reaction Chadwick. J. 1932 Proc Roy Soc H 6 A . 692 The Existence of a Neutron Cox, S.A. ; Williamson, R.M. 1957 Phys Rev 10$, 1799 9 Angular Distribution and Correlation Studies of Be , B / 0, and Mg** (d,p) Reactions - 61+ -Davisson, CM. ; Evans, R.D. 1952 Rev Mod.Phys 2|±, 79 Gamma-Ray Absorption Coefficients Deutsch, M. 1951 Rept Prog Phys XIV, 196 Angular Correlations i n Nuclear Reactions Edwards, M.H. 1951 M.A. Thesis, Physics Dept. University of Bri t i s h Columbia The Design and Operation of a Current Integrator, etc. Evans, N.T.S. ; Parkinson, W.C. 1 9 ^ Proc ,Phys 6Z&, 68% / 0 Angular Distributions i n the B (d,p) B Reaction Evans, R.D. 1955 McGraw-Hill Book Co. Inc., New York The Atomic Nucleus Ferguson, A.J. ; Gove, H.E. ; Litherland, A.E. ; Almqvist, E. ; Bromley, D.A. ; 1957 B u l l Am Phys Soc II, 2. 51 and Nuclear Data Card 57-h-ll B ' 57#5 (verbal) 9 Gamma-Ray Decay Schemes in B / / from the Reaction,Be (He3 , p *) B " Gordy, W. ; Ring, H. ; Burg, A.B. 19*f8 Phys Rev 2it, 1191 / a „ Nuclear Spins and Quadrupole Moments of B and B Green, G.W. 1953 Jour Sci Inst 30, 171 An E l e c t r i c a l l y Operated A l l Metal Capillary Vacuum Valve for Adjustable Gas Flow Heiberg, S.A. 195k Ph. D. Thesis, Physics Dept., University of Br i t i s h Columbia Reactions Induced by Fast Neutrons i n Boron Trifluoride etc. Heydenburg, N.P. ; Temmer, G.M. 195^ Phys Rev 2k, 1252 Z S L ^ Gamma Rays from L i 7 , F , Ne and Na Produced by Alpha-Par t i d e Bombardment of Lithium and Fluorine Jones, G.A. 5 Wilkinson, D.H. 1952 Phys Rev 88, 1+23 The Reaction L i 7 (o£,r) B " and States of B Kaye, G.W.C. ; Laby, T.H. 195° Longmans, Green and Co. Ltd., London Tables of Physical and Chemical Constants, 11th Edition - 65 -Larson, E.A.G. 1957 M.A. Thesis, Physics Dept., University of B r i t i s h Columbia The D (p, fr) He 3 Reaction at Low Energies Lauritsen, T. 1952 Ann Rev Nuc Sci 1, 67 Energy Levels of Light Nuclei Mayer, M.G 5 Jensen, J.H.D. 1955 John Wiley and Sons, Inc., New York Elementary Theory of Nuclear Shell Structure Meyer-Schutzmeister, L. ; Hanna, S.S. 1957 B u l l Am Phys Soc II, 2, 28 and Nuclear Data Card 57-^-10 B 57#f (verbal) Reaction L i 7 B* Moszkowski, S.A. 1955 North-Holland Pub. Co., Amsterdam Theory of Multipole Radiation, Chapter XIII of Beta-and Gamma-Ray Spectroscopy; Siegbahn, K., Editor Robertson, L.P. 1957 M.A. Thesis, Physics Dept., University of B r i t i s h Columbia Rutherford, E. 1919 Phil Mag 2Z? 581 Collision of Alpha Particles with Light Atoms IV Sharp, W.T. ; Gove, H.E. ; Paul, E.B. 1953 A.E.C.L. Chalk River Project; TPI-70 Graphs of Coulomb Functions Shire, E.S. 199+ Jour Sci Inst 31, 192 A Thermally-Operated Gas Valve Swann, CP. ; Metzger, F.R. ; Rasmussen, V.K. 1957 Bull Am Phys Soc II, 2, 29 and Nuclear Data Card 57-^-9 B " 57#3 (verbal) Lifetimes of the h.k Mev Excited States of B " and C Temmer, G.M. 1955 Private communication also Heydenburg, N.P. ; Temmer, G.M. 1955 Phys Rev 100, 150 Coulomb Excitation of Rare-Earth Nuclei with Alpha Particles Tuve, M.A. ; Hafstad, L.R. ; Dahl, 0. 1933 Phys Rev j£, 1055(A) Nuclear Physics Studies Using the Van de Graaff Electrostatic Generator - 66 -Whaling, W. 1957 Kellogg Radiation Lab., Cal Tech, (mimeographed, 57 PP) The Energy Loss of Charged Particles i n Matter Wilkinson, D.H. 195^ Cavendish Lab., Cambridge, (mimeographed, 36 pp) Illustrations of Angular Correlation Computations Using the Racah Coefficient Methods Wilkinson, D.H. 1955 A.E.C.L. Chalk River Project, PD-260 Radiative Transitions i n Light Elements II W i l k i n s o n , D.H. 1957 Phys Rev 105, 666 F i r s t E x c i t e d S t a t e o f B" : P o s s i b i l i t y o f S p i n - F l i p S t r i p p i n g 

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