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A study of the interaction loss of protons and deuterons in NaI Ahmad, Munawar Sultana 1988

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A STUDY OF THE INTERACTION LOSS OF PROTONS AND DEUTERONS IN Nal By MUNAVAR SULTANA AHMAD B.Sc,  University of Dhaka, 1974  M.Sc,  University of Dhaka, 1975  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF PHYSICS  We accept this thesis as conforming to the required  standard  THE UNIVERSITY OF BRITISH COLUMBIA JULY 1988 ©  Munawar Sultana Ahmad, 1988  In  presenting  degree  this  at the  thesis  in  partial  fulfilment  University of  British  Columbia,  freely available for reference and study. copying  of  department publication  this or of  thesis by  this  for scholarly  his thesis  or  her  the  I agree  requirements  for  may  representatives.  It  be is  Department The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3  advanced  that the Library shall make it  I further agree that permission  purposes  an  granted  by the  understood  for extensive head  that  for financial gain shall not be allowed without  permission.  DE-6f3/81i  of  of  my  copying  or  my written  ii ABSTRACT  Interaction  losses  in  sodium  iodide  c r y s t a l s have been d i r e c t l y  measured f o r protons i n the range of energies from 139 to for  deuterons  of 277 MeV.  444  MeV  and  Calculations of the expected loss were made  for protons over the range 151-500 MeV using the best able reaction cross section data.  currently  avail-  Our experimental values are t y p i c a l l y  about 21% lower than the calculated values. The i n t e r a c t i o n loss f o r 277 MeV than  the  calculated  value  obtained  value of Measday and Schneider. deuteron  interaction  for 277 MeV  deuteron i n Nal i s about  lower  using the deuteron cross section  Using t h e i r calculated value of 100  MeV  loss as a reference point, we calculated the loss  deuterons and from a f i t to our data we obtained  section f o r deuterons at an average energy of 188.4 MeV mb,  8%  which i s about 20% lower than the cross section  the  cross  to be 2590 ± 180  obtained  empirical r e l a t i o n that tr(d-A) i s 2_(p-A) at h a l f the energy.  from  the  iii TABLE OF CONTENTS  Page ABSTRACT  i i  TABLE OF CONTENTS LIST OF TABLES  i i i v  LIST OF FIGURES  vi  ACKNOWLEDGEMENT  viii  DEDICATION  1.  2.  ix  INTRODUCTION  1  1.1  I n e l a s t i c nuclear reaction cross section  2  1.2  Motivation of the present work  6  THE EXPERIMENT  9  2.1  Beam l i n e IB  9  2.2  Production of the secondary deuteron beam  12  2.3  Nal c r y s t a l s (TINA and MINA)  13  2.4  Experimental arrangement  15  2.5  Electronics and data a c q u i s i t i o n  22  iv 3.  4.  DATA ANALYSIS  28  3.1  28  Interaction loss of deuterons  3.1.1 RF cut  31  3.1.2 Time of f l i g h t cut  33  3.1.3 Energy loss cut  33  3.1.4 Multi wire proportional cut  33  3.1.5 Energy c a l i b r a t i o n  37  3.2  43  Interaction loss of protons  3.2.1 Protons from p+p-^p+p i n Nal detectors  43  3.2.2 Direct proton beam i n a Nal detector  49  RESULTS AND DISCUSSION  51  4.1  Deuteron interactions  51  4.2  Proton interactions  53  4.3  Discussion  54  4.3.1 Proton data  54  4.3.2 Deuteron data  60  4.4  70  REFERENCES  Summary and conclusion  73  V LIST OF TABLES  Table 2.1  Page The beamline quadrupole values and t h e i r d i r e c t i o n of focus f o r the deuteron beam  14  2.2  Energies of protons i n TINA and MINA  19  2.3  Dimensions of s c i n t i l l a t o r s and MWPCs used i n 1987 run Energies of the proton and the deuteron beam (1987 run)  2.4  21 21  4.1  Interaction loss of deuterons using d i f f e r e n t cuts . . .  52  4.2  E f f e c t of d i f f e r e n t X,Y cuts on the i n t e r a c t i o n loss of deuterons  53  Results of the interaction loss of protons with 5 and 10 MeV cuts  55  Present r e s u l t s f o r the proton i n t e r a c t i o n loss i n Nal detectors using a cut 10 MeV below the peak  56  4.5  Comparison of dE/dX values  58  4.6  Reaction cross section values f o r proton interactions i n Nal, as determined from present data  . . . .  60  Present r e s u l t of the deuteron i n t e r a c t i o n loss  ...  62  4.3 4.4  4.7  vi LIST OF FIGURES  Figure  Page  2.1  TRIUMF beam l i n e s and experimental f a c i l i t i e s  10  2.2  Layout of beam l i n e IB  11  2.3  Schematic of the experimental setup (1986 run)  . . . .  17  2.4  Schematic of the experimental setup (1987 run)  . . . .  18  2.5  Schematic of the electronics  (1986 run)  23  2.6  Schematic of the electronics  (1987 run)  27  3.1  A t y p i c a l deuteron pulse height spectrum i n MINA  3.2  A t y p i c a l scatter plot (energy vs RF time)  30  3.3  A t y p i c a l RF spectrum  32  3.4  A t y p i c a l raw spectrum of time of f l i g h t (TOF) between two s c i n t i l l a t o r s  34  A t y p i c a l time of f l i g h t (TOF) spectrum with RF cut  35  A t y p i c a l deuteron energy loss spectrum i n s c i n t i l l a t o r S2 with RF and TOF cuts  36  3.5 3.6 3.7  ...  29  A t y p i c a l raw spectrum (LI) from a multiwire proportional chamber  37 i  3.8 3.9  A t y p i c a l spectrum (X^ - Ll-Rl) from a multiwire proportional chamber with RF and TOF cuts  39  A t y p i c a l spectrum ( X and TOF cuts  40  P R J  - AX^ + BX ) with RF 2  3.10  A t y p i c a l deuteron energy spectrum i n MINA  41  3.11  A t y p i c a l deuteron energy spectrum showing MINA resolution  42  vii 3.12  A t y p i c a l RF spectrum  3.13  A t y p i c a l scatter p l o t (TINA energy versus MINA energy)  3.14  i n the proton run  44 46  A t y p i c a l background subtracted proton energy spectrum  47  3.15  Energy c a l i b r a t i o n of TINA  48  3.16  A t y p i c a l pedestal subtracted proton energy spectrum i n TINA  50  4.1  Interaction loss of protons i n Nal  61  4.2  Total reaction cross section f o r d + ^ 0 with Glauber theory prediction [32]  4.3 4.4  along  Total reaction cross section f o r d + -*^Ni along with Glauber theory prediction [31]  65 66  Reaction cross section versus A /3 f 2  MeV deuterons  o  r  188.4 69  viii ACKNOWLEDGEMENTS  I  w o u l d l i k e t o e x p r e s s my s i n c e r e g r a t i t u d e and a p p r e c i a t i o n t o my  supervisor,  Professor  David  F.  Measday  f o r h i s guidance,  advice,  p a t i e n c e and encouragement throughout t h i s work. I  would  like  t o thank Dr. M a r t i n Salomon, Dr. Dezs6 H o r v 5 t h , Dr.  S h i r v e l S t a n i s l a u s and Tony Noble f o r t h e i r a s s i s t a n c e i n t h e p r e p a r a t i o n and r u n n i n g o f t h e e x p e r i m e n t s .  Dr. S t a n i s l a u s i s a l s o thanked f o r  many h e l p f u l s u g g e s t i o n s d u r i n g t h e c o u r s e o f t h i s work. I am i n d e b t e d t o Dr. Dave  Hutcheon,  without  whose  expertise  and  p a t i e n c e we w o u l d n o t have found t h e d e u t e r o n s i n t h e f i r s t p l a c e . The  advice  and a s s i s t a n c e  o f Dr. J . L . B e v e r i d g e and Dr. A l a n F r y  d u r i n g my f i r s t few months a t TRIUMF a r e a l s o Thanks  a r e due  thankfully  acknowledged.  t o Mrs. R a n i Theeparajah f o r h e r c a r e f u l t y p i n g o f t h e  thesis. F i n a l l y , I w i s h t o thank my husband, S a l a h u d d i n f o r h i s s u p p o r t enthusiasm for  f o r education,  and  and a l s o b o t h my p a r e n t s and p a r e n t s - i n - l a w  t h e i r c o n t i n u o u s encouragement.  ix  DEDICATION  TO MONJULI  - 1 CHAPTER 1  Introduction  When a charged p a r t i c l e passes through a nuclear  interactions.  In  many  nuclear  material  physics  important to know the number of these interactions. are  basically  of  two  types.  i t can  experiments These  undergo i t is  experiments  In the f i r s t type a counter i s used to  measure the k i n e t i c energy of the charged p a r t i c l e by stopping i t i n material iodide.  such  as  plastic  In the second type,  scintillator, to  reduce  a  s i l i c o n , germanium or sodium the  incoming  energy  of  the  charged p a r t i c l e or to stop i t as i n a range measurement, materials such as aluminum, carbon or copper are used. For total-energy counters only nuclear important.  Elastic  scattering  normally stays within the confines elastic  collision  the  is  inelastic  peaked  of  the  forward, sensitive  interactions  are  and the p a r t i c l e volume.  In  an  energy transfer to the nucleus i s small and for  most cases only a few percent of the energy transfer i s more than 2%  of  the incoming energy [1]. The energy which i s transferred to the nucleus due to an e l a s t i c c o l l i s i o n may not be detected by the counter, but elastically  scattered  particles  which have not undergone  nuclear  r e s o l u t i o n of the counter.  will  not be distinguished from those  interaction  because  of  the  finite  T y p i c a l l y the resolution of the counter i s 1  to 2% f o r 350 MeV proton energy. In an i n e l a s t i c interaction, energy i s l o s t f o r several reasons: a)  the  the negative Q-value of the reactions  - 2 b)  the production of uncharged p a r t i c l e s such  as  neutrons  and  gamma  rays which do not deposit t h e i r energy i n the c r y s t a l c)  the  production of heavier charged p a r t i c l e s such as t r i t o n s , alphas  etc f o r which the s c i n t i l l a t o r response w i l l be non-linear.  One way or other, energy w i l l be l o s t and the the  counter  will  energy  deposited  in  be less than that for protons which do not interact.  Thus f o r the t o t a l energy stopping counters the proton can be considered as  lost  from  the f u l l energy peak i f i t undergoes a nuclear i n e l a s t i c  interaction. Such corrections have been considered by several authors have emphasized energies up to 150  1.1  [2-5]  who  MeV.  I n e l a s t i c nuclear reaction cross-sections  Reaction  cross sections, defined as t o t a l minus t o t a l e l a s t i c cross  sections f o r nucleons incident on properties  needed  for  tions . To describe the multiparameter  nucleus,  are  one  of  the  scattering  basic  an understanding of the nuclear strong interacnucleon-nucleus  interaction  in  terms  o p t i c a l model p o t e n t i a l , one needs experimental  t i o n on t o t a l cross elastic  a  sections, cross  reaction  sections  and  cross  sections,  polarizations  of  the  informa-  differential [6-11].  reaction cross-section i s p a r t i c u l a r l y important f o r l i m i t i n g the  The range  of the imaginary part of the o p t i c a l model p o t e n t i a l . The  nucleon-nucleus  interaction  can  also be described within the  -  3  -  framework o f a semi c l a s s i c a l a p p r o x i m a t i o n cross  sections  t o the transparency  which r e l a t e s  the r e a c t i o n  o f t h e n u c l e u s w h i c h i s d e f i n e d as  the d i f f e r e n c e from u n i t y o f t h e r a t i o o f t h e r e a c t i o n c r o s s s e c t i o n t o the  geometrical  cross  section.  The  reaction  c r o s s s e c t i o n s c a n be  c a l c u l a t e d from a t h e o r y b a s e d on a s i m p l i f i e d model where one c o n s i d e r s the  nucleon-nucleus  tions.  interaction  Here t h e n u c l e u s  nucleons  in a  as  a sum o f n u c l e o n - n u c l e o n  i s c o n s i d e r e d as  nuclear  potential  a  degenerate  Fermi  interacgas o f  of radius R - r_ A  V3. The r e a c t i o n  cross-sections i s a  -  R  *R (1-T)  (1.1)  2  1 - (1 + 2 K R ) e " where  T  -  (1.2) 2K R 2  i s the transparency o f the nucleus. which  characterizes  2 K R  K  2  i s the absorption  t h e a b s o r p t i v e p r o p e r t y o f t h e p o t e n t i a l and i s a  f u n c t i o n o f the cross s e c t i o n f o r nucleon-nucleon is  energy  coefficient  dependent.  formation i s considered  I f t h e Coulomb  scattering,  and  thus  r e p u l s i o n i n compound n u c l e u s  [12], the modified  formula  f o r the r e a c t i o n  cross section i s  a  R  -  ir(r AV3 0  +  % )  2  (  1  .  Z  z  e m  (R+A)E where  E  D  .  T  ]  (  1  .  3  )  Q  i s the incident proton energy and * i s the reduced wavelength  of the incident p a r t i c l e . The  t o t a l reaction cross-sections f o r protons on various nuclei have  - 4 been  measured  by  many  experimenters.  shown that around 200 MeV, section  varies  only  in  the  slightly  Pollock and Schrank [13] have  region  with  where  energy,  the  reaction  cross-  the cross-section can be  f i t t e d to the following r e l a t i o n  _ where r  (fm )  -  2  R  (wr A / 2  - 1.26fm, and so wr «5.Ofm . 2  Q  precise  2  3  Q  - 5.0)  Thus i t  2  0  (1.4)  was  possible  to  make  interpolations for reaction cross-section of elements f o r which  few or no data were available. reaction  cross-section  There i s a clear minimum of  around 250 MeV  the  proton  for most of the elements.  Above  t h i s energy the onset of pion production causes a s l i g h t increase of the cross  section  up  to  600 MeV.  Above 600 MeV  the data are few and  s u f f i c i e n t l y r e l i a b l e to give information  on the high-energy  However,  reaches a maximum around 2  there  are  indications that _  R  and then decreases very s l i g h t l y at higher energies [14,15]. large  errors  on  not  behaviour.  Due  GeV  to the  the measurements i n t h i s energy, Measday and Richard-  Serre [1] chose to assume  a  constant  section for energies greater than 250  value  for  the  reaction  cross  MeV.  Renberg et a l . [16] f i t t e d t h e i r experimental data on reaction cross section (up to 567 MeV curve  (eq.  1.3)  which provided the best values for r  nuclear transparencies transparency  was  incident proton energy on Nal) with a t h e o r e t i c a l  seen  G  and K and hence  of some of the elements could be calculated. to  decrease  with increasing mass number which  implies that the reaction cross section comes closer and closer geometrical cross Measday  and  The  to  the  section. Richard-Serre  [1]  calculated  the  number of nuclear  - 5 i n e l a s t i c interactions of stopping protons i n various the  then known reaction cross sections.  simple step integration particular  material  (-0.1 g/cm ).  method.  The  The c a l c u l a t i o n proceeded by a range  of  the  proton  in  that  was divided into n number of c e l l s of equal length  f  =  1 - exp (- Enjaj.) i  where n^ i s the number of atoms/cm  2  cross  i n the  section i n that c e l l .  dependent, i t was necessary to proton  using  The t o t a l f r a c t i o n of interactions i s then given by  2  average  materials  i n each  cell.  The  ith cell  and  i s the  Since the cross section i s energy  determine energy  (1.5)  at  the  average  energy  of the  the end of the f i r s t c e l l was  calculated using the range-energy programme [17]. The average energy of the  proton i n that c e l l was found, and the corresponding reaction cross  section was interpolated from the then available data. of  interactions  i n the  first  cell  Thus the  was determined.  The integration  continued u n t i l 10 MeV, at which energy the reaction cross all  elements  except  carbon i s assumed to be zero.  i n total  compromise  f o r protons.  2  0.2  g/cm  2  number  of  f o r heavier elements.  peak  had  proved  a  For range measurements this corre-  sponds to an uncertainty i n the peak of -0.1 g/cm and  the  energy counters must define the non-interacting  peak, and a cut at 10 MeV below the maximum of the reasonable  section f o r  This cut-off at 10  MeV was used because a l l experimental determinations of interactions  number  for light  elements  A 10 MeV proton, any way, cannot  penetrate the Coulomb b a r r i e r of most nuclides.  - 61.2  Motivation of the present work  In many nuclear physics appear  s c a t t e r i n g experiments  particles  i n the outgoing channel and detectors are used to detect t h e i r  f u l l energy.  I t i s convenient to use pulse height i n sodium  specify the scattered p a r t i c l e s . for  charged  iodide to  Since the pulse height w i l l be smaller  a p a r t i c l e which has undergone a nuclear interaction, i t i s neces-  sary  to make a c o r r e c t i o n for p a r t i c l e s l o s t from the f u l l energy peak.  This c o r r e c t i o n has been measured experimentally several  authors  which had been  using  available  calculated  [2,3,16,18-21].  energy.  calculated by  data on t o t a l reaction cross section or measured  by  different  groups  A few studies have been made to determine the reaction  p r o b a b i l i t y f o r protons on incident  [3,12],  and/or  sodium  iodide  crystal  as  a  function of  Johnson et a l . [22] were some of the f i r s t ,  measured proton i n t e r a c t i o n percentages  at energies  up  to 68  and they MeV  on  sodium iodide with an o v e r a l l accuracy of 10%. Measday  [4] measured  and calculated  the percentage  undergoing nuclear i n e l a s t i c interactions for energies up The  to 160 MeV.  c a l c u l a t i o n s were performed using an estimated cross section value  from the p l o t of the energy number  given  inaccuracy. up  of protons  dependent  by Johansson et a l . [23].  cross  section  against  The measured values have 4-10%  Palmieri and Wolfe [24] measured t h i s loss f o r  to 150 MeV energy on sodium iodide with a 20% accuracy.  protons  available  of  Measday and  Serre [1] have summarized a l l experimental reaction percentage tion  atomic  informa-  and using the then l a t e s t t o t a l reaction cross section  information have c a l c u l a t e d reaction percentages  f o r protons stopping i n  - 7 various materials including sodium iodide over the range 30-800 MeV with an o v e r a l l accuracy of 5-10%. Sourkes et a l . [25] undertook the i n t e r a c t i o n loss sodium  iodide  in  of  up  on  the energy range 50-150 MeV with an o v e r a l l error of  about 3%, while Goulding and Rogers [26] protons  measurements  to  150  MeV  have  measured  with 2-3% accuracy.  this  loss  of  Goulding et a l . also  calculated t h i s percentage loss f o r 40-240 MeV protons and t h e i r  values  are s l i g h t l y larger than those calculated by Measday and Serre [1]. Cameron  et  a l . [27] and Bracco et a l . [28] measured the e f f i c i e n c y  of sodium iodide counter Cameron  et  protons. where  I  a l . up  for  detecting  energy  telescope  was  defined  as  MeV I/I  0  i s the t o t a l number of protons incident on a counter telescope  and I i s the number of tagged protons which resulted i n signal  protons;  to 150 MeV protons and Bracco et a l . up to 350  The e f f i c i e n c y of a counter Q  intermediate  i n the sodium iodide detector.  a  full  energy  An estimation of the i n t e r a c t i o n  loss could be obtained from t h e i r data which i s the r a t i o of ( I - I ) / I . 0  Renberg et a l . [16] measured several  elements  proton  reaction  than  sections f o r  and compounds, including sodium iodide f o r protons of  energy 220-570 MeV with an error of 3%, which better  cross  0  existing  measurements  was  a  factor  i n that energy region.  t h i s error, the calculated values of the proton i n t e r a c t i o n  of  three  Because of probability  become more uncertain and less dependable as the energy increases. To  obtain  experimental  values  of  the  interaction  protons on sodium iodide f o r energies beyond 150 MeV  where  loss f o r the few  exper-  imental data are available, and above 350 MeV where no experimental data are a v a i l a b l e , we have undertaken the measurements of proton  undergoing  - 8 nuclear  inelastic  interactions  i n Nal f o r the energy range of 139-444  MeV using the TRIUMF cyclotron f a c i l i t y . For heavier p a r t i c l e s , the calculated and experimental data f o r interaction  loss  are  very  few.  Measday and Schneider [5] calculated  t h i s loss f o r deuteron and alpha p a r t i c l e s of up to 160 MeV iodide  and  for  sodium  p l a s t i c s c i n t i l l a t o r s while Bojowald et a l . [29] calculated  i t f o r deuterons of up to 450 agreement  MeV  in  germanium,  which  are  in  good  with the only available experimental r e s u l t of Eisberg et a l .  [30] who measured this loss f o r deuterons of up to 250 MeV Recently N.V.  on germanium.  Sen et a l . studied the e l a s t i c scattering of polarized  deuterons  from  energies.  The data were analyzed i n terms of the o p t i c a l model and  reaction  the  cross  calcium and n i c k e l [31] and oxygen [32] at intermediate  sections  the  deduced were compared to predictions from the  Glauber theory o p t i c a l l i m i t . Watanabe [33] used the WKB  method to calculate the angular  ution and the p o l a r i z a t i o n of 94 MeV  deuterons by carbon.  The r e s u l t of  h i s c a l c u l a t i o n using well parameters which f i t the scattering 40 MeV protons by carbon, was  distrib-  data  of  i n good agreement with the measured values  of the d i f f e r e n t i a l cross section.  This suggests the empirical r e l a t i o n  that cross section f o r deuteron i n n u c l e i i s twice the cross section f o r proton at h a l f the energy.  - 9CHAPTER 2  The Experiment  The aim of the present experiment was to study the i n t e r a c t i o n of  protons  and deuterons i n sodium iodide c r y s t a l s .  ment was performed i n September 1986 elastically loss.  scattered  when  we  used  The f i r s t  loss  experi-  the proton  beam,  o f f a hydrogen target, to study the i n t e r a c t i o n  The f i n a l data taking was done i n March '87 when d i r e c t beams of  protons and deuterons were used.  The experiment was performed using the  p o l a r i z e d proton beam provided by the IB primary  beam  line  (BL1B) at  TRIUMF.  2.1  Beam l i n e IB  The  experiment  cyclotron hydrogen  facility.  was  performed  The  cyclotron  at  the 1BT1 l o c a t i o n of the TRIUMF  accelerates  negatively  ions and a proton beam i s extracted by removing both electrons  from the ions by i n s e r t i n g a stripper f o i l i n the machine. of  the beam  i s variable  ns  bunches  with  a  The  energy  up to a maximum of 520 MeV depending on the  r a d i a l distance of the f o i l i n the cyclotron. 5  charged  time  separation  23.055 MHz cyclotron radio frequency  The beam i s produced i n  of 43 ns corresponding to the  (RF).  Two  beams  are  typically  extracted, one into the proton h a l l , the other into the meson h a l l ( F i g . 2.1).  OQ  IPC  REMOTE HANOIINO EACR.ITV  (D  43 MW ISOTOfC PRODUCTION CYCLOTRON  5" (D «l  § « •9 (A H. If (D  3 rt  R» Ml R»  O  W ION SOUKI 3  r POLARIZED  ION source  •AT HO LABORATORY  THERMAL NEUTRON PACRJTV  MESON HALL SERVICE ANNEX  - 12 The schematic of the primary proton beamline IB 2.2.  Using  Fig.  in  Fig.  magnetic elements (dipole, quadrupole magnets) as shown i n  2.2, the proton beam from the cyclotron  experimental mounted.  i s shown  zone  (1BT1)  where  was  the target  transported to the  and  the detectors were  In our September 86 measurement, a l i q u i d hydrogen target  was  used while i n the March 87 measurement a d i r e c t proton beam was used.  A  secondary deuteron beam was also produced during the March 87 run.  2.2  Production of the secondary deuteron beam  In order to measure the deuteron reaction losses i n Nal c r y s t a l ,  a  low i n t e n s i t y deuteron beam was produced f o r the f i r s t time on beam l i n e IB during the present experiment.  The deuterons were produced from  the  primary proton beam using the reaction p+p->d+w. The deuterons selected +  were those emitted at or very  close  to  the primary  beam  direction,  y i e l d i n g -292 MeV deuterons from a beam of 446 MeV protons. The  deuteron  momentum  i s thus 6% higher than that of the primary  beam, making i t possible to suppress the background of scattered protons using  the magnetic  elements shown i n F i g . 2.2.  The production target  was a 5 5 mg/cm thick polyethylene ( C H 2 ) f o i l i n the beam l i n e 2  section,  just  1  vault  i n front of the bending magnet 1BVB2 (or more simply B2,  as i n Fig. 2.2). The magnetic f i e l d of B2 was set to d e f l e c t the primary beam 3 cm to the  left  of  center onto a lead b r i c k which served as a beam-stop, and  which occupied the left-most 3 5 %  of  the 10  cm  diameter  beam  pipe.  - 13 Quadrupoles upstream of B2 produced a horizontal focus at the beam-stop; thus the p a r t i c l e s getting past to the r i g h t deuterons  or  elastically  scattered  possibly halo from the primary beam. set  of  the beam  stop  were  from the C H 2 target, and  protons  The f i n a l bending  magnet  B3  was  to transport the deuterons of interest and to overbend any protons.  Quadrupole magnets Q7, Q8 and Q9  were  set to produce  an  achromatic  double focus from the CH£ target to the target l o c a t i o n 1BT1. The  quadrupole  and dipole MUX (Multiplex current read back) values  and t h e i r d i r e c t i o n of focus are given cyclotron the  tank,  i n Table  2.1.  Beam  i n the  which i s not stripped and extracted, i s accelerated to  outer edge of the tank where i t s l i p s out of phase with the RF, i s  decelerated  back  to  the stripper  f o i l and extracted.  These protons  a r r i v e at the experiment at a d i f f e r e n t time. A high energy probe can be used to intercept stripping f o i l .  In our experiment a wide f o i l  beam  going  past the  (C type) heavily shadowed  by an high energy probe was used.  2.3  Mai c r y s t a l s (TINA and MINA)  In Nal  t h i s experiment, the i n t e r a c t i o n loss of protons and deuterons i n  were  studied  using  TINA and MINA.  TINA, which stands f o r TRIUMF  Iodide of Natrium, measures 46 cm i n diameter and 51 cm i n length and i s o p t i c a l l y a single unit, viewed by seven phototubes. for  MINA, which stands  Montreal Iodide of Natrium measures 36 cm i n diameter and 36  length  cm i n  and i s also an o p t i c a l l y single u n i t viewed by seven phototubes.  - 14 Table 2.1 The beamline quadrupole values and t h e i r d i r e c t i o n of focus for the deuteron beam (446 MeV protons and 292 MeV deuterons)  Quads  MUX Settings  Direction  Ql  213.6  H  Q2  304.0  V  Q3  341.8  H  QV  39.6  V  Q5  183.8  H  Q6  139.9  V  Q7  127.2  H  Q8  242  V  Q9  272  H  1BVB2  559.8  1BB3  570.6  - 15 Both c r y s t a l s are shrouded by large i r o n walls of  30 cm 4> and 25 cm <f> respectively.  with  reasonable  ment.  resolution  TINA and MINA  [34-39]  including  have  apertures  They are of excellent q u a l i t y and  such detectors are preferred f o r 7-ray detection and  opening  when  100%  efficiency  are important c h a r a c t e r i s t i c s of an experibeen  studies  used  in  many  different  experiments  i n atomic and nuclear physics, but the best  known work has been i n p a r t i c l e physics experiments on the weak interactions  where  several key measurements [40-45] have been made.  MINA have not been used  for  the  detection  of  protons  or  TINA and deuterons  before, although other Nal c r y s t a l s have been often used i n a v a r i e t y of experiments e s p e c i a l l y by the Alberta group [46].  2.4  Experimental arrangement  A schematic of the experimental setup f o r the '86 and the is  shown i n Figs. 2.3 and 2.4 respectively.  '87  runs  We s h a l l f i r s t discuss the  experimental d e t a i l s of the '86 run and then the '87 run. In the '86 run, we used a l i q u i d hydrogen target which was contained in  a  cylindrical  target f l a s k of 5 cm diameter and 5 cm length.  This  was chosen i n such a way that a reasonable event rate was obtained  with  minimum  energy loss of the incoming protons.  The target f l a s k was made  of 0.13 mm kapton and was placed inside an evacuated s c a t t e r i n g which  had  a  kapton  window.  The  e l a s t i c a l l y scattered proton beams  from the p+p-*p+p reaction were detected by the two large TINA  and  MINA  (discussed  chamber  i n Section 2.3).  Nal  detectors  Two p l a s t i c s c i n t i l l a t o r s  - 16 which covered the faces of TINA and MINA were used to particles.  A  small p l a s t i c s c i n t i l l a t o r ( l x 1" x V l 6 " ) n  front of TINA i n order to define the angle. at  identify w  TINA and MINA  a  s  charged u s e c  were  * in  placed  d i f f e r e n t angular positions with respect to the incoming proton beam  and at equal distances from the target (-1.25 m). For a known energy incident proton beam h i t t i n g the l i q u i d target,  hydrogen  the energies of the e l a s t i c a l l y scattered and r e c o i l i n g protons  detected by TINA and MINA at d i f f e r e n t angular positions could be using  the  TRIUMF  TRIUMF KIN2B0DY. MINA  were  kinematic  handbook  [47] and the computer programme  The actual energies of protons detected  slightly  lower  than  the  known  theoretical  by  TINA  and  values given by the  handbook or KIN2B0DY programme because of the energy loss i n the target vessel,  plastic  scintillators,  iron, and aluminum layers i n the front  faces of TINA and MINA. The incident proton energies protons  detected  by  TINA  and  and  MINA  (calculated using TRIUMF computer Table  2.2.  The  the at  energies  of  different  programme  LOSS)  the scattered  angular positions are  summarized i n  primary energy of the proton beam was determined  from  the cyclotron s t r i p p e r parameters and i s accurate to about 1 MeV. In the '87 run as shown i n F i g . 2.4, two multiwire gas proportional chambers  (MWPC)  separated by 0.45 m were mounted immediately a f t e r the  evacuated beam pipe window (.02 particle  trajectories.  The  mm  stainless  multiwire  steel)  to  measure  proportional chambers had four  outputs (XL, XR, Y L , YR) and had a delay l i n e readout system which about  0.5 mm  vertical.  resolution  the  gave  i n the horizontal and 2 mm r e s o l u t i o n i n the  Following the wire chambers was a lead and  steel  collimator  - 17 -  TO BEAM DUMP  ^-LIQUID H-  I F i g . 2.3:  PROTON  TARGET  BEAM  Schematic of the experimental setup (1986 run)  - 18 -  I COLLIMATOR  EXIT 7"  ^  S3  —  S2  'P5  I  LEAD COLLIMATOR  3  _  MWPC 2  MWPC I  PROTON F i g . 2.4:  BEAM  Schematic of the experimental setup (1987 run)  - 19 Table 2.2 Proton energies In TINA and MINA  Incident proton beam energy (MeV)  Angular position of TINA with respect to incident beam 8j  Theoretical proton beam energy i n TINA (MeV)  Actual Angular proton position beam of MINA energy with after respect energy to loss incident correcbeam 6^ tion i n TINA (MeV)  Theoretical proton beam energy i n MINA (MeV)  Actual proton beam energy after energy loss correction i n MINA (MeV)  497  41°  254.1  249.3  42°  242.9  235.8  497  47°  202.5  196.9  36.5°  294.5  288.2  497  54°  146.3  139.3  30°  350.7  344.9  451  41°  232.8  227.7  43°  218.2  210.6  403  41°  210.1  204.7  43.5°  192.9  184.7  - 20 having an opening of 51 mm diameter.  The collimators were of s u f f i c i e n t  thickness to stop any of the p a r t i c l e s from beams.  A  plastic  scintillator  S  2  the primary  or  secondary  was mounted immediately a f t e r the  collimator and about 1.25 m beyond i t a second p l a s t i c  scintillator  was mounted i n front of the Nal c r y s t a l (TINA and MINA).  The f i r s t part  of the '87 run was with the deuteron beam and f o r t h i s S 3 and MINA used.  S3  were  For the second part we studied the reaction loss with the d i r e c t  proton beam and f o r t h i s S 3 and TINA  were  used.  TINA  or MINA  were  mounted i n such a way that the beam could h i t d i r e c t l y the front face of i t , i . e . the angular p o s i t i o n of TINA or MINA with respect beam  was  0°.  The  given i n Table 2.3.  to  incident  dimension of these s c i n t i l l a t o r s and the MWPCs are The energies of the proton and  the deuteron  beam  are given i n Table 2.4. For  a  446 MeV  proton beam which y i e l d s about 291.6 MeV deuterons,  beamline quadrupoles were set to the optimum tune quads  7,  8  and  condition.  In  fact  9 were set to transport deuterons from the production  target to an achromatic horizontal and v e r t i c a l focus at 1BT1. During the '87 run, the d i r e c t beam measurement.  Because  was  used  after  the  deuteron  i t was very d i f f i c u l t to remove the polyethylene  target from the vault section at that moment, i t was l e f t there f o r the rest  of  the experiment but the 8" lead beam stopper was removed. The  dipole and quadrupole magnets were reset f o r protons.  - 21 Table 2.3 Dimension of s c i n t i l l a t o r s and MWPCs used i n the ' 8 7 run  Counters  Dimension  MWPC 1  5" x 5"  MWPC 2  5" x 5"  S2  1 1/4"^ x 1/16"  S3 (TINA)  1" x 1 1/2" x 1/32"  S3 (MINA)  8" x 8" x 1/8"  Table 2.4 Energies of the proton and the deuteron beam ( ' 8 7 run)  Particle  Incoming energy i n MeV  Energy detected i n Nal c r y s t a l a f t e r energy loss correction* i n MeV  446 348  443.9 345.7  291.6  276.8  Energy loss i n p l a s t i c s c i n t i l l a t o r s , aluminum and i r o n layer i n TINA and MINA were incorporated. For protons, additional energy loss i n the deuteron production target C H 2 was also incorporated.  - 22 2.5  E l e c t r o n i c s and data a c q u i s i t i o n  A schematic of the e l e c t r o n i c s used i n the '86 run i s shown i n 2.5.  Fig.  In t h i s diagram the squares l a b e l l e d D, D l , CFD represent d i s c r i -  minators. into  Linear signals above a threshold (set by user) are  logic  signals  by  the discriminators.  CFDs (constant f r a c t i o n  discriminators) are used  where  because  the timing of the output pulse i s r e l a t i v e l y  f o r these  CFDs  the timing  converted  independent of the size of the pulse. logic  fan-in/fan-out  units.  The  information  is  important  The triangles represent l i n e a r or triangles  with  arrows  represent  attenuators and the c i r c l e s give the CAMAC locations of ADC's, bit  registers  etc. which were read by the computer.  l a t e d i n two modes.  scalers,  Data were accumu-  F i r s t with f u l l target and then with  empty  target  to subtract the background. The  cyclotron  radio  frequency  signal,  usually  known  s i g n a l , was transmitted d i r e c t l y from the main c o n t r o l room counting  room  where  as the RF to the M9  the data a c q u i s i t i o n e l e c t r o n i c s and the PDP11/34  computer were located to record the data  on magnetic  tape  f o r each  event. Seven  signals each from TINA ( T l , T2  T7) and MINA (Ml, M2  and three signals from s c i n t i l l a t o r s mounted i n front of TINA and  (T^, Tg  T Q ) and one signal from the s c i n t i l l a t o r mounted i n front of MINA  (M^) f o r charged coincidences were area  M7)  to the counting  room.  transmitted  from  the  experimental  Signals T^ and Tg were from s c i n t i l l a t o r  S^ and Tg was from S 3 , the very small s c i n t i l l a t o r which was front of TINA to define the angle of the proton into TINA.  placed i n  - 23 -  .O-DK to TDC START  TilCHM  to ADC GATES" to TDC START  =UCK>£]  OL>d (D-SHE F i g . 2.5:  Schematic of the electronics (1986 run)  - 24 In t h i s experiment, the phototube signals from TINA and MINA each)  were s p l i t into two parts by a passive s p l i t t e r (PS).  parts (-80% by amplitude) were amplified s i x times amplifier  (LRS 612A) and attenuator  with  combinations  The larger  the help  of  and were fed into  twelve input, high  r e s o l u t i o n CAMAC  (ADC-LRS  Signals from the seven smaller parts (-20% by ampli-  2258A).  Analogue  (seven  tude) were sent to a mixer (MIX) to get a clipped  to D i g i t a l  summed  output  Converters  signal.  A  s i g n a l from the mixer was obtained and a quad l i n e a r fan in/fan  out (LRS428F) was used to fan out this signal i n two parts. The f i r s t part was amplified using an amplifier (LRS612A) was  f e d into CAMAC ADCs.  and  then  The second part a f t e r a m p l i f i c a t i o n was sent  to a constant f r a c t i o n discrimator (CFD-ORTEC 934). Signals from s c i n t i l l a t o r s T  and Tg were sent to a  A  quad  nator (LRS 821Z) from which NIM l e v e l outputs were obtained. and Tg were then fed into a l o g i c fan in/fan output  out u n i t  of which was sent to discrimator DI (LRS621BLZ).  discrimiSignals T  A  (LRS429A) the A s i g n a l from  TQ was also sent through a discriminator; the two discriminator  outputs  and a l o g i c a l output from the CFD were then fed into t r i p l e 4-fold l o g i c coincidence u n i t (TIN-LRS465). adjusted  i n such  between a l l three. was  adjusted  so  a  way  Timing  that  there  of these  signals  S i m i l a r l y timing of the discriminator s i g n a l from M that  there  was  A  an overlap between t h i s and the CFD Two signals from  TIN and  v i a a fan out u n i t were sent to a b i t r e g i s t e r and a v i s u a l scaler.  Another output was sent to the coincidence u n i t known as LAM Me)  were  was clear overlap (coincidence)  s i g n a l coming to the coincidence unit (MIN). MIN  three  and the coincidence  output  was  (Look At  sent to fan out unit (LRS429A).  - 25 Several  outputs  were used from this unit.  The widths of these outputs  were adjusted by sending these signals to discriminators. was  used  as  a  C212 strobe.  used as gates to the ADC. STRl  and STR2  were made. timing  where  output  Two outputs were stretched to 500 ns and  Two outputs were sent  to coincidence  units  coincidences with CFD outputs from TINA and MINA  Output signals from STRl and STR2 having TINA and MINA  respectively  CFD  were used as TDC s t a r t s f o r two 2228A LeCroy Camac  Octal Time to D i g i t a l Converter. Dual  One  An output was stretched to 1 ms  by a  Gate Generator (DGG-LRS222) and was sent to a fan i n unit, where a  computer busy signal was also fed.  An output of this unit was  used  as  an i n h i b i t signal to the coincidence unit known as LAM. There  were  two  types  of data read onto tape.  Type 1 events were  the strobe events while type 2 events were j u s t the s c a l e r s . a c q u i s i t i o n system started with the LAM s i g n a l .  by  TDC  clocks  Thus these TDCs give the  of f l i g h t of the protons to TINA and MINA.  One event was handled  at a time.  A 1 ms gate from the Dual Gate Generator was set which  protection  against  events  occurring  full  gave  immediately afterwards u n t i l the  computer s t a r t s reading the CAMAC module information, was  were  the TINA and MINA CFD signals and stopped by the RF signal  and these are c a l l e d RFT and RFM respectively. time  data  ADC gates were set, and  ADCs provided the energy information i n each counter. started  The  the buffer was transferred to tape.  whenever a buffer  I f the computer was busy  processing an event, the NIM driver sends an i n h i b i t signal to the LAM coincidence u n i t to stop more events from p i l i n g up. For a number of coincidences a b i t was set i n the C212 b i t r e g i s t e r s whenever a strobe f i r e d .  The purpose of this i s that by  examining  the  - 26 b i t pattern we could then reconstruct the event. A 2.6.  schematic of the electronics used i n the '87 run i s shown i n F i g . The MINA (or TINA) signals were treated the same way as described  i n the '86 run. Signals from S 2 and S 3 were delayed and sent to l i n e a r fan outs. output from each of these was sent to ADCs, the other one to CFDs. CFD  output was sent to a coincidence unit  or Event).  (S2.S3  outputs of the Event coincidence unit was sent to the LAM,  that  One  One of the  coincidence  unit  i s , the event trigger was derived from a coincidence between  the two p l a s t i c s c i n t i l l a t o r s , defined  An  by  with  the thick s c i n t i l l a t o r .  the  time  of  the  trigger  being  The TDC clocks were started by the  LAM signal and stopped by the RF s i g n a l . In LAM, a new event was vetoed when arising event.  out  of  the  computer  was  an  inhibit  signal  busy and/or event busy from a preceding  The output signal from LAM were  Fan-out  there  logically  fanned  out  by  the  u n i t and the widths of each outputs were adjusted using d i s c r i -  minators, so that they had s u f f i c i e n t widths to be used as C212 strobes, ADC gates and TDC s t a r t s . then to a TDC stop. from  the  delay  The RF signal was sent to a discriminator and  Signals  line  (X , X , Y , Y ) and W L  R  L  R  2  (X , X , Y , L  R  L  Y ) R  multiwire proportional chambers (W^ and W 2 ) were  delayed and were used as TDC stops. In both experiments, the data were recorded  event  by  event  on  magnetic tape using the TRIUMF standard multi data a c q u i s i t i o n system.  a  - 27 -  o x  F i g . 2.6:  Schematic of the electronics (1987  run)  - 28 CHAPTER 3  Data Analysis  The  data  analysis  computers at TRIUMF.  was  performed  using  the VAX 8650 and VAX 780  The MULTI [48] written raw data were analyzed with  MOLLI [49], the TRIUMF standard program f o r the o f f l i n e manipulation of data, with user  supplied  implemented  obtain  to  subroutines. the  The  different  software  cuts  i n t e r a c t i o n loss f o r deuterons and protons  w i l l be discussed i n this chapter.  3.1  Interaction loss of deuterons  The deuteron pulse height triggered  i s presented  spectrum  i n MINA  f o r a l l the  i n F i g . 3.1 and shows the deuteron peak and a  broad range of pulse heights from the events where the went  a  nuclear  reaction,  coming  from  deuteron  under-  as well as from protons of varying energies  which has scattered i n the beamline. deuterons  events  the  CH2  The primary means  of  identifying  production target was the time of the  event t r i g g e r r e l a t i v e to the cyclotron R.F.  F i g . 3.2 shows  this  time  (for two 43 ns periods, f o r greater c l a r i t y ) versus the energy deposited i n the sodium iodide counter. relative  flight  time  The horizontal p o s i t i o n i s determined  f o r each p a r t i c l e .  The group marked 'a' are the  deuterons produced i n the C H 2 target, 'b' are the deuterons produced the  middle  l e g of  the beamline  by  in  near the beam-stop, and 'c' are the  9000  7200  -  CO 5 4 0 0  -  O O  3600  -  1 800  -  200  400  600  800  1000  Channel  1200  1400  Number  1600  1800  OQ  2000 1 o  1500-  (ft 3  o  >  <D  o  1000-1  rt (6  3  (6 H OQ VI  a CD  o  C LJ  500 H  (n H» ft (ft  a  •—i  »  OQ P> H«  3  u rt  6  i i i i I i i i i I i i i i i i i i i i i i i i i i i l i i i i I i i ii 1000 1200 1400 1600 200 400 600 800 RF  - 31 protons.  The locus of the low-energy p a r t i c l e s breaking o f f to the l e f t  of group 'c' matches that expected of 446 MeV protons which d e f l e c t into the vacuum vessel of the magnet B3, lose energy, and are scattered so as to  emerge  from  B3  back  on the beamline axis.  deuterons and protons i s confirmed by the time plastic  scintillators  l a t o r , but  these  proportional deuterons.  of  The i d e n t i f i c a t i o n of flight  between  the  and by t h e i r pulse heights i n the thick s c i n t i l -  parameters  chambers  were  are  not  so  sensitive.  The  multiwire  used to obtain p o s i t i o n information of the  The X-Y p o s i t i o n information from the wire chambers  enabled  us to confirm that the deuterons from the CH2 target were being focussed as predicted by the beam transport calculations, did  not  strike  the  that  these  deuterons  collimator,  and  that the range i n angles was as  The events used i n determining  the  Nal  calculated.  satisfy  interaction  loss  had  to  the 'good deuteron' condition which consisted of t i g h t r e s t r i c -  tions or cuts on raw data which are as follows:  3.1.1  RF cut  The RF spectrum allows interest,  other  deuterons  us and  to  discriminate  protons.  between  deuterons  As mentioned e a r l i e r i n this  section the group marked 'a' are good deuterons ( F i g . 3.2). RF  spectrum  is  shown  i n F i g . 3.3.  determine the RF cuts to be applied select  only  of  A  typical  The f i r s t pass at the data was to in  the  subsequent  treatments  the good deuterons and thus eliminating useless data.  arrows indicate the cuts imposed on subsequent data.  to The  8000  6000  4000  -  2000  -  O O  0 0  200  400  600  800  Channel  1000  1200  Number  1400  1600  - 33 3.1.2  Time of f l i g h t cut  A t y p i c a l raw spectrum of time of f l i g h t between is  shown  i n F i g . 3.4.  Applying  explains  the  origin  of  scintillators  the RF cut f o r either deuterons or  protons, one obtains a time of f l i g h t spectrum as This  two  shown  i n F i g . 3.5.  the two peaks i n F i g . 3.4.  The time of  f l i g h t cut was selected using the information from F i g . 3.5.  3.1.3  Energy loss cut  The energy loss spectrum f o r the deuterons i n the thick s c i n t i l l a t o r S 2 was generated from the raw data using RF and time of f l i g h t cuts ( F i g 3.6).  This spectrum was used to select the energy loss cut (dE/dx  cut)  and i s also i l l u s t r a t e d i n the S 2 pulse height f o r protons.  3.1.4  Multiwire proportional chamber cut  Two  wire  chambers  (MWPC1  and  MWPC2)  were used i n the experiment.  Each one has four outputs usually known as l e f t , r i g h t , top outputs.  Here  T2,  and B 2 .  histograms f o r LI, R l , T l , B l , L 2 , R 2 , T 2 , and B 2 were generated i n  the present experiment. 3.7.  bottom  we s h a l l c a l l the outputs of the f i r s t wire chamber LI,  R l , T l , and B l and f o r the second wire chamber as L 2 , R 2 , TDC  and  A t y p i c a l raw histogram f o r LI i s shown i n F i g .  Four histograms XI, X 2 , Y l , and Y 2 were then generated where  - 34 -  Fig.  3.4:  A t y p i c a l raw spectrum o f time o f f l i g h t (TOF) between two scintillators  10000 o Proton  8000-  o  o +  w  6000-  o  Deuteron  o  c  o 4000 o  o +  2000  o + o o +  0 400  o  Qa><p(D(D<pq><M>911111111111*"*"  500  600 700 Channel Number  800  36 -  s^unoQ Fig.  3.6:  A t y p i c a l d e u t e r o n energy l o s s spectrum i n s c i n t i l l a t o r w i t h RF and TOF c u t s  S2  7000  OQ CO  6000 »  —\  ft  h o  5000  n p) «! to (D O ft  ^  4000  O  O  3000  -^1  i-h M O  0  2000  H  1000 (H x> ii o •o o  H rt H» O  3  P>  0 500  1 DO 0  Channel  150 0  Number  2000  - 38 XI - LI - R l ;  X2 = L2 - R2  Y l = B l - T l ; Y2 - B2 - T2 These  histograms  show  directions i n the two wire projected  the deuteron chambers.  beam  Two  p r o f i l e i n the X and Y  other  histograms  of the  X, Y coordinates at the f o c a l point Xp^j = AX1 + BX2 and Yp^j  = CY1 + DY2 were also generated where A = C = -3.2; B = D = 4.2. A t y p i c a l XI and Xpgj spectra with RF and time of f l i g h t shown  i n Figs.  3.8  and 3.9 respectively.  cuts are  The wire chamber cuts were  selected from the XI, X2, Y l , Y2, Xpgj and YpRj spectra. After implementing RF, time of f l i g h t , energy loss (dE/dX) and wire chamber cuts, any p a r t i c l e s other than deuterons and any deuterons other than those produced i n the C H 2 target were cuts  removed.  Using  a l l these  the deuteron energy spectrum i n MINA was generated and was used i n  determining the sodium spectrum  iodide  response.  A  typical  deuteron  energy  i n MINA i s given i n F i g . 3.10. The r e s o l u t i o n of MINA i s very  good f o r these deuterons - no worse than 0.7% FWHM i n the peak as  shown  i n F i g . 3.11.  3.1.5  Energy c a l i b r a t i o n  The  protons with 446 MeV energy from the cyclotron produced deuter-  ons of 291.6 MeV energy through the reaction p+p-+d+jr. +  The energy l o s t by the deuterons traversing the distance between the exit  window  and MINA was calculated.  Considering the stainless s t e e l  e x i t window, p l a s t i c s c i n t i l l a t o r s and the aluminum layer i n the front  300 to OO  fl  o > p  ft  250  H  200  H  1 50  H  [Ll  u  &a H  O P « M H»  ft 10 »  ptf o i j rt * E 3 B o. H X O M «•] D f O C i rt 5»J to M Hi O  CO  o o  VO  1 00  H  50  H  B g  h  0 m s  •d  V  s  m  I  \i  \t  1/  (6 H  o o  M rt p> O  3 P  0  V  V  1  -200  0  200  Channel  400  ^  600  Number  800  1000  - 40 -  F i g . 3.9:  A t y p i c a l spectrum ( X  p R J  •= AX1+BX2) with RF and TOF cuts  - 41 -  o o  CM  O O O  O o  o  CO  CD  o  o  o  o  CM  s}unoQ F i g . 3.10:  A t y p i c a l deuteron energy spectrum i n MINA  - 42 -  F i g . 3.11:  A t y p i c a l deuteron energy spectrum showing MINA resolution  - 43 face  of MINA, the deuterons l o s t about 14.8 MeV.  deuteron peak was pedestal  was  obtained  obtained  at channel  number  The 276.8 MeV energy  1190 while  the MINA  at channel number 94. Using these 2 points the  MINA energy was calibrated.  3.2  Interaction loss of protons  The analysis of the data f o r the i n t e r a c t i o n loss f o r protons now  be  discussed.  The September '86 run, used scattered protons from  the p+p-^p+p reaction and w i l l be discussed i n section 3.2.1. '86  will  The March  run used the d i r e c t proton beam into the Nal, and w i l l be discussed  i n section 3.2.2.  3.2.1  Protons from p+p-^p+p i n N a l detectors  During the September '86 run, protons  of d i f f e r e n t  energies  were  used while TINA and MINA were placed at d i f f e r e n t angles with respect to the incoming beam. energies  of  The two c r y s t a l s  were  used  i n coincidence.  The  the incoming proton beam and the corresponding energies of  the protons at TINA and MINA have already been given i n Table  2.2 (p.  19). The  RF  spectrum  f o r TINA  section 2.5) were generated.  and MINA (RFT and RFM as described i n  A t y p i c a l RFT spectrum i s shown  3.12, which shows two proton peaks separated by 43 ns.  in  Fig.  RF cuts f o r TINA  J—i—i—i—i—i  1 200 0  OQ  i  i  i  i  I  i—i—i—I—i—i—i—I—i—I—r  i  i  i  i  i  i  i  i  i  i  i  J  L  S3  10 0 0 0  -  ft  3  O P>  pa *i w •a (D  80 0 0 CO  o rt  60 0 0  -  40 0 0  -  O O o rt O  3  2000  i 4I i  0  100  200  300  400  Channel  50 0  i—i—i—I—i—i—r  60 0  Number  700  800  - 45 were chosen from this spectrum as shown by  the arrows.  Similarly  RF  cuts f o r MINA were also chosen from a RFM spectrum. A scatter p l o t of TINA energy versus MINA energy was generated (Fig. 3.13) which shows the range of proton energies i n TINA and MINA. subsequent  analysis while generating energy spectra i n TINA, a r e s t r i c -  t i o n on the MINA energy spectrum was imposed and vice versa. were  In the  selected  from  the scatter  plot  which  make  These cuts  sure that while a  scattered proton of f u l l energy i s detected i n one of the detectors, the r e c o i l proton i s detected i n the other.  The f i n a l proton energy spectra  i n TINA and i n MINA were obtained using the RF  and the scatter  plot  cuts. Similar  techniques  were applied to generate the energy spectrum i n  TINA and i n MINA f o r empty target runs.  After normalization, the empty  target spectrum was subtracted from the corresponding f u l l target proton energy spectrum to obtain the background subtracted f i n a l proton  energy  spectrum; a t y p i c a l one i s shown i n Fig. 3.14. When  the outgoing  protons  towards the detector, they lose distance  leave some  the target vessel on t h e i r way energy  traversing  half  of the  of the target vessel, p l a s t i c s c i n t i l l a t o r s and the A l layer  present i n the front face of TINA and MINA.  The actual energies at the  c r y s t a l s were given i n Table 2.2 (p. 19). TINA ent  runs.  and MINA energies were then c a l i b r a t e d using data from d i f f e r The TINA energy c a l i b r a t i o n curve i s shown i n Fig. 3.15.  TINA Energy vs. MINA Energy  OQ  800  CO  § s?  i i i  .1 1 I I  i  i  i  * ' t i I r )  1  I  I  L  i  I  I  I  I  i  III!  700  rt> O M OQ  "  i  a.  B"  o. »  » 9 13 w O H« W O  •* 3  rt P> » (-•  >  CD  600  oqo»  [Li oQ]'-• ••)• •  rt  2o Z  Ml  ® (» M OQ (t>  •a o  w H> rt »  >N500 CD  CT>  ^_ CD  L5  400 300 H 200  OQ P>  3 rt  I  200  I  I  I | I  400  i  600  i i i  i  800  i  i i  i  1000  i  i i  i  1200  Energy(MeV)  i  i i  i  1400  i  i i  i  1600  i  i i  1800  - 47 -  o  O O  Lf)  o  CM  CM  o  F i g . 3.14:  o  o  o  o  CD  o  o  Lf)  in  s]unoQ  A t y p i c a l background subtracted proton energy spectrum  - 49 3.2.2  Direct proton beam i n a Nal detector  In the March '87 run, a d i r e c t proton beam of 348 MeV was  used  with  and  446  MeV  TINA as the detector. As usual the RF cut was selected  from the RFT histogram. The proton energy spectrum i n the thick s c i n t i l l a t o r obtained trum. The  using  an  RF cut.  (ES2) was  then  The dE/dX cut was selected from t h i s spec-  The time of f l i g h t spectrum was also generated with  an  RF cut.  cut f o r the time of f l i g h t of the protons between two s c i n t i l l a t o r s  was then selected.  For the d i r e c t beam the vast majority of events pass  a l l these cuts. Using  RF, dE/dX and the time of f l i g h t cuts the f i n a l proton energy  spectrum was obtained. Fig.  3.16.  A t y p i c a l proton energy  spectrum  i s shown i n  6500  CO  O O  5200  -\  3900  H  2600  —\  1 300  H  0  Energy (MeV)  - 51 CHAPTER 4  Results and Discussion  4.1  Deuteron  In  interactions  the deuteron  energy  spectrum i n MINA (Fig. 3.10) the t a i l was  separated from the peak by a cut i n the spectrum maximum  of the peak.  at 5  MeV  below the  We also consider t h i s cut-off at 10 MeV below the  peak to separate the non interacting peak  from  the i n t e r a c t i o n  tail.  With each cut imposed, the peak to t o t a l counts r a t i o improved s l i g h t l y . Table 4.1 shows a comparison of t a i l to t o t a l counts r a t i o tion  loss  with  different  cuts  both  or  interac-  at 5 and 10 MeV below the peak  c u t - o f f point. The f i n a l t a i l to t o t a l counts r a t i o or 276.8  interaction  loss  f o r the  MeV deuterons i n the sodium iodide c r y s t a l was found to be 39.5 ±  1.7% and 38.4 ± 1.7% f o r cut o f f at 5 MeV and 10 respectively,  MeV  below  the peak,  where the errors given are purely s t a t i s t i c a l .  The value  for  the i n t e r a c t i o n loss i s r e l a t i v e l y i n s e n s i t i v e to quite severe  on  RF, time of f l i g h t , and energy l o s s .  cuts  This value f o r the interaction  loss i s s i m i l a r to that found f o r germanium detectors, v i z . -40% [29]. Using standard RF, TOF and dE/dX cuts, sensitivity  we  have  also  of the i n t e r a c t i o n loss to X, Y cuts from wire chamber 1.  Loose, medium and severe cuts were imposed on the X spectrum shown  by  studied the  arrows  marked  which are  i , m, and s respectively i n F i g . 3.8 (p. 39).  - 52 Table 4.1 Interaction loss of deuterons using d i f f e r e n t cuts  Cut o f f at 5 MeV below the peak  Cut  Cut o f f at 10 MeV below the peak  Tail" Total*  Tail* Total*  RF  41.7 ± 1.1  40.0 ± 1.1  RF and time of f l i g h t  42.3 ± 1.1  39.6 ± 1.0  RF, time of f l i g h t and dE/dX  40.9 ± 1.1  39.2 ± 1.0  RF, time of f l i g h t , dE/dX and wire chamber  39.5 ± 1.5  38.4 ± 1.5  Error quoted i s only  statistical  Similar cuts were imposed on the Y spectrum and i t was interaction Table 4.2.  loss  found  that  the  i s more or less i n s e n s i t i v e to these cuts as shown i n  - 53 Table 4.2 E f f e c t of d i f f e r e n t X, Y cuts on the Interaction loss of deuterons  Cut  Cut o f f at 5 MeV below the peak  Cut o f f at 10 MeV below the peak  Tail* Total*  Tail* Total*  Y Loose X Loose Y Medium Y Severe  40.611.1 40.711.1 40.611.4  39.111.1 39.111.1 38.911.3  Y Loose X Medium Y Medium Y Severe  40.,6 + 1..2 40..7 + 1..2 40..8 + 1..5  38 .9 + 1,.1 39,.0 + 1,.2 38,.8 + 1,.4  Y Loose X Severe Y Medium Y Severe  41..0 + 1..4 41..0 + 1..4 41..1 + 1..8  39,.4 + 1..4 39 .4 + 1,.4 39,.1 + 1..7  Error quoted i s only  4.2  statistical  Proton Interactions  In the proton energy spectrum (Fig. separated  from  the  maximum of the peak. past  the  10  MeV  peak  3.14) the i n t e r a c t i o n  was  by a cut i n the spectrum at 10 MeV below the  I f we look at the spectrum c a r e f u l l y we  see  that  cut, a few bins contain counts some portion of which  could be a t t r i b u t e d to the t a i l and some to the peak. in  tail  A l i n e was  drawn  the t a i l region (as shown i n F i g . 3.14) which was extended up to the  - 54 cut o f f l i n e , 10 MeV below the peak.  Counts above t h i s  line  in  these  bins were a t t r i b u t e d to the peak and the rest to the t a i l . Thus  the t a i l to t o t a l ( t a i l + peak) r a t i o or the i n t e r a c t i o n loss  was calculated. cut  This r a t i o was also calculated i n the same way with the  5 MeV below the peak.  S i m i l a r l y i n the f i n a l proton energy spectra  of the March '87 run (Fig. 3.16), the 10 MeV and 5 MeV were used to calculate the t a i l over t o t a l r a t i o .  cut o f f points  The r e s u l t s from both  the runs are given i n Table 4.3.  4.3  Discussion  4.3.1  Proton  data  In both the March '86 and the September '87 runs, the thickness all  the materials  present  calculated i n g/cm . materials  i n the beam path towards the detector was  Considering the interaction loss i n each of  2  (hydrogen,  plastic,  aluminum  detector etc.) to be 1% per g/cm  2  then  calculated.  of  layer  i n front  [47], the t o t a l i n t e r a c t i o n  these  face of the loss  was  The i n t e r a c t i o n loss i n these materials introduces a  correction and one of the systematic uncertainty i n our f i n a l results of the  proton and the deuteron i n t e r a c t i o n loss i n Nal was taken to be 20%  of t h i s correction.  The ambiguity  of separating  the reactions  into  e l a s t i c and i n e l a s t i c regions also introduces an uncertainty i n the t a i l to t o t a l r a t i o .  The e f f e c t of changing the p o s i t i o n of the cut by 5 MeV  on the present data i s on the average -1.5%.  We have considered h a l f of  - 55 Table 4 . 3 Results of the Interaction loss of protons with 5 and 10 MeV cuts  Proton energy ( i n MeV)  Interaction Loss (%) Cut o f f at 10 MeV Cut o f f at 5 MeV below peak below peak  139. 3  13. 1 + 0.4  14.2 + 0. 4  184. 7  21. 0 + 0.2  22.9 + 0. 2  196. 9  21. 7 ± 0.5  23.1 + 0.,5  204..7  21.,7 + 0.2  22.9 + 0.,2  210.,6  24. 2 + 0.2  25.3 + 0. 2  227.,7  27.,5 + 0.2  29.0 + 0.,2  235,.8  29..5 + 0.4  31.0 + 0,.4  249,.3  29,,1 + 0.4  30.7 + 0,.4  288 .2  38,.4 + 0.6  40.2 + 0 .6  344 .9  45,.5 + 0.7  47.2 + 0 .7  345 7**  45 .8 + 0.8  47.2 + 0 .8  443 .9**  58 .4 + 0.4  59.9 + 0 .4  Error quoted i s only s t a t i s t i c a l From the March '87 run  - 56 t h i s difference as the uncertainty. results  (Table  4.4)  systematic errors.  includes  the  Hence the error quoted i n our f i n a l statistical  error  as well as the  The s t a t i s t i c a l error and the systematic errors were  added i n quadrature to obtain the f i n a l error.  Table 4.4 Present r e s u l t s f o r the proton Interaction loss i n Nal detectors using a cut 10 MeV below the peak  Energy (MeV)  Interaction l o s s * (%)  139.3  13, .1 ± 0.9  184.7  21, .0 ± 0.9  196.9  21.,7 ± 1.0  204.7  21, ,7 ± 0.9  210.6  24, ,2 ± 0.9  227.7  27, ,5 ± 0.9  235.8  29,.5 ± 1.0  249.3  29,.1 ± 0.9  288.2  38 .4 ± 1.1  344.9  45 .5 ± 1.1  345.7  45 .8 ± 1.2  443.9  58 .4 ± 0.9  Total error incorporating s t a t i s t i c a l and systematic  - 57 In  the  present  experiment, the i n t e r a c t i o n loss of protons i n Nal  obtained over the range 139-444 somewhat  smaller  than  the  MeV  and  calculated  tabulated  values [1,26].  values of Goulding and Rogers are s l i g h t l y higher Measday  and  C.  Richard-Serre.  measured loss at 146 Because  of  these  interaction loss.  MeV  from  larger  inconsistencies we  and  than  4.4  is  The calculated the values  of  Roger's experimentally  than  our  measured  value.  have decided to recalculate the  The procedure we have undertaken i s as follows:  The tabulated values of obtained  Goulding  i s also  i n Table  the  CERN  energy  report  E  and  dE/dX  f o r proton  i n Nal  [1] were f i t t e d , using TRIUMF MINUIT  program, with a function Y  -  Ax" + C  where Y i s the f i t t e d dE/dX, X i s the energy. assigned  (4.1)  B  About 1% uncertainty  to the dE/dX data up to 300 MeV and 0.5% up to 500 MeV.  was Para-  meters obtained from the best f i t are A - 213.8940, B - 0.8976 and  C  -  0.8949. The  original  dE/dX  data  and the data obtained using the best f i t  parameters are shown i n Table 4.5 f o r comparison. To c a l c u l a t e the i n t e r a c t i o n loss, f o r convenience that  i t was  assumed  the Nal c r y s t a l was divided into c e l l s of various thickness where,  i n each c e l l , protons lose 1 MeV i n energy. assuming  500  MeV  incoming  We started our  calculation  protons and continued d i v i d i n g the c r y s t a l  into c e l l s u n t i l the proton energy dropped to 150 MeV. 350 c e l l s of various thickness.  Thus there  were  We were p a r t i c u l a r l y interested i n the  - 58 Table 4.5 Comparison of dE/dX values  dE/dX (MeV/g/cm ) from CERN report  dE/dX (MeV/g/cm ) from f i t  100  4.330  4.322  200  2.734  2.734  300  2.167  2.173  400  1.881  1.882  500  1.711  1.703  Energy (MeV)  energy  range  z  of  150-500  MeV  2  because there i s a lack of data i n this  energy range. The t o t a l f r a c t i o n of i n t e r a c t i o n i s given by f-l-exp(-£ i i) where i n  n^  i s the  number  of atoms/cm  2  cross section i n that c e l l . protons  i s g/cm  2  was  i n the i t h c e l l and  a  i s the reaction  For each of the 1 MeV c e l l s , the  range  of  calculated using the f i t t e d dE/dX value f o r the  proton energy i n that c e l l . of atoms/cm  Using the range values f o r the 1 MeV c e l l s ,  the  number  a^'s  f o r each c e l l , the i n t e r a c t i o n loss f o r protons i n the energy range  2  (n^'s) were then calculated.  Knowing n^'s and  - 59 151-500  MeV  can  be calculated.  We started with 151 MeV protons whose  i n t e r a c t i o n loss could be found using the following expression:  I  151  "  n  151 151 a  +  I  150  <  x  " 151 151> n  (->  a  4  where I 1 5 0 i s the i n t e r a c t i o n loss of 150 MeV protons i n Nal, the of  which  was  obtained from the CERN report [1],  loss f o r 152 MeV proton, I 1 5 2  w a s  2  value  Thus the i n t e r a c t i o n  computed using the value obtained  for  and so on. We f i r s t assumed an energy independent range 151-500 MeV The X  2  cross section a i n the energy  and the i n t e r a c t i o n loss of  proton  were  calculated.  calculated values were then compared with our measured values using minimization technique keeping a as a free parameter.  f i t , a = 1273 ± 24 mb was Since  the  From the  best  obtained.  reaction cross section a i s not a c t u a l l y energy  indepen-  dent, we t r i e d to calculate the loss assuming an energy dependent a. have  fitted  the  existing  results  of  We  reaction cross-sections versus  energies [1,16] with an energy dependent function -  a  p + QE + RE  (4.3)  2  and obtained the parameters p - 1634.27, Q •= -0.235797, from  the best f i t .  R  =  The experimental values were then compared with the  calculated values obtained using a — K(p + QE + RE ),  where  scaling  and  2  factor.  Keeping  K  as  a  free  parameter  minimization technique, we obtained K - .79 ± .02 Table  0.0006311  from  K  using  the  is  the  a  best f i t .  4.6 shows the calculated reaction cross section from the best f i t  to data at some energies as well as the energy independent  a.  Present  - 60 r e s u l t s a r e shown i n F i g . 4.1 along The  with  our  calculation  calculation  distinguishable  f o r the p r o t o n  using from  loss  u s i n g the energy dependent c r o s s  energy the  interaction  independent  calculation  with  cross  section  in  Nal  section.  is  hardly  an energy dependent c r o s s  section.  Table  4.6  Reaction cross section values f o r proton i n t e r a c t i o n s i n N a l , as d e t e r m i n e d from p r e s e n t d a t a  E  (MeV)  Energy dependent cross section (mb)  151  1274.3  200  1273.8  300  1280.1  400  1296.3  500  1322.6  4.3.2  Energy Independent cross section (mb)  1273.0  Deuteron data  I n the p r e s e n t e x p e r i m e n t , the t o t a l i n t e r a c t i o n l o s s f o r 276.8 deuterons  in  Nal  was  found t o be  (39.5 ± 1.7%)  as shown I n T a b l e  where the e r r o r quoted i n c l u d e d b o t h the s t a t i s t i c a l and the  MeV 4.7  systematic  - 62 Table 4.7 Present r e s u l t of the deuteron Interaction  Energy (MeV)  Interaction loss (%)*  276. 8  39.5 ± 1.7  Total error incorporating  uncertainties.  On the basis  calculate  reaction  the  loss  s t a t i s t i c a l and systematic.  of  our  interaction  loss  we  wanted  to  cross section f o r deuterons i n Nal and compare  with other r e s u l t s . The i n t e r a c t i o n loss f o r 100 MeV deuterons i n Nal as Measday  and  Schneider  [5]  i s 9.8%.  calculated  Taking t h i s value as a reference  point, calculations have been done assuming that the 276.8 MeV lost  their  energy  in  Nal  by  t i l they reached 100 MeV.  deuterons  From the t o t a l  range of 276.8 MeV deuterons i n Nal, the range f o r 100 MeV deuterons was subtracted  and  were calculated. energy  t h i s range the number of nuclei per cm^(n) i n Nal  The reaction cross section (a) f o r 80  MeV  deuteron was obtained from the paper [5] as 3520 mb.  and o, the found.  with  i n t e r a c t i o n loss  We have included  (1 - e  _ n a  )  for  or  higher  Based on n  deuteron up to 100 MeV  the i n t e r a c t i o n loss f o r 100 MeV  deuterons  was as  9.8% of the surviving p a r t i c l e s (9.8 e" %) and hence the t o t a l interacTU7  tion  loss  was found to be 47.3%.  The i n t e r a c t i o n loss thus calculated  - 63 i s somewhat higher than our experimentally measured experimental effective section  result  for  interaction in  Nal  the  cross  interaction section.  we  Using  can  deuteron  work  our  compute the  reaction  f o r the average deuteron energy of 188.4 MeV  100)/2) was found to be 2590 ± 180 mb. theoretical  The  loss,  value.  I t i s generally known  cross  ((276.8 + from  the  of Watanabe [33] that i n order to explain the angular  d i s t r i b u t i o n s , p o l a r i z a t i o n s etc, the o p t i c a l model p o t e n t i a l parameters are  more  or  less the same f o r 94 MeV deuterons and f o r 45 MeV  scattered by carbon. half  the  deuteron  This i s because each nucleon i n the energy.  well at higher energies. elastic  scattering  of  Recently N.V.  They [32]  cross section (CT - 583 mb) r  deuteron  Sen et a l . ,  [31,32] studied 4  mentioned  that  the  total  much  f o r 400 MeV deuterons i n oxygen deduced from  between  200  I t should be noted here and 231 MeV  were observed beetween 231 and 552 MeV also  found from N.V.  that  protons  of  a  R  —  by  a  R  should  not  since variations of less than 5% i n Renberg's measurement.  I t was  Sen et a l ' s c a l c u l a t i o n that the cross section for  700 MeV deuterons, on oxygen i s also twice the value MeV  reaction  the cross section measured by Renberg et a l . [16] f o r the p  - 1^0 system at 231 MeV. change  the  deuterons from ^ 0 , ^Ca and -*^Ni at  the o p t i c a l model calculations i s p r a c t i c a l l y twice the value 295 ± 12 mb,  has  This r e l a t i o n apparently works reasonably  polarized  intermediate energies.  protons  Renberg  et  al.  measured  for  345  Based on t h i s information i t i s now  generally accepted that the deuteron i n t e r a c t i o n cross section i n matter for  deuteron  energy  E  greater than 94 MeV  i s approximately twice the  proton i n t e r a c t i o n cross section i n that matter f o r protons with E/2.  energy  - 64 With  this  empirical r e l a t i o n , we have estimated the reaction cross  section of 188.4 section  of  94.2  calculated was used  in  deuterons which should MeV  be  protons i n Nal.  found to be 3235 mb.  t h i s c a l c u l a t i o n was  twice  the  reaction  cross  The reaction cross section thus  The proton reaction  cross  section  derived from the e x i s t i n g proton reaction  cross section data f i t t e d with an energy dependent quadratic  function as  mentioned e a r l i e r i n Section 4.3.1. In  Fig.  4.2,  the  total  reaction  compared to Glauber theory predictions tions  based  on  Glauber  points come from Sen  et  theory al's  [32].  are  The  model  energy  as  microscopic  analysis  and  cross  section  the deuteron cross section at f u l l energy.  that above 94 MeV,  a r e  calcula-  from  taken from t h e i r paper [32].  same Figure, we have plotted twice the proton half  section for d + 1^0  given as a continuous l i n e ; data  optical  e x i s t i n g r e s u l t s at lower energies,  cross  the deuteron cross section  agrees  quite  the  On  the  value  at  We can  see  well  with  twice the proton cross section at h a l f the energy. In  Fig.  4.3,  the  total  reaction  compared to Glauber theory predictions. theory  predictions  cross section for d + ^®Ni  are  The data points and the Glauber  are taken from Sen et a l . [31].  On t h i s figure, as  before, we have p l o t t e d twice the proton cross section at h a l f energy as the deuteron cross section at f u l l energy. do not agree. have  however, the two  curves  Since the proton cross sections for Ni are not known,  we  calculated them using values for Fe and making a s l i g h t correction  by s c a l i n g with cross  Now,  section  (discussed l a t e r data  in  this  section).  The  proton  for oxygen and i r o n were taken from Measday and  Richard-Serre [1] and Rehberg et a l . [16].  C.  - 65 -  o o  o o  O O O  (qLu)uoipas F i g . 4.2:  O  o  o  o  00  CD  O O  SSOJQ  Total reaction cross section f o r d + 0 along with Glauber theory p r e d i c t i o n and previous experimental data as mentioned i n Sen et a l . [32] it,  - 66 -  O  CM  HO  >  CD  CD C LU D C D  ~0)  o  "D O  CD  E  "6 5  O  O Q  O  c E  o  tU i_  CD  CO  o <u  o  o a)  c o o  a> to CD  CL  Q_  E b X  - o  c o  l_  o  o o o  O O  CN  CM  F i g . 4.3:  O O  o o r\  o o  LO  (quu ) u o i p a s  o o  o o  o o  SSOJQ  Total reaction cross section f o r d + N i along with Glauber theory prediction [31] and other r e s u l t s as mentioned i n Sen et a l . [31] 5 8  - 67 -  We Mev  f i n a l l y wanted to predict the reaction cross  deuterons  in  Nal  using  For of  for  188.4  extrapolation techniques on the e x i s t i n g  deuteron reaction cross section procedure we  section  results  of  oxygen  and  nickel.  The  followed i s as follows:  230 MeV  protons, the reaction cross sections  [47] as a function  A2/3 were best f i t t e d by a  52.7  -  R  We have selected data at 230 MeV assuming  that  a  find  the  2  3  - 79.1  over 550 MeV  (4.4)  protons as tabulated  [47]  s i m i l a r dependence of reaction cross sections on A i s  true f o r lower proton energies. could  A /  relative  Using the above mentioned r e l a t i o n ,  values  of  the  we  cross sections for Na and I  compared to the cross sections for oxygen and n i c k e l .  a  a  -  1.360CTQ  "I  =  4.90a  Ni  =  1.029a  Fe  Na  -  0.489a  Ni  Na  CT  °1 Using the 188.4 by  Glauber  MeV  1.761a  Ni  deuteron reaction cross section which  theory for oxygen [32] and eq.  cross section i n Nal was cross  -  0  section  found to be  3762  the  predicted  (4.5), the deuteron reaction mb.  Extrapolation  of  the  for high mass iodine on the basis of low mass oxygen  not be very accurate and so the cross section i s Using  is  not  very  dependable.  Gauber theory predicted value of cross section f o r 188.4  deuteron i n n i c k e l [31] and  eq.  (4.5),  the  deuteron  may  reaction  MeV cross  - 68 section i n Nal can be obtained as 2529 Since protons  our were  experimentally somewhat  mb.  measured  smaller  than  expected the same for deuterons.  interaction the  2590 MeV  ±  180 mb;  MeV  Our experimentally measured  MeV  of  ± 1.7%);  found to  be  whereas the n i c k e l data based c a l c u l a t i o n for the 288.4  In F i g . 4.4, 188.4  for  value  deuteron i s (39.5  deuteron reaction cross section was  deuteron cross section i n Nal i s smaller.  for  result  calculated values [1,26] we  the i n t e r a c t i o n loss i n Nal for the 276.8 MeV from t h i s the 188.4  loss  This i s rather  puzzling.  we have plotted the reaction cross section versus  deuterons.  A /3 2  The straight l i n e 1 i s drawn using the oxygen  and n i c k e l data fron Sen et a l . [31,32] and from the extrapolation,  the  deuteron  low  cross section i n Nal i s found to be 2318  and inconsistent with our measurement. using  the  oxygen  mb which i s quite  The straight  line  2  is  drawn  data [32] and the n i c k e l data calculated from proton  reaction cross sections.  The deuteron reaction cross  section  obtained  from l i n e 2 i s found to be 2990 mb. We  suggest that the reaction cross section for deuterons i n n i c k e l ,  calculated on the basis of proton data, Glauber  theory  predictions  [31].  is  more  dependable  was  calculated  to  be 3243 mb.  for  I f we extrapolate  188.4  MeV  the  cross  section i n Na using the oxygen data [32], since t h e i r masses are and  the  which was 188.4  MeV  cross  section  in  close,  iodine using the n i c k e l cross section data  obtained from proton data, deuterons  the  Using the reaction cross section for  n i c k e l based on proton data, the reaction cross section deuterons  than  i n Nal was  the  reaction  cross  found to be 3356 mb.  section  for  These two values  seem more dependable than the other two extreme values of  2529  mb  and  - 69 -  o o  O  CN  CM  00  4.4:  O  O O  O CM  O o  O  o CD  (quj)uoipas  o o  00  CM  o o  SSOJQ  Reaction cross section versus A  2/3 for 188.4 MeV  deuterons  - 70 3762 mb. Again from the empirical r e l a t i o n that a (d-A) energy,  the  188.4  MeV  which i s twice the 94.2 (Section 4.4), for  4.3.1).  2990 mb 188.4  i s 2a (p-A)  half  deuteron cross section i s found to be 3235 mb, MeV  This  proton's cross section i n Nal found from f i t  value  and  the one obtained from l i n e 2 (Fig.  are also dependable values of the reaction  MeV  at  cross  section  deuterons i n Nal which are, as expected, a l i t t l e higher  than our e f f e c t i v e cross section value, 2590 ± 180 mb obtained from  the  fit. Assuming that the reaction cross section i n Na i s the average of the two values obtained from l i n e 1 and 2, the reaction iodine  was  as obtained from the f i t .  third  s t r a i g h t l i n e 3 was  With these values f o r Na  drawn.  from l i n e 3 i s found to be 1181 MeV.  section  for  then calculated from the cross section i n Nal (a(Nal) - 2590  ± 180)  188  cross  mb,  and  I,  the  The n i c k e l cross section interpolated which i s p l o t t e d i n F i g . 4.3  at T  d  -  We observe that the Glauber theory p r e d i c t i o n i s even lower,  which i s puzzling i n the l i g h t of our proton r e s u l t s . We model  thus suggest that the o p t i c a l calculation  model  analysis  and  the  Glauber  of Sen et a l . both give a s l i g h t l y low value for the  deuteron reaction cross section i n the region of a few hundred MeV. strongly  urge  We  p h y s i c i s t s to make a d i r e c t measurement of t h i s quantity  to c l a r i f y t h i s very confused s i t u a t i o n .  - 71 4.4  Summary and  conclusions  We have d i r e c t l y measured the reaction detectors MeV.  losses  of  protons  in  Nal  f o r the f i r s t time at the r e l a t i v e l y high energies of 200-450  The measurements were done i n  constitute  a  excellent  geometry  so  measurement of the e f f e c t i v e cross section.  been able to obtain the i n t e r a c t i o n loss for deuterons  that  they  We have also  of  277  MeV  in  Nal. In the proton measurements the proton beam e l a s t i c a l l y scattered o f f a hydrogen target as well as the d i r e c t beam was measurement  a secondary deuteron beam was  used.  For the deuteron  produced by i n s t a l l i n g a t h i n  CH2 target inside the vault section of the cyclotron and obtained  from  transported obtain  the  primary  proton  reaction  +  of  the  beamline  used.  We  cross sections values f o r protons which are  somewhat below d i r e c t measurements of t h i s some reactions  deuterons  beam from the pp-*dw reaction were  to the normal target l o c a t i o n  effective  the  quantity  and  suggest  that  (viz (p, 2p)) can occur, yet the t o t a l incident energy i s  s t i l l retained within the c r y s t a l . We have recalculated the section  a  —  P + QX + RX  f i t of the recent compared MeV  with  the  with  an  MeV  loss  energy  dependent  section  data.  Our  experimental  calculations were found to be 21% lower.  f o r 100  cross  whose parameters were obtained from the best  deuterons the reaction losses measured was  interaction 188.4  the  cross  2  losses  MeV  (39.5  ± 1.7%).  data  when  For 276.8 Using the  deuterons [5] we calculated the loss for  (average energy) deuteron which was  found to be  47.3%.  f i t to our experimental value, the cross section obtained for  From 188.4  - 72 -  MeV  deuteron was 2590 ± 180 mb, which i s about 20% lower than the  section  obtained  from the empirical r e l a t i o n that cr(d-A) i s 2a(p-A) at  h a l f the energy, which measurement  is  a  is  very  3235  mb.  Our  deuteron  few  measurements  energy range. Model  of  loss  We  Furthermore  there  the deuteron reaction cross sections i n t h i s  Most are results of Optical  calculations.  interaction  useful r e s u l t because no other measurement has  been made i n Nal f o r intermediate energy deuterons. are  cross  show  Model  analyses  or  Glauber  that f o r deuterons on n i c k e l the recent  r e s u l t s of Sen et a l . are somewhat  low,  section  The value f o r n i c k e l was obtained by  lies  above t h e i r values.  because  our  i n t e r p o l a t i o n and t h i s procedure could be questioned. feel  that  effective  cross  Nevertheless  we  the comparison i s i n t e r e s t i n g and indicates that some d i r e c t  measurements of deuteron reaction cross sections are sorely needed. Many e l a s t i c and involve  quasi-elastic  cross  section  measurements  might  the detection of protons and deuterons i n a sodium iodide t o t a l  energy detector and since i t w i l l be sections,  i t is  important  to  used  know  to  measure  absolute  cross  accurately the e f f i c i e n c y of the  detectors f o r obtaining protons and deuterons i n the f u l l  energy  peak.  Since we d i d not obtain a very good agreement between our experiment and the e x i s t i n g calculated values, we f e e l further experiments to  verify  this  important  effect.  the  Nal  calculations  out  to  GEANT  interesting possibility.  could  be  needed  We also caution experimenters that  there might be some dependence on the size of with  are  carried  crystal.  Some  investigate t h i s  - 73 REFERENCES  1. D.F. Measday and C. Richard-Serre, Nucl. Inst. & Meth., J6 (1969) 45, and CERN report 69-17 (1969). 2. R.A. G i l e s and E.J. Burge,  Nucl. Phys. 50 (1964) 327.  3. M.Q. 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