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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  i n 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 f o r the production of beams of singly-charged alpha p a r t i c l e s .  Alterations have been made to  the i o n source, analysing magnet, and reverse electron beam energy s t a b i l i z i n g system.  Well-focussed beams of 10 to 15 microamps  resolved of singly-charged alpha p a r t i c l e s were available, at energies up to above 1.2 Mev. The nuclear reaction L i  7  (oc )f) b" s  was studied by bom-  barding targets of lithium metal evaporated onto copper backings. The gamma rays from the decay of states of B  y/  were observed  with  Nal (Tl) s c i n t i l l a t i o n counters and associated electronic equipment, including a 30 channel Marconi Pulse Amplitude Analyser. In the range of alpha p a r t i c l e energies a v a i l a b l e , 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 p a r t i c ular one at h,k6 Mev. The widths of these resonances were measured respectively as 8, 1 and <1 kev, i n laboratory co-ordinates.  The second of these  values i s s i g n i f i c a n t l y lower than previously reported.  Measure-  ments were also made of the y i e l d s of gamma r a d i a t i o n , and the angular d i s t r i b u t i o n s of c e r t a i n gamma rays from each resonance. Experimental r e s u l t s and calculations have been compared with appropriate t h e o r e t i c a l values to obtain information on the angular  momenta and p a r i t y of c e r t a i n of the B  states.  The zero spin  of the incoming alpha p a r t i c l e s puts a useful l i m i t a t i o n on the input channel spin. Assignments suggested by the data were as follows. the ^.^6  Mev state, 5/2  ; for the 9.28  Mev state, 5 / 2 . +  For  Data  for the 9.19 Mev state cannot d i s t i n g u i s h between 3/2~~and 5/2  ,  while for the 8.92 Mev state, the angular momentum would be r e s t r i c t e d 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 r e s u l t s indicate that the states of B "  are cer-  t a i n l y more complex than the simple s i n g l e - p a r t i c l e picture proposed by Jones and Wilkinson (1952), which i s inadequate to describe the present r e s u l t s .  Further i n v e s t i g a t i o n i s i n v i t e d .  tEJje ptttterstijj of ^§rtttglj Columbia Faculty of Graduate Studies  PROGRAMME OF T H E  FINAL  ORAL  EXAMINATION  FOR THE DEGREE OF DOCTOR OF  PHILOSOPHY  of GILBERT  JAMES  PHILLIPS  B.Sc. University of Manitoba M. A. University of British Columbia  WEDNESDAY,  NOVEMBER  6 t h , 1 9 5 7 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  COMMITTEE I N CHARGE D E A N G . M . SHRUM, Chairman  G. M. GRIFFITHS J. B. WARREN K. C. MANN M. BLOOM  A. EARLE BIRNEY S. W. NASH F. K. BOWERS  -ABSTRACT  Modifications to the University of-British 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 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 L i 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 investigation is invited.  GRADUATE  STUDIES  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 Quantum ' Mechanics  . . . J. S. Blakemore andJ. B. Brown -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 the  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  requirements, f o r an advanced degree at the  University  o f 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 r e f e r e n c e and agree t h a t p e r m i s s i o n f o r e x t e n s i v e f o r s c h o l a r l y purposes may  study.  I further  copying of t h i s  be g r a n t e d by the Head o f  Department o r by h i s r e p r e s e n t a t i v e .  Department  be a l l o w e d w i t h o u t my w r i t t e n  of  The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, Canada. Date  ^3^-  my  I t i s understood  that 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 g a i n s h a l l not  thesis  financial  permission.  Acknowledgements  The author i s pleased to make the following acknowledgements. Dr. J.B. Warren, of the Physics Department, University of B r i t i s h Columbia, Van de Graaff Group Supervisor, has provided advice and d i r e c t i o n during the course of t h i s research. Dr. C.A. Barnes, of the Kellogg Radiation Laboratory, C a l i f o r n i a Institute of Technology, directed the i n i t i a l  stages  of t h i s research programme, i n i t i a t e d many of the modifications to the Van de Graaff Generator, and contributed many h e l p f u l discussions of alpha p a r t i c l e reactions. Dr. G.M. G r i f f i t h s , of the Physics Department, Univers i t y of B r i t i s h Columbia, i n d i r e c t i n g t h i s research,has  contri-  buted his time and advice most generously during the performance of the experiments, analysis of the r e s u l t s , 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. F i n a n c i a l 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.  2.  3.  Production of Alpha P a r t i c l e s (a) (t>)  Ion Source Helium Thermal Valve  5 7  (c)  Operation of the Helium Valve  9  Van de Graaff Modifications (a) Magnetic F i e l d s f o r Deflecting Beams (b) Electron Gun and Energy S t a b i l i t y Beam Path After Acceleration (a) Stops and Beam Shutter (b)  (a) (b) (c) (d) Gamma (a) (b) (c) (d)  6.  C  Target Chambers Lithium Furnace Target Backings Target Preparation Ray Detection S c i n t i l l a t i o n Counters Electronics for Angular D i s t r i b u t i o n Measurements Electronics f o r Angular Correlation Measurements Additional E l e c t r o n i c Apparatus  Targets and Counters • Electronics  Experimental Results and Calculations 1.  Resonance Widths and Gamma Ray Yields (a) (b) (c) (d)  11 11 Ih Ik  16  Experimental Procedures (a) (b)  11  Target Contamination; Background Radiations. 15  k. Targets  5.  5  Measurement Calculation Measurement Calculation  of Widths of Reduced P a r t i c l e Widths of Gamma Ray Yields of Radiation Widths  16 16 17 17 19 19 21 22 25 26 26 27 30 30 30 32 3h 38  2.  Angular Distributions  3.  Measurement of Angular D i s t r i b u t i o n s ........ Corrections  (c)  Calculation of Angular Distributions  Collected Results  Conclusions Appendices I II Ill  P  (a) (b)  Angular Correlations  Table I D E  •..  T  Commercial Components (a) (b)  •  Magnetic Deflection of Charged P a r t i c l e s ... Energy Resolution  Angular D i s t r i b u t i o n Calculations  Bibliography  '  L i s t of I l l u s t r a t i o n s Figure No.  Title  Facing Page  1.  Energy Levels of Boron 11  2.  Ion Source Power O s c i l l a t o r ..  h  3.  Ion Source Components  5  k.  Ion Source Extractor. Canal  6  5.  Helium Thermal Valve  6.  E l e c t r o n Gun Mounting  7.  Magnet Box and Extension Pole Pieces .......  13  8.  Beam Tube and Target Mounting  lh  9.  Lithium Furnace and Target Chamber .........  17  10.  Cathode Follower Header  18  11.  Header with Delay Line Pulse Shaping  19  12.  Spectra from Large Counter  20  13.  Biased Amplifier  21  1*+.  Angular D i s t r i b u t i o n E l e c t r o n i c s ; Block Diagram  22  15.  . 3  , .8  ' •  ,. 12  •  Angular C o r r e l a t i o n E l e c t r o n i c s ; Block Diagram  •  23  16.  Phase Inverter  2h  17.  O.96O Mev Resonance; Thick Target  31  18.  0 . 8 2 0 Mev Resonance; Thick Target  32  19.  O.96O  Mev Resonance;. E x c i t a t i o n Function and  Spectrum  Mt  20.  Magnetization Curve for Analyzing Magnet ...  57  21. 22.  Deflecting Fields for 20 cm Radius Deflecting F i e l d s f o r 30 cm Radius  58 59  23.  Deflecting F i e l d s f o r Singly-Charged Alphas.  60  2h,  Diagram for Energy Resolution Calculation ..  6l  25.  Calculated Energy Spread i n Beam  62  A.Introduction  This thesis describes the modification of the U.B.C. Van de Graaff Generator f o r the acceleration of singly-charged alpha p a r t i c l e s , and an i n v e s t i g a t i o n of c e r t a i n excited states of boron 11 produced by the r e a c t i o n L i (ocjf )B 7  /y  .  Alpha p a r t i c l e s have c e r t a i n advantages over other nuclear p r o j e c t i l e s .  They have zero spin, which l i m i t s the input  channel spin f o r alpha-induced  reactions to a single value, a  simplifying r e s t r i c t i o n f o r .the analysis of nuclear decay schemes. Where a u s e f u l i n t e n s i t y of doubly-charged alphas can be obtained, the energy of the accelerator i s e f f e c t i v e l y doubled, an a t t r a c t i v e p o s s i b i l i t y f o r 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 t o generate usable numbers of the doubly-charged i o n s ,  ( B i t t n e r , 1954; Temmer 1955).  Beginning i n 1911 w i t h R u t h e r f o r d ' s determination of nuclear s i z e by s c a t t e r i n g experiments, nuclear r e a c t i o n s were studied f o r two decades w i t h n a t u r a l alphas as the only p a r t i c l e source.  N a t u r a l alphas produced the f i r s t recognized nuclear  reaction N Be («*»n) C  f ¥  (*,p) 0  / 7  (Rutherford, 1919) as w e l l as the  r e a c t i o n leading t o the discovery of the neutron,  (Chadwick, 1932). A r t i f i c i a l l y accelerated alphas became a v a i l a b l e w i t h the development of p a r t i c l e a c c e l e r a t o r s i n the e a r l y 1930*s, p a r t i c u l a r l y w i t h the c y c l o t r o n .  Though t h e i r production i n Van  de Graaffs was reported as e a r l y as 1933 (Tuve, Hafstad and D a h l , 1933)> i t i s only i n comparatively recent years that e x tensive use has been made of Van de Graaff alphas. As pointed out by Bennett, Roys and Toppel (195D> alpha capture appears t o be a " s i m p l e " process, analogous t o p r o ton capture, r a t h e r than t o the more complex deuteron-induced processes, where the s t r i p p i n g r e a c t i o n s may compete w i t h or r e place compound nuclear f o r m a t i o n .  This i s perhaps not s u r p r i s i n g  i n view of the t i g h t l y - b o u n d alpha s t r u c t u r e . The L i  B  r e a c t i o n was f i r s t reported by  Bennett, Roys and Toppel (1951)> and subsequently by Jones and W i l k i n s o n (1952) and Heydenburg and Temmer (195^)• the known l e v e l s of B  / y  Figure 1 shows  up t o 16 Mev, (Ajzenberg and L a u r i t s e n , 1955).  Be  +  d  15.818  14.0// >>»/////////// 13.2  / / / / / / / / /  / / / /  / / /  //  //////WW / / /  I 1.8  B  1  0  + n  11.459  Be° + p  10.61 10.23  9.19  1 1 2 3 3  986, 9.28 8.57 Li  7.99  7  7.30  6.76  6.81  5 0 3 4.46  Fig  I  E n e r g y  L e v e l s  of  B o r o n  II  +  a  8.667  - 3 Jones and Wilkinson studied the angular d i s t r i b u t i o n s of the gamma rays, and made assignments f o r almost a l l l e v e l s up t o 9.28 Mev on the basis of a s t r i c t s i n g l e - p a r t i c l e s h e l l 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 p l / 2 ) , i . e . the upper l e v e l of the ground-state spin-orbit doublet, and higher states were assumed to be formed by e x c i t a t i o n of the odd proton t o higher levels i n the d,s and f s h e l l s . Considerable information on the B  11  of i t s mirror nucleus C  / ;  actions on B . /<?  l e v e l s , and those  has been obtained from stripping r e -  Evans and Parkinson (195*0» from Butler theory  analysis of data from B  /  0  (dp) B  / /  , obtained r e s u l t s disagreeing  with the assignments of Jones and Wilkinson, p a r t i c u l a r l y f o r the f i r s t excited state.  Their data was somewhat complicated by  compound nucleus interference i n the stripping reaction.  How-  ever, the r e s u l t s of Cerineo (1956) on the mirror r e a c t i o n B  / 0  (dn) C " support the conclusions of Evans and Parkinson with-  out ambiguity.  Recently Wilkinson (1957) has reported that  measurement of the l i f e t i m e of t h i s state by doppler-shift technique supports his e a r l i e r assignment of 1/2 , and suggests that the apparent disagreement  of the stripping data may r e s u l t from  a s p i n - f l i p of the outgoing p a r t i c l e i n the stripping reaction. The mass 11 system appears i n reasonable agreement with the charge-independent  nuclear force picture of mirror n u c l e i up  to the close doublet i n B " at 6.80 Mev where no such doublet has been observed i n C . x /  This might be explained by a s h i f t of the  i-t>  o fc  0<3  > o o > — a OQ_  a  3  •d P (?) CD #>  £  o  oo 10  E E  X  c o CM  £  SI  Vcvl  O  c  >  O  o  O  o  ^ x E a |0o 3 ° c  -  W  N  o CM  o CM  3  s  S —  - X  o  > o o  to CM  cp _ © o. i_ a (0 CO  o  CM  Fig  Ion  Source  Power  Oscillator  .0 V 3  »  *• O  upper l e v e l of the doublet i n C  - r a i s i n g the energy l e v e l from  a position predicted by comparison with the mirror l e v e l i n B when the l e v e l l i e s near the separation energy f o r a p a r t i c l e . Levels of the mass 11 system above 6 Mev are of considerable interest f o r the mirror nucleus picture, and i n v i t e further study, (Lauritsen, 1952). A detailed i n v e s t i g a t i o n of the gamma rays from the three resonances i n L i (e*>^) B energy range has been attempted.  within the Van de Graaff The system appears considerably  more complex than at f i r s t imagined, and a complete interpret a t i o n of the l e v e l scheme up to 9 Mev w i l l require a good deal of further investigation. While t h i s experiment was i n progress, an abstract of a similar study was published (Meyer-Schutzmeister and Hanna, 1957), but  no further d e t a i l s have appeared up to the present time.  >-t>  Em® o O  o  ja 3  a  a  (ft  O  93 CD  > a a  o  >  •o noi  a> A o  9  o  u (D o—9jT)  .2 o  JUUiH w O O CM >  Fig  3  Ion  Source  C o m p o n e n t s  B. Apparatus  1. P r o d u c t i o n of Alpha (a)  Ion  Particles  Source:  P o s i t i v e ions were produced i n a c o n v e n t i o n a l r a d i o f r e C i r c u i t of the 200  quency i o n source. shown i n f i g u r e 2,  watt power o s c i l l a t o r i s  and the arrangement of the i o n source  a s s o c i a t e d equipment i s shown s c h e m a t i c a l l y i n f i g u r e 3»  and Modi-  f i c a t i o n s f o r the p r o d u c t i o n of alpha p a r t i c l e s i n c l u d e d the a d d i t i o n of the helium c y l i n d e r and helium v a l v e , and an improved gas  manifold. During the course of these experiments,  a new  gas mani-  f o l d , w i t h helium-leak t e s t e d t o g g l e v a l v e s , (Appendix I c o n t a i n s data on c e r t a i n commercial components),and an attached gauge, was  installed.  The  Pirani  t o g g l e v a l v e s were s u p p l i e d w i t h  1/k  i n c h pipe t h r e a d s , which had t o be vacuum-sealed t o the manifold and t o adaptors f o r 0 - r i n g c o u p l i n g s .  T h i s was  accomplished  t i n n i n g the threads i n the m a n i f o l d and c o u p l i n g s w i t h  by  indium  metal,(Appendix I ) . P a l l a d i u m l e a k s i n the hydrogen and deuterium c y l i n d e r s have been r e p l a c e d w i t h thermal v a l v e s , s i m i l a r i n o p e r a t i o n , though c o n s i d e r a b l y more compact than the helium v a l v e , t o be d e s c r i b e d below.  These thermal v a l v e s have a s m a l l leakage r a t e  even when n o m i n a l l y c l o s e d , thus a l l o w i n g a s m a l l of one gas by another  i n the d i s c h a r g e .  contamination  Because of the d i f f e r e n c e  i n i o n i z a t i o n p o t e n t i a l s of hydrogen, (or deuterium) and  helium,  Hi  O I  0.25 I I nches  Fig  4  Ion  S o u r c e  E x t r a c t o r  Canal  - 6 a d d i t i o n of hydrogen or deuterium t o a helium d i s c h a r g e a much g r e a t e r contamination  produced  of the i o n beam t h a n 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 t o a hydrogen or deuterium d i s c h a r g e .  Laby, 1956)  The  i o n i z a t i o n p o t e n t i a l s a r e : (Kaye and  v  H  13.598  ev  He  2**.58  "  He*  5k.k  «  Background r a d i a t i o n s due  t o contamination  of  helium  d i s c h a r g e s by deuterium were observed, and w i l l be d i s c u s s e d low.  The  l i n e was  solenoid-operated  t o g g l e v a l v e i n the deuterium  i n s t a l l e d to eliminate t h i s  be-  gas  contamination.  F i g u r e h shows the base of the d i s c h a r g e  tube and  the  e x t r a c t o r c a n a l , through which i o n s l e f t the d i s c h a r g e tube  and  entered  the a c c e l e r a t o r tube.  the e x t r a c t o r c a n a l was  Focussing  of i o n s i n t o and  e f f e c t e d by the shape of the plasma i n  the lower part of the d i s c h a r g e  tube.  Satisfactory extraction  of i o n s depended on the shape of the e x t r a c t o r c a n a l . s t r i c t e d an opening a t the t o p allowed c a n a l by the i o n beam, producing  Too  re-  e r o s i o n of the aluminum  asymmetries i n the e x i t  and metal s p u t t e r i n g of the Vycor tube surrounding trance.  through  hole,  the c a n a l  en-  B o t h these e f f e c t s c o n t r i b u t e d t o poor f o c u s s i n g by  a l t e r i n g f i e l d g r a d i e n t s and i n g the y i e l d of i o n s .  the shape of the plasma, thus lower-  Alpha p a r t i c l e beams were p a r t i c u l a r l y  d e s t r u c t i v e t o i n c o r r e c t l y shaped c a n a l s .  The  p r o f i l e shown i n  f i g u r e h seemed t o reduce the r a t e of s e r i o u s e r o s i o n .  A two l i t e r helium c y l i n d e r was c o n s t r u c t e d of l A inch brass.  One end was removable, and sealed i n place on a  neoprene O - r i n g .  A 150 p s i . pressure gauge and a t o g g l e v a l v e  were mounted on one end, a second t o g g l e v a l v e on the o t h e r . The helium v a l v e was strapped t o t h i s b o t t l e , and connected t o one t o g g l e v a l v e w i t h an O-ring (b)  coupling.  Helium Thermal Valve:. S i n g l y - c h a r g e d alpha p a r t i c l e s were obtained by i o n i z -  ing helium gas i n the r a d i o - f r e q u e n c y i o n s o u r c e . a c o n t r o l l e d f l o w of r e a s o n a b l y fold.  This required  pure helium i n t o the gas mani-  Since t h e d i f f u s i o n r a t e of helium through metals i s a l -  most z e r o , the p a l l a d i u m l e a k , o f t e n used f o r hydrogen or deut e r i u m , c o u l d not be used, and some type o f mechanical v a l v e was required.  For o p e r a t i o n i n a Van de G r a a f f , t h e v a l v e had t o  be rugged and dependable, capable  o f remote c o n t r o l , had t o p r o -  v i d e p o s i t i v e s h u t - o f f , f i n e c o n t r o l o f the gas f l o w , and have a reasonably  short o p e r a t i n g  time-constant.  Valves o p e r a t i n g by t h e d i f f e r e n t i a l thermal  expansion  o f d i s s i m i l a r metals, w i t h e l e c t r i c a l h e a t i n g , f u l f i l l a l l t h e above requirements. S h i r e (195^).  Examples a r e g i v e n by Green (1953)» and  Some d e s i g n s had p r e v i o u s l y been t e s t e d i n t h i s  l a b o r a t o r y , and t h e v a l v e used was developed  from t h e s e ,  (Heiberg,  195^ PP. 65-66). T h i s d i f f e r e n t i a l - e x p a n s i o n needle v a l v e i s shown i n f i g u r e 5.  Body and end-plates  o f the v a l v e were of b r a s s ; the  Fig  5  Helium  Thermal  Valve  needle of a " s t a i n l e s s " type s t e e l , of unknown c o m p o s i t i o n . Copper-plated s t a i n l e s s s t e e l G-rings,(Appendix  I),  provided a  p o s i t i v e s e a l a t the ends t o w i t h s t a n d the o p e r a t i n g of s e v e r a l hundred degrees  temperatures  c e n t i g r a d e , and p r e s s u r e s up t o  100  psig. S a t i s f a c t o r y o p e r a t i o n of such a v a l v e was on the c h o i c e of taper f o r the n e e d l e . used appeared  dependent  The 10 degree h a l f - a n g l e  t o provide r e a s o n a b l y slow opening, and hence f i n e  c o n t r o l without s t i c k i n g i n the s e a t .  I n c o r p o r a t i o n of the  v a l v e seat i n one end-plate r a t h e r than i n the v a l v e body allowed a good match of the t a p e r s on the needle and s e a t , as both c o u l d be c u t on a l a t h e w i t h the same s e t t i n g of the compound-rest. The f l o a t i n g nut a t the f i x e d end of the needle allowed  the  needle t o be lapped onto the s e a t w i t h the v a l v e p a r t i a l l y a s sembled.  F i n a l l a p p i n g was  done^ w i t h no. 1000-grit  l a p p i n g com-  pound . The h e a t i n g element c o n s i s t e d of approximately h meters of 0.010  i n c h nichrome w i r e , t o t a l r e s i s t a n c e 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 w i t h about 6 mm  of asbestos paper.  s u p p l i e d v i a a v a r i a c and a 150  ^00  VA i s o l a t i n g  c y c l e AC  power  was  transformer,(Appendix  I ) . Tank helium was  used,  (Matheson welding grade, 99.99$  p u r e ) , the gas b o t t l e b e i n g f i l l e d by passing the helium a t p s i g . through an a c t i v a t e d c h a r c o a l t r a p a t l i q u i d n i t r o g e n  150  - 9 temperature, (c)  (77 degrees K ) .  Operation of the Helium  Valve:  The helium v a l v e was i n s t a l l e d i n the Van de G r a a f f on October  25, 1955, and operated  s a t i s f a c t o r i l y from t h a t d a t e ,  w i t h no a t t e n t i o n other than p e r i o d i c f i l l i n g bottle. charged  Beam c u r r e n t s o f up t o 20 microamps r e s o l v e d o f s i n g l y alpha p a r t i c l e s were observed; 10 t o 15 microamps were  t y p i c a l l y a v a i l a b l e d u r i n g experiments. ion of  o f t h e helium gas  S u i t a b l e l o a d i n g of the  source o s c i l l a t o r , c o r r e s p o n d i n g t o o s c i l l a t o r p l a t e c u r r e n t s 200 t o 250 ma were obtained a t a power i n p u t of a p p r o x i m a t e l y  55 watts t o the thermal v a l v e .  With the t o p t e r m i n a l o f t h e Van  de G r a a f f open, these o s c i l l a t o r l o a d c u r r e n t s were obtained w i t h i o n source m a n i f o l d p r e s s u r e s o f about 350 When f i r s t  microns.  turned on, the l e a k r e q u i r e d f r e q u e n t a d -  justment f o r a p e r i o d o f about one-half hour.  T h i s presumably  was the time r e q u i r e d f o r t h e l e a k t o r e a c h thermal with i t s surroundings.  Ambient temperature  equilibrium  i n s i d e the top t e r -  m i n a l of t h e Van de G r a a f f a t 50 l b s n i t r o g e n p r e s s u r e , measured w i t h a maximum thermometer over long p e r i o d s , i n c l u d i n g u n i n t e r rupted runs of 16 hours, reached  52 degrees  The helium v a l v e proved  C.  q u i t e s e n s i t i v e t o the r e g u -  l a t i o n of the 110 V, kOO c y c l e AC power i n t h e t o p t e r m i n a l , and d u r i n g p e r i o d s when t h i s r e g u l a t i o n was poor, t h e v a l v e r e quired c o n t i n u a l adjustment  t o keep the l o a d i n g of t h e i o n source  o s c i l l a t o r and t h e beam, c o n s t a n t .  - 10 The thermal, time constant of the helium valve appeared reasonably short; turning o f f the leak power extinguished a normal discharge i n less than 5 seconds. Leakage rate through the closed helium valve into the manifold was observed to give a pressure r i s e of three microns i n one minute i n a volume estimated at 20 cc (manifold and P i r a n i gauge).  This rate did not constitute a serious drain on the  helium supply, and produced n e g l i g i b l e pressure r i s e i n the a c celerator tubes. Although the helium valve was at times observed t o operate without adjustment f o r periods of up t o two hours, more frequent attention was usually required.  A f i n e r adjustment on  the heater power would have been convenient.  Addition of a second  heater winding to the leak, with the variac c o n t r o l l i n g one winding, and the second connected to a constant \oltage source by a switch would give the desired degree of c o n t r o l . Before i n s t a l l a t i o n i n the Van de Graaff, the helium valve was tested on the i o n source of a 50 kev accelerator. At t h i s time the l i n e spectrum of singly-ionized helium was observed, and a search made f o r l i n e s indicating doubly-ionized helium, i n o  e  particular those at *f685.8 A and 6560.1 A, using a d i r e c t v i s i o n spectroscope (Canadian Arsenals L t d . Type 55). not observed.  These l i n e s were  - 11 2.  Van de Graaff Modifications (a)  Magnetic F i e l d s f o r Deflecting Beams: Magnetic d e f l e c t i o n of singly-charged alpha p a r t i c l e s  required s i g n i f i c a n t l y higher f i e l d s than f o r the d e f l e c t i o n of protons or deuterons of_similar energies.  For example, on the  o r i g i n a l 20.3 cm radius i n the deflecting magnet, 1 Mev  protons,  deuterons, and singly-charged alpha p a r t i c l e s required f i e l d s of 7, 10 and Ik kilogauss r e s p e c t i v e l y . field  Appendix II discusses the  requirements. Operation of the beam-deflecting magnet at these higher  f i e l d s raised problems i n machine control which led to several modifications of the Van de Graaff Generator. (b)  Electron Gun and Energy S t a b i l i t y : The accelerating p o t e n t i a l of the Van de Graaff was  stabilized by a beam of electrons injected at the earth end of the d i f f e r e n t i a l pumping tube, and intensity-modulated by a signal derived from the p o s i t i o n of the deflected beam r e l a t i v e to a pair of s l i t s or " s n i f f e r s " , thus f i x i n g the accelerating potent 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 d e f l e c t beams of 0.8 to 1.0 Mev alpha p a r t i c l e s , i t was found that the electron beam ceased to s t a b i l i z e the accelerating p o t e n t i a l , apparently the r e s u l t of the f r i n g i n g f i e l d of the magnet a f f e c t i n g the e l e c tron beam entering the d i f f e r e n t i a l tube.  The base-plates of the  accelerator and d i f f e r e n t i a l tube manifolds were r e l a t i v e l y close  Fig  6  E l e c t r o n  Gun  Mounting  - 12  -  t o the yoke of the magnet ( v e r t i c a l s e p a r a t i o n $k cm) d i s t a n c e was  decreased by the l i f t i n g  d i f f e r e n t i a l s i d e (height of l u g 12  and  l u g on the yoke on  cm).  this the  W i t h the magnet  on,  f l i p - c o i l measurements i n d i c a t e d a p p r e c i a b l e magnetic f i e l d s even between the pumping  manifolds.  O r i g i n a l l y the e l e c t r o n gun was the base-plate  of the d i f f e r e n t i a l m a n i f o l d ,  the l i f t i n g - l u g 2.5  mounted e x t e r n a l t o  on the magnet.  about 10  E l e c t r o n s were i n j e c t e d a t about  kev energy, and d r i f t e d a d i s t a n c e of about 1.5  through the s t e e l pumping manifold tube proper.  cm above  before  meters  up  e n t e r i n g the vacuum-  Magnetic f i e l d g r a d i e n t s 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 , c o u l d a p p a r e n t l y d e f l e c t or  de-  focus the e l e c t r o n beam s u f f i c i e n t l y t h a t i t d i d not a r r i v e at the top t e r m i n a l of the a c c e l e r a t o r . S h i e l d i n g the e x t e r n a l gun s h i e l d , (5  s t r u c t u r e w i t h a mu^metal  i n c h p h o t o m u l t i p l i e r s h i e l d ) , w i t h a 0.25  s t e e l housing, and w i t h t h i s housing l i n e d w i t h 0.25 s i l i c o n s t e e l transformer  laminations  inch mild inches  of  f a i l e d t o produce any  im-  provement. T h i s d i f f i c u l t y was e l e c t r o n gun  f i n a l l y overcome by remounting  s t r u c t u r e on a H-.5  cm diameter b r a s s  i n g up i n t o the base of the pumping manifold about 1 meter.  tube, p r o j e c t -  f o r a distance  T h i s arrangement i s sketched i n f i g u r e 6.  t h i s p o s i t i o n the d r i f t d i s t a n c e f o r the e l e c t r o n s was reduced, and  the gun  s t r u c t u r e was  the  of In  greatly  w e l l removed from the  region  Fig  7  Magnet  Box  and  Extension  Pole  P i e c e s  - 13 of high f r i n g i n g - f i e l d s .  This arrangement has operated  satis-  f a c t o r i l y since February, 1956. Several improvements were made to the analysing magnet. Extensions on the pole faces increased the e f f e c t i v e radius of curvature, from about 20.3 cm t o about 30.5 cm, thus decreasing the f i e l d required t o deflect p a r t i c l e s of any given energy. As o r i g i n a l l y designed, the magnet had 11.5 inch radius c i r c u l a r pole faces with a 5 inch gap, supporting 16 inch square pole faces 2 inches t h i c k , leaving a 1 inch gap. A strong f r i n g i n g f i e l d was produced by the segments of the c i r c u l a r faces extending beyond the square faces, with maximum f r i n g i n g f i e l d s at the p o s i t i o n of entry and exit f o r a beam following an 8 inch radius. Shims were provided only a t the entry p o s i t i o n . 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 i r o n , and bolted to the 16 inch square pole-faces. Each extension was f i t t e d with a s e m i - c y l i n d r i c a l adjustable shim , of 3A- inch radius.  Brass rocker-arms were attached t o the shims.  A new magnet box was constructed of 7 / 8 inch diameter copper tubing.  Two q u a r t e r - c i r c l e s of t h i s tubing were joined  at the entrance p o s i t i o n , and hard-soldered t o a rectangular brass flange, one inch t h i c k .  This flange was bolted t o 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 p o s i t i o n .  Fig  8  Beam  Tube  and  Target  Mounting  - Ik This arrangement permitted r e l a t i v e l y easy removal of the magnet box, and the i n t e r i o r of the copper tubes was conveni e n t l y cleaned with s t e e l wool or chemicals. For t h i s 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 p a r t i c l e required about 10  kilogauss d e f l e c t i n g f i e l d to follow t h i s curvature, compared to about l^f kilogauss with the former arrangement.  Deflecting  f i e l d s f o r the p a r t i c l e s 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  versed by the beam a f t e r leaving the accelerator tube.  tra-  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 t o t a l v e r t i c a l beam. After d e f l e c t i o n , the v e r t i c a l spread of the beam was limited by the gold s n i f f e r s , 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 t a r g e t , i . e . much narrower than t h i s  stop-opening.  - 15 The solenoid-operated beam shutter, which carried a quartz focussing plate, protected the targets from the beam except when making observations, thus prolonging target l i f e .  A  switch on the main control panel allowed remote operation of t h i s shutter. (b)  Target Contamination  and Background Radiations:  Carbon deposits were observed to accumulate on surfaces struck by the beam, p a r t i c u l a r l y on the s n i f f e r s and target. These deposits were a serious source of background r a d i a t i o n s , 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 ,(l.l#). / 3  Carbon deposits were produced from hydrocarbon vapours i n the vacuum system, c h i e f l y from pump o i l s and vacuum grease. To l i m i t these deposits, dry neoprene gaskets were used on a l l s t a t i c joints i n the beam tubes, and vacuum grease on moving seals, (target holder and gate v a l v e s ) , was kept to a minimum.  The beam  tube and magnet box were frequently dismantled f o r cleaning of exposed surfaces, stops and s n i f f e r s . Two l i q u i d nitrogen cold traps were used on the beam tube: a pyrexside-arm  at the e x i t of the magnet box, and a brass  and stainless s t e e l trap a t 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 f a i n t greyish coating during runs of up t o twelve hours, heavier deposits occurred on the s n i f f e r s .  although  - 16 Deuterium contamination i n the i o n beam was another source of background r a d i a t i o n .  With an alpha p a r t i c l e beam  passing through the magnet box, the deuterium f r a c t i o n was  de-  f l e c t e d 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 p a r a f f i n was supported by a Dexion frame so as to surround the beam tube at the e x i t of the magnet box and attenuate radiations from t h i s region. Addition of the solenoid-operated valve i n the deuterium l i n e to the ion source f i n a l l y eliminated t h i s source of background  h.  radiation.  Targets (a)  Target Chambersi Several target chambers were tested during the e a r l y  phases of t h i s experiment.  The f i n a l design i s shown i n f i g u r e 9.  A 2 inch glass port gave a clear view of the i n t e r i o r when making or bombarding targets.  Beam current measurements were f a c i l i t a t e d  by insulating the target stem on a l u c i t e r i n g .  Target backings  were kept cool by an external blast of a i r on the heavy copper target stem. (b)  Lithium Furnace: Thin l i t h i u m targets were prepared by evaporation of  lithium metal onto copper backings i n vacuo.  A lithium furnace  of brass and stainless s t e e l 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  Lucite \  Glass  7  1  Sliding Seal Brass  Body  O  2 I nches  Furnace Tube  T a r g e t  C h a m b e r  Beam Tube O - Ring Qrooves  Cooling Coil  Brass  Steel O i_ Inches Lithium  Fig  9  Lithium  F u r n a c e  and  T a r g e t  F u r n a c e  Chamber  - 17 wound over a mica sheet around the stainless s t e e l tube.  Up to  125 watts were supplied to the heater by a variac and 10:1 stepdown transformer.  The melting and b o i l i n g points of l i t h i u m are,  respectively, 186 and 1380 degrees C. (e)  Target Backings: Evaporated lithium targets were l a i d down on copper  backings 0.015 inches t h i c k .  I t was observed that during some  long runs with f a i r l y large beams (more than 10 mieroamps) the y i e l d from a target decreased slowly with bombarding time, and the surface of the copper developed a b l i s t e r e d appearance over the region where the beam had struck.  S i l v e r backings were tested,  but the y i e l d seemed to decrease more markedly than with copper, although no b l i s t e r i n g was observed.  Cooling the target backings  by blowing a i r on the stem of the target holder appeared  to pre- •  vent t h i s d e t e r i o r a t i o n 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 l a t t e r 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. After a few moments heating, the pressure gauges on the magnet box indicated a sudden, momentary r i s e to pressures of several microns. This probably marked the melting of the l i t h i u m and the l i b e r ation of absorbed gases.  Pressures quickly returned t o the order  of 1 0 " * mm, and the lithium started to appear on the target backing  Fig  10  Cathode  Follower  Header  - 18 a short time l a t e r . evaporation process.  No pressure r i s e was observed during the However, the gauges were situated some d i s -  tance from the target chamber, with three cold-traps intervening, and so d i d 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 b u i l t up, i t became less transparent, and took on" an ashgrey matte surface.  This colour f i r s t appeared when targets were  about 30 kev t h i c k . Several hours of bombardment produced only s l i g h t blackening of the targets, indicating that very l i t t l e carbon was being deposited.  No deposits thick enough to s h i f t the measured  p o s i t i o n of the L i  (*>« ) B  resonances were observed, indicating  that any deposits were less than a k i l o v o l t t h i c k . Thin evaporated targets were quite uniform i n thickness, as indicated by the shape of the e x c i t a t i o n functions.  A very  thick target, made by depositing successive layers of l i t h i u m , was less  uniform. For some tests and c a l i b r a t i o n s , B  get f o r the B " ( p Y) Q f  /2  reaction.  /y  was used as a t a r -  Targets of B "  separated  isotope on 0.002 inch gold f o i l backing were a v a i l a b l e . by the Harwell Electromagnetic  Separator Group).  (Supplied  Fig  u  Header  with  Delay  Line  Pulse  Shaping  -  5«  19  -  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 f o r these experi-  ments.  The f i r s t consisted of a Nal(Tl) c y l i n d r i c a l c r y s t a l 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 photomultiplier.  This w i l l be referred to as the "large" counter.  A  second, to be referred t o as the "small" counter, was a c y l i n d r i c a l c r y s t a l 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.  O p t i c a l connection from the windows of the  c r y s t a l containers to the phototubes was made with Dow-Corning no. 200  s i l i c o n e o i l , v i s c o s i t y 10 * centistokes at 25 degrees C.  Leakage of the s i l i c o n e o i l was prevented  by a rubber sleeve  slipped over the phototube and the c r y s t a l container.  For the  large counter, a sleeve was made by vulcanizing a sheet of 1/32 inch rubber. loon.  For the small one, a sleeve was cut from a toy b a l -  Neither counter has shown any loss of r e s o l u t i o n over a  period of a year. The large c r y s t a l , photomultiplier, potentiometer  chain,  and cathode follower were mounted i n a brass cylinder 9 cm diameter by 38.5 cm long. 10.  The cathode follower c i r c u i t i s shown i n figure  The small c r y s t a l was supported  i n an aluminum tube 5.6 cm  diameter by 5.*+ cm long, attached t o a brass cylinder 7.6 cm d i a meter by 28 cm long. to a pulse-cable. that of figure 10.  Two c i r c u i t s were used to match t h i s detector  The f i r s t was a cathode follower similar to The second, shown i n figure 11 was introduced  Fig  12  Spectra  from  Large  Counter  - 20 when measuring angular c o r r e l a t i o n s .  I t 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 c y l i n d r i c a l for ease i n handling and shielding. T y p i c a l gamma ray spectra for the large counter are shown i n figure 12 f o r C s  / 3 7  , Ra Th, and C ' gamma rays. z  Energy  resolution was about 7% at 2.62 Mev. The e f f i c i e n c y of the large c r y s t a l , as a function of gamma ray energy, had recently been studied experimentally by E.A.G. Larson, and L.P. Robertson, and t h e o r e t i c a l l y by P.P. Singh, a l l of t h i s laboratory. within %  Theoretical c a l c u l a t i o n s agreed  of measured values for Co*° gamma rays (1.17 and 1.33  Mev), and for the 6 . 1 ^ Mev gamma rays from the F reaction.  (p>c*0 0  Mr. Singh supplied a c a l c u l a t i o n of the c r y s t a l e f -  f i c i e n c y appropriate t o t h i s experiment, which w i l l be discussed below. The small counter, used c h i e f l y as a monitor, was supported by an X-ray tube stand, with no shielding on the c r y s t a l . The large counter was mounted inside a set of interlocking lead b r i c k s , having a 9.5 cm hole, lined with l A inch s t e e l tube.  Ad-  d i t i o n a l lead shielding was used around the region of the c r y s t a l ; the counter and shielding were carried on a Dexion t r o l l e y .  - 21 (b)  Electronics f o r Angular D i s t r i b u t i o n Measurements: High voltage for both photomultipliers was supplied by  an I.D.L. Type 532 EHT supply, and a potentiometer with separate adjustments f o r 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 l i m i t e r i n the  cathode follower c i r c u i t shown i n figure 10 prevented severe overloading of the pulse amplifier by cosmic ray pulses. Pulses from the large counter were fed to a Northern E l e c t r i c Model 1W+  wide band amplifier, whose time constants were  used f o r pulse-shaping. Generally a "top cut" (integration time constant) of 1 microsecond, and a "bottom cut" ( d i f f e r e n t i a t i o n time constant) of 5 microseconds were used. Pulses from the Northern E l e c t r i c 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 c o r r e l a t i o n experiments. A Dynatron model 1009A scaler was attached to the d i s criminator output of the Northern E l e c t r i c amplifier to provide a monitor f o r the counts i n the large detector.  This discriminator  was set to a bias l e v e l just above the 2.62 Mev gamma rays from Ra Th. For a number of the angular d i s t r i b u t i o n experiments, the monitor consisted of the small counter feeding pulses to an  Fig  14  Angular  Distribution  Electronics;  Block  Diagram  - 22  -  Atomic Model 20*fB linear a m p l i f i e r , 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 amp l i f i e r , and the bias of the scaler was adjusted to just above 2.62  Mev. A block diagram of t h i s general arrangement f o r angular  d i s t r i b u t i o n experiments i s shown i n figure lk. (c)  Electronics for Angular Correlation Measurements: To observe the angular c o r r e l a t i o n 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 i n 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 i s shown i n figure 15.  The channel from large c r y s t a l to kicksorter  was as described above, with the addition of a delay-line at the input to the Northern E l e c t r i c amplifier, with matching r e s i s t o r s , and operation of the biased amplifier gate i n the c o i n c i d e n c e position. For  the monitor channel, negative pulses from the cathode  follower of the small c r y s t a l were fed to an EKCo Type linear amplifier.  10^9B  Positive pulses of up to 70 v o l t s amplitude  from the EKCo amplifier went to an Atomic model 510 Single Channel Analyser ("SCA") which provided the energy discrimination i n t h i s  P> o  era CD N 03  Fig  15  Angular  Correlation  Electronics ;  Block  Diagram  - 23 channel.  15 v o l t s negative, were i n -  Output pulses from the SCA,  verted by a phase inverter, figure 16, for  to provide positive pulses  operation of the biased amplifier gate. An output point was added to the SCA to provide a p o s i -  t i v e pulse out for each pulse of amplitude  Pulses from t h i s output were coupled by an 80  base l i n e .  cable and pulse transformers scaler.  greater than the  SCA  ohm  (Appendix I) to a Dynatron 1009A  This provided a monitor channel f o r angular  coincidence  measurements, and for some of the angular d i s t r i b u t i o n runs, when t h i s channel was used s o l e l y as a monitor. The SCA was not designed f o r use i n time^coincidence measurements, i t s operation being as follows: Input pulses met a discriminator which defined the "base l i n e . "  A l l pulses of ampli-  tude greater than t h i s base l i n e setting were amplified a factor of ten by an "expansion a m p l i f i e r " , and applied to a second d i s criminator.  This second discriminator determined an  above the base-line s e t t i n g . fed  amplitude  Output of both discriminators was  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 f o r pulses which f e l l within the "window" amplitude. An output pulse appeared only after an input pulse had  crossed the base l i n e , and, without crossing the window d i s c r i m i n ator, had f a l l e n below the base l i n e again, thus i t was the ing  trail-  edge of the input pulse which determined the position i n time  of the output pulse.  For pulses with an exponential decay, pulses  Fig  16  Phase  Inverter  - 2h of d i f f e r e n t amplitude  f a l l i n g within the window width gave a  v a r i a t i o n of up to several microseconds delay i n 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 overcome t h i s d i f f i c u l t y .  This c i r c u i t provided delays-line shaping  to produce "square ' pulses, 2 microseconds long, rather than ex1  ponential pulses, so that there would be much less v a r i a t i o n i n length for d i f f e r e n t pulse amplitudes.  The improvement was  not  as great as had been hoped, as the shaped pulses were s t i l l somewhat rounded on top, and t h i s shape was exaggerated by the expansion amplifier i n the single-channel analyser, so that the output pulse was triggered by the sloping portion of the top of the "square" pulse.  The v a r i a t i o n i n delays was,however, reduced  to  about one microsecond. Satisfactory coincidence operation was achieved by i n serting a delay i n the spectrum channel s l i g h t l y greater than the maximum delay i n the monitor channel, and using a gate pulse of s u f f i c i e n t duration to ensure that a l l truly-coincident pulses entered the biased amplifier without c l i p p i n g .  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 l i n e (Appendix I) provided a t o t a l delay of about 3*5  microseconds.  The gate i n the biased amplifier was greater than approximately  opened by pulses of  10 v o l t s p o s i t i v e , the gate  remaining  - 25 open for the duration of the pulse above t h i s amplitude.  The  out-  put pulse of the SCA had a rounded top, and the phase inverter incorporated a gain c o n t r o l , which allowed a v a r i a t i o n 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 s a t i s f a c t o r y . Pulses fed to the EKCo amplifier were also fed i n para l l e l to a length of cable, with a r e s i s t i v e termination, during experiments. of the SCA. (d)  This cable was  used when setting the window p o s i t i o n  Its use w i l l be discussed below.  A d d i t i o n a l E l e c t r o n i c Apparatus: Beam currents to the target were measured with an e l e c -  tronic current integrator, described i n Edwards, ( 1 9 5 D .  A  300  v o l t battery biased the target positive to suppress secondary electron emission. A system of switching relays gave simultaneous s t a r t i n g and stopping of the current integrator, k i c k s o r t e r , s c a l e r s , and an e l e c t r i c timer.  This system was  controlled by the integrator  to give readings f o r a c e r t a i n number of integrator counts. Pulse generators using Western E l e c t r i c 276D mercury switching r e l a y s , and based on Chalk River designs, were used f o r the setting and c a l i b r a t i o n of the kicksorter (Robertson The pulses were shaped to have approximately as those from Nal crystals (0.25  1957).  the same rise-time  microseconds),  and were of suf-  f i c i e n t l y low l e v e l that they could be fed d i r e c t l y to the photo-  - 26 multiplier headers, through the " t e s t " connector (figures;, 10 and 11) thus providing a check on the whole e l e c t r o n i c 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 i n t e n s i t i e s with angle, measured  with respect t o the beam d i r e c t i o n were observed, using the large counter to examine the spectra and the small counter as a monitor.  For t h i s 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 l i t h i u m when struck by the beam.  Azi-  muthal position of the large counter was set with the a i d of a protractor placed on top of the target chamber, and spacing from target to the counter was determined  by l u c i t e spacing-blocks  used to set the distance from the outer w a l l of the target chamber to the face of the c r y s t a l . Some of the gamma rays studied were of low i n t e n s i t y , and to obtain reasonable counting rates i t was necessary t o 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 r e s o l u t i o n was  - 27 therefore not available f o r these low-intensity t r a n s i t i o n s . However, since the angular d i s t r i b u t i o n functions were not expected to contain terms of higher than the second power i n cos ~6measurements at 0 and 90 degrees with respect to the beam d i r e c t i o n were adequate to determine the angular d i s t r i b u t i o n coefficients.  Accordingly these two angles were used i n the d i s -  t r i b u t i o n measurements. Two 90 degree positions were a v a i l a b l e , one on either side of the target chamber.  Repeated runs i n these  and the 0 degree position were made i n measuring  each d i s t r i b u t i o n .  The target was rotated so that the gamma r a d i a t i o n always passed through the copper target backing to the large counter, i . e . f o r the detector at 0 degrees to the beam d i r e c t i o n , the plane of the target was at approximately h$ degrees to the beam, with the face of the detector "looking a t " 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 c r y s t a l was supported with i t s axis vertical,above the horizontal plane of the beam, allowing maximum clearance f o r the large counter around the t a r get chamber.  For angular c o r r e l a t i o n s , the small counter was  placed with i t s axis i n the horizontal plane, at 135 degrees to the beam d i r e c t i o n , at a distance chosen to make the e f f e c t i v e s o l i d angles of the two c r y s t a l s approximately equal. (b)  Electronics: Channels of the kicksorter were set with the mercury r e -  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 l i n e of the SCA when the small counter was used as a monitor.  Energy calibrations were occasionally checked with the  h.h3 Mev gamma r a d i a t i o n from B  (p,f)C  , and the 6,1k Mev  r a d i a t i o n from F '* (p,<xX) o'*,' To calibrate the SCA f o r energy s e l e c t i o n and coincidence counting, pulses from the small counter were fed t o the Northern E l e c t r i c amplifier i n p a r a l l e l with the EKCo a m p l i f i e r .  A spec-  trum from the small counter was thus displayed on the k i c k s o r t e r . 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 l i n e and window d i s criminators set to include t h i s range of pulses.  The cable to  the Northern E l e c t r i c amplifier was then disconnected and terminated with an equivalent impedance, (about 9 0 ohms) during the experiments. Operating energy f o r the Van de Graaff was chosen by determining an e x c i t a t i o n function over the resonance being studied for each new target, the gamma rays being counted at the output of the Northern E l e c t r i c discriminator, and by the monitor  counter.  A t y p i c a l e x c i t a t i o n function over the O.96O Mev resonance i s shown i n figure 19.  The energy of the accelerator was measured  by a generating voltmeter, and once an operating point was chosen, the electron gun s t a b i l i z i n g system kept the energy constant within narrow l i m i t s , and with only infrequent adjustments.  - 29 Energy r e s o l u t i o n of the analysed  p a r t i c l e 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 s n i f f e r s .  The s i m p l i f i e d  analysis given i n Appendix II indicated that the range of energies i n the beam f o r t y p i c a l s n i f f e r positions was several tenths of a percent, i . e . several k i l o v o l t s at 1 Mev.  However, obser-  vations made while measuring resonance widths indicated that the resolution was one k i l o v o l t or better. A well-focussed  beam formed,at the p o s i t i o n of the s n i f -  f e r s , a l i n e focus about 2 mm wide by 25 mm high.  I t was expected  that the alpha p a r t i c l e f r a c t i o n of the beam was c l o s e l y homogeneous i n energy on leaving the accelerator, and that the rather wide v e r t i c a l spread of the deflected beam represented  a small  range of p a r t i c l e energies, i . e . the analysing system was highly dispersive.  In that case, the range of energies f o r p a r t i c l e s  passing between the s n i f f e r s would have been considerably less than that indicated by the simple geometric c a l c u l a t i o n .  This  energy range was also a measure of the s e n s i t i v i t y 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 k i l o v o l t s  thick were used f o r width measurements.  The shape of the t h i c k -  target e x c i t a t i o n functions at the resonances was determined bymeasuring the y i e l d of gamma rays at closely-spaced energy i n tervals across each resonance.  Alpha p a r t i c l e energies as i n d i -  cated by the generating voltmeter were held constant to about one k i l o v o l t at each point. The t o t a l width P of the resonances,in laboratory coordinates, was determined by f i t t i n g t h e o r e t i c a l curves t o these experimental points.  The Breit-Wigner s i n g l e - l e v e l formula f o r  the cross-section (f (E) i n the neighborhood of a narrow, isolated resonance of the (<*^) reaction i s  (1) 2  (E - E ) SI  r~i  - ( '/  2 )  where:  f1  i s the t o t a l width of the resonance  \2.  "  /y E^  " alpha p a r t i c l e width »  "  t o t a l r a d i a t i o n width  " resonance energy  2.  Hi  in  O  P  6  03 H  o d  10 (0  >  -<J> d  o  (0  d  E *-  o > c  m m d  o m  CD O  in  CD  T" o o ©  10  *-  c  3 O  o o o  o o o  rO  O O O  CM  o o o  o  Fig  17  0.960  Mev.  Resonance;  Thick  T a r g e t  9 C 4)  - 31 =  (2.1  + 1)  (2s + 1 ) weighting  factor  j  ;  j  energy  statistical  ( 2 j , + 1)  s p i n of  incident  "  "  initial  state  "  " compound  "  Integration the  the  for: s  sion for  is  of  y i e l d Y of  E and t a r g e t  this  formula  gamma r a y s  thickness  Y = C  \  particle  gives  as  the  following  a function  of  alpha  expresparticle  t  tan"'  Y  t  l  t  + y  (2)  (y-t)  where: C is y and y and t  are  This  a  = E -  shown t h e  experimental  resonance  rays  and t h e  to  set  a  widths  0.960  the  the  at  of  the  and  limit  These  of <1  kev  widths values  of  /2.  '  to  the  resonances. and  0.820  Mev,  O.MX)  of  fitted  points  small width  centre-of-mass  i n units  f u n c t i o n was  the  for  E  measured  determine  curves  constant  the  on the  points  to  17  a n d 18  are  In figures "best  fit"  Mev r e s o n a n c e s .  because the  experimental  of  the  resonance,  low it  theoretical I n the  yield  of  was  only  co-ordinates  were  case  of  gamma possible  width.  i n laboratory  by m u l t i p l y i n g by  the  factor  reduced  to  Fig  18  0.820/levResonance  •,  Thick  Target  - 32 M  c  / M/ = O.636  where: M  i s the reduced mass  Q  =  M / i s the mass of the incident p a r t i c l e Mj2  i s the mass of the target nucleus  The r e s u l t i n g values of the p a r t i c l e widths f» Resonance Energy  0,kO0 Mev  Lab. Co-ords.  <• 1 kev  Centre-of-mass  <<-l »•  were:  0.820 Mev 1. 0,6k  kev "  0.960 Mev 8. 5.1  kev »  (Experimental r e s u l t s and calculations are collected i n 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 i n Ajzenberg and Lauritsen (1955), p a r t i c u l a r l y for the 0.820 Mev resonance, f o r which the l a t t e r observed a laboratory width of about 6 kev. (b)  Calculation of Reduced P a r t i c l e Widths: The t o t a l width P of a resonance may be expressed as  the sum of reduced p a r t i c l e and r a d i a t i o n widths: P  =  ^  [p ( p a r t i c l e s ) +  fy'(radiation)  In the energy range of these experiments, no p a r t i c l e emission other than the re-emission of alpha p a r t i c l e s was  - 33  -  energetically possible, thus:  r •  + £17  c  Reduced alpha p a r t i c l e widths  o)  a  }f«c were calculated  from the r e l a t i o n , (Blatt and Weisskopf 1952,  r~  -  page  390)  w  — C — 2 K  Vj  R  where: K v  i s the wave-number of the incident p a r t i c l e s i s a factor depending on the height of the coulomb  t  barrier and the angular momentum of the incident alpha p a r t i c l e s , calculated from the tables of Bloch et a l (195D> and from the graphs of Sharp, Gove, and Paul (1953) R  =r  (A,  0  r = I.H-5 x 10  )» the i n t e r a c t i o n radius cm, the value  0  R  2  -/3  , „  using  +A  = 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 c a l c u l a t i o n  of the i n t e r a c t i o n radius i s a matter of some uncertainty.  For  l i g h t n u c l e i , consisting of assemblies of r e l a t i v e l y 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 above value of r  e  or charge-radius i s being measured.  The  seems to be commonly used f o r reactions of l i g h t  nuclei (Moszkowski 1955)•  Note however that Sharp, Gove and Paul  - 3^ (1953) used the expression R  =  „  '/3  1.5 A ,  - / 3  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 p a r t i c l e 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 p a r t i c l e width would have t o be very large i f the t o t a l width were to be measurable, f o r , i f the reduced width i s assumed to be of the same order as the two above, (say 350 kev), the t o t a l width of the resonance would be only about 5 ev, i . e . of the same order of magnitude as the r a d i a t i o n width, as pointed out by Ferguson et a l (1957). (c)  Measurement of Gamma Ray Y i e l d s : Y i e l d s 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 f o r background, normalized, and divided into energy i n t e r v a l s of 2 Mev, each covering the photo-and rays, or cascades.  pair-peaks of one of the gamma-  The number of counts i n these intervals was  then corrected for absorption and f o r counter e f f i c i e n c y .  - 35 Absorption occurred  i n the copper target backing, the  brass target chamber, the l i t h i u m target and the face of the aluminum c r y s t a l container. and were therefore  The l a t t e r two e f f e c t s were small,  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 i n l i n e with the axis of the counter ranged from 0.015 to 0.021 inches (0.0381 to 0.0^37 cm). Since the v a r i a t i o n i n absorption was small over t h i s range, and since the counter subtended a large s o l i d 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) t h i c k , symmetric about the target i n the horizontal plane.  Absorption of gamma rays i n copper and  brass was calculated using t o t a l absorption c o e f f i c i e n t s from the tables of Davisson and Evans (1952). P.P. Singh has calculated the e f f i c i e n c y of the large counter as a function of gamma ray energy up to 10 Mev f o r the following d e f i n i t i o n of e f f i c i e n c y £ „  € (By ) =  at gamma ray energy E y :  no. of counts i n 2 Mev i n t e r v a l below E y  y  t o t a l no. of gamma rays incident on the face of the c r y s t a l This calculated e f f i c i e n c y 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 l e v e l s . The observed 9 Mev peaks included counts due to lower energy cascade gamma rays detected i n coincidence. Corrections were c a l culated f o r such coincidences from the intense r a d i a t i o n due t o cascades through the l e v e l a t h.k6 Mev. I t was necessary to consider two processes: random and true coincidences. The random coincidence rate was N where N  c  c  f  counts per second,  i s the counting rate per second and T i s the resolving  time of the counting apparatus.  T  was taken t o be 5 microseconds,  the decay time-constant used i n the Northern E l e c t r i c a m p l i f i e r . The counting rate f o r true coincidences was a function of N  the number of disintegrations per second giving a cascade  £  the e f f i c i e n c y of the counter  (g)  the s o l i d angle of the counter and of the angular c o r r e l a t i o n between the com-  ponent gamma rays of the cascades.  The angular c o r r e l a t i o n 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 l e v e l from both the 9.28 and 9.J9 Mev levels had very small correlations.  For the purpose of these calculations the c o r r e l a -  tions were assumed to be zero.  I t was further assumed (a rather  crude approximation i n view of the angular d i s t r i b u t i o n data) that the r a d i a t i o n was i s o t r o p i c , and with these assumptions, the  - 37 coincidence counting rate f o r detecting both members of a pair of coincident gamma rays was:  while the counting rate for detecting only one gamma ray from each d i s i n t e g r a t i o n was:  2 N  (a> € and the r a t i o of true c o i n c i -  dences to random counts was therefore:  60 €  For the 9.19 Mev l e v e l , the number of true coincidences was about 50 times the number of random coincidences, and the number of coincidence counts was about k0% of the t o t a l number of observed 9 Mev counts.  For the 9.28 Mev l e v e l , 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 r e s u l t s gave the number of gamma rays i n the s o l i d angle of the counter f o r a given number of incident alpha p a r t i c l e s .  Using the angular d i s t r i b u t i o n co-  e f f i c i e n t s discussed below, the t o t a l number of gamma rays over  V-  was calculated, and the r e l a t i v e i n t e n s i t i e s determined. Relative Gamma Ray I n t e n s i t i e s :  Resonance Energy  OAOO Mev  0.820 Mev  0.960 Mev  9 Mev Radiation  (96$)  1$  12$  8$  13$  91$  75$  7  H  if.5 "  " "  ( W  - 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 The battery voltage was 1 8 9 . 5 V, (Electronic  a r e s i s t o r chain.  Instrument L t d . Model Mf Substandard Meter, no. M + 2 9 7 ) , and the r e s i s t o r chain consisted of four 1 0 megohm Nobeloy 1% r e s i s t o r s . This gave a current of *+.738 microamps, comparable to the beam current during y i e l d measurements. 1 0 9 . 3 microcoulombs  per count,  Integrator s e n s i t i v i t y was  k similar c a l i b r a t i o n , done one  year e a r l i e r , was within 3% of t h i s value. Values of the gamma-ray yields Y per incident alpha p a r t i c l e were: Resonance Energy  O.hOO Mev  0 . 8 2 0 Mev  9  0 . 5 x id""  O.Oh x 1 6 " "  2.3 x 1 6 " " 2.5  Mev Radiation  7  "  "  G.32 x »  h.5  »  "  3.6 x "  (d)  C a l c u l a t i o n of Radiation Widths-  0 . 9 6 0 Mev  15.  x  "  x »  r  Radiation widths were extracted from the t o t a l widths as follows.  The d i f f e r e n t i a l y i e l d dy of gamma rays from  the (o*,V) reaction may be expressed as dy = where:  Q* (E)  dT  - 39 O* (E)  -  i s the cross-section per incident p a r t i c l e of energy E, per target nucleus  Nj  i s the number of incident p a r t i c l e s per second  T  i s the number of target n u c l e i per  cm  The t o t a l y i e l d of gamma rays per incident p a r t i c l e may  be written as: CO  Y =  = N (dx /  y/N;  dE)  CT  (5)  (E) dE  where: N  i s the number-density of the target n u c l e i  dx / dE  i s the r e c i p r o c a l of the energy-loss per  cm,  of the incident p a r t i c l e s i n the target material, assumed to be constant over the «*» 0"  narrow resonances. (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 l i s t e d above,  N  =  n  °  =  h.6h x 10  atoms per  cm  M  where: 23  n  0  i s Avogadro's number, 6.025 x 10  atoms per  gram-atom d  i s the density of lithium, 0.53 *- gms  M  i s the atomic weight of lithium,  1  per  6.9^0  cm  are  - IfO  -  The energy-loss of charged p a r t i c l e s moving through an absorbing medium i s given by the expression:  kTTe z~ 2  dE / dx _  m  0  x  N B  (6)  V  where: e  i s the electronic charge, M-.80 X 10  z  i s the charge on the incident p a r t i c l e , 2, i f the  esu  alpha p a r t i c l e i s assumed to be stripped —29  m  i s the rest-mass of the electron, 9.108 x 10  gm  V  i s the v e l o c i t y of the incident alpha p a r t i c l e s  B  i s the "stopping number" of the absorbing material 2 'm V * B = Z log 0  where:  Z  i s the atomic number of the absorber, 3 f o r lithium.  I  i s the average e x c i t a t i o n p o t e n t i a l of the absorbing atoms.  Direct c a l c u l a t i o n of dE / dx, using the above expressions, was complicated by uncertainty i n the choice of values f o r Z and I to suitably describe the complicated charge-exchange processes occurring as low energy alphas come to rest i n a thick lithium target.  However, the r e l a t i o n s h i p (Bethe, 1936) B = s B (air) may be used to determine  dE / dx, where s i s the "stopping power" r e l a t i v e to a i r f o r the target material  -1+1 dE / dx (lithium) =  N  (  l l t h l u m  >  s dE / dx ( a i r )  (7)  N ( air) J9  N ( a i r ) = 5.276 x 10  3  atoms per cm (15 degrees C and  76 cm) dE / dx ( a i r ) values were taken from the  range-energy-  curves f o r low energy alphas given i n  Bethe (1950) s = 0.53 f o r lithium; Geiger's value, quoted i n Bethe  (1936, page 272). The r e s u l t i n g 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  i n good agreement with those from the data i n Whaling (1957). The i n t e g r a l was evaluated by integrating  the B r e i t -  Wigner s i n g l e - l e v e l formula, (1) above, giving:  a y 2 / f ^  Fr  (8)  r r  We assume that  r  / y i s much less than  imation reducing (8) to  j~i  / «. , and so make the approx-  j»  OOa. Y 2 TT* X  17  (9)  - h2 It was then possible to calculate the values of the from (9) above.  r a d i a t i o n widths Resonance Energy  0.820 Mev  O.hOO Mev  Total . r a d i a t i o n width  These values were:  0.02 ev  0.32  0.960 Mev  ev  1.75 ev  Partial r a d i a t i o n widths: to ground state  (0.019 ev)  0.00^ ev  0.21 ev  to ^.^6 Mev state  (0.001 « )  0.29  "  1.31 "  0.026  "  0.23 "  to 6.8 (?)'»  ««  Ferguson et a l (1957) 96$ and h% Weisskopf•has calculated the l i f e t i m e s of states of l i g h t nuclei against decay by gamma r a d i a t i o n of various multip o l a r i t i e s , assuming the r a d i a t i o n i s produced by s i n g l e - p a r t i c l e t r a n s i t i o n s . The..-radiation widths f o r dipole r a d i a t i o n obtained by Weisskopf are given by:  \r n ]y  (El) = 0.11  E 3  y  A  ev  -  (Ml) = 0.019 E y  (  1  0  )  ev  (Moszkowski 1955) Values of Ey.are i n Mev. Wilkinson (1955)» having surveyed about 100 t r a n s i t i o n s for which there i s strong evidence of dipole character, concluded that f o r E l t r a n s i t i o n s the experimental values are 0.032 times the Weisskopf values, within a spread factor of 7 either way, and that the Ml t r a n s i t i o n s are 0.15 times the Weisskopf values, within a spread factor of 20.  Values calculated from the above expressions,  - ^3  -  and also after m u l t i p l i c a t i o n by Wilkinson's correction factors are l i s t e d below.  These values may be compared with the observed  values given on page k-2. Calculated (a)  r a d i a t i o n widths, i n ev Weisskopf values  state:  El  Ibi  Ial  351.  11.2  38h.  13.5  2.0  El  1.7  Ml to 6.8  0.820 Mev  ial Ml to h.h6 Mev  Wilkinson values  0A00 Mev  Resonance Energy  to ground state:  (b)  0.26  (?) Mev state: E l Ml  2.  Angular (a)  0.960 Mev  1*1 12.3  Ial  IbJ.  396.  12.7  lh.7  2.2  15.2  2.3  52.5  1.7  55A  1.8  2.0  0.3  2.1  0.32  6.7  0.21  7.5  0.2*+  0.26  O.O^r  0.29  0.0*f  Distributions  Measurement of Angular D i s t r i b u t i o n s : Por r a d i a t i o n between states of d e f i n i t e angular  mo-  menta and parity, the angular d i s t r i b u t i o n function i s of the form: W  (-€•)  = £  hi  cos  2i  L  where i takes on a l l i n t e g r a l values from zero to the smallest of 1/ , where 1  /  j  or  1  2  and 1^ are the angular momenta carried by the incoming  p a r t i c l e and the outgoing r a d i a t i o n , and j i s 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 p a r t i c l e capture.  Therefore 1  /  must be =T  1.  It has been assumed that the states were formed by the capture of  - Ulf -  p-wave alpha p a r t i c l e s ( 1 ,  = 1 ) , and the angular d i s t r i b u t i o n  function was thus assumed to be: W ( ^ ) = A + A J J cos* ^  (110  0  and since only r e l a t i v e i n t e n s i t i e s are described by t h i s expression, we let A  0  =  1  Values of the c o e f f i c i e n t A may be determined z  from  measurements made at zero and 90 degrees to the d i r e c t i o n of the incident beam, even with poor angular r e s o l u t i o n .  As some of the  gamma rays were of low i n t e n s i t y , i t was necessary to make measurements with the counter close to the target, reducing angular resolution i n favour of increased counting r a t e .  Details of d i s -  tributions more complex than ( 1 1 ) above would not have been detected with this arrangement. Thin evaporated l i t h i u m targets were used for angular d i s t r i b u t i o n measurements.  E x c i t a t i o n functions were taken over  the resonance being studied f o r each new target, and the alpha p a r t i c l e 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 d i r e c t i o n .  A thin-target  e x c i t a t i o n function and gamma ray spectrum at the 0.960 Mev r e s onance are shown i n figure 19.  Repeated runs were made, using  two 90 degree positions i n the horizontal plane.  Distance from  the counter to the target, and hence the s o l i d angle, was kept constant during each run.  - h5 (b)  Corrections: The spectra were corrected f o r background, normalized  to the monitor counter, and divided into energy regions covering the photo-and pair-peaks of the d i f f e r e n t gamma rays. Intensity of gamma rays i n the counter was proportional to the s o l i d angle subtended by the counter at the target.  This  s o l i d angle was determined i n terms of an " e f f e c t i v e centre" of the large c r y s t a l .  Inverse square measurements with t h i s c r y s t a l  on the 6.1*f Mev gamma rays from F ^ ( p , oc V ) o ( L a r s o n , 1957) /  indicated that t h i s " e f f e c t i v e centre" was h.2 ± 0.2 cm from the front of the c r y s t a l .  Distance from target to c r y s t a l used during  the experiments ranged from 8.2 cm t o 10.8 cm and so the h a l f angle subtended by t h i s e f f e c t i v e centre ranged from about 12 to 15 degrees.  Calculations using the t o t a l absorption c o e f f i c i e n t  of Nal indicated that the p o s i t i o n of the " e f f e c t i v e centre" of the c r y s t a l would be expected to vary only s l i g h t l y 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 l e v e l , the spectrum observed was due t o a pair of gamma rays only s l i g h t l y separated i n energy, and so consisted of s i x overlapping peaks, which coalesced into a single large peak when displayed on the kicksorter with minimum expansion.  To obtain the  d i s t r i b u t i o n s of each of the pair of gamma rays, the d i s t r i b u t i o n of the sum, i . e . of the large peak, was f i r s t obtained. Then the r e s o l u t i o n of the kicksorter was increased t o separate the photopeak of the higher-energy component, and the angular d i s t r i b u t i o n  - if6 of the higher energy gamma ray determined d i r e c t l y , as the d i s t r i b u t i o n of t h i s  photo-peak.  Using a spectrum of the *+.*f3 Mev gamma ray from B *' ( p , 0 C  / 2  , the r a t i o of counts i n the photo-peak to the t o t a l  number of counts i n the photo- and pair-peaks f o r a gamma ray of t h i s energy, was determined.  Using t h i s r a t i o , the contribution  of the higher-energy r a d i a t i o n of the *f.5 Mev cascades was subtracted from the sum, and the d i s t r i b u t i o n of the lower energy peak determined from the remainder. Estimates of errors a r i s i n g 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 i n positioning of the counter with respect to the target, and absorption of r a d i a t i o n by materials i n and near the target chamber.  Probably the greatest  uncertainty was i n the d e f i n i t i o n of the solid-angle of the cryst a l i n terms of i t s " e f f e c t i v e centre" as described above. The absorption corrections were assumed to be constant over the angular region covered, and the geometrical errors were a l l lumped as a probable error i n the s o l i d angle of the counter. S t a t i s t i c a l errors were calculated f o r the spectra, background, and monitor counts. gular d i s t r i b u t i o n c o e f f i c i e n t k A, c o s ^ were:  The r e s u l t i n g values of the anx  i n the expression W  = 1+  - h7 Resonance Energy 9  0.820 Mev  O.U-OO Mev  Mev r a d i a t i o n  - 0.33  0.960 Mev  0.06  1  - 0.h2 ± 0.0V  7  M  n •  * 0.30 ± 0.10  *K5  "  "  - 0.17  1  0.02  + 0.1*6 ± O.Oh  h.k6  »  »  - 0.15  ±  0.02  + 0.10 ± 0.0**  (c)  0.0  ± 0.03  Calculation of Angular D i s t r i b u t i o n s : Following  the Racah c o e f f i c i e n t method outlined by-  Wilkinson (1955)> and using the tables of c o e f f i c i e n t s given by Biedenharn and Rose (1953)» values of the angular d i s t r i b u t i o n coefficient k  were calculated f o r a number of possible tran-  z  s i t i o n s , involving various  spins and p a r i t i e s . The values of  spins and angular momenta involved i n the reactions can be denoted as follows: alpha spin  0  7  +  Li  angular momentum  .  3  /  spin  —>  B  H  spin  > (B spin  )  +  gamma  angular momentum  spin  2  1  and any t r a n s i t i o n may be represented by j/ (1,) j ( 1^)  j^.  i n section 2.(a) above, only p-wave alpha p a r t i c l e s  As discussed  (1/ = 1) were considered, so that a l l calculated t r a n s i t i o n s were 3/2 (1) j ( 1 ) 2  culations) .  2i Z  (see Appendix I I I f o r d e t a i l s of these c a l -  - ho 3»  Angular Correlations Angular correlations'were measured between the pairs of  gamma rays cascading through the l e v e l 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 c o r r e l a t i o n was close to zero.  This  observation has been used i n calculating the gamma ray yields above. Correlations i n a plane normal to the beam required modifications to the target chamber and the mounting of the detectors which had not been made at the time of these experiments.  if9  -  -  Table 1 Collected Results of Experiments and Calculations (a)  P  T o t a l Resonance Widths  Resonance Energy  O.lfQO Mev  0.820 Mev  0.960 Mev 8. kev  Lab. Co-ords.  1 kev  1.  Centre-of-mass  1  0.6*f  (b) 9  "  kev  5.1  »  »  Relative Gamma Ray Intensities (96$)  Mev Radiation  7  "  *f.5  1$  12$  8$  13$  91$  75$  11  "  11  ( W  (c) Gamma Ray Yields Y per Alpha P a r t i c l e 9  • y  0.0U, x 10  -'I 2.3 x 10  0.32 x  «•  2.5 x »  3.6 x  »  .  -•//  0.5 x 10  Mev Radiation  7  "  ^.5  "  (d)  Experimental Radiation Widths  11  "  15. x "  i n ev  0.02  0.32  1.75  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  T o t a l Width P a r t i a l Widths:  (e)  "  Calculated Radiation Widths, i n ev (a) Weisskopf Values  Resonance Energy  lal  t  0  6  ,  8 (  ?  )  stlte:  E  1  *M1  ,0.820 Mev  O.hOO Mev  E l 351. Ml 13.5 to *f.*f6 Mev s t a t e : E l hh. Ml 1.7 to ground state:  (b) Wilkinson Values 0.960 Mev  1*2 I b l l a l  1M  11.2  38*f. 12.3 l ^ f . 7 2.2 52.5 1.7  2.0 l.h  0.26 .  2.0 6  '  7  °0.26  396.  0.3 2 1  7  0.0k  12.7  15.2  2.3  55.^  1.8  2.1  ^  Ibl  °' 0.29  0.32 2 h  O.Olf  - 50 (f)  Experimental Angular D i s t r i b u t i o n Coefficients  Resonance Energy 9  0.*f00 Mev  Mev Radiation - 0.33  1  0.820 Mev  ©.06  0.960 Mev - O.U-2 ± O.O^f  7  "  11  + 0.30 ± 0.10  If.5  "  "  - 0.17  l+.lf6  "  "  - 0.15 - 0.02  1  0.02  0.0  ± 0.03  + 0.lf6 ± O.O^f + 0.10 ± 0.Oil-  Calculated values of the t h e o r e t i c a l angular d i s t r i bution c o e f f i c i e n t s are given i n Appendix I I I .  - 51 D  Conclusions  We now consider what information regarding excited states of B " can be extracted from the above data.  The alpha  p a r t i c l e 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 p a r i t y . The L i ground state i s taken to be 3/2 .  Non-iso-  tropic angular d i s t r i b u t i o n s of gamma rays were observed from the states at 9.28, 9.19 and 8.92 Mev i n B" t i c l e capture.  produced by alpha par-  Consequently the alpha p a r t i c l e s must carry i n an  angular momentum of at least 1,  =  1 (p-wave). 7  Capture of p wave alphas by L i  7  B  would produce states of  with angular momenta of 1/2, 3/2, or 5/2.  The value 1/2,  indicating no o r b i t a l angular momentum,is ruled out by the observed non-isotropic d i s t r i b u t i o n s .  We therefore consider 3/2  or 5/2 as possible angular momentum values f o r these B " states. //  Por these three states of B  , the p r i n c i p a l modes of  decay are either a t r a n s i t i o n d i r e c t l y to the ground state, or a cascade through the l e v e l at h.k6 Mev. i s 3/2~(Gordy, Ring and Burg, 19^8).  For B ,  the ground state  Considerable information  on the h.k-6 Mev l e v e l i s available from the stripping reactions on B  / 0  .  (d,p) B  V  Evans and Parkinson (195 *-) observed i n the reaction 1  B  that this state was formed by the capture of p-wave  neutrons ( l = 1 '•)•• n  This observation has been confirmed by Cox  /0  - 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 l i m i t s the possible angular momenta of the k,h6 Mev l e v e l to the values 3/2, 5/2, 7/2, or 9 / 2 , a l l of negative p a r i t y . The mean l i f e t i m e of t h i s state has been measured by Swann, Metzger, and Rasmussen  hy the scattering of gamma  (1957)  rays on B * , ( E ^ = k.k3 Mev, from N  /  for the l i f e t i m e i s T = 0 . 7 ° x 1 0  S  (p*) Q ) /2  m  The value quoted  seconds, equivalent to a  r a d i a t i o n width of 0 . 8 7 ev, whereas the Wilkinson-adjusted value for a magnetic dipole t r a n s i t i o n of t h i s energy i s about 0 . 2 8 ev, calculated from equation ( 1 0 ) above.  This seems s u f f i c i e n t l y  good agreement to conclude that the t r a n s i t i o n from the h.k6 Mev l e v e l to the ground state has a (magnetic) dipole character, i n which case the possible angular momenta f o r t h i s 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  (1957)•  The observed t r a n s i t i o n s from the 9 . 2 8 l e v e l to the ^.^6 l e v e l and to the  ground state have respectively angular  d i s t r i b u t i o n c o e f f i c i e n t s of + 0,h6 and - 0 . ^ 2 , indicating d i f ferent angular momenta f o r 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 , 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 (d,p) B " r e a c t i o n from either the 2.1*f or the 5.03 Mev l e v e l s , for deuterons of energies 2.5 to 3.9 Mev. S t r i p ping groups were observed with 7.7 Mev deuterons, but were less w e l l defined than those from other l e v e l s . 7/  y o  - 53 state of B " i s 3/2 , we conclude that the h,k6 Mev l e v e l should be assigned the value 5/2. Returning to the 9.28 Mev l e v e l , the r e l a t i v e intens i t i e s of the gamma rays indicated that the t r a n s i t i o n to h.h-6 Mev was favoured over that to the ground state.  The observed  r a d i a t i o n width of the favoured t r a n s i t i o n , 1.31 ev, i s i n reasonable agreement with the Wilkinson-adjusted value of 1.8 ev f o r an E l t r a n s i t i o n , indicating that the 9.28 Mev l e v e l has positive p a r i t y .  The observed angular d i s t r i b u t i o n c o e f f i c i e n t  of + O.h-6 to the h,k6 Mev l e v e l agrees with a 5/2 to 5/2 t r a n s i t i o n , but not with 3/2 to 5/2 (Appendix I I I ) .  Therefore the  9.28 Mev l e v e l i s concluded to be 5/2 , and t h i s assignment also +  gives agreement f o r 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 of the ground state t r a n s i t i o n , 5/2 to 3/2. It might then be suggested that the 9.28 to h.h6 Mev t r a n s i t i o n has a s i n g l e - p a r t i c l e character, while the 9.28 to ground state t r a n s i t i o n involves a single p a r t i c l e t r a n s i t i o n plus some re-arrangement of nucleons i n the p s h e l l , thus providing a possible explanation f o r the r e l a t i v e l y low i n t e n s i t y of the l a t t e r .  Meyer-Schutzmeister  gested 3/2 or 5/2 clusion.  and Hanna (1957) have sug-  f o r t h i s state, i n disagreement  with t h i s con-  Since no d e t a i l s of their work have been published, i t  i s 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 l e v e l the t r a n s i t i o n to the ground state was highly unfavoured. than 2% of that to the  I t s t r a n s i t i o n probability was less Mev l e v e l , compared to about 17$ f o r  - 5^ the comparable r a t i o for transitions from .the 9.28 Mev l e v e l . The observed r a d i a t i o n width of 0.29 ev to the U-.h6 Mev l e v e l agrees with the Wilkinson-adjusted value of 0.3 ev for an Ml t r a n s i t i o n , and i n t h i s case the selection rules allow competit i o n from E2 r a d i a t i o n .  The mixed Ml and E2 transitions allow  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 s to vary over a wide range of values, depending on the mixing r a t i o . ient of - 0.17 would f i t a 5/2 admixture of E2 radiation;  The observed c o e f f i c -  to 5/2~ t r a n s i t i o n , with a large  or a 3/2*" to 5/2~ t r a n s i t i o n with  values of about - 0.2h or - 2.0 f o r o6, the mixing parameter, (see Appendix I I I ) .  The present data i s then unable to d i s t i n -  guish between 3/2 or 5/2 f o r the angular momentum of the 9.19 Mev l e v e l , though negative parity i s suggested. and Hanna (1957)» have suggested 3/2  Meyer-Schutzmeister  or 5/2 f o r t h i s l e v e l . The +  l a t t e r value i s not consistent with the results of the present experiment.  I t should be noted that the angular d i s t r i b u t i o n co-  e f f i c i e n t s to the ^.^6 Mev l e v e l 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 l e v e l , decay d i r e c t l y to the ground state i s highly favoured over any other t r a n s i t i o n (96$, Ferguson et a l 1957).  The observed angular d i s t r i b u t i o n c o e f f i c -  ient of - 0.33 i s consistent with either 3/2 or 5/2 for the angular momentum, but the observed t r a n s i t i o n probability of 0.02 ev Is much smaller than those calculated  for dipole  It does not appear possible at present to further  transitions.  l i m i t the possible  - 55 assignments f o r the 8.92 Mev l e v e l , and the data would suggest that the p o s s i b i l i t y of i t s formation by d-wave (1 = 2) alphas cannot be e n t i r e l y discounted. It i s apparent that the system i s f a r more complex than the simple s i n g l e - p a r t i c l e Wilkinson (1952).  picture suggested by Jones and  Considerably more work must be done before a  complete and consistent l e v e l scheme can be formulated.  - 56 E  APPENDIX I  Appendices  Data on Certain Commercial Components  Toggle Valves: Hoke Inc., Englewood, N.J. Model k$2 1/h inch NPT male f i t t i n g s 200 p s i . 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 properties of the element, i t s current and potential uses, and an annotated bibliography of the scient i f i c l i t e r a t u r e up to 19*+9 may be found i n the book: Indium  Metal 0-Rings:  by Maria Thompson Ludwick: 1950 published by the Indium Corporation of America  United A i r c r a f t Products Inc. Box 1035 Dayton Ohio and 5257 Queen Mary Road, Montreal P.Q.for the helium valve: stainless s t e e l , 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 C i t y , 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  Magnet  Fig  20  Magnetization  C u r r e n t  Curve  for  -  Amps  Analysing  M a g n e t  APPENDIX I I  (a) Magnetic Deflection of Charged  Particles  The equation of motion f o r charged p a r t i c l e s moving normal to a uniform magnetic f i e l d i s : B qv =  mv  (12)  r  where: B  i s magnetic induction, maxwells per cm. (gauss)  q  i s charge on the p a r t i c l e , emu  v is  p a r t i c l e v e l o c i t y , cm per second  m  i s p a r t i c l e mass, gms  r  i s p a r t i c l e path radius of curvature, cm For p a r t i c l e s accelerated through a potential V emu: V q = 1/2 m v  ergs  and equation (12) may be written: B  =  10 r  /  7  where the potential V i s i n Mv. Particle  2 m  V V ' iV '  (13)  Using the values:  Mass  -zv  Charge -zo 1.60199 x 10 emu  p  1.672^8 x 10  d  3.3^35  "  1.60199  QC  6.6^  »  1.60199  6.6M*-2  »  3.20398  the constant 10 7^J~2 m  gm  11  i n equation (13) has the values!  p  l . ¥ i 5 x 10  d  2.0V3  it  06  2.880  »  2.036  "  5  o  an P 0>3 CD Ul CD  0.5  1.0  A c c e l e r a t i n g  Fig  21  D e f l e c t i n g  F i e l d s  1.5  Potential  for  2 0  -  cm  Mv  R a d i u s  2.0  - 58 The above r e l a t i o n of magnetic f i e l d and accelerating potential has been evaluated for these p a r t i c l e s i n the range 0 to 2 Mv, and plotted i n figure 21 f o r 20 cm radius, and i n figure 22 for 30 cm radius.  Figure 23 compares these r a d i i f o r s i n g l y -  charged alphas. On the scale of these f i g u r e s , the curves f o r d and are indistinguishable. The energy of the  p a r t i c l e s i s , of  course, double that of singly-charged p a r t i c l e s accelerated through the same p o t e n t i a l . Figure 20 shows the magnetization ing magnet.  15  The hysteresis loop i s 0.2  curve of the d e f l e c t -  amp wide at a current of  amp. (b)  Energy Resolution The v e r t i c a l separation of the s n i f f e r s and t h e i r d i s -  tance from the centre of the magnetic f i e l d defines a range of energies for the p a r t i c l e s passing between the s n i f f e r s . ing  Neglect-  f r i n g i n g f i e l d e f f e c t s , and assuming a w e l l focussed beam of  p a r t i c l e s entering normal to the magnetic f i e l d , t h i s range of energies may be calculated as follows: (see figure 2*f) r  i s the radius of the path of p a r t i c l e s deflected through 90 degrees, and passing midway between the s n i f f e r s  r'  i s the radius of the highest energy p a r t i c l e s ing  r  a  the s n i f f e r s ; deflected 90 -£degrees  i s the radius of the lowest energy p a r t i c l e s ing  pass-  the s n i f f e r s ; deflected 90 +#degrees  pass-  - 59 *er i s the half-angle subtended at the centre of the magnetic f i e l d by the gap of the s n i f f e r s r < r < r  from figure 2*+: r - r"= AT  r  *r_=  sin ^  =  r ^ sin ^  -  r " (1 + s i n ve-  )  Prom equation (13) above, for accelerating potential V: r  =  k (V)  k  i s a constant  a r _ r " 2 V 4 V  Then  =  V and s i m i l a r l y : For  ^ V V  2/lr =  2 r * s i n ^- .  r  r" ( 1  =  2 r sin r ' (1 - sin*-)  +  sin^-)  /  small angles, both cases may be approximated by:  6 V  2  =  =  200-0$  V T y p i c a l values of  4  V . the energy spread i n the beam, •V  are plotted i n figure 25 f o r four spacings of the s n i f f e r s from the centre of the magnet. was 100 cm.  The spacing used i n these experiments  0  Fig  23  0.5  1.0  A c c e l e r a t i n g  P o t e n t i a l  Deflecting  Fields  for  1.5 -  2.0  Mv.  Singly-Charged  Alphas  -  APPENDIX I I I  60  -  Angular D i s t r i b u t i o n C a l c u l a t i o n s  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 A  z  in  the angular d i s t r i b u t i o n f u n c t i o n : W (#0  = 1 + A  z  cos  z  &  were c a l c u l a t e d w i t h the a i d o f notes by W i l k i n s o n (195*0 and t a b l e s o f c o e f f i c i e n t s by Biedenharn and  (1953)• A n u c l e a r r e a c t i o n i s r e p r e s e n t e d by the n o t a t i o n :  Rose  J,  (1,)  J (I*)  z  z  where J , j , j 7  angular momenta of the i n i t i a l ,  2  are the  i n t e r m e d i a t e , and f i n a l s t a t e s , and  f o r a l p h a p a r t i c l e capture r e a c t i o n s , 1 /  i s the angular momentum  c a r r i e d by the incoming alpha p a r t i c l e , ( s p i n z e r o ) , and 1 £ the m u l t i p o l a r i t y of the emitted gamma r a y , ( s p i n  is  one).  A "pure" t r a n s i t i o n i n v o l v e s the e m i s s i o n of gamma r a y s of a s i n g l e m u l t i p o l a r i t y .  I f more than one m u l t i p o l a r i t y of r a d -  i a t i o n competes i n t h e decay, the t r a n s i t i o n i s termed "mixed". For a r a d i a t i v e capture r e a c t i o n w i t h pure r a d i a t i o n , the angular d i s t r i b u t i o n f u n c t i o n i s o f the form:  kyu. P ^ where K«  2 1, (1/ +  =  2 1/1, A,*. =  F * (1,  + 1)  1)  t h e  =  factor"  -  j) F  (  1  2  %  z  j)  v a l u e s of the F's  g i v e n i n the t a b l e s of Biedenharn P^  tiparticle  and Rose  the Legendre P o l y n o m i a l of order yU.  When the decaying s t a t e 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 v a l u e s of M. appear, the maximum  H)  (ft  •d (» (ft CD  <y>  H  I  c E  V  «  11  w  o  •  9 a "0 9  c  c  U  Pig  2 4  Diagram  for  Energy  Resolution  • o Q.  Calcula  tion  - 61 value  ofy^-  being  the  I n the sisting pole  of  one  part  radiation,  function  has  case  of  of  transitions,  2  of  where  the  smallest  1  mixed  1*  2  -pole  and l  ,  1,  l  or  z  differ  a  by  is  term to  G's  describe  dipole  A  2  one,  parts the  + 2 ^ (-D  of  and  according  to  gives their  interference.  oC  are k  2  given  of  l ' * -  2  distribution  to:  the  *  G ^ U ^1  sum o f  This the  intensities,  2  Z  o) f  expres-  two  plus  2  a  calculated  pure mixing for  below. =1  +  j= j  2  J  + 1)]  z  Coefficients  in W  transitions:  J  i n B i e d e n h a r n and Rose.  1 +  to  the  of  Values  j = 3/2 j^  given  weighted  certain values  Pure  are  normalized  radiations,  cc  con-  form:  [(2j + 1 ) ( 2 1 * + l ) ( 2 1  sion  with radiations  radiation to  ^F^arj-d) The  j.  2  A  5/2  2  c o s ^  j = 7/2  to:  A ^  A^  3/2  - O.ifl  3/2  -  5/2  + 0.125  5/2  + 0.57  5/2  -  7/2  - O.lh  7/2  + 0.80  Pure  quadrupole  j = 3/2 •5,2  to:  transitions:  j=  ^2  0.38  5/2  to:  ^ £  3/2  0.0  3/2  + 0.23  5/2  + 0.5  5/2  - 0.2  7/2  - 0.32  oAl  1.6  0.0  0.4  0.2 Sniffer  Fig  25  C a l c u l a t e d  S e p a r a t i o n  Energy  0.8  0.6  S p r e a d  —  Cms.  in  B e a m  I.  - 62 Mixed  transitions,  magnetic  dipole j  =  and  3/2  electric  to:  A*  J*  3/2 5/2  quadrupole:  + 1  -  - 1  + 0.90  + 1  + 1.^7  - 1  - O.38  j  *  5/2  0.8U,  to:  ©c  3/2 5/2  7/2  + 1  + l.hl  - 1  - 0.8lf  + 1  + 0.16  - 1  + 0.09  + 1  - 0.77 + 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 R e l a t i o n f o r Slow Alpha-Particles and Protons i n A i r  Biedenharn, L.C. ; Rose, M.E. 1953 Rev Mod Phys 2£, 729 Theory of Angular Correlation of Nuclear Radiations Bittner,  J.W. 195^ Rev S c i Inst 2$, 1058 Production of Doubly Charged Helium Ions  B l a t t , J.M. ; Weisskopf, V.F. 1952 John Wiley and Sons, Inc., New York Theoretical Nuclear Physics Bloch, I.; H u l l , M.H. J r . ; Broyles, A.A. ; Bour.icius, W.G. ; Freeman, B..E. ; B r e i t , G. 1951 Rev Mod Phys 22, 1^7 Coulomb Functions f o r Reactions of Protons and AlphaP a r t i c l e s with the Lighter Nuclei Cerineo, M. 1956 Nuclear Physics 2, 113 (North-Holland Publ i s h i n g Co.) Energy Levels of C and Angular Distributions of some Neutron Groups from the B (d,n) Reaction / 0  Chadwick. J . 1932 Proc Roy Soc H 6 A . The Existence of a Neutron Cox, S.A.  692  ; Williamson, R.M. 1957 Phys Rev 10$, 1799 Angular D i s t r i b u t i o n and Correlation Studies of Be , B , and Mg** (d,p) Reactions 9  / 0  - 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 B r i t i s h Columbia The Design and Operation of a Current Integrator, e t c . Evans, N.T.S. ; Parkinson, W.C. 19^ Proc ,Phys 6Z&, 68% Angular Distributions i n the B  /  0  (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 I I , 2. 51 and Nuclear Data Card 57-h-ll B ' 57#5 (verbal) Gamma-Ray Decay Schemes i n B from the Reaction,Be (He , p *) B " 9  / /  3  Gordy, W. ; Ring, H. ; Burg, A.B. 19*f8 Phys Rev 2it, 1191 Nuclear Spins and Quadrupole Moments of B  /  a  and B  „  Green, G.W. 1953 Jour S c i Inst 3 0 , 171 An E l e c t r i c a l l y Operated A l l Metal C a p i l l a r y Vacuum Valve for Adjustable Gas Flow Heiberg, S.A. 195k Ph. D. Thesis, Physics Dept., University of B r i t i s h Columbia Reactions Induced by Fast Neutrons i n Boron T r i f l u o r i d e etc. Heydenburg, N.P. ; Temmer, G.M. 195^ Phys Rev 2k, 1252 ^ Gamma Rays from L i , F , Ne and Na Produced by Alpha-Par t i d e Bombardment of Lithium and Fluorine Z S L  7  Jones, G.A. 5 Wilkinson, D.H. 1952 Phys Rev 88, 1+23 The Reaction L i (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 E d i t i o n 7  - 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 Reaction at Low Energies 3  Lauritsen, T.  1952 Ann Rev Nuc S c i 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 S h e l l Structure  Meyer-Schutzmeister, L. ; Hanna, S.S. 1957 B u l l Am Phys Soc I I , 2, 28 and Nuclear Data Card 57-^-10 B 57#f (verbal) Reaction L i B* Moszkowski, S.A. 1955 North-Holland Pub. Co., Amsterdam Theory of Multipole Radiation, Chapter XIII of Betaand Gamma-Ray Spectroscopy; Siegbahn, K., Editor 7  Robertson,  L.P. 1957 M.A. Thesis, Physics Dept., University of B r i t i s h Columbia  Rutherford, E. 1919 P h i l Mag 2Z? 581 C o l l i s i o n of Alpha P a r t i c l e s 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 S c i Inst 31, 192 A Thermally-Operated Gas Valve Swann, C P . ; Metzger, F.R. ; Rasmussen, V.K. 1957 B u l l Am Phys Soc I I , 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 E x c i t a t i o n 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 E l e c t r o s t a t i c Generator  - 66 Whaling, W. 1957  57 PP)  Kellogg Radiation Lab., Cal Tech, (mimeographed,  The Energy Loss of Charged P a r t i c l e s i n Matter Wilkinson,  D.H. 195^ Cavendish Lab., Cambridge, (mimeographed, 36 pp) I l l u s t r a t i o n s of Angular Correlation Computations Using the Racah C o e f f i c i e n t Methods  Wilkinson,  D.H. 1955 A.E.C.L. Chalk River Project, PD-260 Radiative Transitions i n Light Elements II  Wilkinson,  D.H. 1957 P h y s Rev 1 0 5 , 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 Stripping  of  Spin-Flip  

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