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A comparison of the stopping powers of hydrogen and deuterium and the angular distribution and correlation… Neilson, George Croydon 1952

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fir*  A COMPARISON OF THE STOPPING POWERS OF HYDROGEN AND DEUTERIUM AND THE ANGULAR DISTRIBUTION AND CORRELATION PATTERNS IN PROTON BOMBARDMENT OF F  1 9  AND N  1 5  by George Croydon N e i l s o n  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS , FOR THE DEGREE OF MASTER OF ARTS . i n t h e Department of PHYSICS  We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e s t a n d a r d r e q u i r e d from c a n d i d a t e s f o r t h e degree o f MASTER OF ARTS  Members o f t h e Department of P h y s i c s THE UNIVERSITY OF BRITISH COLUMBIA April,  1952  fix*  ACKNOWLEDGEMENTS  This work was c a r r i e d out under a research grant from the B r i t i s h Columbia Research C o u n c i l .  The author i s g r a t e f u l f o r the c o n t i n u a l encouragement and assistance of Dr..C. A. Barnes, under whose s u p e r v i s i o n t h i s work was c a r r i e d out..  Advice and suggestions from Drs. J . B. Warren and D. B. James were also g r e a t l y appreciated.  The author wishes t o acknowledge the work o f Mr. A. J . Fraser i n connection w i t h the machining of the s c a t t e r chamber.  He i s indebted to Drs. H.'G. Thode and W. H. Fleming, McMaster Univ e r s i t y , f o r the analysis of the deuterium gas.  F i n a l l y , he would l i k e t o thank the B r i t i s h Columbia Telephone Company Limited f o r the scholarship awarded him.  INDEX Page CHAPTER I . A COMPARISON OF THE STOPPING POWERS OF HYDROGEN AND DEUTERIUM I. II.  III.  INTRODUCTION  '...v.  A.  Thin I o n i z a t i o n Chamber  B.  Other Methods of Measuring Alpha P a r t i c l e Ranges  •.  Chamber Electronics .... 1. Power Supplies 2. Pulse Formation and Requirements of A m p l i f i e r ... 3. A m p l i f i e r s C. Deuterium Generator EXPERIMENTAL PROCEDURE  I; 5  F i n a l A m p l i f i e r Adjustments Source Preparation Generation of Deuterium P u r i f i c a t i o n and Handling of Gases C a l i b r a t i o n of the Source Micrometer  7 8 8 8 10 12 13 Ik 15> , 16 17  RESULTS AND DISCUSSIONS A. B. C. D.  VI.  1  DESCRIPTION OF THE APPARATUS '  A. B. C. D. E. V.  '.  METHODS OF MEASURING THE RANGE OF ALPHA PARTICLES  A. B.  IV.  .  Corrections t o Experimental Data Results Possible Sources of E r r o r i n Results Comparison w i t h Previous Data  CONCLUSIONS  CHAPTER II.  19 20 20 23 2U  .  ANGULAR DISTRIBUTION AND CORRELATION PATTERNS IN PROTON BOMBARDMENT OF F  19  AND N  li?  PART A - RADIATION PATTERNS FROM EXCITED STATES OF QI.  INTRODUCTION  26  II.  III.  DESCRIPTION OF APPARATUS A. ELECTRONIC EQUIPMENT NECESSARY  -30  B. REACTION CHAMBER  30 32  FILMS FROM ORGANIC PHOSPHORS  35  IV. . RESPONSE OF THIN ORGANIC FILMS TO ALPHA PARTICLES V. CONCLUSIONS  37  ;  PART B - ANGULAR.DISTRIBUTIONS FOR GROUND-STATE ALPHA PARTICLES FROM N^POQCJ- REACTION 2  38  •I. . INTRODUCTION II. THEORY  39  A. GENERAL PRINCIPLES OF TWO-STAGE PROCESSES B. CALCULATED ANGULAR DISTRIBUTIONS FOR THE GROUND-STATE ALPHA PARTICLES IN THE N III.  (P oc )C  UO  REACTION  DESCRIPTION OF APPARATUS KH  A. REACTION CHAMBER IV.  B. COUNTER AND AUXILIARY APPARATUS DISCUSSION  APPENDIX I  - SAMPLE CALCULATION  .'.  (  HH . H$  ' .'46  APPENDIX II - NUMBER OF SCATTERED PROTONS AS A FUNCTION.OF ENERGY ' • AND ANGLE ... • k9 APPENDIX III - RATIO OF TRUE TO CHANCE COINCIDENCES FOR THE (P-^ ANGULAR CORRELATION EXPERIMENT  50  APPENDIX IV - EXCITON THEORY  52 ..•  APPENDIX V  - ALPHA PARTICLE RANGES FROM THE N^PO^C REACTION AS A FUNCTION OF(^(LABORATORY COORDINATES) AND INCIDENT PROTON ENERGY  53  BIBLIOGRAPHY  $K  ABSTRACT  56  ILLUSTRATIONS Plate I.  II. III. IV. V. VI. VII. VIII. IX. X. XI. XII.  Facing Page The S p e c i f i c I o n i z a t i o n f o r a Single Alpha P a r t i c l e Track, Measured from the End of the Track  2  Comparison of D i f f e r e n t Methods of Measuring Ranges  3  Shallow I o n i z a t i o n Chamber  7  Pulse Formation i n a P a r a l l e l Plate Chamber  9  Pre-Amplif i e r  10  Main A m p l i f i e r  11  Deuterium Generator  13  Signal-to-Noise, Argon i n Chamber S t r a g g l i n g f o r D i f f e r e n t Source Thicknesses  15'  Uncorrected Experimental Number-Distance Curves  20  Experimental Range Number Curve w i t h a•Photo-Multiplier and an Anthracene C r y s t a l Angular C o r r e l a t i o n Between Alpha P a r t i c l e s and Gamma Rays i n the Reaction F (p<x ^ ) 0 19  XIII. XIV. XV. XVI.  XVII. XVIII. XXLX. XX. XXI.  Ill  1 6  2k 27  S c a t t e r i n g Chamber  30  Block Diagram of the E l e c t r o n i c s Required f o r a HighSpeed Coincidence Angular C o r r e l a t i o n Experiment  31  Response of a Thick Section of Anthracene to Alpha P a r t i c l e s of D i f f e r e n t Energy  35  Response of a Thin Section of Anthracene to Alpha P a r t i c l e s of D i f f e r e n t Energy  36  Response of Anthracene to Alpha P a r t i c l e s  37  Thin Window S c a t t e r i n g Chamber  HK  Rutherford S c a t t e r i n g of Protons  h9  R e l a t i v e Response of Anthracene to Alpha P a r t i c l e s and Protons f o r D i f f e r e n t F i l m Thicknesses Range of Ground-State Alpha P a r t i c l e s from N ^(p<x.)C  £2  i n Lab. Coordinates as a Function of (ft and Proton Energy...  $3  1  12  CHATTER I - A COMPARISON OF THE STOPPING POWERS OF HYDROGEN AND DEUTERIUM  I.  INTRODUCTION  The process of energy l o s s dx  by alpha p a r t i c l e s i n passing through •  matter has been i n v e s t i g a t e d by many authors and a t h e o r e t i c a l r e l a t i o n as deduced by Bethe"*" i s given as * "dE = UTTZ e N y i o 2 m v 2  U  z  g  2 )  m  (-—) i s the energy l o s s f o r c o l l i s i o n processes f o r p a r t i c l e s of charge cue eZ and speed v moving through an absorber of e f f e c t i v e nuclear charge Z * , e f f e c t i v e i o n i z a t i o n p o t e n t i a l I and atomic density N. m i s the mass of . an e l e c t r o n . In the d e r i v a t i o n of t h i s formula i t i s assumed that a l l energy i s l o s t i n the i o n i z a t i o n and e x c i t a t i o n of the atoms of the stopping material.  In the case of the two stable isotopes of hydrogen, the i o n i z a t i o n  . p o t e n t i a l of the e l e c t r o n w i l l be only s l i g h t l y a l t e r e d by the presence of the e x t r a neutron i n the deuterium nucleus. 2 3  H  Most previous experimental work ' ' on the stopping powers, of hydrogen and deuterium would seem to i n d i c a t e that the stopping powers are very s i m i l a r , which i s i n agreement w i t h the t h e o r e t i c a l p r e d i c t i o n s .  In 19k9>  however, i t was reported by Harrick and E i c h h o l g ^ that the stopping power of deuterium was approximately 6% greater than the stopping power of hydro-  cm  Z o l . ... i.... i .... t . . . . l.... I.... I .... I 25  2.o  f.S  '.o  o.i  o  cm  THE SPECIFIC IONIZATION FOR A SINGLE ALPHA-PARTICLE MEASURED  TRACK,  FROM WE END OF THE  TRACK  PLATE  I  2 gen.  This r e s u l t cast doubt on the v a l i d i t y of the t h e o r e t i c a l assumption  that the energy l o s s f o r alpha p a r t i c l e s i s due only t o i o n i z a t i o n and e x c i t a t i o n of the atoms. I t was considered necessary, therefore, to make a new measurement of the stopping power of deuterium i n order to resolve the apparent d i s c r e p ancy between theory and experiment.  THEORY The mean range f o r a s i n g l e alpha p a r t i c l e can be convputed from equat i o n ( l ) by using the r e l a t i o n R R  =/  E dx  -/  (-dEj^dE (2) o I dx The stopping power (-i^?.) of an absorber f o r an alpha p a r t i c l e of a dx given energy i s r e l a t e d t o the s p e c i f i c i o n i z a t i o n by ' ;  J  " I  - c p  •  OJ.  £ i s the mean energy associated w i t h the formation of an i o n p a i r .  Plate  I shows the r e l a t i v e s p e c i f i c i o n i z a t i o n f o r a s i n g l e alpha p a r t i c l e , of mean range (3.8U2 cm), measured from the end of the range.  The increase  i n s p e c i f i c i o n i z a t i o n of the alpha p a r t i c l e near the end of i t s range i s expected, since - ^ ^ i j o c p . dx v As each alpha p a r t i c l e makes o n l y a f i n i t e number of c o l l i s i o n s and each c o l l i s i o n has a discrete energy l o s s , i t i s to be expected that the ranges of i n d i v i d u a l alpha p a r t i c l e s w i l l have a d i s t r i b u t i o n about some mean range.  I f R i s the mean range of an alpha p a r t i c l e and ydR gives  the f r a c t i o n of alpha p a r t i c l e s i n the beam which- comes to r e s t between R and R plus dR from the source, then the curve_y can be approximated by the Gaussian r e l a t i o n  •  \c  \  a  •  V  s  3.60  3.70  3.80  V 3.90  4.00  cm  COMPARISON OF DIFFERENT METHODS OF MEASURING RANGES PLATE  H  y  =  ( T r i e ) " W -(R-R) /oc 2  (U)  2  c*; i s the h a l f - w i d t h at i of the d i f f e r e n t i a l range curve ( P l a t e I I ) . e P l a t e I I shows the f o l l o w i n g range r e l a t i o n s f o r polonium alpha p a r t 7  icles i n a i r : Curve a. a number-distance curve w i t h a number-distance extrapolated number range Curve b.  at 3.897 cm  a d i f f e r e n t i a l range curve with mean range 3-8ij.2 cm  Curve c. a p o r t i o n of a s p e c i f i c i o n i z a t i o n curve f o r an alpha p a r t i c l e beam w i t h an i o n i z a t i o n extrapolated range a t 3.870 cm Curve d. a p o r t i o n of a s p e c i f i c i o n i z a t i o n curve f o r a s i n g l e alpha p a r t i c l e of mean range 3»8Ij.2 cm. I t can be seen that the extrapolated i o n i z a t i o n range (Rj) i s not equal to the extrapolated number-distance range.  The r e l a t i o n between B^ and R  i s given by  Rn-R = iTT^oc  (5)  The stopping power of a substance can be defined i n a number of ways, but the most common d e f i n i t i o n i s the r a t i o of the mean range i n the substance to that i n a standard m a t e r i a l , u s u a l l y a i r . The mean ranges are measured at 1J?°C and 760 mm mercury.  II.  A.  METHODS OF MEASURING THE RANGE OF ALPHA PARTICLES  THIN IONIZATION CHAMBER ' 2  8,9  In analyzing data from t h i n i o n i z a t i o n chambers, the usual procedure i s to p l o t a number-distance curve, obtain the extrapolated number range, and determine the mean range by d i r e c t s u b s t i t u t i o n i n t o equation ( 3 ) . In analyzing data from s p e c i f i c i o n i z a t i o n measurements, however, the mean range can be determined from the extrapolated i o n i z a t i o n range only from the e m p i r i c a l r e l a t i o n ^ - R-J--R- -  (.8oC-.06)mm  (6)  Extrapolated number-distance range measurements s u f f e r from chamber depth c o r r e c t i o n s , i . e . one'must know the minimum depth that the p a r t i c l e has to traverse i n s i d e the chamber to produce a pulse that w i l l be counted.  To make t h i s c o r r e c t i o n , i t i s necessary to know the v a r i a t i o n of  i o n i z a t i o n w i t h distance from the end of the range, as w e l l as the s i g n a l to-noise r a t i o , a m p l i f i e r response and bias v o l t s . The observed d i s t r i b u t i o n i n range always has a greater value f o r oc  }  the range s t r a g g l i n g parameter, than the t h e o r e t i c a l value of .062 f o r 8 air.  L i v i n g s t o n and Holloway  have been able to account f o r t h i s increase  by i n c l u d i n g a l l sources of s t r a g g l i n g : 1.  Range S t r a g g l i n g - Defined as the i width of y ( d i f f e r e n t i a l range  curve, P l a t e I I ) at i of i t s maximum. e 2. • Noise S t r a g g l i n g - The pulse produced i n the chamber e i t h e r adds to or"subtracts from the random noise pulses producing a d d i t i o n a l s t r a g gling.  5  3.  I o n i z a t i o n S t r a g g l i n g - The energy required f o r i o n i z a t i o n i s not  constant but v a r i e s about a mean value, approximately 32 v o l t s per i o n pair i n a i r . K* Angular S t r a g g l i n g -  Due to angular d e v i a t i o n s , the paths are not  the same length f o r various alpha p a r t i c l e s , thus a s t r a g g l i n g e f f e c t i s produced. 5>. F o i l S t r a g g l i n g - .Slight non-uniformities i n the f o i l vriiich form the chamber window can l e a d to an increase i n s t r a g g l i n g . 6.  Source Straggling - This and the angular s t r a g g l i n g are the o n l y  e f f e c t s mentioned so f a r t h a t are not symmetrical about the mean range. Source s t r a g g l i n g decreases the mean range and can be caused by source thickness, roughness or d i r t i n e s s .  B. OTHER METHODS OF MEASURING ALPHA PARTICLE RANGES *" 107  1.  D i f f e r e n t i a l I o n i z a t i o n Chamber  18  10  The i o n i z a t i o n from two shallow i o n i z a t i o n chambers w i t h opposite p o t e n t i a l s i s c o l l e c t e d on a common g r i d .  E s s e n t i a l l y , t h i s method meas-  ures the p o s i t i o n of maximum change of i o n i z a t i o n along the path of an alpha p a r t i c l e and leads to a d i r e c t determination of the mean range. 12  2.  S c i n t i l l a t i o n Method Alpha parti.cles may be counted on a ZnS screen placed between the  source and the observer.  Ranges determined by t h i s method are u s u a l l y  short due to the d i f f i c u l t y of counting very small f l a s h e s v i s u a l l y . This method i s much more e f f e c t i v e i f a p h o t o - m u l t i p l i e r tube i s used i n place of v i s u a l counting. 3 . Wilson Cloud Chamber A p a i r of stereoscopic p i c t u r e s enables one t o measure the track ,  lengths and leads d i r e c t l y to a determination of the mean range.  The d i s -  advantages of t h i s method are (a) unknown composition of gases at time of expansion, and (b) the r a p i d f a l l i n g o f f of the i o n i z a t i o n , making the l a s t p a r t of the range hard t o see. h*  Photographic Method Any i o n i z i n g r a d i a t i o n or p a r t i c l e w i l l produce a c t i v a t i o n  absorption i n the emulsion of a photographic p l a t e .  on  This method i s not  too good f o r low energy alpha p a r t i c l e s because of the coarseness of the photographic g r a i n s , and, as a r u l e , i s used only f o r a check on the energy of the alpha p a r t i c l e s . 16,17,18  5.  Magnetic  Deflection  The v e l o c i t y of a charged p a r t i c l e can be found from the amount that i t i s bent when passed through a magnetic f i e l d .  This magnetic  d e f l e c t i o n method leads to very accurate values f o r the alpha p a r t i c l e v e l o c i t y , but, unfortunately, the range can be only approximated from the measured v e l o c i t i e s as there i s no p r e c i s e range energy r e l a t i o n .  0pen  BE>  !  H  '—COPPER  J=iL  )  PREAMPLIFIER MICA  UARTZ/t ^toe/re  ted.  SHALLOW QcOLUMATED SOURCE © A * M PITCH SCREW ® REGISTER  IONIZATION  CHAMBER  © MICROMETER © CHAMBER ® H.T. OUTPUT  PLATE HI  Q ALUMINUM WINDOW (8) COLLECTOR  (5) RUBBER GASKET  D  7  III.  A.  DESCRIPTION OF THE APPARATUS  CHAMBER P l a t e I I I shows a c r o s s - s e c t i o n a l view of the f o u r sections of the  chamber. Section I contains the movable platform upon which the c o l l i m a t e d source i s mounted. mm p i t c h .  The source p o s i t i o n i s set by r o t a t i n g a screw of one  Complete r e v o l u t i o n s are r e g i s t e r e d on a mechanical counter and  p a r t i a l turns are read to the nearest 1/100 mm from a c a l i b r a t e d drum. Section I I shows the t h i n chamber i t s e l f and the method of i n s u l a t i n g the c o l l e c t o r and the high tension face plate-.  The c o l l i m a t e d alpha p a r t -  i c l e s enter the t h i n chamber through an aluminum window which i s pasted to the copper face of the chamber w i t h aqua-dag. The aluminum window has an a i r - e q u i v a l e n t of approximately 1.2 cm.  This thickness f o r the alumi-  num f o i l was chosen f o r a number of reasons: (a) the face must be r i g i d to reduce "microphonics, (b) t h i s thickness i s more uniform than t h i n n e r f o i l s , and (c) the chamber would not be deep enough f o r the f u l l range of a polonium alpha p a r t i c l e i n hydrogen or deuterium without i n c r e a s i n g the pressure above atmospheric or i n t e r p o s i n g other absorbers. I t i s to be noted t h a t the c o l l e c t o r must have the best i n s u l a t i o n p o s s i b l e i n order that none of the charge c o l l e c t e d s h a l l be l o s t through, or soaked up by, the i n s u l a t o r .  The i n s u l a t o r f o r the high voltage e l e c -  trode need not be of such high q u a l i t y , but i t i s necessary that the high voltage input l e a d should have a l a r g e c a p a c i t y to ground i n order t o by-  8 pass any electromagnetic p i c k up before i t reaches the chamber.  I t i s of  the utmost importance that the capacity of the chamber be kept as low as p o s s i b l e so that the voltage w i l l be a maximum f o r a given charge c o l l e c t ed. The chamber depth of 3 mm was chosen f o r t h i s experiment as t h i s i s deep enough to give a good s i g n a l f o r hydrogen and i s l e s s than 1.$% of the t o t a l path length.  B.  ELECTRONICS . 1.  Power Supplies Two regulated power supplies were used to supply the power f o r the  amplifiers.  One was used as a  300 v o l t p l a t e supply and the other as a  v a r i a b l e negative r a i l from -100 to -15>0. In order to ensure complete i s o l a t i o n from e a r l i e r a m p l i f i e r stages and from the f l u c t u a t i o n s that are inherent i n a.c. voltage s u p p l i e s , a b a t t e r y supply was used f o r the p l a t e voltage of the p r e - a m p l i f i e r . - A l l tubes were heated w i t h a 6 v o l t d.c. storage b a t t e r y and thus any a.c. coupling between filaments and cathodes was eliminated. The high voltage supply was a conventional regulated supply and was capable of d e l i v e r i n g 2000 v o l t s w i t h very l i t t l e a.c. r i p p l e .  I t was  necessary to place a f i l t e r network i n the high tension l i n e j u s t before i t entered the chamber, i n order to eliminate any spurious counts due to electromagnetic p i c k up. 2  •  Pulse Formation i n P a r a l l e l P l a t e I o n i z a t i o n Chambers ^1  As a l l g a s - f i l l e d counters and chambers f u n c t i o n by the separation and c o l l e c t i o n of the p o s i t i v e and negative ions formed i n the gas, i t i s important t o know hovir a pulse i s formed.  I f the c o l l e c t i n g electrode i s  p o s i t i v e and has a, capacity C, i t would appear that the change of p o t e n t i a l  t.  t  PULSE FORMATION IN A PARALLEL PLATE CHAMBER  PLATE IV  of the. c o l l e c t o r i s due t o a charge -e being placed on a capacity C.  This  o v e r - s i m p l i f i e d p i c t u r e i s wrong because i t neglects the i n d u c t i o n e f f e c t s which the two ions have been e x e r t i n g since the c r e a t i o n of the i o n p a i r . I f at a time t a f t e r ' t h e i o n p a i r formation, the p o s i t i v e electrode has induced charges - q ( t ) and - q _ ( t ) , the p o t e n t i a l on that electrode w i l l be +  p(t)  = q»(t)+g_(t) C  .....(7)  ;  where P(o) = 0 when.q (o) = -q_(o). +  I t i s i n t e r e s t i n g to note that the charges induced on the other e l e c trode are complementary t o those considered here, and, therefore, the pulses formed on the tyro electrodes are i d e n t i c a l in' form but opposite i n sign.  When the negative i o n has been completely c o l l e c t e d at time t-^, the  p o t e n t i a l of the c o l l e c t o r w i l l be  The s i m p l i f i e d p i c t u r e i n which the p o t e n t i a l would be ~£ when the charge c -e has been c o l l e c t e d i s thus i n c o r r e c t , and corresponds t o the case of complete c o l l e c t i o n of both negative and p o s i t i v e i o n s .  Plate IV shows  the a c t u a l pulse shape. As the c o l l e c t i o n time t  2  (Plate IV) of the p o s i t i v e ions i s more  than 1000 times longer than that of f r e e e l e c t r o n s , i t i s advisable t o construct an a m p l i f i e r with a short time constant so that e l e c t r o n c o l l e c t i o n alone i s responsible f o r the pulse a m p l i f i e d . This i s c a l l e d a f a s t chamber as compared to a slow chamber i n which the p o s i t i v e ions also are c o l l e c t e d and give an a d d i t i o n t o the pulse height (see P l a t e I V ) .  Unfort-  unately, w i t h a slow chamber, the c l i p p i n g time (shortest RG time constant of a m p l i f i e r ) must be made longer than the pulse r i s e time t  2  (Plate IV).  This.method has the disadvantage of a slow maximum'counting r a t e , and  PRE-AMP11F1ER ~ PLATE V  10 g r e a t l y increased microphonics. For a f a s t chamber w i t h e l e c t r o n c o l l e c t i o n only {tr^?  R C ^ t - ^ ) , the  pulse p r o f i l e i s given by P(t) where Q^. =  q (o) = +  =  q-(t)+Q»  constant.  3» A m p l i f i e r s The output s i g n a l of an a m p l i f i e r u s u a l l y has superimposed on i t a v a r i e t y of extraneous s i g n a l components termed "noise".  The various  types of noise can be c l a s s i f i e d according to t h e i r o r i g i n as f o l l o w s : a.  Hum introduced from power supply  b.  microphonic noise  c.  noise picked up from e x t e r n a l sources  d.  noise a r i s i n g from d e f e c t i v e components  e.  inherent tube and r e s i s t o r noise  T h e o r e t i c a l l y , the o n l y type of noise that can not be completely e l i m inated i s that due to tube and r e s i s t o r n o i s e .  In p r a c t i c e , p e r f e c t i o n i s  hard to o b t a i n , but the various types of noise can be g r e a t l y reduced w i t h care.  In c o n s t r u c t i n g the a m p l i f i e r s (Plates V, V I ) , the f o l l o w i n g p o i n t s  were considered. The high mutual conductance pentodes that were used are extremely microphonic as Trail as very s u s c e p t i b l e to hum p i c k up from an a.c. operated heater.  To reduce these f a c t o r s a d.c. heater supply was used and  the a m p l i f i e r and chamber were mounted on s o f t sponge rubber as a p r o t e c t i o n against shock.  A l s o , i t was found necessary to reduce the l o w - f r e -  quency response to l e s s e n microphonic p i c k up. Electromagnetic p i c k up was g r e a t l y reduced by proper s h i e l d i n g of  10 K  + 2<X> 5K  5K IOOK WW  IOOK WU/  50K  68K  «*-—  SOK . •<— ISK  0 (i  B"  B 120K  68*  OOSuF  A'  NH—  HI*  01  Kyi  o/  0/  4o  01 SK  -Hl-o 6"'  /SO  5K  2*F ±* S470K  JuF~>±  47* - Z7K  /OK  S Z7K  < 27*  —  *>Z7K.  '<— J-  X  /20K  /0K  ^—• 47K  -I50V  6AC7U  MAIN  AMPLIFIER  PLATE E Z  1  6,4 <? 7  11 the p r e - a m p l i f i e r which was completely contained i n a copper tube.  Also  a common ground was used i n an e f f o r t to eliminate any electromagnetic pick-up loops. For a pulse a m p l i f i e r having a s i n g l e RC c u t - o f f at low and high f r e quencies, the equivalent rms noise charge q  n  on the capacity of the detec-  19  tor can be c a l c u l a t e d as q  n  "  ( g f R 2 f R i ) T&ttJ  + 2Tr TR (e+ )  +  k  s  (10)  2  C l  Where R i s the input resistance between g r i d and ground, Rg i s the equival e n t input noise resistance of the f i r s t tube due to g r i d current.  R is s  the equivalent s e r i e s g r i d noise r e s i s t a n c e commonly used t o express the magnitude of shot e f f e c t voltages i n the p l a t e c i r c u i t .  C i s the detector  capacity, C-^ i s the input capacitance of the a m p l i f i e r , K i s Boltzman's constant and T i s the temperature.  The frequencies f-^ and fg' are the low-  er and upper §• power frequencies.  To reduce the f i r s t t e r m the g r i d of the  input 6AK5 was l e f t f l o a t i n g ( R — A p l o t o f Q (=  q ) against C (chamber capacity) shows a l i n e a r  n  n  r e l a t i o n e x i s t s between the two; thus the f i r s t two terms, which are due to thermal noise and g r i d current r e s p e c t i v e l y , are n e g l i g i b l e compared to the noise from the shot e f f e c t .  In order t o reduce the shot e f f e c t ,  the input 6AK5> was triode-connected as the mean-square shot noise of a pentode i s g e n e r a l l y three times greater than t h a t of the same tube t r i o d e connected"'' , due to p a r t i t i o n noise. 9  The 6AK5 used was hand-picked f o r  i t s low noise as a l l 6AK5"'s are not e q u a l l y good. Elmore and S a n d s  19  give an experimentally determined curve showing  the signal-to-noise r a t i o as a f u n c t i o n of c l i p p i n g time.  This curve was  found u s e f u l as a guide i n s e l e c t i n g the proper c l i p p i n g time.  12 Some of the advantages of the push-pull main a m p l i f i e r used are: 1.  Changes i n the main supply current are very s m a l l .  The tubes are  self-compensating as p a i r s , r e a c t i o n through the supply l i n e i s t h u s reducv  ed, and the a m p l i f i e r i s more n e a r l y independent of the impedence of the power supply, removing the n e c e s s i t y f o r large decoupling condensers. 2.  E i t h e r sign of i n p u t may be used and e i t h e r sign of output i s a v a i l -  able. 3.  The g a i n i s large only f o r out-of-phase o r d i f f e r e n t i a l inputs at  the g r i d s by .virtue of the use of the cathode-coupling r e s i s t o r s of the long-tail pair.  Hence, in-phase e f f e c t s such as hum on the supply l i n e  cause the g r i d s to r i s e and f a l l , but the cathodes do l i k e w i s e and there is l i t t l e amplification. U.  The gain i s a f u n c t i o n mainly of the tube current and i s more o r  l e s s independent of the combination of g r i d and screen voltages used. More p a r t i c u l a r l y , i t i s independent of the cathode emission and gain i s s t a b i l i z e d against changes i n heater voltage. Gain c o n t r o l i s obtained by the v a r i a b l e low resistance j o i n i n g the cathodes which gives smooth noise-free a c t i o n . 6.  The a m p l i f i e r i s l i n e a r over a l a r g e r range of output pulses than  a s i n g l e tube a m p l i f i e r .  C.  DEUTERIUM GENERATOR The deuterium generator (Plate V I I ) consists of an e l e c t r o l y s i s tube  to generate the deuterium from heavy water, a pressure e q u a l i z e r to keep the deuterium separate from the oxygen, a phosphorous pentoxide dryer, a l i q u i d a i r t r a p , a gas h o l d e r , and a mercury pump.to t r a n s f e r the deuterium i n t o the storage f l a s k .  LIQUID AIR TRAP  RESERVOIR  DEUTERIUM GENERATOR ~  PLATE  M  .1  13  IV.  A.  EXPERIMENTAL PROCEDURE  FINAL AMPLIFIER ADJUSTMENTS The f i n a l value s e l e c t e d f o r the c l i p p i n g time was determined e x p e r i -  mentally w i t h hydrogen i n the chamber as the range of t h i s gas was t o be measured.  The maximum s i g n a l - t o - n o i s e r a t i o was r e a l i z e d w i t h a c l i p p i n g  .time of 10 microseconds, which i s approximately the value p r e d i c t e d by the  19 • curves given i n Elmore and Sands  . I t i s to be noted that t h i s i s not  the optimum value f o r the c l i p p i n g time i f the gas used forms negative ions, as, f o r example, a i r . I t i s advisable, t h e r e f o r e , t o use a gas such as argon f o r a standard because both argon and hydrogen allow e l e c t r o n c o l l e c t i o n and w i l l give pulses o f the same order of r i s e time. I t w i l l be noted that maximum s i g n a l - t o - n o i s e r a t i o does not imply maximum pulse height.  A l a r g e r pulse w i l l be produced i f the c l i p p i n g  time i s made long enough t o include the r i s e due t o the p o s i t i v e i o n c o l l e c t i o n , but when t h i s i s done, microphonics increase the noise l e v e l so that there i s a net l o s s i n s i g n a l - t o - n o i s e r a t i o . An optimum value f o r the chamber voltage was chosen i n much the same -  manner as f o r the c l i p p i n g time, but, as would be expected, the s i g n a l - t o noise r a t i o does not depend on the chamber voltage as long as the voltage i s high enough f o r complete e l e c t r o n c o l l e c t i o n . The chamber i t s e l f was thoroughly washed f i r s t w i t h concentrated n i t r i c a c i d then w i t h a l c o h o l i n an e f f o r t t o reduce the background due t o alpha p a r t i c l e s from the w a l l s , and the i n s i d e was painted w i t h pure  PUTEWT SIGNAL TO NOISE. ARGON IN CHAMBER  S  /  N  -  '9S S55 '495  3000  2000  WNTS PER MINUTE  4000  *  /ooo DISCRIMINATOR  to  f5  20  25  VOLTS 30  36  4o  45  =  8.25  .•nil aqua-dag.  B.  The background f i n a l l y obtained was approximately 30  SOURCE PREPARATION ' > 20  21  counts/min.  2 2  Approximately a dozen o l d radon needles were, a v a i l a b l e f o r the prepara t i o n of a polonium source.  The procedure f o r preparing the polonium  source  "was as f o l l o w s . The radon needles were smashed and d i s s o l v e d i n concentrated n i t r i c a c i d , then evaporated to dryness.  The residue was next d i s s o l v e d i n con-  centrated h y d r o c h l o r i c a c i d and again evaporated to dryness. process was repeated at l e a s t three times.  This l a t t e r  ( A l l evaporation was done w i t h  a water bath, not w i t h an open flame, to avoid apattering.) F i n a l l y , the residue was d i s s o l v e d i n .£N  HC1.  The polonium was then separated from the RaDEF s o l u t i o n as f o l l o w s . A s i l v e r button was mounted on a source holder and p o l i s h e d .  One drop of  'the RaDEF s o l u t i o n was put onto the s i l v e r button, and a f t e r one minute, the button was immersed i n a l a r g e volume of water.  The f i l m of polonium  thus deposited Y/as so t h i n that i t was v i s i b l e only as a s l i g h t c o l o u r i n g to the s i l v e r when placed under, a strong l i g h t . The t h i n source, prepared as o u t l i n e d above, was 'compared to a much stronger source prepared by r o t a t i n g the s i l v e r button i n the RaDEF s o l u -  2'2 t i o n u n t i l a l l the polonium had been deposited by electrochemical a c t i o n P l a t e IX shows the number-distance  curves f o r the two sources.  The  thin  source i s much weaker as would be expected, and, t h e r e f o r e , i t s maximum counting rate has been normalized to that of the stronger source to allow a d i r e c t comparison.  Curves A and B are the curves f o r the t h i c k source  and the t h i n source, r e s p e c t i v e l y , while curve C shows the range s t r a g g l i n g expected f o r an i n f i n i t e l y t h i n source.  I t i s to be noted that curves A  THEORETICAL FOR RANGE  PLATE LX STRUGGLING FOR DIFFERENT  SOURCE THICKNESS  CURVE STRAGGLING  ONLY TUIN THICK  SOURCE SOURCE  3.897  15  and B include other s t r a g g l i n g f a c t o r s besides the range s t r a g g l i n g .  C.  GENERATION OF DEUTERIUM The operation of the deuterium generator can best be understood w i t h  reference to Plate V I I . l y evacuated.  To commence operation the system must be  complete-  This evacuation i s best accomplished..by pumping through taps  8 and 10 simultaneously. Taps 5 and 7 are c l o s e d a f t e r the r e s e r v o i r and mercury pump are f u l l of mercury. h and 6 are open. 2, 3s k,  Tap 9 i s also c l o s e d while taps 1,  2,  When the system has been completely evacuated, taps  3,' 1,  6, 8 and 10 are c l o s e d . Heavy.'water w i t h potassium sulphate .(lgm/  25>cc) as e l e c t r o l y t e can now be introduced i n t o the e l e c t r o l y s i s chamber through tap .10, being sure not to admit any a i r .  The electrodes can  now  be connected and a current of approximately .5 amps passed through the e l e c trolyte.  Thr f i r s t stage i n the operation i s very c r i t i c a l and the gener-  ator must be watched c o n s t a n t l y ; otherwise, too large a pressure w i l l be b u i l t up i n the e l e c t r o l y s i s tube. Taps 1,  2, 3 , h and 5 are opened as atmospheric pressure i s g r a d u a l l y  b u i l t up i n each s e c t i o n of the apparatus.  Stopcock 9 i s l e f t open a f t e r  atmospheric pressure i s obtained i n the tubes'themselves.  Once tap 5 i s  opened the reservoj.r i s connected and the generator can be l e f t to operate by i t s e l f u n t i l the r e s e r v o i r i s f i l l e d .  While the storage tank i s below'  atmospheric pressure, the r e s e r v o i r can be emptied by simply opening tap 6 c a u t i o u s l y and drawing the deuterium i n t o the storage tank.  A f t e r the s t o r -  age tank reaches atmospheric pressure the mercury pump must be used as f o l lows.  The generator i s shut o f f and. tap U c l o s e d . Taps 5 and 7 are then  opened and by lowering.the mercury l e v e l i n the pump the r e s e r v o i r i s emptied.  Now tap 5 i s c l o s e d and tap 6 i s opened, and once more the mer-  16 • cury l e v e l i s r a i s e d , f o r c i n g the deuterium i n t o the storage tank.  The  e n t i r e process i s repeated u n t i l the storage tank contains the required amount' of deuterium.  The phosphorous pentoxide and the l i q u i d a i r trap  remove any water vapour that may come through the o i l pressure e q u a l i z e r . (Water vapour pressure at -190°C i s l e s s than 1 0 ^ mm). -  D.  PURIFICATION AND HANDLING OF GASES As the chamber was pumped down to approximately 10 microns w i t h a  mechanical fore-pump before admitting the gases, any r e s i d u a l gas would amountto o n l y about p a r t i n 10,000, which i s c e r t a i n l y i n s i g n i f i c a n t . The heavy water used i n the deuterium generator was quoted as 99»5% pure heavy water.  Upon f i l l i n g the i o n i z a t i o n chamber w i t h deuterium, the  f i r s t measurements i n d i c a t e d that the stopping power of the deuterium was about 6% greater than that of hydrogen.  The e l e c t r o l y t i c hydrogen and  .argon were obtained i n l e c t u r e b o t t l e s at 15>00 Ibs/sq i n c h and were o f high p u r i t y - b e t t e r than 99.9%.  Water vapour on the chamber was e l i m i n -  ated by means of a l i q u i d a i r t r a p . As the r e s u l t s f o r the stopping power of t h i s deuterium were not cons i s t e n t , i t was decided.that the generator must have o r i g i n a l l y contained some a i r i n the r e s e r v o i r due to f a u l t y pumping, or to a small leak when the r e s e r v o i r was below atmospheric pressure.  In order to save the deuter-  ium already generated, i t was decided to pump the deuterium out of the i o n i zation chamber and p u r i f y i t by passing i t through a palladium l e a d . When t h i s was done, the o r i g i n a l discrepancy between the stopping powers of deuterium and hydrogen was non-existent . For consistency, the hydrogen also was introduced i n t o the chamber through a palladium l e a k .  This process  d i d not change the range, which was i d e n t i c a l w i t h t h a t obtained when the hydrogen was admitted d i r e c t l y i n t o the chamber.  17  As a f u r t h e r check gas samples were taken and sent f o r a n a l y s i s , (see P o s s i b l e Sources of E r r o r i n R e s u l t s , Section V. -C) •  E.  CALIBRATION OF THE SOURCE MICROMETER Even a f t e r a l l p o s s i b l e precautions f o r reducing spurious noise e f f e c t s  had been taken, i t was found necessary t o take a l l readings at night when a c c o u s t i c a l and e l e c t r i c a l noise were at a minimum. The a c t u a l performance of the complete system can be judged by the signal-to-noise r a t i o obtained (see P l a t e V I I I ) f o r 3 mm.  a chamber depth of  With argon i n the chamber a s i g n a l - t o - n o i s e r a t i o of 9 was obtained  and w i t h hydrogen (or deuterium) a r a t i o of approximately 3 was obtained. The reduced signal-to.-noise r a t i o f o r hydrogen i s t o be expected due t o the decreased stopping power of hydrogen. • The s i g n a l - t o - n o i s e r a t i o was dependent upon the state of discharge of the filament b a t t e r y . Therefore, i n order to obtain reproducible r e s u l t s , the b a t t e r y was f u l l y charged before each run and the a m p l i f i e r s allowed to operate f o r about two hours i n order to reach thermal e q u i l i b r i u m .  Also,  i n order to check the a m p l i f i e r s performance, a s i g n a l - t o - n o i s e t e s t was taken immediately before each range measurement. The a c t u a l c a l i b r a t i o n was obtained by p l o t t i n g a number-distance curve f o r hydrogen and using the accepted value f o r the stopping power of hydrogen (.2210^ to c a l c u l a t e the stopping power of deuterium.  Hydrogen  was chosen as. a standard f o r the comparison because hydrogen and deuterium have t h e o r e t i c a l l y very s i m i l a r stopping powers, and, t h e r e f o r e , any e r r o r inherent, i n one measurement should be the same.in the other.  Such an e r r o r  might a r i s e from the chamber penetration c o r r e c t i o n , which can be determined only approximately.  As an a d d i t i o n a l check on the correctness of r e s u l t s  18 each run w i t h hydrogen or deuterium i n the chamber was followed by a s i m i l a r run w i t h argon i n the chamber.  I n t h i s way, the stopping power of  hydrogen was measured i n terms of the stopping power of argon, which was then compared to a i r by using the accepted stopping power of argon compared to a i r (.929) • Two a d d i t i o n a l runs were made i n which the range of argon was compared d i r e c t l y t o that of a i r t o check the accepted value f o r the stopping power of argon. In order that each p o i n t on the number-distance curve should have the same s t a t i s t i c a l weight, the same number of counts were taken f o r each p o i n t on the curve. Since 2% standard deviation on each p o i n t requires approximately 2000 counts, the, source strength was chosen to given approximately 2000 counts per minute.  19  V.  A.  RESULTS AND DISCUSSIONS  •  CORRECTIONS TO.EXPERIMENTAL DATA The mean range i s defined as that range reached by j u s t one-half of  the  p a r t i c l e s that leave the source.  The mean range w i l l depend, of course,  on the s e l f - a b s o r p t i o n of the source, but the stopping power w i l l s t i l l be given by S = fa — provided Rm a i r and Rm gas are measured from the same Rm gas 1 a  source. In f i n d i n g the i n t e r c e p t f o r the extrapolated number-distance range, only the points on the l i n e a r p o r t i o n of the number-distance p l o t (see Plate X) were considered. The background was subtracted from each count, and a s t r a i g h t l i n e was drawn through these points to give the best i n t e r cept.  The best l i n e was determined by tyro separate methods, (a) using a  thread to f i t the l i n e by eye on a l a r g e scale p l o t , and (b) using l e a s t squares.  Both methods gave the same r e s u l t s .  ' Having obtained the i n t e r c e p t , the extrapolated number-distance range was found by considering: 1.  The distance from the chamber face to the source.  (From the c a l i -  b r a t i o n of the micrometer scale w i t h range i n a standard gas.) 2.  The'equivalent range of the aluminum f o i l .  The stopping power of  aluminum was taken as l.J?7 mg/cm , which i s the average of the values given 2  1  1  by Rosenblum , and Marsden and Richardson- -. 3.  1  The chamber depth p e n e t r a t i o n , which was found at l e a s t to a f i r s t  order approximation by using the method described i n Appendix I .  UNCORRECTED EXPERIMENTAL NUMBER DISTANCE CUR /400  ARGON  k  JULY 25 1951  600  HYDROGEN \  SEPT 25 1951  200  300 MICROMETER READING W  o  ,  3.4  3.5  3.6  Vioo g 3.903  \1«>3  o  MICROMETER READING CM I2.Q  20  IN  The c o r r e c t i o n f o r temperature and pressure.  The ranges were reduc-  ed t o standard c o n d i t i o n s . Ro T P  O J  0  B.  =  RP o T  P , RQ r e f e r to. standard temperature, pressure & ranges. 0  T  D  = 288°K,  = 760 mm mercury.  RESULTS TABLE I Stopping Power R e l a t i v e t o Hydrogen  Stopping Power Relative to A i r  Gas  .929  Argon  1  .220  Hydrogen  1.012  .222  Deuterium  Table I shows the r e s u l t s obtained i n t h i s experiment.  The -values  quoted f o r argon and deuterium are the mean of two sets of readings, and those f o r hydrogen are the mean of f o u r sets of readings.  The stopping  power i s defined from the mean range c h a r a c t e r i s t i c of the source. P l a t e X shows a t y p i c a l p l o t f o r a i r , argon and hydrogen.  C.  POSSIBLE SOURCES OF' ERROR IN RESULTS 1.  Statistical The best i n t e r c e p t s obtained from approximately 20 points on the  l i n e a r s e c t i o n of the extrapolated number-distance curve were found i n the l e a s t squares a n a l y s i s to have u n c e r t a i n t i e s of . 0 0 6 , .005 and .015 cm f o r a i r , argon and hydrogen, r e s p e c t i v e l y . . 2.  Foil . Anv e r r o r caused by the f o i l would be due .to choosing the wrong a i r  21  equivalent f o r aluminum. mg/cm 1.62  The stopping power of aluminum used was 1.57  equivalent to 1 cm of a i r , which i s the average of the two values,  and 1 . 5 1 . 1  The u n c e r t a i n t y , t h e r e f o r e , i s plus o r minus .05 mg/cm . o 2  Because of the thickness of the window used ( I . 8 9 0 mg/cm ), there i s a poss i b l e e r r o r of , 0 k l cm i n the range i n argon, o r an e r r o r of 1.6$ i n the stopping power of hydrogen o r deuterium. 3.  Chamber Depth The chamber depth penetrations were 1 . 2 5 , . 9 0 and 2.U0 mm f o r a i r ,  argon and hydrogen (deuterium), r e s p e c t i v e l y . (See Appendix I f o r method of c a l c u l a t i n g ) .  These c a l c u l a t e d values are probably a good f i r s t approx-  imation . I4..  Temperature and Pressure The temperature was read to the c l o s e s t ' \ degree which corresponds  to u n c e r t a i n t i e s of . 0 0 5 , .005* »020 cm f o r a i r , argon and hydrogen, respectively.  The barometer was read to 1/10 mm, g i v i n g an u n c e r t a i n t y too.small  to be considered. 5.  Gas P u r i t y Argon and hydrogen were obtained i n l e c t u r e b o t t l e s and were quoted  as 99.9% pure, thus any e r r o r introduced from t h i s cause was c e r t a i n l y small. As a f u r t h e r check on the p u r i t y of the hydrogen and the deuterium used, a mass spectrometric a n a l y s i s was obtained from Drs. Thode and Fleming, McMaster U n i v e r s i t y . Unfortunately, the hydrogen gas sample was contaminated during t r a n s i t , but the deuterium a n a l y s i s i s as f o l l o w s .  22  H-  D  2  D 0, 2  N  98.33$  2  HDO  1.29 .22  2  A  .011  co  .030  2  29  .008  3  .009  1  32  .019  33  .018  3U  .016  35  .016  36  .018  97.5$  • Atom $ Deuterium  In e x p l a i n i n g the a n a l y s i s , Dr. Fleming stated t h a t the values  given  probably represent a lower l i m i t on the deuterium content, since the most probable sources of e r r o r would r e s u l t i n an apparent increase i n hydrogen content. The appearance of 1.29$  water vapour i n the sample can be  explained  only by assuming contamination of the sample a f t e r i t l e f t the chamber, since a l l water vapour i n the chamber should have been removed by the l i q uid a i r trap.  I f . t h e water content i f ignored, therefore, the lower l i m i t  f o r the deuterium content can be set as 9 8 . 7 9 $ .  The hydrogen impurity,  .83$, would not introduce any appreciable e r r o r i n the stopping power, but the .38$ of other i m p u r i t i e s , mostly n i t r o g e n , could l e a d to an e r r o r of 1.6$  i n the stopping power of deuterium.  I t i s q u i t e p o s s i b l e that some  of the i m p u r i t i e s were introduced i n talcing the sample. Considering the above p o s s i b l e sources of e r r o r , the stopping powers  23  can be quoted w i t h the f o l l o w i n g estimated e r r o r s .  TABLE I I Gas  D.  Estimated Probable E r r o r  Stopping Power  Argon  .929  ^  .007  Hydrogen  .220  ±  .005  Deuterium  .222  *  .005  COMPARISON OF RESULTS WITH PREVIOUS DATA The f o l l o w i n g table l i s t s the values of stopping powers found i n t h i s  experiment and shows the accepted values f o r hydrogen and argon as found by other workers.  TABLE I I I Gas Argon  Shopping Power Previous Work This Work .929^ • 931  Hydrogen  .22U  Deuterium  .22^ .236  .929  ±0.007  .220  ±0.005  .222  10.005  6  3  ±0.0005  The extrapolated range of polonium alpha p a r t i c l e s i n a i r used as a 8 standard was taken from Holloway and L i v i n g s t o n  and i s quoted as being  3.897 cm at l5°C and 760 mm mercury. The stopping powers of hydrogen and argon are i n agreement w i t h the w e l l - e s t a b l i s h e d values as given by G r a y . The stopping power obtained f o r deuterium i s i n accord w i t h the work 3  )4  t  of S c h u l t z , but i s i n disagreement w i t h the work of Eichholz and Harrick  PLATE H EXPERIMENTAL  RANGE  WITH A PHOTO-MULTIPLIER  ANTHRACENE CRYSTAL  700  NUMBER CURVE AND AN  2h  V. CONCLUSIONS  In agreement w i t h t h e o r e t i c a l p r e d i c t i o n s , the stopping powers of hydrogen and deuterium appear to be the same w i t h i n the accuracy of t h i s experiment.  In the t h e o r e t i c a l d e r i v a t i o n of (-—) the assumption i s made dx  that energy l o s s i s due e n t i r e l y t o i o n i z a t i o n and e x c i t a t i o n of the absorbing atoms.  The r e s u l t s of t h i s experiment i n d i c a t e that t h i s assumption i s  a v a l i d one. To detect a d i f f e r e n c e i n the stopping powers of hydrogen and deuterium due to 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 would require an i n crease i n the accuracy of. t h i s experiment by a f a c t o r of 100 o r more. With present experimental techniques, t h i s accuracy would be d i f f i c u l t i f not impossible to accomplish.  .  .  Although the object of the experiment has been met to a reasonable extent, i t i s quite l i k e l y that the t h i n i o n i z a t i o n chamber w i l l be r e p l a c ed by e i t h e r a d i f f e r e n t i a l chamber where chamber penetration d i f f i c u l t i e s are non-existent, or by a s c i n t i l l a t i o n counter using modern photo-multip l i e r tubes as pulse a m p l i f i e r s .  With a p h o t o - m u l t i p l i e r s c i n t i l l a t i o n  counter, i t should be p o s s i b l e to detect 10 KEV pulses as compared.to the 150 KEV required f o r the t h i n i o n i z a t i o n chamber. P l a t e XI shows a p r e l i m i n a r y number-range curve which was obtained from an M I p h o t o - m u l t i p l i e r s c i n t i l l a t i o n counter with anthracene  crystal  without taking any s p e c i a l e f f o r t t o increase the s i g n a l - t o - n o i s e r a t i o .  25  This curve compares very favourably w i t h the ones obtained from the t h i n i o n i z a t i o n chamber a f t e r talcing a l l p o s s i b l e steps to increase t h e . s i g n a l to-noise r a t i o .  26  CHAPTER I I - ANGULAR DISTRIBUTION AND CORRELATION PATTERNS IN PROTON BOMBARDMENT OF F  19  AND N ^ 1  PART A - RADIATION PATTERNS FROM EXCITED STATES OF O  I.  l6  INTRODUCTION  19 When F  i s bombarded by protons there are three, competing reac-  tions ' ^ 2 3  2  1.  F (po<^)0 ^  short range ot  2.  F (p<* ) 0  long range °c  3.  F (pocTT)o  19  19  19  1  1 6  16  short range = v  ( 7T r e f e r s to nuclear p a i r production) The f i r s t r e a c t i o n i s the one of i n t e r e s t i n t h i s experiment.  The y i e l d  of alpha p a r t i c l e s changes r a p i d l y w i t h bombarding energy, and resonance, l e v e l s have been measured and found to occur a t the f o l l o w i n g proton energies (KEV) 3h0, k80, $90, 6 6 0 , 8 2 0 , 8 7 3 , 8 9 0 , 9 3 5 , 1 0 9 2 . I t i s known also t h a t the gamma r a d i a t i o n has three d i s t i n c t energies, approximately 6 . 1 3 , 6.9,  7 . 1 MEV, the r e l a t i v e i n t e n s i t i e s depending'on the bombarding energy  of the protons.  At the lowest resonance  (3U0 KEV proton energy) almost a l l  of the d i s i n t e g r a t i o n s seem to l e a d to the same e x c i t e d s t a t e of 0 . ±o  ma rays 6.13 MEV are then emitted i n the t r a n s i t i o n to the state.  ground-  No long-range alpha p a r t i c l e s ' c o r r e s p o n d i n g t o the d i r e c t  Gam-  30'  60*  ANGULAR  90°  , 5 0  °  l 8 0  °  CORRELATION BETWEEN  oC-PARTICLES AND REACTION  '2"°  Y-RAYSIMTHE  F' (paT) 9  PLATE IE  0"  27  t r a n s i t i o n from the N e  2 0  l e v e l t o the ground-state o f O ^ are observed, 1  though they are much favoured e n e r g e t i c a l l y . Experimental work on alpha gamma angular c o r r e l a t i o n f o r F"^(pot ) O ^ 1  r e a c t i o n has been c a r r i e d on a t Cavendish l a b o r a t o r y f o r the 3I4O KEV resonance  . Both alpha p a r t i c l e s and gamma rays were observed i n a plane per-  pendicular t o the proton beam.  The alpha p a r t i c l e s were detected w i t h a  p r o p o r t i o n a l counter and w i t h a window t h i c k enough t o exclude s c a t t e r e d protons from the t h i c k C a F l  2  target.  with-a lead-walled geiger counter.  The 6 . 1 MEV gamma rays were detected Coincidences between the alpha p a r t i c l e  and the gamma rays were measured as a f u n c t i o n of the-angle between the counters. The angular d i s t r i b u t i o n of alpha p a r t i c l e s w i t h respect to the proton 20 beam i s i s o t r o p i c , and one can take as the simplest assumption that the Ne i s formed by s-protons  . This means that i t has no p r e f e r r e d o r i e n t a t i o n  and i t i s not u n t i l the alpha p a r t i c l e i s emitted that a f i x e d d i r e c t i o n i n space i s defined.  The .gamma r a y then has an angular d i s t r i b u t i o n w i t h  38 respect to t h i s a x i s , as has been found by Barnes e t a l , and the observed • 6_ l a , c o r r e l a t i o n f u n c t i o n has a term i n cos o .  (The r e s u l t s are shown i n  Plate X I I ) I t was concluded from the experimental r e s u l t s that (a) the resonance l e v e l o f neon 20 i s formed by-£ =0 (•£= o r b i t a l momentum) protons and has j = l ( j = t o t a l angular momentum) and i s probably of even p a r i t y because alpha p a r t i c l e emission to the ground s t a t e of O ^ i s not observed, (b) 1  since neon 20 has even p a r i t y and i s formed b y ^ =0 protons, F ^ also has 1  even p a r i t y , and (c) the neon 20 emits alpha p a r t i c l e s w i t h £ = 3 l e a v i n g an e x c i t e d oxygen 16 nucleus w i t h j=3 and odd p a r i t y . In view of the wealth of information which was obtained from the study  28 of only one resonance, i t would be v e r y i n t e r e s t i n g to extend the study of the  angular c o r r e l a t i o n to the higher resonances i n an e f f o r t to  assign quantum numbers to each of the known l e v e l s of 0 " ^ and Ne ^. 2  A very  serious d i f f i c u l t y a r i s e s , however, as the proton energy i s increased.  The  3U0 KEV resonance i s the only one at which the alpha range exceeds the scattered proton range.  For t h i s reason, the protons can be e a s i l y exclud-  ed from the counter by i n t e r p o s i n g absorbing screens while s t i l l admitting the alpha p a r t i c l e s .  Extension of the measurement of the alpha gamma angu-  l a r c o r r e l a t i o n t o the higher resonances, therefore, reduces to the r a t h e r d i f f i c u l t f e a t of designing a counter which w i l l count only alpha p a r t i c l e s i n the presence of a v a s t l y l a r g e r number of more penetrating protons. Appendix I I shows c a l c u l a t e d curves on the number of s c a t t e r e d protons as a f u n c t i o n of angle and energy. Possible Methods of Counting Alpha P a r t i c l e s i n the Presence of a Strong Flux of Protons of Longer Range 1.  Magnetic  Separation  A magnetic analyzer could be used to separate, the two p a r t i c l e s , then a conventional p r o p o r t i o n a l counter could be used f o r counting the alpha p a r t i c l e s .  The disadvantages of t h i s method are (a) c o n s t r u c t i o n of  a magnet capable of r e s o l v i n g the p a r t i c l e s , and (b) v a s t l y reduced  count-  ing rates due to a decrease i n the e f f e c t i v e s o l i d angle of the counter. 2.  Very Fast Coincidence C i r c u i t A very f a s t coincidence c i r c u i t could give a real, to random c o i n -  cidence r a t i o of 1 i f the r e s o l v i n g time was l e s s tnan 5, x 10  . Appen-  dix I I I contains the c a l c u l a t i o n s on r e a l to random r a t i o s . 3.  Coincidence C i r c u i t w i t h Anthracene F i l m A f a s t coincidence c i r c u i t could be used i n conjunction w i t h an  29  anthracene f i l m .  The anthracene f i l m would give pulses which would depend  on the rate of energy l o s s (-^) dx  i n the f i l m , and as  i s greater f o r dx  alpha p a r t i c l e s than f o r protons, the pulses from the alpha p a r t i c l e s would be much .greater than the pulses from protons.  I f t h i s were t r u e , the r e s o l -  ving time of the coincidence c i r c u i t would not have to be so s h o r t .  Recent  p u b l i c a t i o n s , ' ' ' ' ^ however, show that the s p e c i f i c s c i n t i l l a t i o n (—) does dx not increase l i n e a r l y w i t h ( - — ) , but i n s t e a d a s a t u r a t i o n e f f e c t i s obserdx 2  ved.  In s p i t e of t h i s e f f e c t , the pulse from a 2 MEV  alpha, p a r t i c l e  may  be made n e a r l y twice that from a 2 MEV proton by proper choice of the f i l m thickness.  (See Appendix: IV)  ROT AT ABLE INSULATED  GASKET  EMI  TARGET MOUNT  TARGET  -  PHOTO-MULTIPLIER  %<=-snpnoti  PLUG  SCATTERING  CHAMBER—PLATE.  30  II.  A.  DESCRIPTION OF APPARATUS  ELECTRONIC EQUIPMENT NECESSARY P l a t e XIV i s a block diagram of the e l e c t r o n i c equipment that i s  required to perform an alpha gamma angular c o r r e l a t i o n experiment using a fast.coincidence c i r c u i t .  An E.M.I, type p h o t o m u l t i p l i e r tube i s used w i t h A 5819 RCA p h o t o - m u l t i p l i e r  a t h i n anthracene f i l m as the alpha detector.  w i t h a large anthracene c r y s t a l i s used, as the gamma detector.  The high  speed d i s c r i m i n a t o r f o l l o w i n g the Chalk R i v e r design employs an EFP 60 secondary emission tube and is'capable of producing a standard pulse which r i s e s i n a few millimicroseconds.  This d i s c r i m i n a t o r i s being  constructed  by Dr. D. B. James and w i l l be a v a i l a b l e f o r the experiment.  39 The coincidence c i r c u i t i s that of Garwin  7  and has a measured r e s o l v -  8 '"  ing time of 3 x 10~ seconds.  To f u n c t i o n p r o p e r l y the input pulses to the  mixer must be greater than 3 v o l t s .  Atomic instrument  a m p l i f i e r s and s c a l -  ers are a v a i l a b l e t o complete the necessary e l e c t r o n i c s . B.  REACTION.CHAMBER The s c a t t e r i n g chamber (Plate X I I I ) was designed and constructed w i t h  two purposes i n mind: to study the response of t h i n sections of anthracene to protons and t o determine the angular d i s t r i b u t i o n o f the alpha p a r t i c l e s from the F ( p o C ^ ) 0 ^ r e a c t i o n . 19  1  (This angular d i s t r i b u t i o n i s required f o r  •the i n t e r p r e t i n g of the. angular c o r r e l a t i o n experiment.) . The chamber has 12 ports (30° i n t e r v a l s ) i n t o whicfc the magnetically  MUUIPLIBR  MULT I PL l€ft  I  FAST DISCRIMINATOR  FAi DISCKirvti  J1  I +  -  DELAY  DELAY C- > I  +  DELAY f-)  (+)  1  IT  COINCIDE HCE CIRCUIT  COINCIDENCE  AMPLIFIER I  AM PL IFICR IT  DISCRIMIMATOH  DISCRIMINATOR  DELAY (+) JL  CIRCUIT  I  IT  I  SCALERJL  SCALER I  PLATE JJF BLOCK  DIAGRAM  OF  THE  ELECTRONICS  REQUIRED  FOR A HIGH SPEED COINCIDENCE  ANGULAR  CORRELATION EXPERIMENT.  31  shielded s c i n t i l l a t i o n counter can be f i t t e d . ports are made w i t h rubber gaskets.•  .  The vacuum seals f o r a l l  32  III.  FILMS FROM ORGANIC PHOSPHORS  25 - 37 Although there are many references i n l i t e r a t u r e  to organic  s c i n t i l l a t o r s , both l i q u i d and c r y s t a l l i n e , • t h e r e has been l i t t l e work done on t h e i r response to heavy p a r t i c l e s , and the work that has been done i s of very recent o r i g i n .  In f a c t , i t was only a f t e r most of the work  reported here had been completed that anything was published on the r e l a t i v e pulse heights produced by protons and alpha p a r t i c l e s , and nowhere i n l i t e r a t u r e has anyone published a method of producing a t h i n f i l m from organic s c i n t i l l a t o r s . Anthracene and terphenyl of high p u r i t y were chosen as the organic scintillators.  I t i s unfortunate that the pulse r i s e time i n inorganic  s c i n t i l l a t o r s i s so long" '  , because they show a good response t o alpha  particles. Since anthracene and terphenyl have a c r y s t a l l i n e s t r u c t u r e , i t i s not as simple as would be supposed to produce the uniform c l e a r l a y e r of the pure s c i n t i l l a t o r that i s d e s i r e d . . Many d i f f e r e n t methods of f i l m formation were t r i e d and the b e t t e r f i l m s produced were t e s t e d f o r alpha p a r t i c l e response on an 18 channel kick sorter. Techniques Employed i n the Production of Thin Films 1.  Evaporation of an anthracene s o l u t i o n on a water surface. The anthracene was d i s s o l v e d i n a s u i t a b l e organic solvent which  would f l o a t on a water surface and evaporate, l e a v i n g the anthracene as a f i l m on the water surface.  33 The f o l l o w i n g table l i s t s the various solvents t r i e d and the r e s u l t s .  TABLE IV Solvent (Saturated w i t h Anthracene)  Remarks on F i l m Produced on Water Surface  Benzene  Too v i o l e n t a surface e f f e c t F i l m uneven and c r y s t a l l i n e F i l m very t h i n  Chloroform  Density of chloroform too great, does not form a s u i t a b l e f i l m  Ether  Surface tension breaks f i l m as i t i s formed  Carbon Disulphide  Forms granular i s l a n d s  Other solvents such as acetone, amyl a l c o h o l and e t h y l a l c o h o l were t r i e d a l s o , but the s o l u b i l i t y of anthracene i n these was too small to make f i l m formation a p o s s i b i l i t y .  Zapon (commercial laquer) was added to the benzene  s o l u t i o n i n an e f f o r t to reduce surface a c t i v i t y , but i t was found that the f i l m s thus produced d i d not s c i n t i l l a t e . • 2.  •  Evaporation of Anthracene Solutions on Glass Plates • The same solutions as t r i e d above on water were painted onto glass  s l i d e s and allowed to eyaporate to dryness.  In a l l cases, the surface  formed was very uneven due to c r y s t a l formation. The best f i l m produced i n t h i s manner came from a chloroform s o l u t i o n . 3.  C r y s t a l s Grown from S o l u t i o n Saturated s o l u t i o n s of anthracene i n benzene, chloroform and carbon  disulphide were allowed to evaporate slowly at room temperature, producing c r y s t a l s of pure anthracene. The c r y s t a l s formed from a chloroform s o l u t i o n were, needle-shaped, and, therefore, of l i t t l e use, but the c r y s t a l s formed from benzene and  3k  carbon disulphide- s o l u t i o n s were i n a useable l e a f form.  The l e a f c r y s t a l s ,  however, were e i t h e r very small or i f given time to grow to a s u f f i c i e n t s i z e , too t h i c k .  This i s a good method of making f l a t c r y s t a l s of anthra-  cene approximately 1/10 mm h-  thick.  Evaporation of Anthracene onto a Glass Plate i n a Vacuum The anthracene was heated i n vacuo and allowed to condense on a  glass p l a t e . evaporated.  The thickness could be c o n t r o l l e d by the amount of anthracene The required thickness, .J? to 1, mg/cm , could be obtained  e a s i l y but, unfortunately, the.surface formed was not as uniform as would be desired, because the anthracene tends to form c r y s t a l l i n e grains as i t condenses on the g l a s s . 5.  F i l m Produced from an Anthracene Melt F i n e l y powdered anthracene was placed between two glass s l i d e s which  were separated by an aluminum f o i l of the f i l m thickness required (approximately .001 cm).  The anthracene was thus confined to the area not covered  by the aluminum f o i l and was of the proper thickness.  The s l i d e s were  heated (on a hot p l a t e ) u n t i l the anthracene flowed, and then allowed to • cool.  The top p l a t e and the aluminum f o i l were removed when the anthracene  had s o l i d i f i e d , l e a v i n g the required anthracene f i l m .  This procedure r e s u l t -  ed i n a s a t i s f a c t o r y f i l m . 6.  F i l m Produced from a P l a s t i c  Phosphor  The p l a s t i c phosphor c o n s i s t s of a small percentage of terphenyl i n a polymerized monomer of styrene. Uniform t h i n sections were made by d i s s o l v i n g the p l a s t i c i n benzene and p a i n t i n g the s o l u t i o n on a glass s l i d e , but the p l a s t i c f i l m d i d not give the large pulses that were produced by anthracene of the same t h i c k n e s s , 7.  (see next section)  F i l m Produced from Pure Terphenyl The above techniques were t r i e d w i t h terphenyl as w i t h anthracene  and the r e s u l t s were very s i m i l a r ,  (see next section)  PLATE XV  3000  RESPONSE AHWKACENE OF  OF A  THICK SECTION OF  TO ALPHA  DIFFERENT  PARTICLES  ENERGY  ZOOO  i  /ooo  PULSE HEIGHT cC ALPHA PARTICLE ENERGY ARBITRARY  UNITS  / )  35  IV.  RESPONSE OF THIN ORGANIC FILMS TO ALPHA PARTICLES  In order to t e s t the pulses from the f i l m s o f anthracene  and terphenyl,  a l i g h t - t i g h t chamber was constructed w i t h i n which was mounted a movable alpha source.  I t was thus p o s s i b l e to have any.desired f r a c t i o n of the  alpha range f a l l w i t h i n the f i l m . Plate XV shows the pulses formed by a c r y s t a l of anthracene grown from a carbon disulphide s o l u t i o n .  The c r y s t a l was much t h i c k e r than the equiv-  alent range of polonium alpha p a r t i c l e s i n anthracene.  Therefore, the  pulses diminished i n sige as the source was moved f a r t h e r from the c r y s t a l . P l a t e XVI shows s i m i l a r curves f o r a t h i n f i l m produced by method 5« The thickness of t h i s f i l m as determined by weighing was 1.1. mg/cm . Assuming that I.I4. mg/cm  of anthracene i s equivalent t o 1 a i r cm, t h i s  corresponds  to an equivalent range i n a i r of approximately 0.8 cm. The pulse height does not decrease as the source i s moved away from the f i l m , showing that the f i l m i s much thinner than the range of the alpha p a r t i c l e s (3«8U cm). Very similar' r e s u l t s were obtained using pure terphenyl i n place of anthracene, but the p l a s t i c phosphor gave a much smaller p u l s e .  The pulses  produced i n the p l a s t i c phosphor are roughly one-half the s i z e of those produced i n anthracene or terphenyl f o r the same energy of alpha p a r t i c l e s . From the pulse heights observed f o r a t h i c k s e c t i o n of anthracene, P l a t e XV, i t i s p o s s i b l e t o p l o t the response of anthracene to alpha p a r t i c l e s i n the energy range 0 . 5 to 5.0 MEV. Taylor e t a l have published a response curve f o r alpha p a r t i c l e s of energies from 2 MEV to 20 MEV. The  3000  PLATE RESPONSE ANTHRACENE  2000  IOOO  o  OF A THIN SECTION OF T O ALPHA PfiRTiCLeS  36  i n s e r t i n P l a t e XVII shows t h i s curve.  The r e s u l t s obtained i n t h i s exper-  iment are p l o t t e d and f i t t e d to t h i s curve at h MEV  (Plate X V I I ) , and  are  seen to be a smooth continuation of the r e s u l t s obtained by Taylor et a l  37  V.  CONCLUSIONS  From the preceding s e c t i o n , i t i s concluded that a s a t i s f a c t o r y and r e l a t i v e l y simple method'of producing t h i n s c i n t i l l a t i o n f i l m s of anthracene has been developed.  The response of these f i l m s to alpha p a r t i c l e s  of varying energy agrees w e l l w i t h the e x c i t o n theory of B i r k s (see Appendix I V ) . 'Assuming t h a t t h i s theory c o r r e c t l y p r e d i c t s the response of these f i l m s t o protons, i t would appear d i f f i c u l t t o d i s c r i m i n a t e between protons and alpha p a r t i c l e s i n organic phosphors on the b a s i s of pulse s i z e alone.  As soon as a resolved beam of protons i s a v a i l a b l e from the Van de  Graaff generator, the response of these f i l m s to protons w i l l be checked. I f i t proves impossible to d i s c r i m i n a t e between protons and alpha p a r t i c l e s on pulse s i z e alone, i t w i l l be necessary to decrease the r e s o l v ing time of the coincidence mixer to about 5 x 1 0  - 1 0  seconds.  The Garwin  c i r c u i t i s probably not capable of such a short r e s o l v i n g time, but a s u i t able coincidence c i r c u i t f o r t h i s work i s being developed by Dr. D. B. James.  38  PART B - ANGULAR DISTRIBUTIONS FOR GROUND-STATE ALPHA PARTICLES FROM N ^ C p o c ) ^  1 2  REACTION  I . INTRODUCTION  In view of the power of the angular d i s t r i b u t i o n and c o r r e l a t i o n method, i t i s n a t u r a l to look at the analogous set of r e a c t i o n s f o r the proton bardment of N  .  bom-  These r e a c t i o n s are l -! 12 (poCtf)C 1  N  15  N  short range alpha p a r t i c l e s  12 (poc)C  long range alpha p a r t i c l e s  The y i e l d f o r the r e a c t i o n s N^^(p<x ^ ) C  1 2  and N"^(p°c)C  12  has been measured 16  resonance s t a t e s of the 0  up to a proton energy of 1.2 MEV,  nucleus occuring at proton energies of 0 . 9 , 1 . 0 , 1.2 MEV^.  compound For the reson-  c  IP ance at 1.2 MEV,  both s t a t e s of C  can r e s u l t , the c r o s s - s e c t i o n being 0 . 6 12  and 0.2 barn f o r the r e a c t i o n l e a d i n g to ground and e x c i t e d states of C. respectively.  The gamma ray t r a n s i t i o n energy i s h»k£& MEV.  reports an energy of h-h$  Wilkinson  .01+'MEV and a high order of a n i s t r o p y of order  14- 0.3 c o s 0 near the 900 KEV 2  level.  In order to assign the angular momentum and p a r i t y of the luU6|? MEV state of C , 12  the angular, d i s t r i b u t i o n of the gamma rays w i t h respect to  the proton beam i s i n s u f f i c i e n t by i t s e l f . angular momentum of the O ^ 1  M ^(poc)C 1  12  A knowledge of the p a r i t y and  e x c i t e d state could be determined by the  r e a c t i o n , and would probably enable an unambiguous assignment  of quantum numbers to a l l s t a t e s i n v o l v e d . I f necessary f u r t h e r knowledge could be obtained by examining the alpha gamma angular c o r r e l a t i o n .  39  '  - ^.  I I . THEORY '  GENERAL PRINCIPLES OF TWO-STAGE PROCESSES Reduced to i t s simplest terms, the two-stage process i s e s s e n t i a l l y  a fluorescence problem.  In fluorescence, l i g h t of one wave-length i s  absorbed by a system and the capture cross s e c t i o n of atoms f o r r a d i a t i o n i s l a r g e s t when the t o t a l energy ocrresponds t o a s t a t i o n a r y state of the system.  Subsequently, some other l i g h t i s emitted.  l i g h t i s described i n roughly the same terms.  The d i s p e r s i o n of  The e s s e n t i a l form of the  d i f f e r e n t i a l cross s e c t i o n i n the analogous case where a heavy p a r t i c l e (proton) i s absorbed and a heavy p a r t i c l e (ex. alpha p a r t i c l e ) i s emitted i s given as  In t h i s formula gg(E) and g^<(E*) represent s l o w l y varying functions of energy and serve as parameters when one compares theory w i t h  experiment.  They represent something l i k e i n t r i n s i c p r o b a b i l i t i e s of r e a c t i o n once one has brought the n u c l e i together.  P^ and P^' are b a r r i e r p e n e t r a b i l i t i e s  f o r the i n c i d e n t and emitted p a r t i c l e s , r e s p e c t i v e l y .  The s u b s c r i p t r  r e f e r s to the various resonances and the Y ^ r e f e r s to the associated Legendre polynomials. ^  o r b i t a l angular momentum of i n c i d e n t p a r t i c l e .  A *-X  Z-component o f ^ , and i s zero because of the choice of Z-axis  j  t o t a l s p i n angular momentum of i n c i d e n t p a r t i c l e and t a r g e t nucleus  j  Z-component of j  J  t o t a l angular momentum of compound nucleus  z  ho  J Jl  Z-component of J  z  3Xid.Jl  are the o r b i t a l angular momentum and i t s z-component f o r the emitted p a r t i c l e  z  . j'and ^  are the spin angular momentum and i t s z-component of the r e s u l t a n t p a r t i c l e s  The transformation c o e f f i c i e n t s ( ^ j j z  Shortley, pages 73—78.  z  | J J ) are l i s t e d i n Condon and Z  Since conservation of angular momentum holds i n  these problems  I t - U J  - Jz  s i n c e  z  J^z "  + j)  0  A l l p o s s i b l e angular d i s t r i b u t i o n s up to J equals h f o r the compound nucleus have been worked out and are l i s t e d i n the s e c t i o n below.  B.  CALCULATED ANGULAR DISTRIBUTION FOR THE GROUND-STATE ALPHA PARTICLE IN THE N ^ p t x Q C  1 2  REACTION  The d i s t r i b u t i o n has been c a l c u l a t e d assuming f i v e overlapping e x c i t ed s t a t e s i n 0"^ w i t h spins of o+, 1-, 2+, 3 - , U+- where the signs i n d i c a t e the p a r i t y of the state (-, odd p a r i t y , -+- even p a r i t y ) . The f o l l o w i n g assumptions f o l l o w i n g e a r l i e r experimental r e s u l t s were made (a) N ^ has a s p i n of \ and odd p a r i t y , and 1  12  (b) C  has a s p i n of 0 and even p a r i t y .  12  Therefore, C +• °C has a s p i n of 0 and even p a r i t y . A l l p o s s i b l e proton and alpha p a r t i c l e angular momenta which are cons i s t e n t w i t h the above assignment t o the O ^ compound nuclear states have 1  been i n c l u d e d . In order that unknown nuclear f a c t o r s , ex. p e n e t r a b i l i t y , resonance denominators,  can be allowed f o r , each alpha p a r t i c l e has .assoc-  i a t e d w i t h i t a separate amplitude and phase f a c t o r of the form Ae "A" i s the amplitude and "a" i s the phase angle.  , where  ill  Including t o t a l angular momentum of the compound nucleus up to k, there are nine ways i n which the r e a c t i o n can-take p l a c e . These are l i s t ed below. No  Total Spin of N + p  T o t a l Spin-  ol6  15  C  1 2  V  Amplitude and Phase  1  1  1  0+"  0  0  A, a  2  1  0  1-  1  0  B, b  2  1-  1  0  I, 7  1  1 '  2 +  2  0  D,  1  3  2 +  2  0  E, e  6  1  2  3-  3  0  F,  7  1  U  3-  3  0  G, g  8  1  3  U  0  H, h  9  1  5  ii -  0  K, k  .1 ;  3 k  Any combination of the f i v e states of the O ^ 1  d  f  compound nucleus can be  taken by c o l l e c t i n g those terms which contain the amplitude and phase f a c t ors corresponding to them.  Ex:  Assuming 0  l 6  to have two overlapping l e v -  e l s of (0 4-) and ( 3 - ) , the f o l l o w i n g terras must be c o l l e c t e d , / A + F H G 4 AFcos(a-f) 4- AGcos(a-g) +• FGcos(f-g) 2  2  2  E s s e n t i a l l y , t h i s i s a procedure whereby the amplitudes of the unwanted states are put equal to zero. The•angular d i s t r i b u t i o n s of ground-state alpha p a r t i c l e s from the N ^(poC)C 1  r e a c t i o n are thus as f o l l o w s .  1 2  The abbreviation c  i s used throughout. O ^ Spin States , • Involved 1  (04-)  Angular D i s t r i b u t i o n  -  2  1/6  A^  n  = cos  11  k2 0  Spin States Involved  (1-K1-)  Angular Distribution 3/2B  (Cont'd)  2  3/20Y (l+-3[C ) 2  2  3 A J 2 7 £ BYcos(b-y) ( l - 3 c ) 2  (24)(24) 5/12  D (l+-3c ) 2  2  15/56 E ( l - 2 c + 5 c ) 2  2  [ t  5/8 4 2/7 DE cos(d-e)(-l + 1 2 c - l 5 c ^ ) 2  (3-K3-)  21 A O  F (l-2c -»-5c ) 2  2  i ;  7/288 G ( 9 + l i 5 C - l 6 5 c ^ - « - 1 7 5 c ) 2  2  7/16 (h+)(k+)  6  FGcos(f-g)(3-69c 4- 2 2 5 c ^ - 1 7 5 c ) 2  6  9/22U.H (9-»A5c -l6Sc U- 1 7 5 c ) 2  2  [  6  U5AU08 K (9936c +29Uc -6[^c -+-itUlc ) 2  9 M (o*)(l-)  J 5/77  2  lt  6  8  HKcos(h-k)(-9-»-360c -2130cV3920c -2205c ) 2  I ABcos(a-b)(-c) 1/JlO AYcos(a-y)(-Hc)  (0-*)(24)  1/6 J ^ A ADcos(a-d)(l-3c ) 2  l A J 5 7 7 AEcos(a-0,)(-l4-3c ) 2  (0+)(3-)  1 A . 4 ^ 7 5 AFco.s (a-f) ( 3 c - 5 c ) 3  £ 47/27 AGcos(a-g)(-3c-»-5c ) 3  (o+)(U+)  3/8 J 5 7 2 1 AHcos(a-h)(-3 +-'30c -3£ck) 2  3/16 J5/33 AKcos(a-k)(3-30c ^ 3 5 ^ ) 2  (l-)(2+-)  I 4l0"BDcos(b-d)(  c)  6  8  O  16  Spin States Involved  Angular D i s t r i b u t i o n •. (Cont'd)  (l-)O-)  _  .  f >)63/5 BFcos(b-f ) ( - l - h 3 c 1/2U J l l  )  BGcos(b-g)(-3H-30c -35c ) 2  It  3/UO J l i r Y F c o s ( y - f ) ( - H - 1 2 c - l 5 c ) 2  1/16  u-)(a+)  l i  YGcos(y-g)(-3-6c -H25c ) 2  Ii  .3/2 4 3 A BHcos(b-h)(-3c4-£c ) 3  3/16 > | l 5 / l l B K c o s ( b - k ) ( - l 5 c 4 - 7 0 c - 6 3 c ^ ) 3  3/16 >|6/35 Y H c o s ( y - h ) ( - 2 1 c + 1 1 0 c - 1 0 5 c ^ ) 3  3/16 J6/11 YKcos(y-k)(-3c - 1 0 c 4 - 2 1 c ^ ) 3  (2+)(3-)  • |4lirDFcos(d-f )(c ) 3  1/U8 470/3 DGcos(d-g)(-21c  +110c -105c^) 3  3/8 EFcos(e-f ) ( - 5 c 4-26c -25'c^) 3  l / 8 j V 3 EGcos(e-g)(3c-10c 4- l $ c ^ ) 3  1/16J30/7 DHcos(d-h)(-3-6c -4- 25c^) 2  5/32^6/11 DKcos(d-k)(3-75c 4- 2 U 5 c ^ - l 8 9 c ) 2  6  3 / l l 2 j l ? EHcos(€-h)( 3 - 6 9 c 4 - 225c^-175c ) 6  2  15/32J3/77 EKcos(e-k)(-3 4-l5c -U5c -+- h9c6) 2  (3-)(U+)  J4  3 / 8 j p / 5 FHcos(f-h)(3c-10c -4-30c ) 3  5  ' 3 / 3 2 J 2 1 / I I FK c o s ( f - k ) ( 2 1 c - 2 0 5 c + U 5 3 c ^ - 3 l 5 c 3  1/32 '  :  GHcos(g-h)(8lc-795c +  1/16 J3 5/11  1775c^-1225c )  3  7  GKcos(g-k)(30c -8Uc 4-70c ) 3  5  7  7  BALL BEARING STOP  ROTATING ARM  — COUNTER'ADJUSTMENT  THIN WINDOW. SCATTERING  CHAMBER  PIATElUIl  hk  III. A.  DESCRIPTION OF APPARATUS  REACTION CHAMBER •Calculations (see Appendix V) shovf that the range of the alpha p a r t -  i c l e s at 180° to the beam direction i n the l a b o r a t o r y system of coordinf  ates would have a range of only 2.3 cm i n a i r .  The chamber shown i n  P l a t e XVIII was constructed w i t h 21 windows a l l of which have an equival e n t a i r range of l e s s than 1.56 cm.  The windows on one side of the  chamber are 1 0 ° apart, while the three on the other f o r monitoring purposes are placed at 1|0 , 90° and 1 3 0 ° , r e s p e c t i v e l y .  The p r o p o r t i o n a l  counter can be a c c u r a t e l y moved from window to window by a c a l i b r a t e d arm w i t h a b a l l - b e a r i n g stop every 1 0 ° . The counter can be moved towards or away from the target by means of a screw.  B.  COUNTER AND AUXILIARY APPARATUS A p r o p o r t i o n a l counter i s used to d i s t i n g u i s h between alpha pulses  and any other pulses from other sources. The counter i s shown i n P l a t e X V I I I .  A very t h i n window i s the main  feature of the p r o p o r t i o n a l counter ( 0 . 5 cm a i r e q u i v a l e n t ) .  At 180°  the alpha p a r t i c l e ' w i l l thus expend O.I4.MEV (2.30-2.06=0.2l|. cm) i n the counter, which i s s u f f i c i e n t t o give a good-sized p u l s e . The necessary e l e c t r o n i c c i r c u i t s have been constructed and t e s t e d and have been found t o be s a t i s f a c t o r y .  An a u x i l i a r y r e a c t i o n chamber  has been constructed f o r the measurement of the gamma r a y angular d i s t r i bution.  IV.  DISCUSSION  A l l t e s t s of equipment i n d i c a t e that the experiment i s f e a s i b l e and completion of 'the experiment awaits a stable resolved beam from the Van de Graaff generator.  he  APPENDIX I  SAMPLE CALCULATION The experimental extrapolated range f o r a i r corresponded to a reading of 3 « 7 1 2 on the micrometer.  To f i n d the a c t u a l distance from the  o r i g i n , the known value of the extrapolated range f o r a i r at l£°C and 760 mm, i . e . 3 . 8 9 7 cm, was used.  Now, not a l l of the 3 . 8 9 7 cm i s i n a i r .  The aluminum window has an a i r equivalent of . 9 6 8 cm, therefore, the actual range i n a i r i s 3 . 8 9 7 - . 9 6 8 = 2 . 9 2 9 cm from the o r i g i n , i f the experimental range was at l£°C and 760 mm mercury.  But since the exper-  imental temperature and pressure d i f f e r e d from these values, a c o r r e c t i o n i s necessary to make the two i d e n t i c a l . R  =  1  RQPQT  PT  0  Therefore, a reading of 3 . 7 1 2 cm on the micrometer corresponds to an actual distance of 3 . 0 2 6 .  The micrometer c o r r e c t i o n is. then  •3.712 - 3 . 0 2 6  =  . 6 8 6 cm  For argon, which was found to have an uncorrected extrapolated range corresponding to a distance of U.003 om on the micrometer, the f o l l o w i n g corrections are applied. • 1.  Micrometer Correction R  1  -  U.003 -  .686  =  3.317  cm  hi  2. Temperature and Pressure C o r r e c t i o n R  o  °  R  '^£  ~  3-317  x .968  =  3.210  PT 0  3.  Chamber Depth Correction Since the signal-to-noise r a t i o i s greater f o r argon than f o r a i r ,  the alpha p a r t i c l e m i l not have to penetrate the chamber as f a r to produce the same s i z e pulse i n argon as i n a i r .  This means that the o r i g i n  from which we measured the a i r range w i l l have s h i f t e d toward the f r o n t of the chamber f o r argon.  In order to have the o r i g i n the same, we must sub-  t r a c t the difference i n chamber penetration from' the observed argon range. Experimentally, the signal-to-noise r a t i o f o r a i r at the maximum of the Bragg curve was 6 (see Plate V;1U). Since the maximum s p e c i f i c i o n i z a t i o n i s approximately 6000 i o n p a i r s per mm- , a chamber depth of 3 mm would correspond to.a t o t a l of 18,000 i o n p a i r s formed.  I f the s i g n a l - t o -  noise r a t i o i s 6, then 1/6 x 18,000 or. 3000 i o n p a i r s are. required before a pulse i s recorded. By numerical i n t e g r a t i o n of the s p e c i f i c i o n i z a t i o n D curve f o r a s i n g l e alpha p a r t i c l e - , the penetration required to produce 3000 i o n p a i r s was found to be 1.25  mm.  For argon, the signal-to-noise r a t i o was found to be approximately 8 1/3.  Therefore, 25/18 times as many ions were formed by argon i n the  3 mm as were formed from a i r .  I f the r e l a t i v e i o n i z a t i o n i s constant over  a l l energies f o r a i r to argon, one would assume that the penetration would be given by 18/25 :o.f the value found f o r a i r . 18/25 x 1.25 .90 mm The c o r r e c t i o n i s , therefore, 1.25  - .90 = .35 mm, which i s subtracted  from 3.210 to give a corrected extrapolated range of 3 . 1 7 5 . The mean ranges are now e a s i l y found from the graph by subtracting  •  the observed s t r a g g l i n g parameter, S = R  e x  m  Mean Range i n A i r  =  2.929 -  .087  -  2.8U2  Mean Range i n Argon  =  3.175  .108  =  3.067  -  Therefore, the stopping power of argon i s given by'  Rm argon  =  2.8l>2  3 .067  »  -  U8  - R , from the corrected e x t r a -  polated range.  Rm a i r  •  .927  RUTHERFORD SCATTERING  OF PROTONS——  PLATE.  h9  APPENDIX I I  Number of Scattered Protons as a Function of Energy and Angle P l a t e XIX shows the f a m i l y o f curves obtained when the number of protons scattered at various angles i s p l o t t e d against the energy of the i n c i d e n t protons. The curves were c a l c u l a t e d from the Rutherford  N  scattering-formula.  number of i n c i d e n t p a r t i c l e s per second  = Q  N  =  number of atoms/cc i n target  t  =  target thickness cm  e  =  e l e c t r o n i c charge  Z  *» charge on i n c i d e n t p a r t i c l e  Z'  =  atomic number of target  •§mv •- energy of the i n c i d e n t p a r t i c l e The curves, were c a l c u l a t e d f o r an aluminum target of 2 mm a i r equivalent thickness.  C l e a r l y the number of s c a t t e r e d protons could be f u r t h e r  reduced by using a thinner target of low atomic number.  Thin f i l m s of  c o l l o d i o n or formar would reduce the- number of scattered protons.  50  APPENDIX I I I  Ratio of True to Chance Coincidences f o r the F ( p o c y ) 0 1 9  Correlation  l 6  Angular  Experiment  The number of true coincidences i s given by Np =  ^ ^^\^7^ 0  where k = p r o b a b i l i t y t h a t the i n c i d e n t p a r t i c l e s h a l l produce the r e q u i r ed r e a c t i o n , and N  D  -  number of i n c i d e n t p a r t i c l e s per second  ^ ^=  the e f f i c i e n c i e s of two counters  "»flk  the s o l i d angle subtended by the counters  (  7 ss  The number of chance counts i s given by N T  c  = 2N N C 1  2  i s the r e s o l v i n g time i n seconds, N-j_ and N  ing r a t e s .  2  are the s i n g l e channel count-  If. N]_ r e f e r s to the alpha counter, then the scattered protons  w i l l determine the counting rate i n t h a t channel because t h e i r number f a r exceeds the number of alpha p a r t i c l e s i n the r e a c t i o n . N]_  -  N X, where X i s the Rutherford scattering, p r o b a b i l i t y 0  then the r a t i o of true coincidences to chance coincidences i s  2N _N f ]  2  2N X C 0  For the experiment to be f e a s i b l e , R should not be l e s s than u n i t y . I f we substitute the f o l l o w i n g numerical values  51  k = 10  , W  0  = 6 x K r V s e c = 1 microamp of beam £  ^.= 0 . 2 5 , y[ = ^ t  we obtain  2* =  2  ;  -  1,  = 1 0 ~ , and K = l o f y s e c ,  £ x 10~  2  1 0  sec.  The value of N]_ above was c a l c u l a t e d f o r 2 mm a i r equivalent thickness of aluminum . By s u b s t i t u t i n g a thinner hydrocarbon f i l m , N]_ can be reduced by a f a c t o r of 100 without too much d i f f i c u l t y . ing- time i s f  Then the required r e s o l v -  - 5 x 10~ which i s e a s i l y obtainable.  Equivalent Air Range of Film 0.2 cm  0.5 cm I.O cm  UJ  a b_ o o  !<  oc:  PROTON  ENERGYH>  MEV  PLATtXST RELATIVE RESPONSE OF ANTHRACENE TO ALPHA PARTICLES AND PROTONS FOR  DIFFERENT  FILM  THICKNESSES  52  APPENDIX IV  Exciton Theory The v a r i a t i o n of — ( s p e c i f i c fluorescence) w i t h (-—) ( s p e c i f i c enerdx dx gy l o s s ) may be explained using the e x c i t o n t h e o r y ^ . 2  On t h i s theory, the  e l e c t r o n i c energy e x c i t e d by the i o n i z i n g p a r t i c l e (the exciton) i s t r a n s f e r red from molecule to molecule w i t h i n the c r y s t a l , u n t i l i t i s e i t h e r emitted as r a d i a t i o n or quenched by a damaged molecule. I f the number of excitons produced per u n i t path length i s A^. and the dr dE l o c a l concentration of damaged molecules i s B-?~ molecules ner undamaged dx molecule and the e x c i t o n capture p r o b a b i l i t y of a damage molecule r e l a t i v e to an undamaged molecule i s k, then the s p e c i f i c fluorescence i s dE dL dx~ dx 1 kBdE dx _ A  =  +  The values f o r anthracene are A = 82.5 and kB = 7 . 1 5 , as c a l c u l a t e d from the experimental data on alpha p a r t i c l e s . In Plate XX> the r a t i o of the s p e c i f i c fluorescence of alpha p a r t i c l e s to the s p e c i f i c fluorescence of protons i s p l o t t e d against proton energy f o r f i l m s of d i f f e r e n t t h i c k n e s s . assumed to be 2 MEV.  The i n c i d e n t alpha p a r t i c l e energy i s  PLATE MI RANGE OF GROUND-STATE ALPHA PARTICLES FROM N' (p 5  *)c'  2  IN LAB. COORDINATES AS A EttMTlON OF 0 AND PROTON ENERGY  _  N " ALPHA PARTICLE RANGE SCATTERED PROTON RANGE  53  APPENDIX V  Alpha p a r t i c l e ranges from the  (p o<.)C  r e a c t i o n as a f u n c t i o n of  (ft (lab coordinates) and proton energy have been c a l c u l a t e d from the gene r a l formula A ME:\  =  L i 2' — ( M ^ ) ^ Cos(^+(MM Q +• MQM^E-^ - M-jMgE-^sin (f)* 2  3  The subscript 0 r e f e r s to the target nucleus, 1 to the i n c i d e n t p a r t i c l e , 2 t o the emitted p a r t i c l e , and 3 t o the r e s i d u a l nucleus.  MQ...M^  are the  masses of the four n u c l e i , and M the mass of the compound nucleus. EQ...E  are the k i n e t i c energies of the p a r t i c l e s .  Plate XXI shows the s c a t t e r e d proton range a t of energy.  •  = 0 as a f u n c t i o n  9x BIBLIOGRAPHY  1.  L i v i n g s t o n and Bethe  Review of Modern P h y s i c s - 9 , 2 6 3 ,  2.  Rutgers and M i l a t z  Physica  3•  Gray  Proc. Cambridge P h i l . S o c .  U.  Schultz  Phys i c a l Review  5.  N. J . Harrick  M.A.  6.  H a r r i c k , Eichholz  P h y s i c a l Review  7.  Halliday  Introductory Nuclear Physics Wiley, 1950  8.  Holloway and L i v i n g s t o n  P h y s i c a l Review  9.  M i l a t z and Rutgers ,  Physica VI  10.  Lewis and Wynn-Williams  Proc.Royal S o c i e t y  11.  Lewis  E l e c t r i c a l Counting Cambridge U n i v e r s i t y Press  1937  7 , 5 0 8 , I9U0 72, 19UU  53,62 2, 193 8  Thesis, U n i v e r s i t y of B.C. A p r i l , I9I+9 76,589,  19U9  5 U , l 8 , I938 529,  1939  13>6,3k9, 1932 19U2  12.  Hoag and K o r f f  E l e c t r o n and Nuclear Physics Van Nostrand, 19U9  13.  Hoag  E l e c t r o n and Nuclear Counters Van Nostrand, 1938  lU.  Wilkinson  I o n i z a t i o n Chambers and Counters Cambridge U n i v e r s i t y Press 1950  15.  Curran and Craggs  Counting Tubes 19U9  Academic Press Inc. 16.  Mano  17.  Chang  18. Wadey  Annales de Physique  • 1,72,  193U  P h y s i c a l Review  6 9 , 6 0 , 193H  P h y s i c a l Review  7 U , l 8 U 6 , 19U8  19.  Elmore and Sands  20.  Rutherford, Chadwick and E l l i s  •Electronics McGraw H i l l , 19^9 Radiations from Radioactive Substances Cambridge U n i v e r s i t y Press 1930  21.  Hevesy and Paneth  Radioactivity . Oxford U n i v e r s i t y Press  1938  55  22.  Bjorksted, M i t c h e l l '  P h y s i c a l Review  U6,629,  193U  23.  Chao, F o l l s t r u p , Fowler and Lauritsen  P h y s i c a l Revie?f.  79,108,  1950  22,357,  1950  2U.  Hornyak, L a u r i t s e n , Morrison and Fowler  Review of Modern Physics  25.  S. B. B i r k s  P h y s i c a l Review  8U,36ii,  1951  26.  Taylor, Remley, Jentschke and Kruger  Physical. Reviexv  83,169,  1951  27.  Frey, Grim, Preston and Gray  P h y s i c a l Review  82,170,  1951  28.  Robinson, Cook and J e f f e r s o n  Journal Chem. Physics  l8,lU8,  1950  29.  Jordan and B e l l  Nucleonics  30, Oct.l9U9  30.  Scharr and Farmer  P h y s i c a l Review  81,891,  P h y s i c a l Review  80, U7UA950  31.  . Scharr and F r a n k l i n  1951  Birks  Proc.Physical Soc. London A 63,129U,  33.  Reynolds  Nucleonics  3U.  Hartmut Kallman and Furst  Nucleonics  35.  Koski  P h y s i c a l Review  36.  Gettings  P h y s i c a l Review  37.  Bell  P h y s i c a l Review  77,li|.05, 19U8  38.  Barnes, French and Devons  Nature  I66,lii5,  1950  39.  Garwin  R.S.I.  21,569,  1950  Uo.  Schardt, Fowler and L a u r i t s e n  P h y s i c a l Review  80,136,  1950  ill.  W. R. Arnold  P h y s i c a l Review  8o,3U,  1950  U2.  French  Mimeographed Lecture Notes Cambridge, 1950  32.  5, 1,  1950  May-1950  U9;JUiy-i950y 76,308,19^9 75,205,  19U9  •ABSTRACT  The stopping powers of hydrogen and deuterium have been compared, using a t h i n i o n i z a t i o n chamber.  The r e s u l t s were found to be c o n s i s t e n t  w i t h the preseht-day theory on the method of energy l o s s .  A method f o r the preparation of t h i n f i l m s of organic phosphors has been devised and the response of these f i l m s to alpha p a r t i c l e s has been tested.  • •  A l l necessary apparatus f o r the study of angular c o r r e l a t i o n and d i s t r i b u t i o n patterns f o r F (p<*.t)0^ and N ( p a c ) C l!?  constructed. U (p«)C ?  l 5  1 2  r e a c t i o n s has been  The t h e o r e t i c a l angular d i s t r i b u t i o n patterns f o r the  r e a c t i o n have been c a l c u l a t e d .  

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