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He3 filled ionization chamber as a neutron detector Healey, Dennis Charles 1965

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A HE-3 FILLED IONIZATION CHAMBER AS A NEUTRON DETECTOR by DENNIS CHARLES HEALEY B.Sc,  The University of British Columbia, 1963  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF SCIENCE in the Department of PHYSICS  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA April 1965  In presenting this thesis i n p a r t i a l fulfilment of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t freely available for reference and study.  I further agree that permission  for extensive copying of this thesis for scholarly purposes may  be  granted by the Head of my Department or by his representatives. It i s understood that copying or publication of this thesis for f i n a n c i a l gain shall not be allowed without my written permission.  Department of  "Vhysics  The University of B r i t i s h Columbia, Vancouver 8, Canada, Date  flj>r  i<s-  :  \<H,<T  ABSTRACT 81  81  The threshold energy for the reaction Br (p,n)Kr and found to be 1.133 .020 Mev. ±  The threshold for C d  l l 6  was measured  (p,n)ln  1 1 6  was  searched for up to 1.8 Mev but was not found.  face.  The density of cosmic neutrons was measured at the earth's sur-9 3 It was found to be 4.2±.7*10 n/cm over land with 66$ i n thermal "9 3  equilibrium.  Over the sea, this density was 3.72±.98xK>  i n the thermal peak.  n/cm with 64$  The earth's albedo or reflectivity to neutrons imping-  ing on i t from the atmosphere was estimated to be . 2 2 . ACKNOWLEDGEMENTS I wish to express my sincere gratitude to Dr J.B. Warren for his kind supervision of this research project and his willing guidance throughout my research career.  The assistance of Dr B.L. White, Dr G. Jones and  Dr R.M. Pearce proved invaluable and was greatly appreciated. I am deeply indebted to the National Research Council for the two scholarships held during the course of this work. I also wish to express my gratitude to Dr G.L. Pickard and Dr B.M. Bary of the Institute of Oceanography for their aid i n obtaining for me the use of CNAV Whitethroat.  - i i -  TABLE OF  CONTENTS  page CHAPTER I  INTRODUCTION  1  CHAPTER I I  THE  1  CHAPTER I I I  NEUTRON THRESHOLD MEASUREMENTS I N B r  I O N I Z A T I O N CHAMBER 8  1  AND  Cd.  1 1 6  ,  4  1.  Introduction  4  2.  Shape o f t h e N e u t r o n Y i e l d Curve  4  3.  Neutron  5  4.  M o t i v a t i o n f o r the B r  5.  Threshold  f o r Li''(p,n)Be''' 8 1  (p,n)Kr  and  8 1  Cd  l l 6  (p,n)ln  1 1 0  T h r e s h o l d Measurements  6  Targets  8  a) M a t e r i a l s Used  8  b) Manufacture  9  of Targets  6.  A r r a n g e m e n t o f T a r g e t Chamber a n d D e t e c t o r  11  7.  Electronics  11  8.  Background Counting Rate  12  9.  E n e r g y C a l i b r a t i o n o f t h e v a n de G r a a f f G e n e r a t o r  14  rt-l  10.  Threshold Energy of Br  11.  Threshold Energy of C d ^ C p ^ I n  CHAPTER I V  MEASUREMENT OF THE  THE  (p,n)Kr  14 1  1  16  6  COSMIC NEUTRON F L U X  EARTH'S SURFACE  AT 19  1.  Introduction  19  2.  Arrangement of E x p e r i m e n t a l Apparatus  20  3.  Chamber F i l l i n g  20  4.  Chamber E f f i c i e n c y f o r N e u t r o n  5.  E f f i c i e n c y o f Cadmium S h i e l d i n g  Detection  21 22  -iii6.  Chamber counting Rate and Neutron Density  23  7.  Measurement of the Cosmic Neutron Density over the Sea  25  8. Estimation of the Earth's Albedo to Cosmic Neutrons  27  9. Comparison to other Neutron Density Measurements  27  APPENDIX A  To Show cr°<l< at Neutron Emission Threshold  28  APPENDIX B  Wall and End Effects  30  APPENDIX C  Background Counting Rate  34  APPENDIX D  The Counting Rate of a Black Neutron Detector  M  in an Isotropic Neutron Flux  36  APPENDIX E  Integral Evaluation  37  APPENDIX F  Estimation of the Earth's Albedo to Cosmic Neutrons  41  -ivLIST OF FIGURES to follow page 1.  Ionization Chamber  2  2.  Ionization Chamber Dimensions  2  3.  Details of Collector Support  2  4.  Electrode Voltage Supply Circuit  2  5.  Graph of Y and Y ^  6.  Target Chamber and Neutron Shielding  11  7.  Block Diagram of Electronics  11  8.  Electronics Used i n Energy Calibration and Beam Monitoring  12  9.  Y versus Proton Energy for NaBr and BaB^ Targets  15  10.  Y^  versus Proton Energy for NaBr and BaBr^ Targets  15  11.  Y  versus Proton Energy for BaBr Target  15  12*  Neutron Yield from Evaporated Cd Target showing  2  versus Proton Energy for Id7(p,n)Be  7  5  2/3 2  37 Resonances Due to C l  37 (p,n)A  16  13.  Neutron Yield for C l ( p , n ) A  14.  Cadmium Evaporator and Target Chamber  15.  Neutron Yield from Ta Target Backing and Beam  37  37  (Schoenfeld)  Dependent Background 16.  17 17  17  Block Diagram of Electronics for Measuring Cosmic Neutron Flux  20  17.  Chamber Efficiency  21 .  18.  Cadmium Shielding Efficiency  22  Bl.  Spectrum Shape for Wall and End Effects  30  B2.  Schematic Diagram Showing Wall Effect and F u l l Energy Peak;  Typical Neutron Peak  31  -V-  to follow page B3.  Proton Range i n Gases  31  Cl.  Neutron Specturm for Background Estimation  34  Fl.  Spectrum Shape of Differential Neutron Flux  41  -1CHAPTER I  INTRODUCTION  3 O v e r t h e p a s t f e w y e a r s , a He  filled  i o n i z a t i o n chamber h a s b e e n  u s e d i n t h e U.B.C. v a n d e G r a a f f l a b o r a t o r y t o s t u d y t h e p h o t o d i s i n t e g r a t i o n of  3  He .  3 Due t o t h e l a r g e c a p t u r e c r o s s s e c t i o n o f He-' f o r n e u t r o n s ,  chamber c a n a l s o be u s e d a s a n e u t r o n d e t e c t o r . b e c a u s e t h e c a p t u r e r e a c t i o n He ( n , p ) T causes of  the neutron  energy  spectrum  i s exothermic  b y .765 Mev.  useful This  t o be r a i s e d o u t o f t h e e l e c t r o n i c  t h e a m p l i f i e r s and t h e e l e c t r o n p i l e up o f t h e i o n i z a t i o n chamber.  t h i s t h e s i s , t w o u s e s o f t h e He^ f i l l e d detector are discussed. in  I t i sparticularly  this  Firstly,  i o n i z a t i o n chamber a s a  noise In  neutron  t h e c h a m b e r was u s e d a s a n e u t r o n d e t e c t o r  some ( p , n ) t h r e s h o l d m e a s u r e m e n t s a n d s e c o n d l y , i t was u s e d a s t h e  n e u t r o n d e t e c t o r i n a measurement o f t h e cosmic  neutron  f l u x at the earth's  surface.  CHAPTER I I  THE I O N I Z A T I O N CHAMBER  The n e u t r o n d e t e c t o r u s e d w a s a c y l i n d r i c a l g r i d d e d  ionization  3 chamber f i l l e d  with a mixture  shown i n t h e f o l l o w i n g  o f He , a r g o n  a n d methane t o t h e p r e s s u r e s  table:  Chamber F i l l i n g He CH Argon 3  4  Pressure  ( A t m a t 0°C)  1.41 0.19 1.36  The g e n e r a l f e a t u r e s c o n s i d e r e d i n t h e d e s i g n o f t h i s  chamber  -2have been d e s c r i b e d described  b r i e f l y i n conjunction  in  2.  figure  The  inches  with  on t h e side nearest  pump ( B ) ( M a c D o n a l d , 1963) purifier  dioxide time.  alpha  t h e gamma r a y s o u r c e u s e d d u r i n g Opposite t h i s  and a p u r i f i e r  (e).  The i n t e r i o r  c o n t a i n i n g a Ca-Mg e u t e c t i c  end b y a g l a s s kovar s e a l ( j ) and a t t h e other  The  grid  i n diameter.  strands  These s t r a n d s  t u r n mounted on l a v a d i s c s  fte P o at  5.30  a  s t r u t s ( i ) . The supported a t  end b y a g l a s s bead  were mounted on r i n g s  (k).  0.004  ( l ) w h i c h were i n  s h a p i n g r i n g s were mounted o n  The d e t a i l s o f t h e c o l l e c t o r s u p p o r t a r e  shown i n f i g u r e 3 a n d t h e c i r c u i t  shown i n f i g u r e  carbon  i n place by  o f e q u a l l y spaced s t e e l w i r e  ( m ) . The f i e l d  insulated e l e c t r i c a l terminals. are  ( c )behind  i n c h d i a m e t e r German s i l v e r t u b i n g  of fifteen  mixture.  structure of c o l l e c t o r ( f ) , grid (g)  one  consisted  pulse  t h e passage o f  k e l - F 0 - r i n g s ( d ) and h e l d  s h a p i n g r i n g s ( h ) were h e l d on a system o f t h r e e  c o l l e c t o r was made o f .025  inches  the study  The b r a s s e n d p l a t e s o f t h e chamber w e r e  t o t h e c y l i n d r i c a l slides w i t h  field  65ST6  s i d e were mounted a  s o u r c e was c o n c e a l e d i n a b r a s s h o l d e r  operated i r o n f l a p .  aluminum r i n g s and  f i g u r e 1 and t h e t a b l e o f dimensions  and w a t e r v a p o u r w h i c h c o l l e c t e d i n t h e chamber w i t h  magnetically  w i l l be  removed t h e t r a c e amounts o f h y d r o g e n , o x y g e n , n i t r o g e n ,  A Po  sealed  (1964) a n d  e c c e n t r i c a l l y on a l a t h e t o r e d u c e one s i d e t o  o f t h e p h o t o d i s i n t e g r a t i o n o f He .  The  MacDonald  c y l i n d r i c a l w a l l , A , was made o f ,25 i n c h t h i c k A l c a n  aluminum t u b i n g , turned 0.05  (1963) a n d  by Robertson  for the electrode  voltage  supply i s  4« 2 1 0  alpha  source, used t o give an energy c a l i b r a t i o n p o i n t  M e v f o r t h e c h a m b e r , was made b y e v a p o r t a i n g  a b o u t one m i l l i m i c r o -  210 curie l/8  o f s o l u t i o n c o n t a i n i n g Po  inch i ndiameter.  on a h i g h l y polished  T h i s d i s c was h e l d  stainless steel disc  i nt h e source holder  ( c ) b y means  Figure 2  Chamber Dimensions Dimension  Inside radius of cylinder wall  5.72 ± . 0 5 cm  Radius of collector  0.0507± . 0 0 0 6 cm  Mean radius of grid  0 . 3 8 5 d . 0 0 5 cm  Diameter of grid wires  0.0058 cm  Radius of inner guard ring  1.75 cm  (to centre of ring) Radius of outer guard ring  3.65  Distance between grid supports  1 4 . 4 * . 0 2 5 cm  cm  (length of active volume) Inside length of chamber  2 1 . 5 cm  Approximate t o t a l volume of chamber  2.2 liters  Total volume i n active region  1480±15  cm  3  Volume of electrode support as a percentage of V^ot  2.20#  Volume enclosed by grid as a percentage of V^ ^ Q  0.45*  Active volume  1455*15  Measured chamber capacity  10 * 2 pf  Chamber capacity and amplifier  18t3 f  ; input capacity  p  cm  3  Figure 3 * Deisils  a{  Collector  Siuj)por"l  Figure 4  {  Elec4ro<Je  l/ol-tage  Supply  Circuit  50 f  HT  P  to  (3000v) (ceramic  All ca-pcxitors paper unless o+Vierujise specified  -franSf'ttino)  -3of Edwards Picien vacuum wax.  After purifying the chamber by passing the  gas through the Ca-Mg eutectic at a temperature of 300°C for about 24 hours, a resolution of about 3% (or 160 kev) was obtained i n the alpha peak. This i s compared to the intrinsic resolution of the preamplifier and amplif i e r system, as checked by a pulser, which was about 2% at 5,3 Mev. The residual alpha activity of the chamber arises largely from the aluminum walls, which emit .31 alphas/cm -hr with an energy above 250 kev (Sharpe, 1955) < > If the chamber walls are coated with aquadag, an aqueous dispersion of graphite, this i s reduced to about .07 alphas/cm^-hr.  With  this ionization chamber, further reduction was obtained by lining the inside surfaces with Mylar, a polyester film produced by Dupont. The Mylar was coated on both sides by an evaporated gold film, to render the surface conducting and so avoid field distortion due to accumulated charge.  This  reduced the alpha particle background to .02 alphas/cm^-hr, uniformly distributed over an energy range from 0 to 7 Mev. The chamber was normally operated at a center wire potential of 3000 volts.  The voltage of the grid and f i e l d shaping rings was then set  by the dropping resistors as shown i n figure 4.  The chamber was free from  breakdown up to 4000 volts—the rating of the collector decoupling condensor.  However breakdown d i f f i c u l t i e s were encountered i n the electrode  voltage supply circuit when the chamber was used on the roof of the Physics Building during the monitoring of the cosmic neutron flux.  This breakdown  was overcome by enclosing the chamber i n a cardboard box covered with a plastic dropsheet. Due to the capture of electrons by electronegative atoms and the recombination of ion pairs produced i n the chamber at the high pressure used, the size of the voltage pulse produced by some event depended on the rate  -4at which the electrons were collected onto the center wire; that i s , depended on the center wire voltage.  Above a collector voltage of 2500 volts, the  pulse height for 5 . 3 Mev alpha particles from Po  210  increased f a i r l y l i n -  early with voltage, progressing from a relative height of 4.0 units at 2500 volts to 5 . 0 units at 4000 volts.  Over a period of weeks, this pulse height  for fixed collector voltage decreased due to the generation of electronegative gases i n the chamber, removing increasing numbers of electrons from the fast component of the voltage pulse.  For prolonged periods between  purifications, the pulse height could decrease to 50$ of i t s i n i t i a l value.  CHAPTER III NEUTRON THRESHOLD MEASUREMENTS IN B r 1.  8 1  AND  Cd  1 1 6  Introduction The measurement of neutron thresholds by bombardment with charged  particles gives f i r s t of a l l the Q-values for reactions involving ground states and excited states of nuclei.  This w i l l i n turn establish isotopic  mass differences i n the f i r s t ca.se and w i l l locate excited states and measure their energy i n the second case.  A considerable amount of precise mass  data has been accumulated i n this way. .2.  Shape of the Neutron Yield Curve The potential barrier to the emission of neutrons from a nucleus  i s of the form  4  , ,  Thus at threshold, unless there i s some selection rule operating, there w i l l be a large component of X-0 neutrons.  The energy dependence for the total  reation cross section, Wigner (1948) and Guier ( 1 9 5 7 ) , i s shown in Appendix A to have the form, for s-wave neutrons,  « k  0-  n  w h e r e !<„ i s t h e n e u t r o n wave n u m b e r . Since  k -  ~  n  and/\ = —  , then the t o t a l cross  s e c t i o n dependence on  final  neutron energy has t h e form  The n e u t r o n e n e r g y E the  threshold  the  recoil  n  i s t h e d i f f e r e n c e between t h e bombarding e n e r g y and  energy, n e g l e c t i n g  t h e s m a l l amount o f e n e r g y t r a n s f e r r e d t o  nucleus.  h The r e s u l t 0" <* f that  n  i s , f o r a thin target.  i s the cross Integrating  e n e r g i e s r a n g i n g f r o m z e r o t o E„( \  the y i e l d  Hence f o r t h e y i e l d f r o m a t h i c k t a r g e t  it  3.  over a t h i c k target f o r  one h a s  so f o r a l i n e a r e x t r a p o l a t i o n t o z e r o y i e l d t o g e t t h e t h r e s h o l d , i s necessary t o plot  versus  N e u t r o n T h r e s h o l d f o r Id7(p,n)Be  a  x ) ( t h a t i s , t o p l o t Y^  p l o t , a r u n was made t o m e a s u r e t h e t h r e s h o l d The t a r g e t  c h a m b e r u s e d was t h a t  7  A target  o f a b o u t 10 k e v t o 2 M e v  A graph showing b o t h t h e n e u t r o n y i e l d and ( n e u t r o n y i e l d ) b o m b a r d i n g e n e r g y i s shown i n f i g u r e 5. a  of the Y plot.  of the y  f o r the reaction Id7(p,n)Be .  shown i n f i g u r e Vh.  l i t h i u m was e v a p o r a t e d t o a t h i c k n e s s  versus  3  7  To c h e c k t h e e x p e r i m e n t a l s e t u p a n d t h e u s e f u l n e s s  Y  energy,  yields  mg>  and  section f o r a single neutron  I n t h i s case, l i n e a r  of natural protons.  versus extrapolation  /3  plot gives  a value about 1 kev below l i n e a r e x t r a p o l a t i o n o f t h e  I n the case o f a y i e l d  curve with  a smaller  slope, t h i s  error  Figure 5 :  Cr.rap)i o r  sn«J (jJeudron  A/eu4ran yfal^  "Plotted flyunst A/eu-f ron  BomDSrcLimj  Yield)  Energy  416000  -\ /4ooo  Y © H /2ooo  10000  6000  2ooo  1.850  Proton  1,154  Bomba^dmo  I.2S8  Energy  I.9b2  jVi  l.?(,6  Mev  1.270  (i)r\ca\\brei^)  would be larger. 4. Motivation for the B r ( p , n ) K r 81  81  and C d  ll6  (p,n)In  116  Threshold  Measurements The primary motivation for studying these reactions was the uncertainty i n the mass values for either the target nucleus or the product nucleus.  This i s illustrated i n the following table (Everling). Mass Excess (C = 0)  Error  -77.510 Mev  .035 Mev  I2  Br Kr  8 1  -77.680 Mev  .090 Mev  Cd  1 1 6  -88.480 Mev  .300 Mev  In  1 1 6  -87.890 Mev  .170 Mev  Further considerations i n the choice of reactions to study were the necessity that the threshold be below 3 Mev, since the device available to accelerate the protons was a 3 Mev van de Graaff generator, and the need for the reactions to have the correct changes of parity and angular momentum to go at low energies. The Q-values for the two reactions, calculated using the mass values from Nuclear Data Tables ares Br (p,n)Kr  81  Q= -1.030 ± .090 Mev  Cd^tp^In  1 1 6  Q= -1.370 ± .340 Mev  81  The values for the angular momenta and parities of the states involved are shown i n the following energy level diagrams. (Nuclear Data Sheets)  _&89 0-64  0.19 z -  x  _o.qr  Kr*  1  0-0  Br  8 1  o.«i  0.22.  0.07  life 0.0  C d 116  The t r a n s i t i o n from t h e ground s t a t e o f B r of Kr  i n v o l v e s a p a r i t y shange and A J / C B  f o r the plot of Y One  0  t o t h e ground  The o u t g o i n g neutrons  v e r s u s bombarding energy t o y i e l d a s t r a i g h t  u n i t o f a n g u l a r momentum change can come from t h e i n t r i n s i c  momentum o f t h e bombarding p r o t o n and d e p a r t i n g neutron.,  state  need  JL O a  line. angular  The o t h e r u n i t  can come from t h e o r b i t a l a n g u l a r momentum o f t h e bombarding p r o t o n , which a l r e a d y needs X odd t o p r o v i d e f o r t h e p a r i t y change, and hence t h e r e a c t i o n w i l l go w i t h p-wave p r o t o n s .  81 The t r a n s i t i o n t o t h e f i r s t e x c i t e d s t a t e o f K r r e q u i r e s no p a r i t y change and AT* 1 . s-wave p r o t o n s .  a t .19 Mev  T h i s can be accomplished  with  -8The  t r a n s i t i o n from t h e ground s t a t e o f Cd  o f I n ^ " ^ i n v o l v e s n o p a r i t y c h a n g e a n d AT = 0 o r i . be  a c c o m p l i s h e d b y s-wave  5.  116  t o t h e ground  state  I n e i t h e r case, t h i s can  protons.  Targets a) M a t e r i a l u s e d The  m a t e r i a l used f o r t h e v a r i o u s  i n n a t u r a l i s o t o p i c abundances. stable isotopes  Br  7 9  Br  8 1  Cd  1 0 6  Cd  1 0 8  contained  The Q - v a l u e s f o r ( p , n ) r e a c t i o n s  % Natural Abundance  (p,n)  50.57  -2.404 ±.005 M e v  49.43  -1.030 + .090 M e v  1.22  Cd °  12.43  -4.742 i .040 M e v  Cd  1 1 1  12.86  =2.020 ±.210 M e v  Cd  1 1 2  23.79  =3.398i .019 M e v  Cd  1 1 3  12.34  -0.473 ±.010 M e v  Cd  1 1  28.81  -2.203± .020 M e v  Cd * 1  6  a r e shown  Q-Values  =5.880± .100 M e v  ^  f o r the  Tables)  .89  n  B r and Cd  o f Cd and B r , a s c a l c u l a t e d f r o m t h e mass v a l u e s ,  below. (Nuclear Data  Isotope  targets  7.66  -1.370±.340 Mev  Thus i n n a t u r a l l y d i s t r i b u t e d b r o m i n e , t h e n e u t r o n t h r e s h o l d w i l l be t h a t o f Br  81  .  113 However, i n n a t u r a l l y d i s t r i b u t e d cadmium, Cd ^ had t h e l o w e s t 113  threshold. next  page.  The e n e r g y l e v e l s k e t c h  f o r Cd  113 (p,n)In  i s shown o n t h e  -9= 5,9  .  (f|  awj  1  J-  0-0 Cd"  I n order t o y i e l d  Q.393  a  3  o-o  f  s-wave n e u t r o n s , one needs g-wave protons t o the ground  113 state of In  o r p-wave protons t o t h e f i r s t two  e n e r g i e s i n v o l v e d are  .47  Mev,  .86 Mev  and 1.12  excited states.  Mev,  S i n c e the  these r e a c t i o n s are  116 unlikely.  (p,n)In^"° i s 0 ->  On the o t h e r hand, the r e a c t i o n Cd  +  T h i s r e a c t i o n i s p o s s i b l e w i t h s-wave p r o t o n s .  The  only other  d i f f i c u l t y i s t h a t no e s t i m a t e i s made o f the Q-value f o r Cd  (p , 1*). . +  remaining  106,  106  x  (p,n)In  However, t h i s v a l u e i s p r o b a b l y g r e a t e r t h a n t h a t f o r C d ^ ( p , n ) l n ^ 8  (-5.88  Mev)  because C d ^ ^  i s even more d e f i c i e n t i n n e u t r o n s than  8  Cd^ . 8  81 The B r  t a r g e t s c o n s i s t e d o f e i t h e r NaBr(AR) o r  o r a t e d onto copper b a c k i n g s .  BaB^CR)  The neutron t h r e s h o l d f o r Na i s  5.053  evapMev  ( N u c l e a r Data T a b l e s ) and the lowest t h r e s h o l d among t h e v a r i o u s i s o t o p e s  138 o f Ba i s t h a t o f Ba The C d " ^ l u r g y Dept, U.B.C.  which i s 2.3 t a r g e t was I t was  t o a t h i c k n e s s o f .030  a  Mev.  o b t a i n e d from Dr I.H. Warren o f the M e t a l -  99.999$  pure cadmium b a r which had been r o l l e d  inches,  b) Manufacture o f T a r g e t s i ) NaBr About 2 grams o f NaBr(AR) was in a bell-jar. 10~^  The  p l a c e d i n a t a n t a l u m boat  p r e s s u r e i n the b e l l j a r was  t o r r and the t a n t a l u m boat was  enclosed  reduced t o about  s l o w l y heated by p a s s i n g an  -10alternating current through i t to drive off the water of hydration of the NaBr. I f the,boat temperature was raised too quickly, severe decrepitation of the hydrated NaBr occurred, rapidly emptying the boat of a l l NaBr. When decrepitation of the NaBr had ceased  -5 and the bell-jar pressure had fallen to about 2x10  torr, the boat  temperature was raised to about 1000°C (orange colour) and the NaBr evaporated onto a copper plate,which had been etched i n dilute HNO^,  placed about 6 centimeters above the boat.  The f i n a l target  size was about 1.5 inches square and had a thickness of about .02 inches of NaBr. i i ) BaBr  2  BaBr2 was evaporated onto copper backings i n nuch the same manner as was NaBr. The principal differences weres 1) Hydrated BaBr decrepitated more violently than NaBr and had 2  to have a longer heating time. 2) BaBr2 would not adhere to the etched copper surface but would adhere to a sandblasted surface. 3) The BaBr targets were much thinner than the NaBr ones (about 2  .001 inches). i i i ) Cadmium The- cadmium target was used i n the form provided (see page 9). A piece 1.5 inches by 2 inches was soft soldered to a copper piece of the same dimensions to serve as a heat sink because i t was found that the  unsupported cadmium targets tended to melt where struck  by the proton beam. The surface of the target was cleaned by washing with acetome. Further cleaning resulted due to slow evaporation of the target surface when i f was heated by the bom-  -11barding proton beam. Other cadmium targets were made by milling the surface of a cadmium piece soldered to a copper backing and by evaporation of cadmium from a tantalum boat onto a sandblasted copper backing. 6.  Arrangement of Target Chamber and Detector The arrangement of targets, target chamber, detector and  shielding i s shown i n figure 6. a pyrex tee.  The target was mounted on a brass rod i n  The brass rod was held i n a sliding seal so that the target  could be turned around by means of a cord passing to the outside of the wax shielding.  This made i t possible to run protons f i r s t on the target to get  the reaction count rate.  Then, by turning the target mount, protons were  run on a platinum target to get the background counting rate.  The brass  rod was drilled out through the center to allow the passage of a current of water to cool the target. When desired, the target could be retracted and a quartz piece lowered into the beam path for the purpose of focusing the beam. The detector and target chamber were surrounded by about one inch thickness of wax.  This served to moderate and trap the neutrons coming from  the target and so increase the efficiency of the detector.  Around the mod-  erator was placed neutron shielding consisting of .048 inches of cadmium and twelve inches of wax.  This served to shield out neutrons originating  from sources other than the target chamber. 7. Electronics A block diagram of the electronics used i s shown i n figure 7. The H. T. on the collector of the ionization chamber was derived from a 0-5000 volt North-East Power Supply,  The pulses from the ionization cham-  ber were fed through a Dynatron type 1430A preamplifier and main amplifier  Ti  9i*eA  UJ<X*  hiob'ila  ro  ch^r^Ler  O)  cka.mber_ H OJ  water lines Card. —  :  o  v. ' (retracted )  5  )  cr  J)  ra  proton be~aw  0>  beam coHinno-W-  3  4arqe.t • p_yr&i, tee de-teoW — nea+v-on moderod-or shield.—  7  'Block  icjure 7  of  T3isgr"flvr>  .c 3 2.  T3 n  IL  C-  a) i.  a:  o  a)  EI«cfromcS  -12-  unit  i n t o 128 c h a n n e l s o f a N u c l e a r D a t a 120 p u l s e h e i g h t a n a l y z e r .  h e r e , t h e e n e r g y s p e c t r u m o f p u l s e s o b t a i n e d c o u l d be electric The  typewriter or displayed  p r i n t e d out on an  on a model 701 F a i r c h i l d  IBM  oscilloscope.  i n t e g r a t i o n and d i f f e r e n t i a t i o n t i m e c o n s t a n t s u s e d o n t h e D y n a t r o n m a i n  a m p l i f i e r were b o t h 8 m i c r o s e c o n d s . w i n d o w o f t h e ND r e a d i n g due  120 k i c k s o r t e r was  The  a t t e n u a t i o n u s e d was  s e t so as t o g i v e a b o u t  16 d b .  1$  The  deadtime  t o e l e c t r o n i c and chamber n o i s e .  The in  From  f i g u r e 8.  e l e c t r o n i c s u s e d t o m o n i t o r t h e p r o t o n beam c u r r e n t a r e shown A 90 v o l t s p o s i t i v e b i a s was  a p p l i e d t o the t a r g e t t o r e -  d u c e t h e c u r r e n t due t o s e c o n d a r y e l e c t r o n s k n o c k e d t h e i n c i d e n t p r o t o n beam.  The  c u r r e n t was  out o f the target  by  t h e n passed t h r o u g h an E l d o r a d o  C u r r e n t I n t e g r a t o r , M o d e l C I - 1 1 0 , w h i c h m o n i t o r e d c u r r e n t and  accumulated  charge.  8.  Background  Counting Rate  The b a c k g r o u n d  c o u n t i n g r a t e was  produced p r i n c i p a l l y by  two  sources? a ) Beam d e p e n d e n t 90°  background  coming  b e n d i n g magnet a t t h e base  accelerating  l a r g e l y f r o m t h e magnet b o x o f t h e  o f t h e v a n de G r a a f f g e n e r a t o r  column.  b ) Time dependent  background  coming  l a r g e l y from cosmic neutrons.  As a check t h a t t h e time dependent t h e cosmic n e u t r o n f l u x , a measure o f t h i s f r o m t h e v a n de G r a a f f l a b o r a t o r y . n e u t r o n p e a k was dependent  f l u x was  c o u n t i n g r a t e was  s h i e l d e d b y wax  and  was  due  largely  to  made a t some d i s t a n c e  count r a t e o b t a i n e d i n the t h e r m a l  a b o u t 470 n e u t r o n s / h o u r f o r t h e w h o l e  background  b e r w h e n i t was  The  background  chamber.  The  time  a b o u t 100 n e u t r o n s / h o u r i n t h e cham-  cadmium.  T h i s c o u l d be a s c r i b e d t o  fast  Elec+romcs  Used in \/Br\ de Qradff  Enera y  u.lo.4edL P.O.  ft Vovwi t Hig h VoHouje.  power Supply  -Pou>ev- Supply  N a l  (Tl)  A/D 501 Single Ctowwcl ?ulse  Height  A n a Is****  £lec4romcs  Used  + 90 _ vohts  to MOVUTOY- Beam  10  Current  Curreirfc Tn+e^rator  (2slibr<x.+  -13neutrons i n the cosmic neutron flux. Consisting of two components, the background was combatted i n two ways. It was found that the beam dependent background was due chiefly to deuterium contamination i n the HF ion source, accelerating column and magnet box.  This contamination was highest immediately after deuterium  ions had been accelerated for some experiment and therafter decreased with time as the deuterium was pumped out of the system.  It was found  that after about three days with no deuterium acceleration, the beam dependent background was sufficiently low to be tolerable.  At a bombarding  energy of 1.2 Mev, the beam dependent background was comparable to the time dependent background and together they were about equal to the neutron yield from Br ^(p,n)Kr "*" about 100 kev above threshold when a 5 microampere 8  8  At energies of 1.6 Mev and higher, where the search for the  beam was used. Cd"^(p,n)In^  1  threshold was carried out, the beam dependent background  was up by a factor twenty and constituted more than ninety percent of the t o t a l background.  At the beam currents used, this was about .3 counts  per microcoulomb. The time dependent background was reduced by increasing the proton current incident on the target.  This was accomplished by using larger  heat sinks as target backings and by using a large beam spot (about 1 cm square) to avoid local heating of the target. The method used to monitor the background for the Br "Hp,n)Kr ^" 8  8  threshold measurement was to run on a .002 inch platinum f o i l , indium soldered to a copper heat sink,  immediately after each run on the target.  This run was carried out for the same  current, charge and beam focusing  conditions as the primary target run. Thus the only change effected was to remove the primary target and put a platinum one i n i t s place.  It was found  that about the same background counting rate was achieved whether one ran  -14on the platinum target or on a stop outside of the wax and cadmium shielding, indicating that l i t t l e or none of the background counting rate originated inside the target ahamber. For the Cd^^(p,n)In^"^ threshold search, the background was estimated i n a similar way by running on a tantalum piece. However, i n this case, the background counting rate was higher than that obtained by running on a stop outside the wax and cadmium shielding—probably due to increased coulomb scattering of higher energy protons onto the chamber walls. 9.  Energy Calibration of the Van de Graaff Generator The machine energy was calibrated by means of resonances i n the 19  reaction F  16 (p,<*#)0  and .9353 Mev.  at proton bombarding energies of .669 Mev,  .8735 Mev  The resulting gamma ray flux was monitored with a 2 and  3/4 inch diameter by k and 1/2 inch long Nal(Tl) s c i n t i l l a t i o n counter. The electronics used are shown i n figure 8.  The output of the photomul-  t i p l i e r was fed to a Nuclear Data amplifier Model 501.  The amplifier also  served as a single channel pulse height analyzer. The discriminators of this analyzer were set approximately so that a l l pulses greater than counter.  were  The anticoincidence pulse from the discriminator was then fed into  a Model U.B.C.-N.P.-II scaler and there counted The target was made by evaporating 10 mg of CaF2vCP) onto copper backings which had been polished smooth. The CaF£ was evaporated from a tantalum boat at a temperature of about 1400°C (white hot). The copper backings were held about 15 cm from the boat and the resulting targets had a thicKness of less than 5 kev. 10.  81  Threshold Energy for Br  81  (p,n)Kr  Graphs of the neutron yield near threshold are shown for NaBr  -15-  and BaBr  2  targets i n figure 9 .  The curve for the yield from the NaBr target  shows a linear low energy t a i l extending down to about 700 kev. not  This does  appear i n the yield curve for the BaBr^ target nor does i t s shape 8/3  obey any c ( »^ law. n  rn0l  Hence i n using the data from the NaBr target, this  t a i l was extrapolated up and subtracted out of the yield curve. The resulting NaBr target data was then used just as a check on the more precise results gained from the BaBr target. 2  A graph of yield raised to the 2/3 power plotted against bombarding energy for the BaBr target i s shown i n figure 1 0 . 2  The f i r s t eleven  points on this curve were fitted with a straight line by means of least squares. 1,133 Mev.  The energy intercept of this line, giving the threshold, i s Also shown on this graph i s a similar plot for the corrected  yield from the NaBr target.  This gives as the energy 1.10 Mev, a value  sufficiently close to the BaBr result i n view of the approximate nature 2  of the NaBr target results. A further graph of Y ' versus energy for the yield from the BaBr target i s shown in figure 11. 2  ion,  This shows a higher energy linear reg-  extending from about 1400 kev to about 1550 kev.  This may be due to  81 at .19 Mev.  neutron emission to the f i r s t excited state of Kr a threshold would tend to linearize the Y  That such  plot i n the presence of the  ground state threshold which has l e f t the linear region may be due to the fact that i t proceeds by s-wave protons (see page 7) whereas the ground state threshold proceeds by p-wave protons. Hence the cross section for  81 neutron emission to the f i r s t excited state of Kr the  i s probably larger than  cross section for neutron emission to the ground state.  Another reason  why such a threshold could linearize the graph i s that the detecting system i s more sensitive to slow neutrons to the f i r s t excited state than to the  Figure 9  (  -I  l_  -1681 fast neutrons to the ground state of Kr • The threshold value of 1.133 Mev can be converted to a Q-value by means of the approximate r e l a t i v i s t i c relation given by Langsdorf  where m^ and m are the atomic masses of the incident particle and target 2  respectively.  This yields the result Q = -1.120 Mev  This agrees with the value of -1.030^.090 predicted from the mass values. The standard deviation i n this result, taken from the standard deviations shown i n figure 10, i s about 20 kev.  Since this i s by far  the dominant source of uncertainty, the the threshold can be quoted as I. 133 .020 Mev. ±  II.  Threshold Energy for Cd^"^(p,n)In^ 116, . 116 A search for the threshold of the reaction Cd (p,n;In was  carried out for proton energies ranging up to 2.0 Mev using a procedure 81, . 81 similar to that used to measure the Br  (p,n;Kr  threshold. Below a proton  energy of 1.60 Mev, no neutron production which could be ascribed to cadmium was observed.  Above an energy of about 1.64 Mev, many neutron resonances  were observed (see figure 12). cadmium targets were  Similar results were obtained whether the  used as obtained from the Department of Metallurgy,  had the surface milled off or were made by evaporation of cadmium onto a sandblasted copper backing.  Since the cadmium target was many Mev thick,  these neutrons could only proceed from a thin target deposited on the surface of the cadmium target. The material making up this thin target has a 37 37 (p,n) threshold at 1.64 Mev. This f i t s the reaction C l (p,n)A which has  Figure 12. ;  Neutron  Yield  Snooomj  "Resonances  ^ accumulated  •prom  Evaporated* Due T o  prc4ov\  Cs^wwum  T~e?rje"t.  37  Cl^pjh l°oo^yo\,coul J  chgrcje  9oo j-7041— 600I-  Sou|  300  2.00  .5) 5  1 0 0  ± «* J  QJ  "2:  So 8  70  j  So 4.0  36  10  |.60  J 1.61-  I-72  L  -I  I.76  L. -J  /.80  L  "Proton  '  »  /.92  Energy  (^ei/)  ' /.96  '  2,oo  -17-  a threshold at  1.6U1- .002  M e v ( S c h o e n f e l d ) a n d h a s many r e s o n a n c e s  corres-  38 ponding t o excited kev.  levels i nA  The n e u t r o n y i e l d  , w i t h an average  s e p a r a t i o n o f about 5  g r a p h o b t a i n e d b y S c h o e n f e l d i s s h o w n i n f i g u r e 13  and i n g e n e r a l a g r e e s w i t h t h a t  shown i n f i g u r e 1 2 , t a k i n g i n t o a c c o u n t a n  energy s h i f t o f about 8 k e v — a n  amount Within t h e c o m b i n e d  energy uncer-  t a i n t y o f t h e two measurementso From t h e graph o f f i g u r e 1 2 , i t i s apparent t h a t t h e C d " ^ ( p , n ) 116 In  t h r e s h o l d i s p r o b a b l y a b o v e 1.72 M e v , s i n c e t h e n e u t r o n y i e l d f r o m t h e  cadmium t a r g e t a t t h i s p o i n t d i p s t o t h e v a l u e s o b t a i n e d An  below  i n v e s t i g a t i o n o f t h e v a l l e y a t 1.92 Mev gave a s a n u p p e r  60 n e u t r o n s f o r a p r o t o n c h a r g e o f 4000 m i c r o c o u l o m b s . f o r t h e p e n e t r a b i l i t y o f a coulomb b a r r i e r T  1.60 Mev.  limit  o f about  Using the formula  (Bohm 1 9 5 1 )  =  where  c  o  s  *  = J%  w  _  (3  ,  (/  81 116 the r a t i o o f the p e n e t r a b i l i t i e s f o r Br and Cd i s Penetrability  (Cd  1 1 6  )  Penetrability Assuming  the yield  c u r v e from Cd  116  (Br  8 1  h a s t h e same s h a p e  t h e n t h i s would  put a lower l i m i t  Cd'^tp^In "^  f r o m n e u t r o n s i n v a l l e y a t 1.92 M e v .  1  .04  ) 81 as t h a t from B r ,  o f a b o u t 1.5 M e v o n t h e t h r e s h o l d o f  I n a f i n a l e f f o r t t o produce  a cadmium t a r g e t f r e e o f s u r f a c e  c h l o r i n e c o n t a m i n a t i o n , t h e t a r g e t chamber i l l u s t r a t e d  i n figure  1 4 was u s e d .  U s i n g t h i s c h a m b e r , t h e cadmium t a r g e t c o u l d b e e v a p o r a t e d i m m e d i a t e l y b e f o r e u s e a n d t h e n d r a w n u p i n t o t h e p r o t o n beam w i t h o u t b e i n g e x p o s e d t o  figure  |3 '  ^eu+ro*  Yield  for  -f-ke  'Reac+io^  Cl^pjnJA  ( Schoenfeld)  (4 -  1.920  |,?40  i960  "Proton  I.880 Energy  1,900 (Mev)  ,920  Figure 14 * .  Csdrniuvn  Evapora-for  Tsrozk  Chgrnber  Fifjuve. 15" '  /Veu-rrow  Y\e,\d pro™  "B^tlcv^  gv\d Beewv Depended B^you^d*  "  Tsn+aluw  P  r  o  Target  t  o  n  E  n  e  r  the atmosphere. o f about 1 0 0  The  cadmium t a r g e t s p r o d u c e d  by  t h i s method had  a thickness  kev.  R u n n i n g on t h e t a n t a l u m t a r g e t b a c k i n g b e f o r e e v a p o r a t i o n o f cadmium gave t h e n e u t r o n y i e l d mium t a r g e t was  evaporated  curve  shown i n f i g u r e  The  Neutron Y i e l d Cd Beam D e p e n d e n t  Mev  900yt<coul  286  244  42  1.600  Mev  9 0 0 y*COUl  235  180  55  1.700  Mev  900 y*coul  320  217  103  1.720  Mev  600  214  1.800  Mev  600y*coul  197  121  The T h i s agrees  yield  at 1.720  the y i e l d  Mev,  c l o s e l y with the 3 2 0  shows t h a t t h e c h l o r i n e at 1.700  Mev  normalized to 900yucoul, i s 321 obtained at 1.700  counts  c o n t a m i n a t i o n produced and  1.720  Mev.  T h u s i t w o u l d seem t h a t t h e c h l o r i n e atmosphere. the  surface chlorine  between  from the n e u t r o n y i e l d s ) , t h e n an a t m o s p h e r i c  from  the  ( l e s s t h a n 40 e v ,  chlorine  a  contamination.  surface i s chemically quite  were q u i t e t h i n  12  Figure  o f a b o u t two  contamination originated  Since a f r e s h l y evaporated  c h l o r i n e t a r g e t s produced  a ratio  Mev.  counts.  Hence t h i s method o f p r o d u c i n g  cadmium t a r g e t a p p a r e n t l y e l i m i n a t e s t h e  and  Difference  1.500  318  obtained  the neutron d e t e c t o r .  Accumulated Charge  yUcoul  cad-  shown i n t h e  beam d e p e n d e n t b a c k g r o u n d was  r u n n i n g on a q u a r t z s t o p about 3 meters from  Proton Energy  A f t e r the  onto the b a c k i n g , the neutron y i e l d s  f o l l o w i n g t a b l e were o b t a i n e d . by  15.  the  active estimated  contamination  of  n 1  in  10  pheric  would p r o d u c e t h i s t a r g e t ( b a s e d o n t h e a s s u m p t i o n t h a t a n a t m o s chlorine  atom m i g r a t e s  about 1 0 0 meters i n the  mium t a r g e t i s e x p o s e d t o t h e a t m o s p h e r e ) .  The  period the  atmospheric  cad-  chlorine  -19contamination might come from such sources as freon used i n the van de Graaff pressure tank or trichlorethylene used as a solvent i n the lab. Comparison of the difference between the neutron yield of the cadmium target and the beam dependent background with the graph i n figure 15 yields the following tables Proton Neutron Yield (norma!L i z e d to 1800 coul) Difference Energy Cd Target-Beam Depentent Ta Target-Beam Dependent (Mev) Background Background 1.60  110*40  138*30  -28±50  1.70  206±46  121*30  87±60  1.80  363±66  257*34  106±70  The numbers under Difference would ordinarily be ascribed to the neutron yield from cadmium,, However, the numbers obtained have large uncertainties attached to them due to the large background counting rate and also do not exhibit any shape characteristic of a threshold.  Hence i t i s not possible  to identify a (p,n) threshold for cadmium below 1.8 Mev, which i s i t s e l f above the upper limit of 1,71 Mev set by the table of consistent Q-values (Nuclear Data Tables). CHAPTER IV MEASUREMENT OF THE COSMIC NEUTRON FLUX AT THE EARTH'S SURFACE 1.  Introduction During a measurement of the threshold energy of the reaction 81  Br  81  (p,n)Kr  , i t was found that a large part of the background counting  rate was independent of the bombarding proton beam,. This count rate was about 120 counts per hour and was comparable to the count rate for the reac=  -20-  tion itself. To  T h i s background was  check t h i s , i t was  T h i s measurement was  decided  t e n t a t i v e l y a s c r i b e d t o cosmic n e u t r o n s .  t o measure the  c a r r i e d out on the  cosmic n e u t r o n f l u x d e n s i t y .  r o o f o f the P h y s i c s B u i l d i n g  64  3 f e e t above ground l e v e l making use  o f the He  f i l l e d i o n i z a t i o n chamber as  the neutron d e t e c t o r . 2.  Arrangement o f E x p e r i m e n t a l Apparatus The  in  arrangement o f the apparatus i s shown i n the b l o c k  figure 1 6 .  r i n g s o f the Corporation  The  h i g h t e n s i o n f o r the  i o n i z a t i o n chamber was 5000  centre wire,  g r i d and  s u p p l i e d by a North E a s t  v o l t s power s u p p l y , Model  RE=5001AW1.  The  i o n i z a t i o n chamber were f e d t h r o u g h a model  1430A JDynatron  main a m p l i f i e r u n i t i n t o a N u c l e a r Data 101  multichannel  lyzer.  From here the  i n f o r m a t i o n was  power t o run t h i s assembly was  pressor to eliminate voltage  3.  Chamber  shaping  Scientific s i g n a l s from the  preamplifier  read out n o n - d e s t r u c t i v e l y e i t h e r on electric  typewriter.  spikes„  Filling  He  chamber c o n t a i n e d ?  3  1.41  CH^  ol9  A total  atm  (0°C)  atm  1.36  atm  2.96  atm  At the time o f the n e u t r o n f l u x d e n s i t y measurement, t h i s had (0°C).  Using  and  ana-  f e d through a r a d i o i n t e r f e r e n c e sup-  •When i n i t i a l l y f i l l e d , the  2 „ 7 1 atm  field  pulse height  a Model 7 0 1 F a i r c h i l d o s c i l l o s c o p e o r by means o f an IBM The  diagram  a law o f the form  dP cit  JlJ  y  f a l l e n to  Figure  16  Block iVemfron  Diagram  of  Eledromcs  far  Vie.asunfxj  Cosmic  Flux  Ht>.  ''ficr  flmoll Pier  -f i f«e<4  ch3wib«>"  kicksor+e*(3ooc i/o fe)  t)sct"osc«-pe.  »>>erfe rev-ice.  -21whereP- partial pressure m = m o l e c u l a r weight k = constant yields  as p a r t i a l pressures at the time  He  o f t h e measurements  3  1.21  atm  .19  atm  1.31  atm  2„71  atm  CH^ A total  4.  Chamber E f f i c i e n c y f o r N e u t r o n  Detection  A s s u m i n g a n i s o t r o p i c d i s t r i b u t i o n o f n e u t r o n t r a c k s i n t h e chamb e r , t h e a v e r a g e p a t h l e n g t h .in t h e a c t i v e v o l u m e o f t h e c h a m b e r was c u l a t e d t o b e 8.0  cal-  cm.  3 U s i n g t h e t w o v a l u e s o f He the  chamber n e u t r o n  capture No  number d e n s i t y a n d a v e r a g e p a t h l e n g t h ,  e f f i c i e n c y was c a l c u l a t e d  from t h e f o r m u l a  e "  where 1 - -  - chamber  v\ ~ 3.25  X"  8.0  10  efficiency He  19  3  atoms/cm  3  cm  o" = cross s e c t i o n for n e u t r o n c a p t u r e b y He  (Neutron  Cross  Sections) The g r a p h  o f t h e chamber e f f i c i e n c y v e r s u s n e u t r o n e n e r g y  l o g - l o g and l o g - l i n e a r  1)  log-linear  plot  i s figure  plot, valid  Efficiency  17.  for  i s shown i n b o t h  The s t r a i g h t - l i n e e q u a t i o n s  10° <£<10°^ 8  Mev  = -1.901 - J 5 0 S JUi£  ares  Fioure Efficiency Stale  17 s  Chamber  Efficiency  J  Linear Stale  jVeurfron  £r\era  \  /Mai')  =22=  2) l o g - l o g p l o t , v a l i d  =7 -2 f o r 5 10 '<£< 10 Mev -.479  Z- 4 3*/o~ £  Efficiency ~8 Below a neutron energy 100%,  o f 10  ^ Mev, t h e chamber e f f i c i e n c y i s a p p r o x i m a t e l y  The f o l l o w i n g t a b l e g i v e s t h e v a l u e s o f chamber e f f i c i e n c y i n t h e  various neutron  energy  Neutron  ranges. Chamber  Energy  Mev  1.0  5 10 •9<£ < 1 10  Mev  -1.901~.1505(lnO  Mev  2.43  6  E f f i c i e n c y o f Cadmium  X  10~ (fc'~° 4  4 7 9  )  Shielding  During part o f the experiment, a box which  Efficiency  £ < 5 10  1 10° <£ < 1 1 0 ~  5.  4  t h e n e u t r o n d e t e c t o r was p l a c e d i n  h a d w a l l s l i n e d w i t h .020 i n c h e s o f c a d m i u m .  Using the law  -oAn  A/  N = //  e  e  .4^3"10  where n= i ~  23  Cd atoms/cm  3  .020 i n c h e s  = .0508 cm O"-  capture neutrons  one  o b t a i n s the graph  shield  c r o s s s e c t i o n o f Cd f o r (Neutron Cross  Sections)  i n f i g u r e 18 s h o w i n g t h e e f f i c i e n c y o f t h e c a d m i u m  f o r the capture o f neutrons.  The e q u a t i o n o f t h e s t r a i g h t  p o r t i o n o f the curve i s  Jb^  (CA £#iciencyj  •= " K>. 95 - Z.G i*g £  where €= n e u t r o n energy  i n Mev  H e n c e o n e g e t s t h e f o l l o w i n g t a b l e f o r t h e cadmium  efficiency?  line  Figure  18 Cadmium  Shielding  Efficiency  -23-  Cadmium E f f i c i e n c y  Neutron Energy =6  1.0  £ < .3 10 .3 1 0 ° < € < 1.0  10~  6  1.0 6.  Mev 6  I^IO^E" ' ) 2  Mev  6  .014  10" <€ 6  The Chamber Counting Rate and Neutron Density In water, the d i f f u s i o n length of thermal neutrons i s about  2.85  cm (Beckerly)o  Based on the density change, t h i s indicates a d i f f u s -  i o n length of more than 46 meters i n a i r .  Hence the presence of the chamber  w i l l not appreciably change the neutron f l u x i n the neighbourhood of the counter. A t y p i c a l neutron spectrum i s shown i n figure B2„  I t shows a large  low energy noise peak, l a r g e l y generated by the leading tube i n the dynatron preamplifier, a f l a t v a l l e y , due t o the end and w a l l e f f e c t s i n the chamber (see appendix B), and the c h a r a c t e r i s t i c thermal peak, extending over about 200 kev due t o the chamber and amplifier re solution o. The e f f e c t i v e neutron f l u x can be related t o the chamber counting rate i n the following ways 4 where C/R.= count rate (counts/sec) >fy - e f f e c t i v e f l u x density ** A  counter surface area  This i s shown i n appendix D ** I f <KE) i s the d i f f e r e n t i a l neutron f l u x , then the t o t a l neutron f l u x is  4>= J 4 (f)dE . >  <  $  &  i s defined as  4> = E  w (^) A't  where  e  0  4> ( ) = 4 > ( € ) y [ c h a m U r E  £  etf.c.ency]  '  T  h  a  t  is  > %,  i  s  j  u  s  the t o t a l f l u x density which i s counted i n the chamber.  t  t  h  a  t  p  a  r  t  °  f  -24The neutron f l u x was monitored with the counter by i t s e l f and with the counter surrounded by various amounts of cadmium shielding. chamber counting rate, the background pendix C) was  To get the  count rate of 1 0 . 2 counts/hour (ap~  subtracted from the f u l l energy peak and the r e s u l t was mul-  t i p l i e d by the appropriate factor (appendix B) to correct f o r the w a l l effect.  The values of c p  obtained under various conditions are shown  &  below. Time  Type of Bun  No Cd shielding  3  . 0 2 " Cd s h i e l5d around chamber  3 2  Counts i n F u l l Chamber Energy Peak Counting Rate (counts/hour) .  .  4 hr  0  15797*122  hr  6619 ± 8 1  8 . 0 5 ± . 2 1 * 1 0  128*2  1.96-t.06*10~  5  hr  701  2 9 8 * 1 4  . 0 3 2 " Cd s h i2e l d. above chamber  5  hr  9 5 0  4 0 7 * 1 6  e  e  5 2 5 * 4  . 0 3 2 " Cd s h i2e l d. below chamber  Values of 4>  4> » (n/cm -sec)  4  are not calculated f o r the l a s t two cases above because the  anisotropic cadmium shielding removes the i s o t r o p i c neutron f l u x and thus one of the conditions f o r the derivation of the formula  CR. i s not  4>- A  fulfilled. The f i r s t two entries i n the above table enable one to evaluate  a neutron density d i s t r i b u t i o n function of the form (Westcott)  w h e r e  o (*>) ^ n  i l l  e A = I for E>J^ A = o fV £ yukT  r  rS i s the v e l o c i t y of a neutron of energy  kT  -25"  T h i s d i s t r i b u t i o n c o n s i s t s o f a M a x w e l l i a n peak o f t h e r m a l n e u t r o n s  (^V(A/)  p l u s a h i g h e n e r g y t a i l w i t h a l / E d e p e n d e n c e ( ^ C«/) )<> T h e c o n s t a n t y < i s e  used t o determine  a low energy  cut-off t othis t a i l .  F o r neutrons from a  m o d e r a t e d r e a c t o r , a v a l u e o f jm_- 5 w a s f o u n d t o w o r k a n d t h i s was adopted h e r e .  value  The t w o c o n s t a n t s l e f t t o e v a l u a t e a r e n , t h e t o t a l  neutron d e n s i t y , and p , the f r a c t i o n o f neutrons i n t h e e p i t h e r m a l t a i l . To  f i n d t h e s e t w o c o n s t a n t s , t w o i n t e g r a t i o n s w e r e made? ( 1 ) w i t h no cadmium <b  =  shielding^  8 . 0 5 ± .37 * ! 0 ~  •^(A^) [ c h s w U r (2) w i t h cadmium s h i e l d i n g  (j>  =  |.96 * J O  x  efficiency  .AT'  .020 i n c h e s t h i c k a r o u n d  the counters  - 4  10  - J <}> (AT) [ l n BK«Ler c  4  (ficiencyj [ [ - CA e rfluencyj  e  Some o f t h e d e t a i l s o f t h e s e i n t e g r a l s , i n c l u d i n g c o m p u t e r p r o g r a m s i n t h e i r e v a l u a t i o n , a r e d i s c u s s e d i n a p p e n d i x E. two  The  l i n e a r e q u a t i o n s i n t h e t w o unknowns, n (1)  Yi(l-f) [l.63lo]  (2)  n  (i-f)  and  + n f [ 2 . 6 2 38]  [-.olfes] + n f [ 1-4216]  f i r s t term i n t h e second  The i n t e g r a l s  used  yielded  f. »  .- 9  8 . 0 5 ± . 3 7 * l >o " 1.94 ±  e q u a t i o n was t a k e n t o b e z e r o .  .10  ,-9  xi©  This yielded  f - .328i.03 4.2±.7*10~  9  T h i s i n d i c a t e s t h a t , a t t h e e a r t h ' s s u r f a c e , t h e cosmic neutron d e n s i t y i s about  4.2±.7*10~  9  n/cm  3  and about  67$ o fthese a r e t h e r m a l i z e d .  These r e -  s u l t s a r e c o m p a r e d w i t h t h o s e o b t a i n e d b y R . F . M i l e s i n s e c t i o n 8.  7.  Measurement o f t h e Cosmic Neutron D e n s i t y over t h e S e a I t was r e p o r t e d b y Goshkov, Z y a b k i n and T s v e t k o v  (1965) t h a t t h e  )  -26. n e u t r o n d e n s i t y i n t h e a t m o s p h e r e o v e r a n e x t e n d e d b o d y o f w a t e r was  three  times lower than that over land.  A c c o r d i n g l y , a m e a s u r e was  neutron counting rate at l a t i t u d e  4 9 ° 25.44« N a n d l o n g e t u d e 1 2 3 ° 2 3 . 8 8 •  T h i s was  made o f t h e  i n Howe S o u n d b e t w e e n G a m b i e r , K e a t s a n d Bowen I s l a n d s .  o f w a t e r was  about  800  f e e t and  the d i s t a n c e from  s h o r e was  The  i n excess  W.  depth of  3 one m i l e .  The  He  filled  i o n i z a t i o n c h a m b e r was  suspended  t w e l v e f e e t f r o m t h e s i d e o f t h e s h i p CNAV W h i t e t h r o a t a n d the water t o be  surface.  The  Time  four feet  box  from  r e s u l t s a r e shown i n t h e f o l l o w i n g t a b l e , w h i c h i s 24.  compared t o t h a t on page  Type o f Run  i n a plywood  Counts Energy  in Full Peak  Chamber Counting Rate  2  (n/cm  -sec)  Cd S h i e l d  1.33 h r  578124  480*20  7.36-+.43*10  . 0 2 0 Cd S h i e l d a r o u n d Chamber  4.20 h r  514*23  123^6.0  1.89*.12*10~  No  I n s e r t i n g t h e s e v a l u e s i n t o e q u a t i o n s (1)  (2)  and  o n p a g e 25  =4  4  yields  .358=* .072 n= 3 . 7 2 ± . 9 8 * 1 0 " where  9  n/cm  3  f r a c t i o n of neutrons i n epithermal tail n ~ density of  T h i s i n d i c a t e s t h a t t h e n e u t r o n d e n s i t y i s about t h a n over the land.  which has been reduced.  sea, then i t i s the d e n s i t y o f thermal  T h i s i s p r o b a b l y due  neutrons, the capture cross s e c t i o n of water average  lower over the  S i n c e t h e c o u n t r a t e s f o r t h e cadmium s h i e l d e d  a r e t h e same o v e r l a n d a n d  weighted  10$  neutrons  3.7  barns.  counter  neutrons  t o the f a c t t h a t , f o r thermal i s about  110  barns but  of the capture cross sections of the p r i n c i p a l  o f the e a r t h ' s c r u s t i s about  sea  the  constituents  -27-  8.  E s t i m a t i o n o f t h e E a r t h ' s Albedo t o Cosmic  The calculated  albedo o r r e f l e c t i v i t y o f t h e e a r t h t o cosmic  i n t h e f o l l o w i n g way ( a p p e n d i x F ) .  all  r e f l e c t e d neutrons were t h e r m a l i z e d o  mic  neutron energy  reflected  spectrum  The  assumed  that  Then, t a k i n g t h e shape o f t h e c o s -  a t h i g h a l t i t u d e s where t h e d e n s i t y o f n e u t r o n s  T h i s e n a b l e d one t o e s t i m a t e t h e d e n s i t y o f  n e u t r o n s and hence t h e i n c i d e n t a n d r e f l e c t e d n e u t r o n f l u x  densities.  r a t i o o f . t h e s e two t h e n gave t h e a l b e d o . reflected albedo =  9.  I t was f i r s t  n e u t r o n s was  from t h e e a r t h i s small, t h e r a t i o o f t h e thermal t o e p i t h e r m a l  n e u t r o n d e n s i t y was f o u n d . reflected  Neutrons  Comparison The  flux  — — — - — — — — — incident flux  =  .22  t o Other Neutron D e n s i t y Measurements n e u t r o n d e n s i t y i n t h e atmosphere h a s b e e n measured b y R.F.  M i l e s (1964).  He u s e d  a b a l l o o n borne  B^F^ filled  c a r r i e d o u t h i s measurements a t a magnetic t u d e s f r o m 8 0 0 gm/cm  i o n i z a t i o n chamber a n d  o l a t i t u d e o f 41 N and f o r a l t i -  t o t h e t o p o f t h e atmosphere.  By extrapolating h i s  2 m e a s u r e m e n t s t o a p r e s s u r e o f 1 0 3 0 gm/cm , o n e g e t s a v a l u e o f a b o u t lO^xlO"  9  n/cm . 3  measured here.  This i s approximately a f a c t o r two greater than the value However, t h e f a c t t h a t t h e e a r t h a c t s a s a good  of  neutrons  ( r e f l e c t i n g o n l y about  at  t h e e a r t h ' s s u r f a c e b y a f a c t o r o f about  ments i n rough  agreement.  22$)would  reduce t h e n e u t r o n  1.6.  absorber density  T h i s puts t h e two measure-  -28APPENDIX A I t w i l l b e shown t h a t t h e f o r the  energy dependence o f the  e m m i s s i o n o f s-wave n e u t r o n s f o r e n e r g i e s  cross  above t h r e s h o l d  section i s o f the  form  cr * k The  expression  malized  f o r the  be  cross  s e c t i o n f o r the  t lux) f t oo u n i t fI-LUX; i r o m t hn e  surface  (nor-  nucleus i s  i  over which the  current  a sphere w i t h a r b i t r a r i l y  d e n s i t y T i s i n t e g r a t e d i s assumed t o  l a r g e r a d i u s R a n d "f i s a p u r e l y  forces present,^  must  any k .  outgoing  1  s o l u t i o n o f S c h r o d i n g e r ' s equation,,  f o r l a r g e R and  escape o f one p a r t i c l e  - Md1-(+V+-<tv<**)  -jaw The  n  For t h i s  case, with  only  short  range  satisfy  T h e o u t g o i n g t y p e s o l u t i o n may b e w r i t t e n a s  4(A) -a(kK^V(l<K)"" 'IH*  |<R  tt  "R»0  t/  ,  k = (2«f) Here  ( P i p e s , 1958) a n d 3(k)  i s a Hankel function o f order  f u n c t i o n o f p a r t i c l e momentum t o b e e s t i m a t e d p o s i t i v e i m a g i n a r y s o t h a t *\> damps o u t low  threshold.  that the  S u b s t i t u t i n g the  energy dependence o f the  |B(k)  later.  /h  i s some  k i s taken  F o r E<0,  exponentially f o r a l l energies b e -  expression cross  z  f o r 0" shows  f o r ifCR) i n t o t h a t  s e c t i o n i s o f the  form  Z  ITT Now  3(k)  depends o n a complete s o l u t i o n o f the boundary value  e l u d i n g a d e t a i l e d c o n s i d e r a t i o n o f the j u s t above t h r e s h o l d , one can 3 00 b y r e q u i r i n g "p m u s t n o t  f i n d the  short zeroth  ranged f o r c e s . order  become i n f i n i t e n o r  problem  in=  However,  e n e r g y dependence o f  i d e n t i c a l l y vanish  over a  -29f i n i t e region of space as k-» 0 . Af  Hence  c*  Thus one requires  jL*.  ,  0 ( 1 )  and so the zeroth order energy dependence of the cross  section i s  As an estimate of the range of validity of this law, the criterion  kR«l  i s used (Marion, 1963). Here k i s the wave number and TS the interaction radius of the entrance channel. Using TO" <° E « ISO kev  cm gives the requirement  -30APFENDIX B  W a l l and End E f f e c t s  Some o f t h e n e u t r o n  capture  events  occurring i nthe ionization  chamber do n o t appear i n t h e . f u l l e n e r g y peak because one o r o t h e r o f t h e r e s u l t i n g p r o t o n o r t r i t o n s t r i k e s t h e c y l i n d r i c a l w a l l o r end o f t h e chamber before  expending a l l o f i t s energy.  the t h e r m a l neutron peak.  T h i s i s termed t h e "wa.ll e f f e c t " .  c o n t r i b u t i o n t o t h e low energy t a i l due  t o neutron  field ive  capture  This c o n t r i b u t e s a low energy t a i l t o  events  A further  i s made b y t h e " e n d e f f e c t " , w h i c h i s  o c c u r r i n g i n t h e end r e g i o n s s h i e l d e d b y t h e  shaping r i n g s but having t r a c k s which p r o j e c t p a r t i a l l y i n t o t h e a c t -  chamber volume.  The s p e c t r u m s h a p e s d u e t o t h e w a l l a n d e n d e f f e c t s  have been c a l c u l a t e d b y Robertson The 1)  (1963) a n d a r e shown i n f i g u r e B l .  a s s u m p t i o n s made i n R o b e r t s o n ' s  c a l c u l a t i o n were:  The c u r v a t u r e o f t h e c h a m b e r w a l l c a n b e n e g l e c t e d . a good a p p r o x i m a t i o n er the  provided  This i s  the radius o f curvature i s great-  t h a n t h e t r a c k l e n g t h , and t h e g r e a t e r i t i s , t h e b e t t e r approximation.  2) T h e t r a c k d i s t r i b u t i o n i s i s o t r o p i c . 3)  The s t o p p i n g power  ^ dx  i s constant.  4) T h e r e a c t i o n s a r e u n i f o r m l y d i s t r i b u t e d t h r o u g h o u t This last but The  c o n d i t i o n i s n o t v e r y w e l l met i n t h i s  experiment  a c o r r e c t i o n f o r i t i s d i s c u s s e d i n t h e next  paragraph.  large value o f the thermal neutron  enhances t h e w a l l e f f e c t because t h e neutron t h a n t h a t a t t h e c e n t r e o f t h e chamber. cal  t h e chamber.  capture  cross section  flux at the walls i s greater  This applies only to the c y l i n d r i -  w a l l s o f t h e chamber s i n c e t h e r e i s a b o u t 3»3  cm o f g a s b e t w e e n t h e  Figure  B i  Spedrum  Shape  -for-  UAxIl  Effect  1 1 3E  *  (1)  Spec4yum  Shape  f**-  £nd  "-tot  f t  Effect  i 1*r -L _1T  1 4 E,  At" * -tot  "y ^ ( ^ ^ i » t )  l s  ^£  tW  probsbilrfy  e>pendin<j between V= S~  cheater surface of  E  of 3 neu.+rovi  a^J E+d€  IM  c<^p+ure event  -f-lne c^o^ber  acWe. i/olume area  ends  of  4t>v-  dchve.  (2)  volume 4w  (I)  gncl  3*^3  -31-  ends and the active volume. Hence the neutron flux at the ends of the active volume i s set approximately by the cylindrical geometry.  The ratio,  G, of the neutron flux at the walls to the average flux throughout a semiinfinite absorbing cylinder has been calculated by Kushneriuk (1957). For the  wall effect calculation, the area of the cylindrical walls i s increased  by the factor G. A typical neutron spectrum i s shown in figure B2. t a i l extends from about -2-  (570 kev) to i- E  E t o t  TOT  The low energy  (190 kev), where i t i s  lost i n the electronic noise. To calculate the f u l l chamber counting rate from the counting rate in the f u l l energy peak, the following relationship, developed by Robertson (1963), was used:  -p  PCR)  -  I  b  L  where "P(R)* fraction of tracks of length "R originating in active volume which strike wall or end of active volume R=  combined range of proton and triton i n chamber  L = length of active volume b = radius of active volume C\= ratio of neutron flux at surface of active volume to average flux throughout volume. The proton and triton ranges i n the chamber were derived from the formula (Robertson)  where "P , T^and *P  cH  n  1} , ^ R  Since "R (E) - S'R ( %) T  H e  and "Tl^  are partial pressures i n atmospheres are ranges taken from the graph i n figure B3  (Nuclear Data Tables) and the triton energy was so  low (about 200 kev) as to put i t on the linear portion of the range-energy  F»9 u r e Schematic  Energy  Spccfvum  Shouimj  VJcW  Ef/ecl  ghd*  full  Peak  no 100  g  %0  3 ^  40  tot 10  3£ 100  J  300  L  ^.oo  j-oa  I  4  1L 0 0  tot  -typical  200  300  4°U  $"00  60O  ^OQ  9oo  v\ea4v"o/i  /OOO  Enev^^y "Released m Chsmnker (kek'J  p<  -32-  'R(e')  curve, then  T  p r o t o n and t r i t o n  s /  R (E) . p  the  ranges a r e :  7l H H e n c e "R=  100 k e v ,  F o r n e u t r o n e n e r g i e s below about  .67 cm  p  = .14 cm  T  . 8 1 cm a n d "P(- &l)=.135 f o r t h e r m a l n e u t r o n s w h e r e G = 1.5 <  f X . 9 l ) = .099 The wall effect  f o r f a s t n e u t r o n s where G=  1.0  s c h e m a t i c s p e c t r u m shown i n f i g u r e B 2 shows t h a t p a r t o f t h e  i sburied i n the f u l l  energy peak.  The f r a c t i o n o f t h e w a l l  e f f e c t t h u s b u r i e d i s t a k e n t o be t h e f r a c t i o n o f t h e a r e a on t h e schematic spectrum which i s included i n t h e f u l l  energy peak.  This fraction i s  f = .129 using  11^=  .67  'Rj «  cm  .14  cm  ' 765 k e v SE * 100 k e v Now one c a n g e t f r o m t h e s c h e m a t i c s p e c t r u m t w o s t a t e m e n t s ! (1)  (Peak count r a t e ) = ( F u l l energy count r a t e ) t fp(^)(Chamber  count rate)  (2)  (Chamber c o u n t r a t e ) = ( F u l l e n e r g y c o u n t r a t e ) + P(R)(Chamber c o u n t rate)  where (Peak count r a t e ) = t h e c o u n t i n g r a t e i n t h e f u l l (ie:  energy peak  counts f a l l i n g between E  -S"f a n d f  "tot  TJOt  ( F u l l energy c o u n t r a t e ) - count r a t e due t o e v e n t s w h i c h expend a l l . t h e i r e n e r g y i n t h e chamber ( C h a m b e r c o u n t r a t e ) = c o u n t r a t e due t o a l l n e u t r o n c a p t u r e events occurring i n active  volume.  Combining t h e s e two e q u a t i o n s y i e l d s : Peak count Chamber count r a t e  rate  —  1 - P(R)(1 - f ) Thus f o r t h e r m a l neutrons  (G =  1.5)  Chamber count r a t e = 1.13(Peak count and f o r f a s t neutrons  (G =  rate)  1.0)  Chamber count r a t e « l,09(Peak count  rate)  The c h i e f source o f e r r o r i n t h e s e statements a r i s e s from t h e v a l u e s a s c r i b e d t o t h e ranges o f the p r o t o n and t r i t o n . p r o b a b l e d e v i a t i o n o f about 10$.  This introduces  These have a  a probable d e v i a t i o n o f  10$ i n t o P(R) and an e r r o r o f about 1% i n t o t h e chamber count r a t e .  APPENDIX C  Background Counting  Rate  T h e r e a r e two ways t o f i n d t h e b a c k g r o u n d c o u n t i n g r a t e . to  s h i e l d the counter  from neutrons.  However t h i s  i s not p o s s i b l e because  s h i e l d i n g only attenuates r a t h e r than eliminates t h e neutron  flux.  4  insensitive.  r a t h e r t h a n He  identical.  Hence t h e b a c k g r o u n d c o u n t i n g r a t e must bd e s t i m a t e d r a t h e r t h a n T h i s e s t i m a t i o n i s done w i t h t h e a i d o f t h e n e u t r o n T h i s s p e c t r u m was t a k e n o v e r a p e r i o d o f 23.7  w a s s h i e l d e d b y .020  and  T h i s method i s n o t v e r y p r a c t i c a l , however, s i n c e  t h e r e i s no w a y o f v e r i f y i n g t h a t t h e t w o c h a m b e r s a r e i n f a c t  Cl.  The o t h e r  3  m e t h o d i s t o u s e a n i d e n t i c a l c o u n t e l r c o n t a i n i n g He hence n e u t r o n  One i s  i n c h e s o f cadmium.  measured.  s p e c t r u m shown i n f i g u r e hours while the counter  The b a c k g r o u n d c o u n t i n g r a t e was  a s s u m e d t o come f r o m t w o s o u r c e s : 1) c o u n t i n g d u e t o e l e c t r o n i c n o i s e .  This f a l l s  o f fexponentially with  energy, 2)  c o u n t i n g due t o n a t u r a l a l p h a p a r t i c l e chamber i t s e l f . to  a b o u t 7 Mev.  e m i s s i o n from t h e w a l l s o f t h e  T h i s i s assumed t o f o r m a f l a t Those a l p h a s  p l a t e a u from zero up  a b o v e a b o u t 5 M e v p r o b a b l y come f r o m  r a d o n e m a n a t i n g f r o m t h e Ca-Mg p u r i f y i n g  eutectic.  A l s o i n f i g u r e C l , t h e graph o f t h e l o g a r i t h m o f t h e counts is  shown f o r t h e r e g i o n o f e l e c t r o n i c n o i s e .  i n t o t h e r e g i o n o f t h e peak t o e s t i m a t e w a s 5»3 * .5 to  counts/hour.  versus t h e energy  This graph i s e x t r a p o l a t e d  t h e b a c k g r o u n d due t o n o i s e .  The t e n c h a n n e l s  This  f o l l o w i n g t h e peak were a v e r a g e d  g i v e a n e s t i m a t i o n o f t h e b a c k g r o u n d c o u n t i n g r a t e due t o n a t u r a l a l p h a  e m i s s i o n i n t h e chamber.  T h i s gave a c o u n t i n g r a t e o f 4.9±  .5  counts/hour  Rfjure  C l  T  A/eu4ron  Time  Courier  Spedrum £.3,7 flours  shielded  h>y .020 indies  o f Ccl  -35i n the f u l l energy neutron peak. Thus the background counting rate from the two sources i n the f u l l energy peak was taken to be 10.2 ±.7 counts/hour.  -36APPENDIX D The Counting Rate of a Black Neutron Detector i n an Isotropic Neutron Flux <£>(/o) * A ^ r\(v)  The d i f f e r e n t i a l neutron flux i s where p i ^ d ^  = vv  (total neutron density)  and  =  (total neutron flux)  |~^(/u)d/0  Consider an element of surface area d A of the counter A parallelpiped of length AT" i s projected from this area i n direction (G , <j> )  The volume of the parallelpiped i s Ay6 A cM> © The number of neutrons in the parallelpiped with velocity between A/ and A/+ d A/ i s  r  ,  u  1  v  .^  The fraction of these neutrons with velocity vector along (0 pointed towards dA . i s  , sin9  , ,  ded4  Hence the flux of neutrons through clA from direction between  Q  and  0 +  between / J and  and between <p and +J  <P-fd<t>  with velocity A*-  1  is [n(*>)e}*>lA>dA  Hence, integrating over  8>4 » )  AT*  and  A,  ocrtg)>^n-6  one gets for the  chamber count rate Count rate =  —  4  dA  d©d<£  A/ n(/o)J/o j o e i © ^<^e»  d<9  r  d*  -37APPENDIX E To evaluate the i n t e g r a l s : (1)  J <t>M  [c&vmbe/b  j^iofi^cj]  [cQa/r»be^ X^ICA^C^J^I - Ci  (2)  1$\UA™C^J  Since the chamber counting rate above neutron energies of about 100 kev was  small and inseparable from the background  counting rate and also t o make  the i n t e g r a t i o n easier, i t was decided t o set the upper l i m i t s of the i n t e grals at v e l o c i t i e s corresponding to 100 kev energy. The functions involved i n the i n t e g r a l s are: (1)  f^Y\{y)  <{>(/•) =  where  n(^)-  *  *f^(v)  »  ^  f chamber  5  1.0  e< sxio'tfei/  efficiency « j-|.9oi-ASosJU\€ -4  I 2.43 */o  £  -.-"9  %+\°\€< l.oxio Mev 6  .  I.OVIO < € < i . o x i o |vAev  (3) l-O  €<  iciencv - j |.I2 *|o  4  ^ev  ,3-xlo" <€< |.o*io ^ei/  6  -Ol4  i.oxio~ <£ b  Some of these functions are expressed i n terms of neutron energy and others i n terms of neutron v e l o c i t y .  For the i n t e g r a l s , i t was decided t o express  everything i n terms of the neutron energy £  (6  i s i n Mev).  Thus i t was  necessary t o f i n d an expression f o r the neutron f l u x i n terms of energy, that i s , to f i n d cj)(e) „  The integrated neutron f l u x i s  -38-  / o  Hence  ««)  Therefore  in <j>(e)  = i v^ae*)  °  '  £  ^(s€«) f  («€*)]  Thus the integrals to be evaluated are la)  2a)  £  ^ [ c W b e r  ^  eff»a«"cyjd'€  $(*) [ c U w U * effifciewcy][|- Cd Efficacy] cl€  The i n t e g r a l 2a can be evaluated by f i n d i n g  3a) and  j" <K^ [chav«W efficiency] [cd «fficie«*yj  d£  combining i t with l a . These i n t e g r a l s , because of the ranges of the functions  broke up into sixteen i n t e g r a l s .  involved,  Of these i n t e g r a l s , two were n e g l i g i b l y  small, two were evaluated on the UBC Computing Center's 7040 computer using a Simpson's rule program and the rest were evaluated a n a l y t i c a l l y . oo  the a n a l y t i c a l solutions involved  sums of the form £  were also calculated with the use of the 7040 computer. The program used to evaluate 2 flBFTC THESIS DOUBLE PRECISION SUM DIMENSION N(3J),X(3) N(l) 10  N(2) 50 N(3) 200 X ( l ) -.2 X(2) -12.0 X(3) -40.0 DO 100 K 1,3 SUM 1.0  i s l i s t e d below:  Two of  n  .  These sums  -39-  3  2 1000 1 100  J N(K)-1 EN N(K) PRINT 3,X(K) FORMAT(5H X ,F5.l//5X,lHM,13X,3HSUM//) DO 1000 M 1,J EN M SUM SUM*X(K)*(EN-EM)/(EN-EM 1.0)**2 SUM SUM 1.0 PRINT 2,M,SUM F0RMAT(I6,E16.9) CONTINUE SUM SUM*X(K) PRINT 1,SUM FORMAT(//7H SUM ,El6.9//) CONTINUE STOP END  $ENTRY The program used to evaluate the i n t e g r a l s by Simpson's rule i s l i s t e d below t IBFTC THESIS  A 5.0E-09 B 3.0E-07 N 100 CALL SIMP (A, B, N, AREA) 10 TEST AREA N 2*N CALL SIMP(A, B, N, AREA) DIFF ABS(AREA-TEST) PRINT 31»N,AREA,TEST,DIFF 31 FORMAT(3H N ,15,6H AREA ,E15.7,6H TEST ,E15.7,6H DIFF ,E15.7) IF(DIFF-AREA*1.OE-04)20,20,10 20 PRINT 41,N,AREA 41 FORMAT(5H N ,I5,8H AREA ,E15.7) STOP END IBFTC SIMP SUBROUTINE SIMP (A, B, N, AREA) AN N . H (B-A)/N SUM1 0.0 SUM2 0.0 CALL AUX (A,Y) YA Y CALL AUX (B,Y) YB Y X A-H NN N/ 2 DO 30 I 1,NN 30 X X 2.0«H  -40CALL AUX (X,Y) SUM1 SUM1 Y XA DO 40,1 2,NN X X 2.C*H CALL AUX (X,Y) SUM2 SUM2 Y AREA H/3.0*(YA 4.0*SUM1 2.0*SUM2 YB) RETURN END IBFTC AUX SUBROUTINE AUX (X,Y) T -(.4E 08)*X Y X*AL0G(X)*EXP(T) RETURN END $ENTRY  -41APPENDIX F Estimation of Earth's Albedo for Cosmic Neutrons The shape of the differential cosmic neutron flux density i n the atmosphere has been calculated by Lingenfelter, assuming the solar proton spectrum to be of the form ^  = Ke  ° . This graph i s shown in figure  dr  F l where the curve has been approximated by three straight line segments: 1.38*10 £ 10  1  2.63*10~ £ " 5  ,  1  , 9  1.67*10~ £ - * 5  € < 9 10"  7  8  9 io" <e < 1.0 io"  °  8  6  1.0 10" < € < 1.0 1 0 " 2  9 3  6  1  2  Lingenfelter calculated curves for pressures of -100 gm/cm , 200 gm/cm and 300 gm/cm . These curves were almost parallel (within about 10$) and hence i t was assumed that the curve shape was the same at 1030 gm/cm^. The cadmium ratio (Westcott) for this spectrum shape was calculated by finding the relative counting rates for a l/v counter by means of the two integrals  (  -9  Thus  € '  ./t(E) ^  J -9 5*1° f««)U-CJ  and  Effc-vJ j  £  Cadmium Ratio = R_ , Cd  ^Vz  6  €  = 2.62 This value i s related to f , the fraction of the neutrons in the epithermal component, by the formula (Westcott) f - i.oiK PrT f j T = .82  where K= 2.07 T. = 293*60 K r=280°K  are  Fd :  Spec4rum  Shape  o f D i f f e r e n t is I  A/eu4ron  Enerq y  (Me*/  Cosmic  -42I t was found i n the measurement done a t the earth's surface that  -9  3  ri=-4.2*10  the density of neutrons was i n the epithermal component.  n/cm  and of these only 33$ were  I t was assumed that at the earth's surface,  the neutron f l u x consisted of three components* 1) an incident epithermal component 2) an incident thermal component 3) a r e f l e c t e d thermal component ( i e j r e f l e c t e d from the earth) The number density o f the incident epithermal component i s •33*(4.2xlO  -9  n/cm"*) or 1.4*10~ n/cm . 9  neutron density.  This comprises 82% of the incident -9 3  3  Hence the incident thermal neutron density i s .3*10  n/cm .  By d i f f e r e n c e , t h i s leaves the r e f l e c t e d thermal neutron density as  2.4xl0~ n/cm . 9  3  From these neutron d e n s i t i e s , one oa$ estimate the incident and r e f l e c t e d fluxes as followst Incident fast Incident .:  A  A  flux  = 1-4  flux - .3Mo  *io« [<*  9  ^  J« e  o  T  Reflected thermal f l u x = 2 . 4 * l o  j ^  —  a  e,  JA/  o „4  _ l O . S x |o  -3  Hence the incident f l u x density i s i s 1.05*10" . 3  4.7x10  and the r e f l e c t e d f l u x density  This y i e l d s albedo =  reflected flux incident f l u x  ,-3  1.05 10  4.7 10"  = .22  3  BIBLIOGRAPHY Beckerly, J.G., Neutron Physics, AECD -2664 Bohm, D., Quantum Theory, Prentice-Hall Inc. (1951) Everling, F., K'onig,. L.A., Mattauch, J.H.E., and Wapstra, A.H., Nuclear Physics 18 529 (i960) Guier, W.H. and Hart, R.W.,  Phys. Rev. 106 296 (1957)  Goshkov, Zyabkin and Tsvetkov, Atomnaia Energiia 12 429 (1965) Kushneriuk, S.A., AECL Report 462 (1957^ Langsdorf, A.S., Monahan, J.E., and Reardon, W.A.,  ANL-5219 (1954)  Lingerfelter, R.E., and Flamm, E.J., Journal of Geophysical Research 6£ 2199 (1964) Miles, R.F., Journal of Geophysical Research 6£ 1277 (1964) Neutron Cross Sections, BNL 325, Second Edition Nuclear Data Sheets, National Academy of Sciences—National Research Council Nuclear Data Tables (I960), Consistent Set of Q-Values (Part 2), United States Atomic Energy Commission Pipes, L.A., Applied Mathematics for Engineers and Physicists, page 354, McGraw-Hill Book Company, Inc. (1958) Robertson, L.P., (1963), Ph.D. Thesis, University of British Columbia Schoenfeld, W.A.,  Duborg, R.W.,  Preston, W.M.  and Goodman, C , Phys. Rev.  8£ 873 Westcott, C.H., Walker, W.H.and Alexander, T.K., AECL-612 (1958) Wigner, E.P., Phys. Rev. 22 1002 (1948)  

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