TRIUMF: Canada's national laboratory for particle and nuclear physics

REVMOC : a Monte Carlo program for calculating charged particle transmission through spectrometers and… Kitching, P. Apr 30, 1971

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R E V M 0  CA MONTE CARLO PROGRAM FOR CALCULATING CHARGED PARTICLE TRA N SM ISS IO N  THROUGH SPECTROMETERS AND BEAM LINESP. KitchingMESON FAC I L I TY  OF:UNIVERSITY OF ALBERTA SIMON FRASER UNIVERSITY UNIVERSITY OF VICTORIA UNIVERSITY OF BRITISH COLUMBIA TR I - 7 1 - 2TRIUMFTRIUMFT R I - 7 1 - 2R E V H O CA MONTE CARLO PROGRAM FOR CALCULATING CHARGED PARTICLE TRANSMISSION THROUGH SPECTROMETERS AND BEAM LINESP. K i t ch i ngPostal  Address:Nuc lear  Research Centre  U n i v e r s i t y  of  A l be r t a  Edmonton,  A l be r t aCanada A p r i l  1971C O N T E N T SPage1. INTRODUCTION 12. DESCRIPTION OF PROGRAM 23. PHYSICAL INTERACTIONS 33.1 Decay 33.2 Nuc lear  Absorp t ion 43.3 Nuc lear  E l a s t i c  S c a t t e r i n g 63 .b Mu l t i p l e  S c a t t e r i n g 63-5 Energy Loss 64. DATA INPUT 94.1 General 9b.2 Sign Convent ions 10b . 3 Ta r ge t  Geometry 11b.b D r i f t  Region 124.5 Quadrupole Magnet 134.6 Uni form F i e l d  Bending Magnet 144 . 7 Double Focusing Magnet 164 . 8 Beam Spot Parameters 174.9 Interchange of  Axes 184.10 P a r t i c l e  Momentum Parameters 184.11 P a r t i c l e  Mass and Other  Parameters 194.12 I n i t i a l i z a t i o n  of  Random Number Generator 204.13 Number o f  T r i a l s 214.14 Di s t r i b u t  ions 214.15 End o f  Case and End o f  Data 245. ERROR MESSAGES 256. EXAMPLES 266.1 Example 1 266 .2 Example 2 366 .3 Example 3 53Acknowledgements 75References 75i i1. INTRODUCTIONREVMOC is a Monte Ca r l o  computer  program,  w r i t t e n  in FORTRAN I V ,  fo r  the design and ana l y s i s  o f  magnet ic  spect rometers  and beam t ranspo r t  systems.  In t r a c i n g  charged p a r t i c l e s  through a system of  magnets,  f i r s t  o r de r  t heory  is used by the program,  t ha t  i s ,  in a T a y l o r ' s  se r i e s  expansion about the p r i n c i p a l  t r a j e c t o r y ,  second and h i ghe r  o r de r  terms are neg lec ted .  The program attempts to s imula te  the phys i ca l  p rocesses ,  such as decay,  mu l t i p l e  s c a t t e r i n g ,  nuc l ea r  s c a t t e r i n g  abso rp t i on ,  and ca l c u l a t e s  c o r r e c ­t i ons  f o r  any loss o r  gain  of  p a r t i c l e s  from these causes.  The program w i l l  a l so  g i ve  d i s t r i b u t i o n s  o f  p a r t i c l e s  accepted by the system as a f unc t i on  of  a v a r i e t y  of  v a r i a b l e s ,  i f  t h i s  is des i r ed .. b .2.  DESCRIPTION OF PROGRAMThe program ca l cu l a t es  the p r o b a b i l i t y  that  a p a r t i c l e ,  in t r a ve r s i n g  a gi ven  exper imental  system,  w i l l  be l os t  from that  system by means of  decay,  s c a t t e r i n g ,  absorp t i on  or energy  loss in mater ia l  in the p a r t i c l e  path.To s imula te  a gi ven exper imental  system,  a se r i e s  of  regions  is s p e c i ­f i e d .  Regions which may be s pec i f i ed  a re :1) d r i f t  region2) quadrupole magnet3) un i form f i e l d  bending magnet bending in theM   ^  ^  ^ h o r i z o n t a l  planedouble focus ing  spect rometer  magnetAny number o f  regions in any o rde r  may be s p e c i f i e d ,  prov ided  the t o ta l  number is not  more than f i f t y .  The f i r s t  region is the exper imental  t a r g e t .  Parameters ,  such as magnet ic  f i e l d s ,  l eng ths ,  d e n s i t i e s ,  atomic spec ies ,  e t c . ,  are s p ec i f i e d  f o r  each element  on data ca rds .  The program t races p a r t i c l e s  through the system us ing ' f i r s t  o r d e r 1 t heory  to c a l c u l a t e  d i s ­placements and d ev i a t i ons  caused by magnet ic  f i e l d s .I n i t i a l  parameters f o r  each p a r t i c l e  are determined by the program from uni form random d i s t r i b u t i o n s  w i t h i n  s p ec i f i e d  l im i t s  on the momentum range Ap,  p o s i t i o n  in the t a r g e t ,  and i n i t i a l  d i splacements  AX-j., AY^. and d ev i a ­t i ons  AX- j/, AY-j.^ in the ho r i z o n t a l  and v e r t i c a l  p l anes .  The p a r t i c l e  is then t raced  through the system.  At  the end of  each d r i f t  region a t es t  is app l i ed  to see i f  the p a r t i c l e  displacement  l i es  w i t h i n  s p ec i f i e d  l i m i t s ,  given by counter  and s l i t  s i zes  in the actual  exper imental  system.  I f  a p a r t i c l e  s a t i s f i e s  a l l  the t e s t s ,  then t h i s  p a r t i c l e  w i l l  be counted in the system in the absence of  decay,  s c a t t e r i n g ,  e t c .  The p a r t i c l e ,  w i t h  the same i n i t i a l  parameters ,  is then t raced  through a second t ime ,  t h i s  t ime being al lowed to decay,  s c a t t e r ,  e t c . ,  w i t h  a pp rop r i a te  p r o b a b i l i t i e s .  The same tes ts  are app l i ed  at  the end of  each d r i f t  reg ion to determine whether  the p a r t i c l e  remains in the exper imental  system.  The whole process is repeated fo r  a l a rge  number of  p a r t i c l e s ,  each p a r t i c l e  being t raced  through tw i ce ,  once w i t hou t  ' p hy s i c a l  processes'  such as decay,  s c a t t e r i n g ,  e t c . ,  and once wi th  these processes .  Should ,  however ,  i nco rpo r a t i o n  o f  these ' p hy s i ca l  processes'  not  be requ i red  in a r un ,  the second t r ace  f o r  each p a r t i c l e  is not done.. 2 .3.  PHYSICAL INTERACTIONS3.1 DecayThe decay length Ad of  the p a r t i c l e s  is ca l cu l a t ed  from the l i f e t ime  and momentum by means of  the r e l a t i o nAd = 30 M ( pQ/mc) cmwhere x = l i f e t im e  in nsecp0 = cent ra l  va lue  o f  momentum in GeV/c m = rest  mass o f  p a r t i c l e  in GeV/c2 .The va lue  of  Ad obtained  is t he re fo re  on l y  c o r r e c t  when the momentum o f  the p a r t i c l e  is equal  to i t s  cent ra l  v a l ue .  T h i s  should not lead to l arge  e r r o r s  prov ided  Ap/pQ is not  too l a r ge .A two-body f i n a l  s t a t e  is assumed to r e s u l t  from p a r t i c l e  decay.  The decay angle is chosen randomly from a un i form d i s t r i b u t i o n  in the cent re  of  mass o f  the decaying  p a r t i c l e .  T h i s  procedure is c o r r e c t  on l y  i f  the f i na l  s t a t e  has o r b i t a l  angu lar  momentum of  z e r o ,  such as:+ +it itU j -*+ +c itU \ -\+ +c itU  -*c itUc -> TT° 7T°The energ ies  of  the decay products  are then determined from t h e i r  masses,  which are s p ec i f i e d  as input  data .  One of  the decay products  is t raced  through the rest  of  the system,  which one being determined by the input  data .  I t  is assumed that  t h i s  decay product  undergoes no a bso rp t ion ,  nuc l ear  s c a t t e r i n g ,  energy  loss o r  decay in t r a v e r s i n g  the rest  of  the system.  Mu l t i p l e  s c a t t e r i n g ,  however ,  is a l lowed to occu r .  Up to two d i f f e r e n t  two-body decay modes may be s p e c i f i e d .  The branching  r a t i os  and masses o f  the products  are gi ven  as input  data .  The program randomly chooses v i a  which decay mode a gi ven  p a r t i c l e  decays,  w i t h  p r o b a b i l i t i e s  gi ven  by the branching  r a t i o s .  I f  the sum of  the two branching  r a t i o s  is less than u n i t y ,  the remainder  of  the decays are assumed to be i n to  threei  n ior  more body f i n a l  s t a t e s ,  and are l o s t  to the system immediatel y .In o r de r  to ob ta i n  b e t t e r  s t a t i s t i c s  in cases where the p r o b a b i l i t y  fo r  decay in the system is sma l l ,  a sca le  f a c t o r ,  SCALE,  may be s p e c i f i e d .  T h i s  m u l t i p l i e s  the p a r t i c l e  l i f e t im e  by SCALE.  Thus ,  i f  SCALE = 0 . 1 ,  ten t imes as many p a r t i c l e s  w i l l  undergo decay in the system.  App r op r ia t e  c o r r e c t i o ns  are made so that  the number o f  undecayed p a r t i c l e s  at  the beg inn ing  of  each region is equ i va l en t  to the number which would be there  i f  SCALE = 1 .0 .  The r es u l t s  are normal i zed  to what would be obta ined  i f  SCALE = 1. The on l y  r e s u l t  is to increase the s t a t i s t i c a l  accuracy  of  the d i s t r i b u t i o n s  of  decay p roduc ts .  I f  the value  o f  SCALE is not  s p e c i f i e d ,  i t  is assumed to be uni ty .3.2  Nuc lear  Absorp t ionFor  each region in the system,  a nuc l ea r  absorp t i on  length Aa is c a l ­cu l a ted  as f o l l ows .  The absorp t i on  cross sec t i on  per  nucleon og f o r  the p a r t i c l e  is s p ec i f i e d  as input  data .  For  each atomic spec i es ,  the absorption cross sec t i on  per  nucleus is ca l cu l a t ed  from an emp i r i ca l  formula by W i l l i  ams1a = kit A0 ' 69 _1_ _11 + 0.039 A 3 (a -  33) -  0.0009 A 3 (a -  33 ) 2 a a mbwhere A = atomic weight  of  nucleusa = absorp t i on  cross sec t i on  per  nucleus in mb.Th i s  formula is expected to be accurate  to about  5% f o r  s t r o n g l y  i n t e r ­ac t ing  p a r t i c l e s  w i t h  energ ies  g r ea t e r  than 1 GeV. For  the best  value  of  ag to use,  the reader  is r e fe r red  to W i l l i ams '  paper .From the dens i t y  of  mater ia l  in the region and the p ropo r t i ons  by weight  of  each atomic spec ies ,  which are s pec i f i ed  as input  data ,  the absorpt ion  l ength Aa is c a l c u l a t e d .  Up to three  d i f f e r e n t  atomic species may be s p ec i ­f i ed  f o r  each reg ion .3. 3 Nuc lear  E l a s t i c  S c a t t e r i n gThe nuc l ear  s c a t t e r i n g  length Ae is obta ined  from the nuc l ear  absorp­t i on  length Aa by means of  the r e l a t i o nAe = (ct / a  ) Aa a e. o .where = nuc l ea r  s c a t t e r i n g  cross sec t ion  per  nucleon and is s p ec i f i e d  in m i l l i b a r n s  as input  data .The angu la r  d i s t r i b u t i o n  of  the e l a s t i c a l l y  s ca t te red  p a r t i c l e s  is assumed to be a forward d i f f r a c t i o n  peak of  the formto  ,  ae - ( 9 l a b ^ o ) 2 labi 2where 0Q2 = y  A3 ( p0/ n y c ) 2= mass of  pionA = atomic  weight  o f  nuc leus .T h i s  d i s t r i b u t i o n  is in reasonably  good agreement w i t h  exper imental  data in the GeV energy  r ange .2 The d i s t r i b u t i o n  f unc t i on  is ca l cu l a t ed  fo r  each atomic species in the r eg ion .  When a p a r t i c l e  is being t raced  through the system and a nuc l ea r  s c a t t e r i n g  o ccu r s ,  the atomic species on which the s c a t t e r i n g  takes p lace is determined w i t h  p r o b a b i l i t i e s  g i ven  by the p ropor ­t i on  by weight  and t o t a l  e l a s t i c  cross sec t i on  f o r  each spec ies .  The s c a t t e r i n g  angle  is randomly chosen from the above d i s t r i b u t i o n ,  and the p a r t i c l e  is assumed to lose no energy  in the s c a t t e r .  The sca t te red  p a r t i c l e  is then t raced  through the res t  o f  the system,  in which f u r t h e r  i n t e r a c t i o ns  such as decay,  a bso rp t i o n ,  s c a t t e r i n g  o r  energy loss may occu r .For  each region of  the system a to ta l  i n t e r a c t i o n  length A is def ined by the r e l a t i o n1 =  J -  + _ L + _ LA Ad Aa Ae *As a p a r t i c l e  is t raced  through the system,  the d i s tance  i  to the nexti n t e r a c t i o n  is determined at  the beg inn ing  of  each region by the usual  Monte-SL/ACar l o  techn ique ,  from the d i s t r i b u t i o n  e . I f  S. is g r ea t e r  than the length of  the r eg i on ,  then no i n t e r a c t i o n  ( decay ,  absorp t i on  o r  nuc lear  s c a t t e r i n g )  is assumed to o c c u r ,  and the p a r t i c l e  is t raced s t r a i g h t  through to the beg inn ing  of  the next  r eg ion .  I f  I  is less than the length of  the r eg io n ,  then the p a r t i c l e  is t raced  up to £ ,  when an i n t e r a c t i o n  is assumed to occu r .  The type of  i n t e r a c t i o n  is decided w i t h  p r o b a b i l i t i e s  determined by the r e l a t i v e  magnitudes o f  Ad,  Aa and Ae.. t .3.4  Mu l t i p l e  S c a t t e r i ngThe program assumes that  mu l t i p l e  s c a t t e r i n g  w i l l  occur  in any region in which the dens i t y  o f  mater ia l  is non - ze r o .  Both s c a t t e r i n g  angles ( u 1) and d isplacements  (u)  are ca l cu l a t ed  in the ho r i z o n t a l  and v e r t i c a l  p lanes ,  and are chosen randomly from d i s t r i b u t i o n s  deduced by M o l i e r e . 3In o r de r  to c a l c u l a t e  these d i s t r i b u t i o n s  the program assumes that  the p a r t i c l e  t r a v e l s  a d i s tance  d through the m a t e r i a l ,  and tha t  the p a r t i c l e  energy is constant  and equal  to i t s  va lue  ha l f - way  through the r eg ion .  Ino rde r  that  these assumptions may not  lead to l a rge  e r r o r s ,  i t  may be necessary  to s p l i t  regions ( e . g .  range c oun t e r s ) ,  in which the mu l t i p l e  s c a t t e r i n g  and energy  loss are l a r g e ,  i n to  a se r ie s  of  sma l l e r  r eg ions .  Since up to three  atomic  spec ies  may be s p ec i f i e d  in each r eg i on ,  the p ro ­gram ca l c u l a t e s  average Mol i e re  d i s t r i b u t i o n s  in a s u i t a b l e  way.4 C a l c u l a ­t ions  are c a r r i e d  out  up to and i nc l ud in g  the second c o r r e c t i o n  term in the Mol i e re  d i s t r i b u t i o n ,  h i ghe r  o r de r  c o r r e c t i on s  being ignored.I f  a p a r t i c l e  undergoes a ' phys i ca l  i n t e r a c t i o n '  i ns ide  a r eg i on ,  the mu l t i p l e  s c a t t e r i n g  is c a l c u l a t e d  up to the po in t  where the ' i n t e r ac t i on '  o ccu r s ,  and then f o r  the rest  of  the reg ion a f t e r  the new angles o r  energy r e s u l t i n g  from the ' i n t e r a c t i o n '  have been c a l c u l a t e d .3 .5  Energy LossI o n i z a t i o n  energy  lossCharged p a r t i c l e s  t r a v e r s i n g  mat ter  lose energy  through i n e l a s t i cc o l l i s i o n s  w i t h  the atomic e l ec t rons  of  the ma t e r i a l .  Because of  thes t a t i s t i c a l  nature  of  the i o n i z a t i o n  p rocess ,  the energy  l os t  e w i l l  havea spread Ae about the most p robable  energy  loss Epro^* Suppose ^max isthe maximum energy  t r a n s f e r  (determined by k i nemat i cs )  to an atomic electronin a s i n g l e  c o l l i s i o n .  Then i f  Ae «  VI , the d i s t r i b u t i o n  of  energymax. a .losses is Gauss ian ,  and £prob is equal  to the average energy  loss of  the p a r t i c l e s . 5 I f  Ae << Wmav however ,  the d i s t r i b u t i o n  of  energy  losses is that  c a l c u l a t e d  by Landau . 6 T h i s  d i s t r i b u t i o n  is asymmetr i c ,  w i t h  a long t a i l  on the s i de  of  h igh energy  losses which f a l l s  o f f  as e- 2 .The program decides which type o f  d i s t r i b u t i o n  is a pp l i c a b l e  f o r  each region in t u r n .  I f  Ae ~ Wmax, and n e i t h e r  d i s t r i b u t i o n  is a p p l i c a b l e ,  a message is p r i n t e d .  The va lue  o f  Epro jj ' s c a l c u l a te d  from the exp ress i on7= At' probAt'  52B + 1 .06 + 2£n + £n --S-Mc 32 i 2 -  63k. 32 + 2£n ^  -  2 £n l  + £ n ^ - - B 2 - < 5 - Uwhere p Imomentum o f  p a r t i c l e  o f  mass M, v e l o c i t y  Be i o n i z a t i o n  po te n t i a l  o f  mater ia l  in eV th i ckness  of  mater ia l  in g/cm2z )tA = 0.1536 AB = £niX c2x 10” 3 f o r  t p rok in GeV 1061The d en s i t y  e f f e c t  c o r r e c t i o n  6 is c a l cu l a t ed  from formulae due to S t e rn he ime r : 8= 0A . 606 X + C + a ( X j - X )  A . 606 X + C 1og1Q (p/Mc)mX < x 0 X 0 < X <. X j  X0 > Xjand a ,  C,  m, X , and X1 are constants  depending on the ma t e r i a l .  I t  is assumed that  the she l l  c o r r e c t i o n  term U is n e g l i g i b l e .  T h i s  assumption is good when the v e l o c i t y  o f  the p a r t i c l e  is much g re a te r  than the v e l o c i ­t i e s  of  the atomic  e l e c t r o n s .  The express ion  f o r  £prob is v a l i d  f o r  both e l ec t rons  and heavy p a r t i c l e s .  The program a l so  c a l c u l a t es  the width  of  the d i s t r i b u t i o n ,  which is t y p i c a l l y  about 20% o f  £pro^ -  Where necessary ,  £prob anc* Ae are averaged over  the atomic  spec ies  in the region,  us ing Bragg ' s  Law.As p a r t i c l e s  are t raced  through the system,  the i o n i z a t i o n  energy  loss e f o r  each reg ion is se lec ted  randomly from the r e l evan t  d i s t r i b u t i o n ,666X. % .using the va lues  of  £pr ob and Ae p r e v i o u s l y  c a l c u l a t e d  f o r  t ha t  r eg ion .Since the d i s t r i b u t i o n  is obtained  from a t a b l e ,  l i n e a r  i n t e r p o l a t i o n  is used to ob ta i n  va lues  i nte rmedia te  between those gi ven  in the t a b l e ,  except  where the va lue  o f  e > 8 A e , when the d i s t r i b u t i o n  is assumed to go as e“ 2 f o r  the Landau cu rve .Rad i a t i ve  energy  lossFor  a l l  p a r t i c l e s  except  e l e c t r o n s , t h e  r a d i a t i v e  energy  loss is assumed to be n e g l i g i b l e .  T h i s  is t r ue  except  at  ve ry  h igh ene rg i es .  I f  e l ec t r ons  are to be t raced  through the system, the  th i ckness  L in r a d i a t i o n  lengths of  each reg ion is c a l c u l a t e d  us ing a formula due to R o s s i . 9 Let  W(EQ, E , L ) d E  be the p r o b a b i l i t y  that  an e l ec t r on  w i t h  i n i t i a l  energy  EQ has energy  between E and E + dE a f t e r  t r a v e r s i n g  the r eg ion .  Bethe and H e i t l e r 10 g i ve  an express ion  f o r  W(E0 , E , L )  o f  the formwfr  r  L l d r  -  dE C^n(En/E)  ] (L/5'n2 " D  W(E0 , E , L ) d E  -  _ T T r 7 £ - ^ -  .The program c a l c u l a t es  and s to res  a t ab l e  of  the i n t eg ra lW(E0 , E , L )  =EW(En , E , L ) d EE0at  5% i n t e r v a l s  in ( E q -  E ) / E q f o r  each r eg ion .When an e l e c t r on  is t raced  through the system i t s  r a d i a t i v e  energy loss is chosen randomly in each region,  us ing the s tored  d i s t r i b u t i o n  tab les  of  ESON F O F A C I I n t e r p o l a t i o n  between the ca l cu l a t ed  values  of  ESON FO FAC is done as f o l l o w s :a) For  energy  losses <5% of  EQ , i t  is assumed thatW(E0 , E , L )  ~ U n  E0/ E ) E/)ln2b)  For  energy  losses >5% o f  EQ , i n t e r p o l a t i o n  is c a r r i e d  out  us ing ageneral  quad ra t i c  f i t  to the three  nearest  values  of  W(E0 , E , L ) .Any photons o r  secondary  e l e c t r ons  which might  be emi t ted  in ther a d i a t i v e  energy  loss process are neg lec ted .Note that  s i nce  £prob and W are ca l c u l a t e d  us ing the cent r a l  momentum p0 of  the p a r t i c l e s ,  e r r o r s  may a r i s e  i f  the momentum spread of  the p a r t i c l e s  is too l a r ge .  The program does not at tempt  to c a l c u l a t e  any energy loss f o r  decay products  t r a v e r s i n g  the system.DATA INPUT4.1 GeneralThe f i r s t  data card must conta in  NEL,  the number of  d i f f e r e n t  regions in the exper imental  system being cons idered .  The t a r g e t  counts as one reg ion .The t o t a l  number o f  regions  must be 50 o r  l ess .T h i s  card has FORMAT( 12 ) .The f o l l ow i n g  cards s pec i f y  the e lements ,  i . e .  the d i f f e r e n t  regionsand i n i t i a l  cond i t i ons  f o r  the system.  Each element  is s p ec i f i e d  by an inputcard o f  the formELMENT , I C , 1 1 , I NDEX , ( DUM ( l ) , 1 = 1 , 6 ) ,  whereELMENT is a type code which determines the kind  o f  element .IC is a code used f o r chang i ng  e lements ,  w i t h  the f o l l ow i ng  meanings:IC=0 means the element  is being s p ec i f i e d  f o r  the f i r s t  t ime ,  o r  is being changed.  In the l a t t e r  case the parameter  values  on the remainder  of  the card are s u bs t i t u te d  for those a l ready  in memory.I I  g i ves  the number o f  the element  being changed.  Elements arenumbered s e q u e n t i a l l y ,  w i t h  va lues  of  I I  i nc reas ing  by u n i t y ,  on f i  r s t  being r ead .IC=1 causes the reg ion  s p ec i f i e d  by I I  to be deleted  and the old valueo f  I I  f o r  each f o l l ow i ng  element to be decreased by u n i t y .IC=2 causes an e x t ra  r eg i on ,  w i t h  the parameters s p ec i f i ed  on the card,t h t hto be i nser ted  between the o l d  I I  and ( i l + l )  r eg ions .  The o ld  va lue  of  I I  f o r  each succeeding region is increased by unity.INDEX is a code dete rmin ing  whether  the region is o r  is not  vacuum.INDEX=0 means the region conta ins  no app rec i ab l e  mater ia l  which could cause s c a t t e r i n g ,  energy  l oss ,  a bso r p t i o n ,  e t c .INDEX=1 means the reg ion does conta in  app rec i ab l e  mater ia l  which could cause s c a t t e r i n g ,  energy  l o ss ,  e t c .( D U M ( i ) ,1=1 ,6)  are the parameter  values  ( t o  be descr i bed  in the f o l l ow ­ing s ec t i ons )  f o r  the element .The card has FORMAT(5A1 , 1 1 , 2 1 2 ,6F10 . 0 ) .I f  INDEX=1,  the f o l l ow i n g  two cards s p ec i f y  the mater ia l  in the r eg ion .The f i r s t  f o l l ow i ng  card conta ins  the parameters FRAC and RHO, whereFRAC = f r a c t i o n  o f  cross sec t i ona l  area o f  ape r tu re  covered byma t e r i a l .  Normal l y  FRAC = 1 . 0 ,  except  for spark chambers,  where the wi res  cover  on l y  some f r a c t i o n  o f  the ape r tu re .RHO = d en s i t y  of  mater ia l  in the r eg ion ,  in g/cm3 .T h i s  card has FORMAT(1 OX,2F10 . 0 ) .The second f o l l ow i n g  card conta ins  the parameters (PROP( j )  , Z ( j ) , J = 1 ,3)wherePR0P( J ) =  p ro po r t i o n  by weight  of  mater ia l  w i t h  atomic  number Z ( J ) .Up to  three  d i f f e r e n t  atomic  spec ies  may be s p ec i f i e d  f o r  any one r eg ion .Th i s  card has FORMAT (10X ,6F10 . 0 ) .Note that  w i t h  the format  F10 .0 ,  the decimal  po in t  may be placed any­where i ns ide  the f i e l d .h.2 Sign Convent ionsWhen f ac i ng  along the d i r e c t i o n  of  t r ave l  of  the p a r t i c l e ,  X is negat i ve  to the r i g h t ,  p o s i t i v e  to the l e f t ,  and Y is p o s i t i v e  up,  negat i ve  down. The va lues  of  X'  and Y '  are p o s i t i v e  when the p a r t i c l e  d isplacement  is i n c r e as in g ,  and negat i ve  when i t  is decreas ing .. i- .P a r t i c l e  going i n to  paper .. ii4 .3  Ta r ge t  GeometryHor i zon ta l  Planebut i ons  o f  w idth  XMAX, DXMAX and L^ ,  r e s p e c t i v e l y  (see Sect ion  4 . 8 ) .The d i s tance  t r a v e l l e d  by the p a r t i c l e  through the t a r ge t  (d)  is then c a l c u l a t e d ,  and the e f f ec t s  of  mu l t i p l e  and nuc l ea r  s c a t t e r i n g ,  abso rp t i on ,  energy  loss and decay in the t a r ge t  mater ia l  are a l so  c a l c u l a t e d .  The t a r get  wa l l s  must be put  in as a separate  region i f  they have a s i g n i f i c a n t  e f f e c t .  I f  L.j- o r  0^ . are s u f f i c i e n t l y  smal l  that  p a r t i c l e s  leave the t a r ge t  v i a  i t s  downstream face ,  t h i s  is c o r r e c t l y  c a l cu l a t ed  by the program.V e r t i c a l  PlaneThe s t a r t i n g  co - o r d i na t es  in the v e r t i c a l  p l ane ,  Y^., Y-j/ are chosen from uni form d i s t r i b u t i o n s  o f  w id th  YMAX and DYMAX, r e s p e c t i v e l y  (see Sect ion  4 . 8 ) .  The e f f e c t  o f  Y-j/ , the i n i t i a l  angle  in the v e r t i c a lplane on the d i s tance  d t r a v e l l e d  through the ta rget ,  is sma l l ,  and is ignored in t h i s  c a l c u l a t i o n .. ib .The values  o f  and X^ . are s p ec i f i e d  on the input  data card as f o l l ows :  1 . Type code = TARG#2.  I I , I N D EX  (see Sect ion  4 . 1 ,  Data Input  -  General )3.  DUM( l )  = Length of  t a r ge t  L-j., in cm4.  DUM(2)  = Ho r i zon t a l  w idth  o f  t a r ge t  X ^ , in cm5.  DUM(3) to DUM(5)  are blank6.  DUM(6)  = Ho r i zon t a l  angle  0^ . between i nc i den t  p r imary  beam andp r i n c i p a l  t r a j e c t o r y ,  in degT h i s  card is FORMAT(5A1 ,V> ,212 ,6F10 . 0 )  .4 . 4  D r i f t  RegionIPOSIT IVE |IPRINCIPAL I TRAJECTORY ;INEGATIVE |JThe c o - o rd in a t es  at  the end of  the d r i f t  reg ion are obta ined  fromx x"jrAt  the end of  each d r i f t  space the c o - o rd i n a te s  are tested  to see i f  they a r ew i t h i n  l i m i t s  s p e c i f i e d  as input  to the program.  The l im i t s  can be thought  o f  as a d e f i n i n g  s l i t  o r  counter  at  the end o f  each d r i f t  r eg ion .The counter  can be set  at  an angle  U to the normal  to the beam, in the ho r i z o n t a l  p lane.  As shown above, U is p o s i t i v e .The parameters are s p ec i f i e d  as an input  data card  o f  the f o l l ow ingtype :1 L 0 0 x00 1 0 0 V0 0 1 L Y00 0 0 1 Y o'. i2 .4 .5  Quadrupole MagnetThe program ca l c u l a t e s  the p a r t i c l e  c o - o rd i n a te s  r e l a t i v e  to the p r i n ­c i pa l  t r a j e c t o r y  from the equati: i onfX xox " . X Sy r Vwhere. bcos kL -k s i n  kL 0 0s in  kL kcos kL 0 000cosh kL k s i nh kL00sinh kL kcosh kLwhere k = 1 2 no 2t3000pL = e f f e c t i v e  length of  quadrupole .Th i s  is f o r  a quadrupole  which focuses in the ho r i zo n t a l  p l ane ,  which is s i g n i f i e d  on the data cards by a p o s i t i v e  va lue  o f  the f i e l d  g r ad i en t .1. Type code = DR I FT2.  I C , I I , I N D E X  (see Sect ion  k .1 , Data Input  -  Genera l )3.  DUM( l )  = Length of  region L in cmk.  DUM(2)  = Upper l i m i t  on x at  end of  region X ^ , in cm5-  DUM(3)  = Lower l i m i t  on x at  end o f  region X. , in cm(norma l l y  negat i ve )  L6.  DUM(A) = Upper l i m i t  on y at  end of  region V , in cm7. DUM(5) = Lower l i m i t  on y at  end of  reg ion Y. , in cm(normal  1y negat  i ve)8.  DUM(6) = Angle U between l i m i t i n g  ape r tu re  and normal top r i n c i p a l  t r a j e c t o r y ,  in deg The magnitudes of  Xu , XL , Y , Y^ must be less than 10 m The card is F0RMAT(5A1,11 , 1 2 , 1 2 , 6F10 . 0 )  .. iL .A negat i ve  va lue  o f  the f i e l d  g r ad i en t  means a v e r t i c a l l y  f ocus ing  quadru­po le ,  in which case the two p a r t i a l  mat r i ces  above are i nterchanged .The p r i n c i p a l  t r a j e c t o r y  must en t e r  the quadrupole  normal to the magnet ic  f i e l d .  The parameters are s p ec i f i e d  on an input  data card as f o l l o w s :1 . Type code = QUAD#2.  I C , I I , I N D E X  (see Sect ion  A . l ,  Data Input  -  General )3. DUM( l )  = E f f e c t i v e  length o f  quadrupole  L ,  in cm*f. DUM(2)  = F i e l d  g r ad i en t  in, kG/cm5. DUM(3)  to DUM(4)  are blank6.  DUM(5)  = D i f f e r ence  T  between path l ength  o f  p r i n c i p a l  t r a j e c t o r yin quadrupo le ,  and e f f e c t i v e  l ength  L,  in cm7. DUM(6) is b lankThe card is FORMAT(5A1 ,11 ,212 ,6F10 . 0 ) .Here and f o r  bending magnets the d i f f e r en ce  T  (6, above)  must be s pec i f i e d  i f  phys i ca l  processes such as decay s c a t t e r i n g  o r  absorp t i on  occur  in the reg ion s i nce  the p r o b a b i l i t y  o f  these o c c u r r i n g  is p ropo r t i ona l  to the d i s t ance  the p a r t i c l e  t r a v e l s  in the r eg ion .  Normal l y  T  w i l l  be small  in comparison w i t h  L ,  and need on l y  be c r ude l y  est imated .  I f  the region is vacuum and the p a r t i c l e  cannot  decay,  T  may be l e f t  ze ro .A .6 Uni form F i e l d  Bending MagnetThe bending magnet bends in the h o r i z o n t a l  p l ane ,  a p o s i t i v e  value  of  the magnet ic  f i e l d  bending to the r i g h t  i f  one t r a v e l s  w i t h  the p a r t i c l e s .  The angle  U is p o s i t i v e  as shown. The angle  V is nega t i ve .. io .The c o - o r d i na tes  of  the p a r t i c l e  a f t e r  the magnet is in the ho r i z on t a l  plane r e l a t i v e  to the p r i n c i p a l  t r a j e c t o r y  are ca l c u l a t e d  assuming that  the p a r t i c l e  f o l l ows  a c i r c u l a r  path in the magnetic f i e l d , t h e  radius  of  cu r va ­tu re  beingP = 3335.6 P/B w i t h  Pn = 3335.6 P0/ BAcmfo r  the p r i n c i p a l  t r a j e c t o r y .The v e r t i c a l  c o - o r d i na t es  a f t e r  the magnet are obta ined  from the equat  i on Nj  j 0   v '  .  jwhere1 0 1 pe 1 0M = +tan V1 0 1-  tan U iP1P1where 0 is angle  through which the p a r t i c l e  is bent  by the magnet.The parameters are s p ec i f i e d  on an input  data card as f o l l ows :1 . Type code = BENDbJ2.  I C , I I , I N D E X  (see Sect ion  4 . 1 ,  Data Input  -  General )3.  DUM(1)  = E f f e c t i v e  length L o f  magnet ic  f i e l d ,  in cm4.  DUM(2)  = Magnet ic  f i e l d  s t reng th  B,  in kG5. DUM(3)  = Angle co between ent rance  and e x i t  face of  magnet, in deg6.  DUM(4) is blank7. DUM(5)  = D i f f e r ence  T  between path l ength  i f  p r i n c i p a l  t r a j e c t o r ythrough magnet,  and e f f e c t i v e  l ength  L,  in cm8.  DUM(6) = Ent rance angle  U between p r i n c i p a l  t r a j e c t o r y  and normalto magnet f ace ,  in degFor  more i n format ion  on T  (7 above ) ,  see the remarks at  the end of  Sect ion  4.5*. it .A .7 Double Focusing MagnetThe program ca l cu l a t es  the p a r t i c l e  c o - o rd i n a te s  r e l a t i v e  to the p r i n c i ­pal  t r a j e c t o r y  from the equat ion' ■X x 0x ' X oV= Mj y ' >whereM =-  1-ncos /I - n  <o s i n /T-rFcos i n /l  - n co/l  - n  cos /1-n000000COS /FT 10./j7 L i n /FT to00p s i n  /FT co cos /FT cowheren =(o = angle of  bend p = radius  o f  cu r va tu reThe p r i n c i p a l  t r a j e c t o r y  is assumed to ente r  and e x i t  the magnet normal 1y .The parameters are s p e c i f i e d  on an input  data card as f o l l ows :. ia .1. Type code = SPECT2.  I C , I l , I N D E X  (see Sect ion  4 . 1 ,  Data Input  -  Genera l )3. DUM( l )  = E f f e c t i v e  length L of  magnet ic  f i e l d  between ent ranceand e x i t  o f  p r i n c i p a l  t r a j e c t o r y ,  in cm4.  DUM(2)  = V5.  DUM(3)  = Angle  w through which p r i n c i p a l  t r a j e c t o r y  is bent ,i n deg6.  DUM(4) to DUM(6) are b lankThe card is FORMAT (5A1 , 1 1 , 2 12 , 6 F 10 . 0 ) .b .8  Beam Spot ParametersEach input  deck o f  data cards must conta in  two cards s p e c i f y i n g  the beam spot  and angu lar  range in which p a r t i c l e s  are produced.  These cards are of  the f o l l ow i n g  k i nd :Fi r s t  Card1. Type code = XSIZE2.  I C , I l  (see Sect ion  4 . 1 ,  Data Input  -  Genera l )3-  DUM( l )  = Ho r i zon ta l  f u l l  w i d t h ,  XMAX, of  beam spot  on t a r g e t ,  in cm4.  DUM(2)  = Fu l l  w i d t h ,  DXMAX, o f  un i form i n i t i a l  d i s t r i b u t i o n  inho r i zo n ta l  angle  X y ' ,  in mrad5.  DUM(3)  = Cent ral  va lue  xc of  beam spot  on t a r ge t  in ho r i z on ta ldi r e c t i o n , in cm6.  DUM(4)  = Cent ra l  v a l u e ,  DXMAXC, of  un i form i n i t i a l  d i s t r i b u t i o n  inho r i z o n t a l  d i r e c t i o n  X y ' , in mrad7. DUM(5)  and DUM(6)  are blankSecond Card1 . Type code = YSIZE2.  I C , I l3 - 6 .  Same as f i r s t  c a rd ,  r ep l a c i ng  h o r i z o n ta l  by v e r t i c a lparametersThese cards are FORMAT (5A1 , I l ,12 , 2 X , 6 F 1 0 . 0 ) .The values  of  DXMAX and DYMAX should be chosen l arge  enough to f i l l  the ape r tu re  o f  the apparatus ,  i . e .  a p l o t  o f  accepted events  versus  i n i t i a l  angle  should go to ze ro  at  the ends.. i% .Making DXMAX or  DYMAX too l a rge  merely  reduced the e f f i c i e n c y  o f  the program,  s ince  then a l a rge  number o f  p a r t i c l e s  have no chance o f  being accepted by the system.4 .9  Interchange of  AxesAt  any po in t  in the system the h o r i z o n t a l  and v e r t i c a l  axes may be i nterchanged .  T h i s  is used,  f o r  example,  when a bending magnet bends the beam in the v e r t i c a l  d i r e c t i o n ,  o r  when the v e r t i c a l  d i s t r i b u t i o n  o f  p a r t i c l e s  at  the end of  some d r i f t  reg ion is des i r ed .  A s i n g l e  input  data card is needed each t ime the axes are interchanged1 . Type code = ROTAT2.  I C , 1 1 (see Sect ion  4 . 1 ,  Data I npu t -Gene ra l )3. DUM( l )  to DUM(6)  are blankThe card is FORMAT ( 5A1 , 1 1 , 1 2 ,2X,6F10 . 0 ) .4 .10  P a r t i c l e  Momentum ParametersEach input  deck of  data cards must conta in  a card s p ec i f y i n g  the p a r t i c l e  momentum parameters .  T h i s  card is of  the f o l l ow i n g  k i nd :Type code = P O t f l ( 0 = a l phabe t i c )I C , I 1  (see Sect ion  4 . 1 ,  Data Input  -  General )1 . .3- DUM(l )  = Cent ra l  momentum p , o f  un i form i n i t i a l  momentum d i s t r i ­but i on ,  i n GeV/c4.  DUM(2)  = Fu l l  w idth  PMAX o f  un i form i n i t i a l  momentum d i s t r i bu t i on ,in GeV/c5.  DUM(3)  = Momentum of  p r i n c i p a l  t r a j e c t o r y  p , in GeV/c.  T h i st r a j e c t o r y  is the reference  t r a j e c t o r y  w i t h  respect  to which a l l  d i splacements  are measured.  I f  pc is l e f t  b l ank ,  the program au t oma t i c a l l y  puts pc = pQ.. i/ .6.  DUM(4)  = T h resho ld  energy  TTHR,  below which p a r t i c l e s  are assumedto be l os t  to the system,  in GeV.7.  DUM(5) and DUM(6)  are blankThe card is FORMAT ( 5A1 , 1 1 , 1 2 ,2X,6F10 . 0 ) .The va lue  o f  PMAX should be g r e a t e r  than the momentum acceptance of  the system,  i . e .  so that  a p l o t  o f  accepted events  versus i n i t i a l  momentum goes to zero  at  the e x t r em i t i e s :Making PMAX too l a rge  reduces the e f f i c i e n c y  of  the program,  s ince  then a l a rge  number of  p a r t i c l e s  have no chance of  being accepted by the system.4.11 P a r t i c l e  Mass and Other  ParametersEvery  input  deck of  data cards must conta in  a card g i v i n g  i nformat ion  about the p a r t i c l e s  being t raced  through the system.  T h i s  card is of  the f o 11ow i n g k i nd :1. Type code = MASS#2.  I C , I I , I N D E X  (see Sect ion  4 . 1 ,  Data I nput -Genera l  for IC ,11)Here,  i f  INDEX ^ 0 ,  t h i s  means that  the p a r t i c l e  can decay,  and a f o l l ow i n g  card is needed to s pec i f y  the decay p r o du c t s .3. DUM(l )  = P a r t i c l e  mass, in GeV/c24. DUM(2)  = Absorp t i on  cross sec t i on  a o f  the p a r t i c l e  on a nuc leon,di n mb5.  DUM(3)  = Nuc l ear  s c a t t e r i n g  cross sec t i on  a of  the p a r t i c l e  on aenu c l e on , in mb. b- .6.  DUM(^) = L i f e t ime  of  p a r t i c l e  x in nsec7.  DUM(5)  = Scale  f a c t o r ,  SCALE (see sec t i on  3 . 1 ,  Decay)8.  DUM(6)  is blankThe card is FORMAT (5A1 ,11 ,212 ,6F10 . 0 ) .I f  INDEX ^  0 ,  the f o l l ow i ng  card must con ta i n  the parameters :1 . 10fc$2.  DUM(l )  = Branching r a t i o  a ( l )  i n to  f i r s t  two-body f i n a l  s ta tedecay mode3. DUM(2) = Mass of  decay product  of  f i r s t  two-body decay mode,in GeV/c2 , which is to be t raced  on through the system a f t e r  decay4.  DUM(3) = Mass o f  o t he r  decay product  of  f i r s t  two-body decay mode,in GeV/c25.  DUM(4) = Branching  r a t i o  a ( 2 )  i n t o  second two-body f i n a l  s t a tedecay mode6.  DUM(5)  = Mass of  decay product  o f  second two-body decay mode, inGeV/c2 , which is to be t raced  on through the system a f t e rdecay7-  DUM(6)  = Mass of  o the r  decay product  of  second two-body decay mode, in GeV/c2The card is FORMAT (1 OX ,6F10 . 0 ) .4.  12 I n i t i a l i z a t i o n  of  Random Number GeneratorEach input  deck o f  data cards must conta in  a card to i n i t i a l i z e  the random number genera to r .  The random number genera tor  operates  by mu l t i p l y i n g  an i n tege r  by 65539 to form a new i n t ege r .  The l eas t  s i g n i f i c a n t  par t  of  the new i n tege r  is then normal i zed  to be between 0 and 1 to g i ve  the requ i red  random number.  The new i n tege r  is used to form the next  random number,  and so on.  A t o t a l  o f  229 random numbers is obtained  before the sequence s t a r t s  to repeat .The s t a r t i n g  i n t ege r  is s p ec i f i e d  on a data card as f o l l ows :1. Type code -  INI T#2.  I C , 1 1 (see Sect ion  4 . 1 ,  Data Input  -  General )3.  DUM(1)  = RANDOM NUMBER I N I T I AL I ZER ,  any odd number ^  9 d i g i t s  inlength. bi .4. DUM(2)  to DUM(6)  are blankThe card is FORMAT(5A 1 ,11 , 1 2 , 2X , F 10 . 0 ) .When changes are made to a system,  and i t  is des i r ed  to see the e f f e c t ,the random number i n i t i a l i z e r  should be reset  to the va lue  used in the f i r s trun.  T h i s  reduces s t a t i s t i c a l  f l u c t u a t i o n s .4 .13 Number o f  T r i a l sEach input  deck o f  data cards must conta in  a card s p ec i f y i n g  the number o f  p a r t i c l e s  to be t raced  through the system.  T h i s  card is of  the f o l l ow i ng  k i nd :1. Type code -  GROUP2.  I C , I 13. DUM(1)  = Number of  b l ocks ,  NSET,  o f  p a r t i c l e s  to be t raced  throughthe system4.  DUM(2) = Number of  thousand p a r t i c l e s ,  NT ,  in each b lock5.  DUM(3)  =* A parameter  NORM6.  DUM(4) to DUM(6)  are blankThe program p r i n t s  out  the cumulat i ve  r e s u l t s  up to that  po in t  a f t e r  each b lock  of  p a r t i c l e s .  A t o ta l  o f  NSET x NT x 1000 p a r t i c l e s  is t raced in a s i n g l e  run.  I f  the f i n a l  r es u l t s  are to be normal i zed  to the f i n a l  numbero f  p a r t i c l e s  accepted by the system,  then the va lue  of  NORM should be g r ea t e rthan z e r o ;  o the rw i se  the non - normal i zed  r es u l t s  w i l l  be p r i n t e d .T h i s  card is FORMAT(5A1 , 11,12  ,2X , 6 F 10 . 0 ) .4 .14  Pi s t r i b u t i o n sP a r t i c l e s  accepted by the system may be c l a s s i f i e d  i n to  " b i n s "  to g i ve  d i s t r i b u t i o n s  in a v a r i e t y  of  ways.  T hus ,  f o r  i ns tance ,  the program w i l l  g i ve  the number o f  accepted events  in ' b i n s '  co r responding  to the i n i t i a l  momenta o f  the p a r t i c l e s ,  i . e .  a d i s t r i b u t i o n  o f  accepted events  as a func ­t i on  of  i n i t i a l  momentum may be obta i ned .  In t h i s  case the ' space '  cons i s t s  o f  j u s t  one ' d imens i on ' ,  i n i t i a l  momentum. More compl i cated  d i s t r i b u t i o n s  may be c a l c u l a t e d ,  f o r  i ns tance  the number o f  accepted events as a func t i on  of  both i n i t i a l  momentum of  the p a r t i c l e s  and h o r i z o n ta l  p o s i t i o n  at  the end of  some s pec i f i e d  d r i f t  r eg ion .  In t h i s  case the ' space '  has two. bb .' d imens i ons ' .  D i s t r i b u t i o n s  in ' spaces '  o f  up to twenty  ' d imens ions '  may be ob t a i ned ,  w i t h  a maximum of  999 ' b i n s '  in any ' d imens i o n ' .  In any one run up to seven ' spaces '  may be de f i ned ,  prov ided  the t o ta l  number o f  ' b i n s '  in a l l  ' d imensions '  is less than 15,000.  The t o t a l  number of  ' b i n s '  , ND, inDa l l  ' d imensions '  is g i ven  by:Ng = £ PRODUCT (no.  o f  b ins  inspaces dimensions each dimension)in each spaceD i s t r i b u t i o n s  in a l l  ' spaces '  s p ec i f i e d  are p r i n t e d  out  at  the end of  the run.  Any o f  the f o l l ow i n g  ' d imens ions '  may be s p e c i f i e d :a)  I n i t i a l  momentum of  the p a r t i c l e sb)  S t a r t i n g  p o s i t i o n  along the length of  the t a r ge tc)  I n i t i a l  d i splacement  o r  d ev i a t i on  in the ho r i z o n t a l  planed) I n i t i a l  d i splacement  o r  d e v i a t i o n  in the v e r t i c a l  planee)  Momentum at  the end o f  some s pec i f i ed  d r i f t  region in the systemf )  Ho r i zon ta l  d isplacement  o r  d e v i a t i o n  at  the end o f  some s pec i f i e d  d r i f t  region in the systemThe feature  enab l i ng  i nterchange  of  v e r t i c a l  and h o r i z o n ta l  axes may be used to ob ta i n  d i s t r i b u t i o n s  as a f unc t i on  of  v e r t i c a l  d i splacement  o r  d e v i a t i o n  at  the end of  any d r i f t  r eg ion .D i s t r i b u t i o n s  may be obta ined  f o r  the f o l l ow i n g :g)  P a r t i c l e s  i n i t i a l l y  accepted by the system,  in the absence of  decay,  s c a t t e r i n g ,  absorp t i on  or  energy  lossh)  P a r t i c l e s  f i n a l l y  accepted by the system,  in the presence o f  decay,  s c a t t e r i n g ,  absorp t i on  and energy  lossi )  Decay products  on l yThe necessary  parameters are s p ec i f i e d  on data input  cards of  thef o l 1owi ng t y p e :Fi  r s t  card1 . Type code = NSPAC2.  I C , 1 1 (see Sect ion  4 . 1 ,  Data Input  -  General )3.  DUM(1)  = Number of  ' spaces '  , NSPACE = 0 ,  in which d i s t r i b u t i o n s  arerequ i r ed .  I f  NSPACE = 0 ,  no mu l t i d imens iona l  ana l y s i s  isdone.. b2 .4.  DUM(2)  = A code parameter  NW, f o r  whichNW = 0 g i ves  d i s t r i b u t i o n s  o f  p a r t i c l e s  i n i t i a l l y  accepted by the system (g above)NW = 1 g i ves  d i s t r i b u t i o n s  of  p a r t i c l e s  f i n a l l y  accepted by the system (h above)NW = 2 g i ves  d i s t r i b u t i o n s  fo r  decay products  on l y  ( i  above)5.  DUM(3) to DUM(6)  are blankT h i s  card is FORMAT ( 5A1 ,11 , 1 2 , 2 X , 6 F 1 0 . 0 ) .Second card1 . 1002.  DUM( l )  = Number o f  ' d imens ions '  in f i r s t  ' space '3.  DUM(2)  = Number of  ' d imens ions '  in second ' space 'Up to N S P A C E T h i s  card has FORMAT ( 1 0 X J F 1 0 . 0 )Up to seven 'spaces'  may be s p ec i f i e d  in one run.A s i n g l e  card now f o l l ows  f o r  each ' d imens ion '  in each ' s pa ce ' .  Eachcard conta ins  the f o l l ow i n g  parameters:1. The type of  ' d imension '  Ja)  = 0P = momentumb) = 0X = displacement  in h o r i z o n ta l  planec)  = DX = d ev i a t i o n  in ho r i z o n t a l  planed) = 0Y = displacement  in v e r t i c a l  planee)  = DY = dev i a t i on  in v e r t i c a l  planef )  = 0T = s t a r t i n g  p os i t i on  along length  of  t a r ge t2.  DUM( l )  = Region number I  where d i s t r i b u t i o n  o f  t h i s  ' d imension 'is r equ i red3. DUM(2) = Number of  b ins  r equ i red  in t h i s  dimension4.  DUM(3) = Fu l l  w id th  S o f  dimension J ,  in app rop r i a te  un i t s(GeV/c)5.  DUM(4) = Cent ra l  va lue  C of  dimension J ,  in app rop r i a te  un i t s(GeV/c,  cm or  mrad)6.  DUM(5)  to DUM(6)  are b lankT h i s  card is FORMAT ( A2 , 8X , 6F10 . 0 ) .. bL -D i s t r i b u t i o n s  o f  type d)  , e)  o r  f )  above may o n l y  be obta ined  f o r  I  = 1,  i . e .  at  the t a r g e t .  I f  v e r t i c a l  d i s t r i b u t i o n s  are r equ i red  e l sewhere ,interchange  of  ho r i z o n t a l  and v e r t i c a l  axes can be used.4.  15 End of  Case and End of  DataThe program w i l l  do up to ten cases o r  runs w i t h  one b lock  of  data ca rds .  A f t e r  a l l  the data cards f o r  one case have been read i n ,  a card of  the type1. Type code = END##causes the program to begin c a l c u l a t i o n s  on that  case.Changes may be made in the parameters f o r  p a r t i c u l a r  elements f o r  the next  case us ing the code ( I C )  as s p ec i f i e d  in Sect ion  4 . 1 ,  Data Input  -  Genera l .  A f t e r  a l l  the changes have been made, a card w i t h  type code = END w i l l  cause the case to be run.  When a l l  cases have been run ,  the program isterminated  by means o f  a card o f  the type1 . Type code = F I N I .. bo .5.  ERROR MESSAGESOn encounte r i ng  c e r t a i n  input  e r r o r s ,  e r r o r  message are p r i n t e d  out  andexecut i on  of  f u r t h e r  c a l c u l a t i o n  is stopped.  Most of  these messages ares e l f  e xp l ana t o r y .  C a l c u l a t i o n  is stopped f o r  the f o l l ow i n g  reasons:1) I n v a l i d  ELMENT code parameter  -  The e n t i r e  input  card and i t s  p os i t i on  in the data deck is p r i n t ed  ou t .  Execut ion  is te rminated .2)  I nco r r ec t  number of  t r an spo r t  elements -  I f  the number of  t r anspo r t  elements read is less than or  g r ea te r  than NEL,  the a pp rop r i a te  message is p r i n t ed  and execut i on  t e rminated .3) IC  > 2 -  A change parameter  not  one of  0,  1 o r  2 is meaning less ,  and execut i on  is terminated  w i t h  app rop r i a te  message.4)  I n v a l i d  reg ion parameter  ( I 1) -  I f  in the second and subsequent  runs a reg ion number is undef i ned ,  the o f fend i ng  card input  is p r i n t ed  and execut i on  te rmina ted .  I t  should again be s t ressed  that  i f  an element  has been deleted  ( i n s e r t e d )  a l l  region numbers are decremented ( i n c r e ­mented)  by u n i t y  immediately  upon d e l e t i o n  ( i n s e r t i o n ) .5)  Normal run t e rmi na t i on  -  When FINI  has been read a message is p r i n t ed  out  and execut i on  te rminated .EXAMPLES6.1 Example 1A quadrupole  spec t rometer  us ing t ime of  f l i g h tThe spect rometer  cons i s t s  of  a quadrupole t r i p l e t  f ocus ing  protons onto a de t ec to r  ten metres from the t a r g e t .  The r equ i red  f i e l d  g r ad i en t s  in the quadrupoles were f i r s t  c a l c u l a t e d  us ing the program TRANSPORT.11 The present  program was then used to c a l c u l a t e  the s o l i d  angle  and momentum acceptances of  the spec t rometer .  The data cards used are shown on page 28.  Note the f o l l ow i ng  p o i n t s :1) The t a r ge t  length was assumed to be n e g l i g i b l e .  Hence 0^ . is notimpor tant  and was put equal  to ze ro .2)  Cards 3 and 5 def i ne  the ent rance  and e x i t  aper tu res  o f  the f i r s t  quad­r upo l e ,  which are assumed to be 4"  x V  squares.  Cards 6 ,  8 and 9 ,  11 do the same t h i ng  f o r  the o the r  two quadrupoles .3) Card 13 def  ines the ape r tu re  of  the d e t e c t o r ,  2 x 2  cm2 .b) The t a r ge t  spot  s i ze  was 0.5 x 0 . 5  cm2 and the cen t r a l  momentum was 200 MeV/c.5) The system was assumed to be vacuum throughout .The f o l l ow i n g  pages g i ve  the output  from the program.  The program f i r s t  p r i n t s  out  the input  parameters ,  w i t h  some minor  changes.  These are :1) angles are in radians2)  the l i f e t im e  is in secondsThe program then p r i n t s  out  the r es u l t s  of  i t s  c a l c u l a t i o n s .  Most of  t h i s  is s e l f  e xp l ana to r y  except  f o r  the f o l l ow i n g :1) The most impor tant  r e s u l t  of  the c a l c u l a t i o n  isSOL I DANGLE*M0M. RES = 0.291 937E-i+ STERAD-BeV/c The quoted e r r o r  is the s t a t i s t i c a l  e r r o r  a r i s i n g  from the number of  p a r t i c l e s  t raced  through the system.  I f  the va lues  of  PMAX, DXMAX or  DYMAX were too sma l l ,  however ,  unknown sys temat i c  e r r o r s  would a r i s e .2)  The c o r r e c t i o n  f a c t o r  g i ves  the r a t i o  o f  PARTICLES ACCEPTED IN I T IALLY/PARTICLES ACCEPTED FINALLY.  The same c ons i de r a t i ons  about the quoted e r r o r  apply  here.  In t h i s  p a r t i c u l a r  case,  s i nce  no phys i ca l  i n t e r ­ac t i ons  such as decay,  s c a t t e r i n g ,  e t c . ,  take p l ace ,  the c o r r e c t i o n  f a c t o r  is i d e n t i c a l l y  equal  to 1 .0 .. ba .3) In the d i s t r i b u t i o n  of  p a r t i c l e s  as a f unc t i on  o f  i n i t i a l  c ond i t i o n s ,  the columns headed F INAL .NOT ( I N I T I AL )  g i ve  the number o f  p a r t i c l e s  f i n a l l y  accepted which were i n i t i a l l y  r e j e c t e d ,  as a f unc t ion  o f  the va r i ous  parameters .  Here i n i t i a l l y  means w i t h  no s c a t t e r i n g ,  decay o r  energy  l o ss ,  and f i n a l l y  means w i t h  s c a t t e r i n g ,  decay and energy  l oss .  In t h i s  p a r t i c u l a r  spec t rometer ,  s i nce  there  is vacuum th roughout ,  and no p a r t i c l e s  decay,  these columns are always ze ro .. b% .13TARG 0 .0DRIFT 150.0 +5 . 08DRIFT 10.0 +5 . 08QUAD 24.765 - 0 . 2922DRIFT 0.001 +5 . 08DRIFT 20.000 +5 . 08QUAD 24.765 +0.5186DRIFT 0.001 +5.08DRIFT 20.000 +5 . 08QUAD 24.765 -0 . 2922DRIFT 0.001 +5 . 08DRIFT 10.0 +5 . 08DRIFT 715.0 +1 . 0I N I T 123456789.NSPACGROUP 1 .0 2 .0XSIZE 0 .5 75.0YSIZE 0 .5 100.0PO 0 .2 0 .15MASS 0.938ENDF IN I- 5 . 0 8 +5 . 08 - 5 . 0 8- 5 . 0 8 +5 . 08 - 5 . 0 8- 5 . 0 8 +5 . 08 - 5 . 0 8- 5 . 0 8 +5 . 08 - 5 . 0 8- 5 . 0 8 +5 . 08 - 5 . 0 8- 5 . 0 8 +5 . 08 - 5 . 0 8- 5 . 0 8 +5 . 08 - 5 . 0 8- 5 . 0 8 +5 . 08 - 5 . 0 8- 1 . 0 +1 . 0 - 1 . 0. b/ .MCNTE CARLO CALCULATICN FOR COUNTER cXPEfiIMENTS   BEGIN CALCULATION NUM3FR 1SYSTEM PARAMETERS DERIVED FROM INPUT   (L(K))   11121 12112111♦ TARC- * SETTING UP REGION 1 IDENTIFIER = 1DATA! 1 , J ) = 0.0 0.0 0.0 0.0 0.0 0(1) = 0.0VACUUM IN THIS ELEMENT•DRIFT*   SETTING UP REGION 2   IDENTIFIER = 20ATA< 2 . J ) = ISO.00000 5.08000 -5.06000 5.08000 -5.080C0UI 2 J = 0.0VACUUM IN THIS ELEMENTTCTAL INTERACTION LENGTH=C•1000E 31 ABS PR08ABILITY=0.0 3-BODY DECAY PROBABILITY = 0.0 REGION 2•DRIFT*   SETTING UP REGION 3   IDENTIFIER = 3DATA! 3 . J ) = 10.00000 5.Ce000 -5.08000 5.08000 -5.08000U( 3 ) = 0.0VACUUM IN THIS ELEMENTTOTAL INTERACTION LENGTH=C.100OF 31 ABS PROEA8ILITY=0.0 3-BODY DECAY PROBABILITY=0.0 REGION 3♦ OUAC * SETTING UP PfcCICN 4 IDENTIFIER = 4DAT A( 4 , J ) = 24.78500 -0.29220 0.0 0.0 0.0U C 4 I = 0.0VACLLM IN THIS ELEMENTTCTAL INTERACTION LENGTH=0.10OOE 31 ABS PROEABI LITY = 0.0 3-BODY DECAY PROBABILITY=0.0 REGION 4♦DRIFT*   SETTING UP REGION 5   IDENTIFIER = 5DATA! 5 . J ) = 0.00100 5.C8000 -5.08000 5.08000 -5.08000UC 5 ) - 0.0VACLLM IN THIS ELEMENTTOTAL INTERACTION LENGTH—0. 1000E 31 ABS PRCBAEILITY—0.0 3-BOOY OECAY PROBABILITY = 0.0 REGION 5. 2- .♦DRIFT*  SETTING UP REGION 6 IDENTIFIER = 6DATA! t . J ) = 20.00000 5.08C0O -5.03000 5.08000 -5.08000U( 6 I - 0.0VACOOV IN THIS ELEMENTTOTAL INTERACTIC N LENGTF=0. 1000E 31 AES PROEABILITY=0.0 3-BODY DECAY PROBABILITY = 0.0 REGION 6♦ OUAC * SETTING UP REGION 7 IDENTIFIER = 7DATA! 7 . J ) -= 24.76500 0.51860 0.0 0.0 0.0U( 7 ) = 0.0VAC U U N IN THIS ELEMENTTCTAL INTERACTION LENGTH —0 • 1000E 31 ABS PROB AB 1L I T Y= 0 . 0 3-HODY DECAY PROBA BI L I T Y = 0 .0 PEGION 7♦DRIFT*   SETTING UP REGION 8   IDENTIFIER = 8DATA! 8 . J ) = 0.00100 5.08000 -5.08000 5.08000 -5.08000UI 6 J = 0.0VACUUV IN THIS ELEMENTTOTAL INTERACTION LENGTH=C.100Ot 31 ABS RRObABILITY=0.0 3-BCDY DECAY PROBABILITY=0.0 REGION 8♦DRIFT*   SETTING UP REGION 9   IDENTIFIER = 9DATA! 9 « J ) = 20.00000 5.08000 -5.08000 5.08000 -5.08000UI 9 ) = 0.0VACULX IN THIS ELEMENTTOTAL INTERACTION LENGTH=C.1000E 31 ABS PRCBABILITY=0.0 3-BODY DECAY PROBABILITY=0.0 REGION 9♦ QUAD * SETTING UP REGION 10 IDENTIFIER = 10DATA! 10 . J J = 24.7650C -0.29220 0.0 0.0 0.0U( 10 ) = 0.0VAC 0 0V IN THIS ELEMENTTOTAL INTERACTION LENGTH-C.1000E 31 ABS PROEAEILITY=0.0 3-BODY DECAY PROBABILITY=0.0 REGION 10♦ DRIFT* SETTING UP REGION 11 IDENTIFIER = 11CA T A( 11 , J ) = 0.00100 5.C80C0 -5.08000 5.08000 -5.080000(11) = 0.0VACUOM IN THIS ELEMENTTOTAL INTERACTION LENGTH=0.1OOOE 31 ABS PROBABILITY=0.0 3-BODY DECAY PR08A8ILITY=0.0 REGION II♦DRIFT* SETTING UP RFGION 12 IDENTIFIER = 12CATAI 12 . J ) = 10.00000 5.08C00 -5.08000 5.08000 -5.08000U< 12 > = 0.0VACUUM IN THIS ELEMENTTCTAL INTERACTION LENGTR=C . 10OOE 31 ABS PROBABILITY=0.0 3-BODY DECAY PROBA81LITY=0.0 REGION 12♦ DRIFT* SETTING UP REGION 13 IDENTIFIER = 13CATAI 13 . J ) = 715.00000 l.CCOCO -1.00000 1.00000 -1.00000L( 13 ) = 0.0VACUUM IN THIS ELEMENTTOTAL INTERACTION LENGTH=0 . 10OOE 31 ABS PROBABILITY=0.0 3-BODY DECAY PROBABILITY=0.0 REGION 13♦ IN I I * SETTING UP REGION 14 IDENTIFIER = 14RANDOM NUMBER INITIALIZER = 123456789♦ NSFAC* SETTING UP REGION 15 IDENTIFIER = 15N S F ACE =0 N * =0♦ GRGLF* SETTING UP REGION 16 IDENTIFIER = 16CALCULATIONS FOR 1 FLOCKS OF 2 TFOUSANO EACHNCRMAL IZATION FACTOR = 0♦XSIZE*   SOTTING UP REGION 17   IDENTIFIER =17XMAX = C.50CCC DXMAX = C.075CCXC = 0.0 DXMAXC = 0.0. 2b .♦ YSIZE* SETTING UP REGION IB ICENTIFIER = 18YMAX = C.SCCOC DY MAX = O.IGOOOYC = 0.0 DYMAXC = 0.0*PU * SETTING UP REGION 19 IDENTIFIER = 19PC = 0.2COOO PM A X = 0. 15000 PC = C.20000TTHR = 0.0♦ MASS * SETTING UP RE GI ON 20 IDENTIFIER = 20PASS = 0.93eC0 SIGA = 0.0 SIGE = 0.0TAUO = 0.0 SCALE = l.CCOOOCECAY MOOES S ALF(l) = 0.0 A3I1I = 0.0 AA(1) = 0.0ALFI2I = O.G A 3{2) = 0.0 A4I2) = 0.0. 22 .IN THE FCLLCWING TAEUCATICN IF RESULTSINITIAL OR INITIALLY MEANS PARTICLES MERE TRACED THROUGH SYSTEM KITH NO DE C A Y , SC A T T E R I N G , AB SORP T I ON OR ENERGY LOSS FINAL OR FINALLY MEANS PARTICLES WERE TRACED THROUGH SYSTEM WITH DEC A Y . SC A TT EP IN G, ABSCJRPT I CJN AND ENERGY LOSS TCTAL N L MEE R OF TRIAL PARTICLES TRACED THROUGH SY S TE M= 2000 , NUMBER OF ('ARTICLES ACCEPTED IN I T I ALLY = 46 NUNEER UF PARTICLES ACCEPTED FINALLY= 46.00PARTICLES INITIALLY REJECTED FRCM TOTAL TRIALSOUTSIDE FCRIZONTAL LIMITS OUTSICE VERTICAL LIMITS AT 1 TARC 0.0 0.0AT 2 DRIFT 2C7.000 613.000AT 2 DRIFT 76.C0O0 76.0000AT 4 COAL 0.0 0.0AT 5 DRIFT 21S.000 21.0000AT 6 DRIFT 169.COO 0.0 AT 7 CLAD 0.0 0.0AT E CRIFT ll.CCOO 12.0000AT 9 DRIFT 0.0 104.000AT 10 CLAC 0.0 0.0AT 11 DRIFT 0.0 49.0000AT 12 CRIFT 0.0 l.OOCOOAT 12 DRIFT 3 S 7.000 33.0000SCL1C ANC-LE*MCM .PE S .= C.25E750E-04 STERAO-bEV/C FRACTIONAL ERRCIR= 0. 147442E 00 TOTAL CORRECT ION FACT CR= 0.100000E 01 FRACTIONAL ERROR= 0.20Q514E 00DISTRIBUTIONS OF ACCEPTED PARTICLES AS A FUNCTION OF STARTING CONDITIONS OF PARTICLE AT TARGETMOMENTUM!GEV/C) POSITION ALONG TARGET(CM)CEV/C INITIAL EEAM FINAL BEAM F INAL.NOT( IN ITIAL ) CM INITIAL BEAM FINAL BEAM FINAL.NOT I INITIAL)O.12E7S0 0.0 C.O 0.0 0.0 46.0000 46.0000 0.00.136250 0.0 0.0 O.C 0.0 0.0 0.0 0.00.143750 0.0 0.0 0.0 0.0 0.0 0.0 0.00.15125C C.O 0.0 0.0 0.0 0.0 0.0 0.00.1SE75C 0.0 0.0 0.0 0.0 0.0 0.0 0.00.1662SC 0.0 0.0 0.0 0.0 0.0 0.0 0.00.173750 0.0 0.0 0.0 0.0 0.0 0.0 0.00.iei25C 1.00000 l.OOOCO 0.0 0.0 0.0 0.0 0.00.1EE750 6.COOOO 6.00000 0.0 0.0 0.0 0.0 0.00.196250 I2.CC00 12.0000 0.0 0.0 0.0 0.0 0.00.2C3750 13.0000 13.0000 0.0 0.0 0.0 0.0 0.0       0.2IE750 4.CC000 4.00000 0.0 0.0 0.0 0.0 0.00.226250 1.00000 1.00000 0.0 0.0 0.0 0.0 0.00.233750 2.CC0C0 2.0COCC 0.0 0.0 0.0 0.0 0.00.241250 0.0 0.0 0.0 0.0 0.0 0.0 0.00.246750 C.O 0.0 0.0 0.0 0.0 0.0 C.O0.256250 0.0 0.0 C.O 0.0 0.0 0.0 0.00.263750 1.00000 1.00000 0.0 0.0 0.0 0.0 0.00.271260 0.0 C.O 0.0 0.0 0.0 0.0 0.0P0S1TILN IN HORIZONTAL PLANE(CM) ANGLE IN HORIZONTAL PLANE(MR)CM INITIAL BEAM FINAL BEAM FINAL.NOT(INITIAL) MR INITIAL BEAM FINAL BEAM FINAL.NOT(INITTAL)0.227500 2.C0000 2.00000 0.0 -35.6250 0.0 0.0 0.0O.2125C0 l.CCCCO l.OOOCO 0.0 -31.8750 0.0 0.0 0.0 !0.1E7600 2.00000 2.00000 0.0 -2e.l2S0 0.0 0.0 0.00.1625C0 3.CCCC0 3.CC000 0.0 -24.3750 0.0 0.0 0.00.137500 3.00000 3.C00C0 0.0 -20.6250 0.0 0.0 0.00.112500 4.00000 4.00000 0.0 -16.8750 2.00000 2.00000 0.00.3750COE-01 2.CCCC0 2.0C0C0 O.C -13.1250 3.00000 3.00000 0.00.625000E-01 0.0 0.0 0.0 -9.37500 I.00000 1.00000 0.0O.37SC0CE—01 4.COOOO 4.00000 0.0 -5.62500 7.00000 7.00000 0.00.125000E—01 l.COCOO l.CCOCO 0.0 -1.87500 9.00000 9.00000 0.00.1250C0E-01 2.00CC0 2.C000C O.C 1.87500 11.0000 11.0000 0.00.375G0CE—01 l.COOOO 1.00000 0.0 5.62499 6.00000 6.00000 0.00.625000E—01 3.00000 3.CC00C 0.0 9.37499 2.00000 2.00000 0.00.875C00E—01 2.00000 2.00000 0.0 13.1250 2.00000 2.00000 0.00.112500 l.CCCOO l.CCOOC 0.0 16.8750 2.00000 2.00000 0.00.137500 3.C0C00 3.00000 0.0 20.6250 1.00000 1.00000 0.0O.1625C0 6.CCCC0 6.00000 0.0 24.3750 0.0 0.0 0.00.167500 l.OCOOO l.OCOCO 0.0 28.1250 0.0 0.0 0.00.212500 3.00000 3.0C000 O.C 31.8750 0.0 0.0 0.00.237500 2.C0000 2.00000 0.0 35.6250 0.0 0.0 0.0i  35  iC  O 7  • •t O CJ<2Ac  o  o  c • t •o  o  c©o o o co o o o o o o o  o  o  c  c  o  oO o o o O o o o o c2 O o o  O c o o o o o c o o C o o o o oUj o o o o o o o o o oX o O o o o o o o o oO c o o o t t t • t t t t t t o o os X t t t # t TY: UV X  O'  ro t t tW < o o o o o o o o!" zz •—< x-Ja- j 2< < O o o o o o o o o o# !" o c o o o o o o o oX o o o o o o o o o oo o o o c o o o c oa -1 o o o o o c o c o oUj < o o c o o t t t t t t t t t t o o o> • t t t t " — 1 X  O'  <*  _l t t t o c c o o o o oz t$•— $\UJX©z< o o o o o o o o o o o O' o o o o o oo o o o o o o o o o o O' c o o o o oo c o c o o o o o o o O' o c o o o ca in in in in in in in m o o o O' in in in in in in t t t t t t t # in in m t t t t t tp- c\i rv % X & ' & t t t t & ' &  &  <■   ()" %)" — —  %)" % ' % ()" n *o  ot •o  oI I I I I I I I I Io  o  o  o  O  o& +,iu  o  o4L • •t o oi"<2X©o  o  o• t •0 0-0© o  o  ©t t • to  o  o  oo  o  o  ot t t •o  o  o  oo  o  ot • to  o  o2 2 < <  MEE SO-J X ^ <©  2o  o  o  o  o  o  o  o  o  oo o o o O  o  o  o  o  o  c o oo  o  o  o  o  o  oo  o  o  o  o  o  o  O  o  o  o  o  o  o  oo © o  o  o © o o o © • t oo  o  o  o  o o o  o  © o2 < O o o o o o o o o o o o o o o o oUJ o o o o CJ o o o o o o © o o © o ©X o © o o o o © CJ o © o © o o o Q o2 o © o o © o o o o © o o © o © O ovJ -1 o o o o © o o © o © © © © o © © ©*“• < t t t t t t t • t • o t • • t t o t t oX 44 -* eg © fO ig eg © t ro eg •4 •«< t w t—< X o o o10 <—•G 2Xj-* wt "4 •H *4 «-*01 o■ o 01 01 01 o o1UJiUJ X1X1X1X1XIXo a o o o o o o o o o o o o o o o o o ©© © o o CJ o o o o © o o © © o © © © o ©uj u : u> in a; U) o o o o o o © © UJ UJ in UJ UJ UJ2 X eg x eg Is* eg in n in Ui Uj U) UJ U) eg x eg l*» eg l>-© n aj ■u n -4 x eg x ig eg X eg x •o X X »oeg •g -* H 44 aj © ro 44 —• n X X •4 —* —< eg egt t t t t t t t t • # • # • t t t t t to o o o o o o o o o o o o o o o O o o oo-IaNFSOaXGoX%SA 10 2 NF a -J *- © t- 2  GC  Mu  <x 2 K< (/)<h-z 5_o2oz01a:«-i"I I I IH XQ in O o*-« X t t2. eg N Is-< t m* eg oX tX a< a2 K— (XX tor in X oh* o eg roZ eg "■) tX t . t4 au o o 1 X□2G2•-*o 21 UX X 1-42 K in o o K< G © t t <X >-• eg Is- XCD * t 44 eg Xo ©J X< <44 ©H©z 2*X in X o GX o eg ro X0* eg  t Xz t t -4 □ o o 1 XuaXXj-* X© IX LL ►-2 2 2> —> w XX X X u© X X ©>4 © © 22 2 2 XG < <H X2 J X XX < <1 1—12 H- © XU 2 442 U b- Xrg X u ex * au 2X  h-22X//  rJ  ©. 2t .6. 2  Example 2A s i n g l e  bending magnet spect rometerT h i s  spect rometer  cons i s t s  o f  a s i n g l e  bending magnet ,  w i t h  an angle of  bend o f  27 deg,  and w i t h  spark planes on e i t h e r  end of  the magnet and 200 cm f o r  the e x i t  o f  the magnet.  A s c i n t i l l a t i o n  counter  f o r  t r i g g e r i n g  purposes is p laced j u s t  in f ron t  of  the magnet.  The program ca l cu l a t ed  two cases in t h i s  run:1) The s o l i d  angle  and momentum acceptance o f  the t o t a l  systemI t  is a l so  des i r ed  to know the number of  p a r t i c l e s  w i t h  a g i ven  i n i t i a l  momentum as a f unc t i on  o f  p o s i t i o n  in the f i n a l  spark p lane.  T h i s  is accompl ished by cards 12, 13,  14 and 15,  which s pec i f y  a ' space '  o f  two d imensions ,  P at  the t a r g e t  and X in the f i n a l  spark p lane .  The system is assumed to be vacuum throughout  except  f o r  the s c i n t i l l a t i o n  counter  ( cards 4 ,  5 and 6 ) .2)  The momentum r e s o l u t i o n ,  assuming w i r e  spacings o f  0 . 10 ,  0 . 14  and 0 .24  cm in the f i r s t ,  second and t h i r d  w i r e  p lanes ,  r e s pe c t i v e l ySince the angu la r  acceptance of  the s i ng l e  w i r e  spacings is ve ry  small  in the ho r i z o n t a l  d i r e c t i o n ,  the va lue  o f  DXMAX is reduced as wel l  as PMAX, to keep a reasonable e f f i c i e n c y .  T h i s  example i l l u s t r a t e s  how elements are changed and how d i s t r i b u t i o n s  as a f unc t i on  of  des i red  v a r i a b l e s  are obtained  us ing NSPAC.One po in t  in the output  deserves ment ion.  In the 'DISTRIBUTION OF PARTICLES FINALLY ACCEPTED'  is gi ven the number o f  p a r t i c l e s  as a func t i on  of  P ( t a r g e t )  and X ( a t  region 6 ) .  The f i na l  number f o r  each value  of  X (6)  is the t o t a l ,  summed over  a l l  momenta, counted at  that  p o s i t i o n .  T h i s  is the s i n g l e  number which appears every  second l i ne .. 2a .01-   231+4   i 5 i531+4  6  i - i 785 6 927 :;<3 9 2 79931+4  2 i2 5 i531+4  2 i2  i+<+ -1!  <=0%     6 5  6  29  =+>;  =+>;  5 5 60== 879;<331+4 6  - i - i  5 231+4   -5 i5 -5 i531+4   - i -5 i5+<+ 5 <=0% 8 =+>;   ;<34+<+6.  2% .MCNTF CAKLO CALCULAT ICN FOR COUNTER EXPEP1MENTS  BEGIN CALCULATION NUMBER 1SYSTEM R A R A M E T E R S DERIVED FROM INPUT (L(K)I 1113 11♦ TARO *  LETTING UP REGILN 1 IDENTIFIER = 1DATA! 1 . J ) = O.UOOIO l.CCOCO C.O 0.0 0.0 U( 1 ) = 0.78540VACLLM IN THIS ELEMENTTOTAL INTERACTILN LENGTH=C.1COOE 31 ABS FKOEABILITY=0.0 3-3CDY DECAY PROBA6 ILITY = 0.0 REGION 1♦DRIFT*   SETTING OF RtGION 2   IDENTIFIER = 2OATAT 2 . J ) = 2CO.OOOGC 10.00000 -10.00000 7.50000 -7.50000U( 2 I = 0.0VACLLM IN THIS ELEMENTTOTAL INTERACTION LENGTH=0. 1000E 31 ABS PROEAEILITY = 0 . 0 3-GGDY DECAY PROSA 8 ILITY = 0.0 REG I ON 2♦DRIFT*   SETTING UP REGION 3   IDENTIFIER = 3CATAI 3 . J ) = O.lfcOCO SO.CCOOO -50.00000 50.00000 -50.00000UI 3 ) = 0.01CC.0C00 X LF AFERATURE CCVLRED BY MATFRIAL A IT H DENSITY 1 .0300 CM ✓ CC CCMFCSITICN OF MATERIAL rOLLOWS :R BH-7 AO 12POGD2A EDPH ATOMIC N J Z 6.0 0.S157C01 .C C.C643C00.0 O.C1/E SCATT.ANGCE=0.16645-02 l/E DISPLACEMENT=0.1380E-03 THICKNESS IN RADIATION LENGTHS=0.3607E-02 IONISATION ENERGY LOSS DISTRIBUTION IS OF LANCAd TYPE.AVERAGE = 0•5 967E —03 Al IDTh=0. 1643E-03 GF V TOTAL INTERACTION LENGTE = 0 . 1OOOE 2i A‘3S PRCl-AE IL I T Y = 0 . 0 3-BODY DECAY PRQ3AB I LI TY =0 . 0 RFC TON 3♦ UENC *---- SETTING UP REGION 4 IDENTIFIER = 4DATA! 4 . J ) — 80.10000 14.C0CCC C.O 0.0 0.0. 2/ .GREESNGRE G I PREG IONONREGPUY - 0Y-0Y = 05 38END=CFDEC A3-BOD500 G3-iiOOY DECAY PRO500000000003—300 Y DECAY PROBC< A ) = 0.£4£25PARAMETERS FOR CENTRAL 1RAJECTORY TFRGUGH BENDING MAGNET RADIUS OF CURVATURE^ 186.6 CMS.INPUT ANGLE= 13.6 VACUUM IN THIS ELEMENTP.P2A DKPOV2TPDTK LLNGTh=0.1000E 31 ACS PRLEAEILITY=0.0IFT* SETTING UP rcEGIGN 5 IDENTIFIER -CATA( 5 • J ) = l.UOCCO 1 4 . C 0 0 0 0 -14.00000PRCEAFIS ELEVENCUUMENGT F=CCNRACALDENNG-?4 .GCOOO00£4<=00)0 E A EB5FIS ELLMEACUUML ENGTh=0ERACALDENN 7CNNGUMBER♦ GRCUHCU SANCNS FCR 1 BLOC ILN FACTOR =C^LCUL NCR MALDENONG UNSP/ICE =1 N* =1 MLL I I-C I *ENS I INAL A N AL Y S I S • NU » E Eh LF SFACES= I NUMfcJEF OF CIMENEICNS IN EACH SF ACE— 2i2 io c.tccc g.?oco x e 2- « e. c o c c. L- .XMAX = C.2C0CQ DXMAX - C.1SGCCAC = C.O DX MA XC = C.O♦YSI2E+ SETTING UP REGION 11 1CENIIF I£R = IIYMAX = C.5CCCC OVKAX - C.C7C0CYC = 0.0 CYMAXC = C.O♦PC. ♦ SETTING UF REG IC N 12 IDENTIFIER - 12PC = C.7C0CC PM A X = 0.6CCCC PC = 0. 70000TTEft - C.C♦ MASS ♦ SETTING UF REGION 13 IDENTIFIER = 13l“ASS = C.S3E0C SIGA = O.C SIGE = 0.0 TACO = C.O SCALE = 1.00000CECAY MCOES : ALFI 1 ) = O.C A3I1) - 0.0 AA(1 ) = 0.0ALF(2) = 0.0 A3(2) = 0.0 A4(2) = 0.0Li .IN THE FOLLOWING TAEULATICN CF RESULTSINITIAL 01 INITIALLY MEANS PARTICLES WERE TRACED THROUGH SYSTEM wITH NO DECAY,SCATTERING,ABSORPTI ON OR ENERGY LOSSFINAL OF FINALLY MEANS PARTICLES WERE TRACEO THROUGH SYSTEM WITH DEC AY,SCATTER ING,ABSORPTI ON ANO FNERGY LOSSTOTAL NUMBER CF TRIAL PARTICLES TRACEC TERCUCE SYSTEM= 15000NUMEER OF PARTICLES ACCEPTED INITIALLY^ 3928NUMBER OF PARTICLES ACCEPTED FINALLY= 3882.PARTICLES INITIALLY REJECTED FRGM TOTAL TRIALSOUTSIDE HORIZONTAL LIMITS OUTSIDE VERTICAL LIMITS AT 1 T ARC 0.0 0.0AT 2 DRIFT 4 92 E.00 0.0AT 3 DRIFT 0.0 0.0AT A EENC 0.0 0.0AT 5 DRIFT 1632.00 1399.00AT t DRIFT 3112.00 C.OPARTICLES FINALLY REJECTED FROM THOSE INITIALLY ACCEPTEDLNERCY TCC LOW MULTIPLY SCATTERED OUT ABSORBED 3-BODY DECAYS TOTAL NUMBER REJECTEDAT1TARG 0.0 0.0 0.0 0.0 0.0 AT 2 CRIFT O.C C.C C.O 0.0 0.0AT 3 DRIFT 0.0 0.0 0.0 0.0 0.0AT 4 BEND C.C 0.0 0.0 0.0 0.0AT 5 DRIFT 0.0 58.0000 0.0 0.0 58.0000AT t DRIFT 0.0 57.0000 0.0 0.0 57.0000CVJcO -  42 -OooavDPARTICLES FINALLY ACCEPTED FRCM THCSE INITIALLY REJECTED BECAUSE C1F INTERACTIONS OF THE FOLLOWING TYF>ESCATTERING FRUM NUCLEUS 1 SCATTERING FRDM NUCLEUS 2 SCATTERING FROM NUCLEUS .3 DECAY-MODE 1 OECAY-MUDE 2OCCUR 1NG IN1TARG 0.0 0.0 0.0 0.0 0.0OCCLRING IN 2 DRIFT 0.0 0.0 0.0 0.0 0.0OCCLRING IN 3 DRIFT 0.0 0.0 0.0 0.0 0.0OCCLRING IN4EEND 0.0 0.0 0.0 0.0 0.0OCCURINC- IN 5 DRIFT 0.0 0.0 0.0 0.0 0.0OCCURING IN t CRIFT 0.0 0.0 0.0 0.0 0.0TOTAL EXTRA PARTICLES PUT INTO EEAMISUNMED OVER ALL REGIONS)MUl. T .SCATT .= C.69CCC0E 02 NLC.SCATT= 0.0 DECAY MODE 1= 0.0 DECAY MODE 2= 0.0 TOT AL= 0.69001PARTICLES FINALLY REJECTED FRCM THOSE INITIALLY ACCEPTED BECAUSE OF INTERACTIONS OF THE FOLLOWING TYPESCATTERING FROM NUCLEUS I SCATTERING FROM NUCLEUS 2 SCATTERING FROM NUCLEUS 3 DECAY-MODE I DECAY—MODE 2OCCLRING IN 1 TARG 0.0 0.0 0.0 0.0 0.0OCCURING IN2DRIFT 0.0 0.0 0.0 0.0 0.0OCCLRING IN 3 DRIFT 0.0 0.0 0.0 0.0 0.0OCCLRING IN 4 BEND 0.0 0.0 0.0 0.0 0.0iTTtcDKh DK n gGD7P oIo oIo oIo oIo oIoOCCLRING IN 6 DRIFT 0.0 0.0 0.0 0.0 0.0TOTAL PARTICLES PEMCVEC FROM EEAM(SUM ML D OVER ALL REGIONS)MULT.SCATT.= 0.115CCCE C3 NLC.SCATT= 0.0 DECAY MODE 1= 0.0 DECAY MODE 2- 0.03-eCCY D E C A Y-= C.C AESQRPT I CN-= 0.0 TOTAL= 0.11E000E 03SCL1C ANOLE*MLM.RES .= C.1G4976E-G2 STERAD—EE V/C FRACTIONAL ERROR= 0. 159556E-01TOTAL CLRRECTICN FACTLR= 0.1011 BEE 01 FRACTIONAL LRR(JR= 0.22O314E-01. L2 .D IS TR I FLITIONS CE ACCEPTED PARTICLES AS A FUNCTION CF STARTING CONDITIONS OF PARTICLE AT TARGETMGMENTLM1 C-EV/C ) POSITION ALONG TARGET(CM)CEV/C INITIAL BEAM FINAL BEAM F INAL.NET ( IN ITIAL) CM INITIAL BEAM FINAL BEAM FINAL.NOT( INITIAL)0.415300 0.0 0.0 0.0 -0.475000E-04 197.000 198.000 3.000000.445CC0 0.0 C.O O.C - 0.42 500 0F.-04 162.000 161 .000 2.00000O.475CC0 0.0 0.0 0.0 -0.J75000E-04 195.000 191.000 3.000000.5CEOCO 18.0000 16.COOC 3.C0000 -0.325000E-04 197.000 194.000 2.000000.535000 IOC.000 97.0000 4.C0000 -0.2750OOE—04 177.000 170.000 I.000000.56 5 0 CO 179.OCO 172.OOC 3.C0C00 -0.225000E-04 195.000 191 .000 3.000000.5950C0 230.000 225.000 5.C0C00 - 0. 17500OE-04 179.300 181 .000 5.000000.625000 296.COO 288.000 5.CCOOO -0.1250OOE-04 195.000 193.000 6.000000.655C0Q 331.000 323.000 2.COOOO -0.7500OOE-05 189.000 186.000 4.000000.685000 399.000 389.000 4 .C0C00 - 0.25000CE-05 191.000 186.000 3.000000.715CC0 395.OOC 294.000 7.00000 0.250000E-05 209.000 204.000 4.000000.745000 271.COO 36e.OOC 7.C0000 0.750000E-05 187.000 189.000 6.000000.7750CC 318.000 215.OOC 3.00000 0.125000E-04 220.000 221.000 5.000000.8C50CO 277.COO 273.OOC 4.COOOO 0.175000E-04 208.000 205.000 4.000000.e35000 247.000 245.OOC l.CJOOO 0.225000E-04 191.000 190.000 5.00000o.eefcco 193.000  194.000  5.C0000 0.275000E-04 219.000 216.900 3.000000.895000 169.COO 173.OOC 6.00000 0.325000E-04 199.000 194.000 1.00000O.925C00 156.OCO 155.OOC 2.C0C00 0.375000E-04 207.000 204.000 0.00.955000 130.000 130.000 2.00000 0.425000E-04 209.000 209.000 4.000000.9e50C0 119.000 125.OOC 6.CCC00 0.475000E-04 202.000 199.000 5.00000PCSITICN IN HORIZONTAL PLANE I CM) ANGLE IN HORIZONTAL PLANE(MR)CM INITIAL EEAM FINAL BEAM FINAL.NOT(INITIAL) MR INITIAL BEAM FINAL BEAM FINAL.NOT( INITIAL)— 0.9500COE—01 192.OCO 189.000 2.00000 Z14.148 0.0 0.0 0.0-0.65CCC0E-01 204.COO 201.000 2.CC000 721.648 0.0 0.0 0.0— 0.T5CCCCE —01 187.000 185.000 7.COOOO 729. 148 0.0 0.0 0.0-0.649999E—01 189.000 184.000 4.COOOO 736.646 213.000 214.000 1.00000— 0.55CCCCE —01 179.COO 177.COO E.CCCOO 744. 148 338.000 331 .000 3.00000— 0.4ECCCCE — 01 210.OCO 21 1 .000 5.00000 751 .648 323.000 325.000 7.00000—0.35CCC0E—C1 ie9.CCC 184.OCO l.CCOOO 759.148 357.000 350.000 1.00000-0.25CCCCE-01 205.000 204.OOC 4.CC000 766.648 366.000 358.000 7.00000-0.IECCCCE-01 167.CCO 184.OCO 3.00000 774.148 351.000 346.000 7.00000— 0.5CC0CIE —02 183.000 180.OOC 4.COOOO 781 .648 306.000 302.000 8.000000.499999E—02 215.COO 210.COC 2.0CC00 789.148 292.000 239.000 5.000000. 15 0 0 0 CE —0 1 185.CCC 184.CCC 4 .00000 796.648 271 .000 268.000 4.000000•25C C COE —01 196.COO 194.OOC 4.CCC00 604. 148 267.000 268.900 7.000000.3SOCCCE-01 213.OCO 211.000 5.00000 811.648 261.000 258.900 6.000000.45000CE-01 lac.eco lei.coc 3.cocoo 8i9.i48 229.000 227.900 3.000000.55CCC0E-J1 195.000 193.000 2.CG000 826.648 203.000 205.900 6.000000.64S999E—01 220.CCO 216.OOC 2.00000 334.148 146.000 141.000 4.000000.749999E — 01 2C8.000 205.OOC 3.CCC00 841 .648 0.0 0.0 0.0C.e5CCCCE-01 194.000 196.000 5.C0000 849.14e 0.0 0.0 0.0C.95C0CCE—01 197.000 193.000 2.CC000 856.648 0.0 0.0 0.0. LL .POSITION IN VERTICAL PLANE!CM) ANCLE IN VERTICAL PLANE(MR I CM INITIAL E E AM FINAL eEAM F INAL.NOT( INITIAL ) MR INITIAL BEAM FINAL BEAM F INAL.NOT{ INITIAL)-0.237SC0 174.COO 166.000 1.00000 -33.2500 0.0 3.00000 3.00000-0.212500 160.000 177.OOC 3.C0000 -29.7500 79.0000 eH.0000 16.0000-0.1675CO 164.000 177.000 1.00000 -26.2500 220.000 206.010 0.0 -0.1625CC 2C9.C00 2C6.0CC 4.0(000 -22.7500 236.000 232.000 3.00000-0.137500 216.000 213.000 4.CC000 -19.2500 240.000 236.000 1.00000— 0. 1 125C0 176.000 176.000 5.00000 -1 5.7500 252.000 249.000 1.00000-0.67£0 COE-0 1 196.OCO 196.000 3.00000 -12.2500 256.000 257.000 2. 00000—0.625000E—01 195.COO 196.000 5.C0000 -8.75000 221.000 217.000 1.90000-0.3750CCE-C1 229.000 229.000 6.00000 -5.25000 251.000 251.000 5.00000-0.125000E-01 176.CCO 179.000 6.COCOO -1.75000 270.000 267.000 1.000000.125CC0E—01 163.000 162.000 i.CCOOC 1.75000 215.000 217.000 2.000000.375CC0E-01 214.COO 210.000 1.00000 5.25000 241.000 239.000 3.000000.625000E—01 181.000 173.000 2.C0G00 8.74999 232.000 228.000 1.000000.e75CC0E-01 199.000 202.000 8.00000 12.2500 232.000 235.000 3.000000.11^500 215.COO 215.OCC 4.00000 15.7500 23O.000 236.000 4.000000.137500 184.000 160.000 2.00000 19.2500 221.000 221.000 3.000000.1C2500 222.000 219.000 2.00000 22.7500 220.000 222.000 5.000000.ie7£00 203.OCO 197.OOC 4.C0000 26.2500 227.000 216.000 1 . 000000.212500 206.COO 204.000 1.00000 29.7500 77.0000 68.0000 12.00000.2375C0 162.000 161.000 4.00000 33.2500 0.0 2.00000 2.00000CENTRAL VALLES AND WIDTHS CF D I STR10UT I ONS IN STARTING MOMENT A AND ANGLES (THESE RESLLTS ARE ROUGH ESTIMATES CNLV-FCR ACCURATE VALUES THE DISTRIBUTIONS SHOULD BE PLOTTED)INITIAL BEAM FINAL BEAM ( CENTRE WIDTH CENTRE WIDTH MOMENTUM(GEV/C I 0.742 0.3 15 0.744 0.315 * HCRIZCNTAL ANGLE(MP) 781. 94.9 781. 95.2 *VERTICAL ANGLE(MR) -0.313 55.0 -0.324 55.1 (DISTRI e L TICN CF PARTICLES FINALLY ACCEPTED SPACE 1X 6 F 1 0.430 0.490 0.550 C.610 0.67C 0.730 0.790 0.850 0.910 0.970°*° I6-° 55.C 89.0 70.0 23.0 0.0 0.0 0.0 0.0 293._*e,e 0.0 0.0 72.0 85.0 79.0 67.0 0.0 0.0 0.0 0.0 303 .~12"° 0,0 0,0 56.C 85.0 76.0 7-5.0 37.0 0.0 0.0 0.0 329 .~7*20 °*° 0.0 41.C 84.0 89.0 94.0 68.0 2.00 0.0 0.0378 .~2*40 °*° °*° S.CC 70.0 80.0 79.0 83.0 50.0 0.0 0.07 •2*4C °*° °*° 0-0 54.0 92.0 84.0 85.0 76.0 39.0 0.0 430.7,20 °*° °*° °*° 38.0 71.0 93.0 91 .0 70.0 64.0 16.0443 .12.0 0.0 0.0 0.0 8.00 83.0 77.0 77.0 92.0 79.0 91.0507 .lt*e °*° °*° °*0 0.0 56.0 85.0 75.0 7.1.0 69.0 69.0427.21*6 0*0 0*0 0.C 0.0 16.0 85.0 72.0 76.0 77.0 79.0405 .SUMS CF COLUMNS ARE0*0 16.0 269. 513. 712. 762. 588. 439. 328. 255.I CJi ILt .MONTE CARLO CALCULATION FOR COUNTER EXPERIMENTS   BEGIN CALCULATION NUMBER 2SYSTEM PARAMETERS DERIVED FROM INPUT   <L(K)>   111311ATARG * SETTING UP REGION 1 IDENTIFIER = 1C AT A( 1 , J ) = O.OOOIO 1 .00000 0.0 0.0 0.0 U{ 1 ) = 0.78540VACUUM IN THIS ELEMENTTOTAL INTERACTION LFNGTH=0.1OOOE 31 ASS PROBABILITY = 0.0 3-BODY DECAY PR08A8ILITY = 0.0 REGION 1ADRIFT*   SETTING UP REGIGN 2   IDENTIFIER = 2DATA! 2 . J > = 200.00000 0.05000 -0.05000 7.50000 -7.50000U( 2 ) = 0.0VACUIM IN THIS ELEMENTTOTAL INTERACTION LENGTH=0.100OE 31 ABS PROBABILITY=0 . 0 3-BOOY DECAY PROBABIL1TY = 0.0 RFGION 2ADRIFT*   SETTING UP RFGION 3   IDENTIFIER = 3DATA! 3 . J ) = 0.16000 50.00000 -50.00000 50.00000 -50.00000U ( 3 ) = 0.01CC.0C00 X OF APERATURE COVERED BY MATERIAL WITH DENSITY 1.0300 GM / CC CCMPCSIT ION OF MATERIAL FOLLOWS :Z PROP CF MATERIAL WITH ATOMIC NO Z6.0 0.9157001.0 0.C843000.0 0.01/E SCATT.ANGLE=0.1664F-02 1/E DISPLACEMENT=0.1380F-03 THICKNESS IN RADIATION LENGTHS=0.3607F-02 ICNISATION ENERGY LOSS DISTRIBUTION IS OF LANDAU TYPE.AVERAGE^O.5967F — 0 3 WIOTH=0.1643E-03 GEV TCTAL INTERACTION LENGTH = 0 . 1000F 31 ABS PROBA01LITY=0.0 3-RODY DECAY PROBABILITY=0.0 REGION 3ABEND A SETTING UP REGION 4 IDENTIFIER = 4C AT A < 4 , J ) = 80.00000 14.00000 0.0 0.0 0 ..0. La .U< 4 ) = 0•24225PARAMETERS FOR CENTRAL TRAJECTORY THROUGH BENDING MAGNETRADIOS OF CURVATURE= 166.8 CMS.INPUT ANGLF= 13.8800 ANGLE OF BEND= 27.7538 OUTPUT ANGLF= -13.8738 DEGREES VACUUM IN THIS ELEMENTTOTAL INTERACTION LENGTH=0.1OOOE 31 ABS PROEAEIL1TY = 0.0 3-BODY DECAY PROBARXL ITY=0.0 REGION LADRIFT*   SETTING UP REGION 5   IDENTIFIER = 5DATA! 5 . J ) = 1.00000 0.07000 -0.07000 7.50000 -7.50000U( 5 ) = 0.0VACUUM IN THIS ELEMENTTOTAL INTERACTION LENGTH=0.1OOOE 31 ABS PROBABILITY=0.0 3-BODY DECAY PRORABI LITY = 0.0 REGION 5ADRIFT*   SETTING UP RFGION 6   IDENTIFIER = 6DATA! 6 . J ) = 200.00000 0.12000 -0.12000 15.00000 -15.00000U1 6 ) = 0.0VACUUM IN THIS ELEMENTTOTAL INTERACTION LENGTH=0.1OOOE 31 ABS PROBABILITY=0.0 3-BODY DECAY PROBABILITY=0.0 RFGION 6*IN IT A SETTING UP REGION 7 IDENTIFIER = 7RANOCM NUMBER INITIALIZER = 111111111AGROUF* SETTING UP REGION 8 IDENTIFIER = 8CALCULATIONS FOR 1 BLOCKS OF 15 THOUSAND EACH NORMALIZATION FACTOR = 0ANSPAC*   SETTING UP REGION 9   IDENTIFIER = 9NSPACE =0 N* =0AXSIZEA SETTING UP REGION 10 IDENTIFIER = 10XMAX = C.20000 DXMAX = 0.00150.  L% .• •XC = 0.0 DXMAXC = 0.0AYSIZE* SETTING UP REGION 11 IDENTIFIER = 11YWAX = C.50000 DY MAX = 0.07000YC = 0.0 DYMAXC = 0.0♦ PCI * SFTTING UP REGION 12 IDENTIFIER = 12FC = 0.70000 PM AX = O.OOAOO PC = 0.70000TTHG = 0.0AMASS A SETTING UP REGION 13 IDENTIFIER = 13MASS = 0.93800 SIGA = 0.0 SIGE = 0.0 TAUO = 0.0 SCALE = 1.00000DECAY MODES : ALF<1) = 0.0 A3(l> = 0.0 A4<1) = CALF < 2) = 0.0 A312) = 0.0 A4(2) = 0. L/ .IN THE FOLLOWING TABULATION OF RESULTSINITIAL OP INITIALLY MEANS PARTICLES WERE TRACED THROUGH SYSTEM WITH NO DECAY.SCATTFRING.ABSORPTI ON OR ENERGY LOSSFINAL OR FINALLY MEANS PARTICLES WERE TRACED THROUGH SYSTEM WITH DECAY,SCATTERING.ABSORPTI ON AND ENERGY LOSSTOTAL NUMBER OF TRIAL PARTICLES TRACED THROUGH SYSTEM= 15000 NUMBER OF PARTICLES ACCEPTED INIT IALLY= 1465NUMBER OF PARTICLES ACCEPTED FINALLY= 719.0PARTICLES INITIALLY REJECTED FROM TOTAL TRIALSOUTSIDE HORIZONTAL LIMITS OUTSIDE VERTICAl LIMITS AT 1 TARG 0.0 0.0AT 2 DRIFT 10010.0 0.0AT 3 DRIFT 0.0 0.0AT 4 BEND 0.0 0.0AT 5 DRIFT 1088.00 697.000AT 6 DRIFT 1740.00 0.0PARTICLES FINALLY REJECTED FRCM THOSE INITIALLY ACCEPTEDENERGY TOO LOW MULTIPLY SCATTERED OUT ABSORBED 3—BODY DECAYS TOTAL NUMBER REJFCTEDAT 1 TARG 0.0 0.0 0.0 0.0 0.0AT 2 DRIFT 0.0 0.0 0.0 0.0 0.0AT 3 DRIFT 0.0 0.0 0.0 0.0 0.0AT 4 EENC 0.0 0.0 0.0 0.0 0.0AT 5 CRIFT 0.0 856.000 0.0 0.0 856.000AT 6 CRIFT 0.0 280.000 0.0 0.0 280.000PARTICLES FINALLY ACCEPTED FROM THOSE INITIALLY REJECTED BECAUSE OF INTERACTIONS OF THE FOLLOWING TYPFSCATTERING FROM NUCLEUS I SCATTERING FROM NUCLEUS 2 SCATTERING FROM NUCLEUS 3 DECAY-MODE 1 DECAY-MODE 2OCCURING IN 1 TARG 0.0 0.0 0.0 0.0 0.0OCCURING IN 2 DRIFT 0.0 0.0 0.0 0.0 0.0OCCURING IN 3 DRIFT 0.0 0.0 0.0 0.0 0.0OCCURING IN 4 BEND 0.0 0.0 0.0 0.0 0.0OCCURING IN 5 DRIFT 0.0 0.0 0.0 0.0 0.0OCCURING IN 6 DRIFT 0.0 0.0 0.0 0.0 0.0TOTAL EXTRA PARTICLES PUT INTO BEAM!SUMMED OVER ALL REGIONS)MULT.SCATT.= 0.390000E 03 NUC.SCATT= 0.0 DECAY MODE 1= 0.0 DECAY MODE 2= 0.0 TOTAL- O.39O909F nPARTICLES FINALLY REJECTED FROM THOSE INITIALLY ACCEPTED BECAUSE OF INTERACTIONS OF THE FOLLOWING TYPESCATTERING FROM NUCLEUS I SCATTERING FROM NUCLEUS 2 SCATTERING FROM NUCLEUS 3 OECAY-MOOE 1 DECAY-MODE 2OCCURING IN 1 TARG 0.0 0.0 0.0 0.0 0.0OCCURING IN 2 DRIFT 0.0 0.0 0.0 0.0 0.0OCCURING IN 3 DRIFT 0.0 0.0 0.0 0.0 0.0OCCURING IN 4 BEND 0.0 0.0 0.0 0.0 0.0OCCURING IN 5 DRIFT 0.0 0.0 0.0 0.0 0.0OCCURINC- IN 6 DRIFT 0.0 0.0 0.0 0.0 0.0TOTAL PARTICLES PEMCVED FROM BEAM(SUMMED OVER ALL REGIONS! (MULT. SCATT. = 0.113600E 04 NUC.SCATT= 0.0 DECAY MODE 1= 0.0 DECAY MODE 2= 0.0salTTd gOT2dr oIo 2ln.GBPD.Kr oIo P.P 2Ar .ID esuooO ov N ISOLID ANGLE*MOM.RES.= C.410199E-07 STFRAD—BEV/C FRACTIONAL ERROR= 0.26I265E-0!TOTAL CORRECTION FACTOR= 0.203755E 01 FRACTIONAL ERROR= 0.455348E-01. oi .DISTRIBUTIONS OF ACCEPTEO PARTICLES AS A FUNCTION OF STARTING CONDITIONS OF PARTICLE AT TARGETMOMENTUM!GEV/C) POSITION ALONG TARGET(CM)GEV/C INITIAL BEAM FINAL BEAM FINAL.NOT(IN ITIAL) CM INITIAL BEAM FINAL BEAM FINAL.NOT(I NITTAL>o.cseicc o.o s.ooooo 9.00000 -0.475000E-04 71.0000 26.0000 18.00000.698300 5.00000 11.0000 10.0000 —0.4250 OOE —04 76.0000 37.0000 14.00000.658500 15.0000 14.0000 1 1.0000 - 0.375000E-04 77.0000 36.0000 22.00000.656700 22.0000 18.0000 13.0000 -0.325000E-04 65.0000 35.0000 21.00000.658900 45.0000 26.0000 19.0000 -0.275000E-04 67.0000 29.0000 14.00000.699100 53.0000 41.0000 21.0000 -0.225000E-04 61.0000 33.0000 19.00000.655300 101.000 35.0000 12.0000 -0.175000E-04 83.0000 34.0000 16.00000.659500 122.000 37.0000 10.0000 ' -0.125000E-04 72.0000 38.0000 22.0000 0.655700 164.000 38.0000 10.0000 -0.750000F-05 79.0000 32.0000 16.00000.699900 170.000 51.0000 9.00000 -0.250000E-05 73.0000 38.0000 21.00000.7C0100 167.000 51.0000 7.00000 0.250000F-05 76.0000 37.0000 18.00000.700300 154.000 36.0000 11.0000 0.750000E-05 64.0000 43.0000 26.00000.7C0500 119.000 52.0000 22.0000 0.125000E-04 84.0000 34.0000 17.00000.7C0700 101.000 59.0000 29.0000 0.175000E-04 65.0000 40.0000 20.00000.700900 86.0000 49.0000 24.0000 0.225000E-04 74.0000 31.0000 17.00000.701100 43.0000 44.0000 35.0000 0.275000E-04 71.0000 37.0000 23.00000.7C1300 31.0000 45.0000 38.0000 0.325000F-04 70.0000 36.0000 18.00000.701500 13.0000 36.0000 34.0000 0.375000E-04 69.0000 40.0000 21.00000.7C17C0 7.00000 37.0000 36.0000 0.425000E-04 85.0000 47.0000 26.00000.7C1900 3.00000 30.0000 30.0000 0.475000E-04 83.0000 36.0000 21.0000POSITION IN HORIZONTAL PLANE(CM) ANGLE IN HORIZONTAL PLANE(MR)CM INITIAL BEAM FINAL BEAM F IN AL. NOT ( INITI AL) MR INITIAL BEAM FINAL BEAM FIN AL • NOT ( INIT I, AL ) 1-0.S500C0E-0I 64.0000 42.0000 25.0000 784.685 0.0 0.0 0.0-0.850000E-01 71.0000 33.0000 16.0000 784.760 0.0 0.0 0.0 ^—0.750000E—01 72.0000 35.0000 14.0000 784.835 18.0000 7.00000 4.00000-0.649959E—01 73.0000 43.0000 25.0000 784.910 29.0000 13.0000 7.00000 *-0.550000E—01 77.0000 45.0000 27.0000 784.985 65.0000 29.0000 13.0000—0.450000E—01 51.0000 27.0000 15.0000 785.060 93.0000 42.0000 19.0000-0.35000CE-01 72.0000 37.0000 26.0000 785.135 97.0000 44.0000 22.0000—0.250000E—01 79.0000 29.0000 15.0000 785.210 124.000 61.0000 31.0000-0.1S0000E-01 84.0000 38.0000 22.0000 785.285 173.000 60.0000 29.0000-0.5000C1E-02 65.0000 31.0000 18.0000 785.360 147.000 74.0000 49.00000.499999E—02 81.0000 43.0000 25.0000 785.435 155.000 93.0000 56.00000.150000E—01 72.0000 34.0000 16.0000 785.510 149.000 78.0000 40.00000.250000E-01 80.0000 34.0000 17.0000 785.585 135.000 62.0000 34.00000.350000E-01 67.0000 39.0000 25.0000 785.660 94.0000 40.0000 18.00000.450 0 COE—01 65.0000 34.0000 16.0000 785.735 89.0000 55.0000 29.00000.550000E—01 76.0000 32.0000 16.0000 785.810 58.0000 36.0000 23.00000.649999E—01 76.0000 39.0000 19.0000 785.885 30.0000 17.0000 11.00000.7499S9E-01 76.0000 25.0000 11.0000 785.960 9.00000 B.00000 5.000000.850000E—01 73.0000 33.0000 19.0000 786.035 0.0 0.0 0.00.950000E—01 91.0000 46.0000 23.0000 786.110 0.0 0.0 0.0. ob .POSITION IN VERTICAL PLANE(CM) ANGLE IN VERTICAL /0<4(1?CM INITIAL BEAM FINAL BEAM F INAL.NOT(INITIAL) MR INITIAL BEAM FINAL BEAM FINAL.NOT{I NTT 1 At-0.237500 77.0000 37.0000 19.0000 -33.2500 0.0 0.0 0.0 -0.212500 64.0000 32.0000 22.0000 -29.7500 20.0000 16.0000 12.0000-0.187500 80.0000 40.0000 18.0000 -26.2500 85.0000 42.0000 22.0000-0.162500 83.0000 36.0000 20.0000 -22.7500 98.0000 44.0000 30.0000-0.137500 86.0000 42.0000 21.0000 -19.2500 72.0000 32.0000 22.0000-0.112500 77.0000 34.0000 21.0000 -15.7500 89.0000 42.0000 22.0000-0.e75000E-01 67.0000 32.0000 20.0000 -12.2500 103.000 40.0000 12.0000-0.625000E-01 71•0 C 00 40.0000 22.0000 -8.75000 95.0000 53.0000 28.0000—0.3750COE—01 65.0000 38.0000 19.0000 -5.25000 83.0000 48.0000 28.0000-0.125000E-01 57.0000 25.0000 16.0000 -1.75000 92.0000 44.0000 23.00000.1250C0E—01 75.0000 27.0000 13.0000 1.75000 86.0000 44.0000 23.00000.375000F—01 56.0000 41.0000 26.0000 5.25000 81.0000 46.0000 28.00000.625000E—01 74.0000 31.0000 19.0000 8.74999 86.0000 38.0000 17.00000.875000E—01 77.0000 37.0000 17.0000 12.2500 81.0000 39.0000 23.00000.112500 82.0000 46.0000 25.0000 15.7500 84.0000 45.0000 28.00000.137500 73.0000 38.0000 24.0000 19.2500 87.0000 41.0000 22.00000.162500 78.0000 43.0000 19.0000 22.7500 96.0000 48.0000 24.00000.ie7500 68.0000 35.0000 17.0000 26.2500 90.0000 44.0000 19.00000.212500 82.0000 27.0000 18.0000 29.7500 37.0000 12.0000 6.000000.237500 73.0000 3e.0000 14.0000 33.2500 0.0 1.00000 1.00000CENTRAL VALUES AND WIDTHS OF DISTRIBUTIONS IN STARTING MOMENTA AND ANGLES (THESE RESULTS ARE ROUGH ESTIMATES ONLV-FOR ACCURATE VALUES THF DISTRIBUTIONS SHOULD BF PLOTTED)INITIAL BEAM FINAL BEAM CENTRE WIDTH CENTRE WIDTH MCMENTUM(GEV/C ) 0.700 0.174E-02 0.700 0.385E-02HORIZONTAL ANGLE C MR) 785. 0.731 785. 0.616VERTICAL ANGLE(MR ) 0.295 57.9 0. 173 57.2END CF FILE ENCOUNTERED FOLLOWING CALCULATION NUMBER 2 . STOP .STOP C EXECUTION TERMINATED6.  3 Example 3A spect rometer  c o n s i s t i n g  of  a quadrupole  p a i r  and two bending magnetsT h i s  spect rometer  cons i s t s  of  a quadrupole  p a i r  f ocus ing  the p a r t i c l e s  through two v e r t i c a l  45 deg bends onto a spark chamber p lane .  P a r a l l e l  to po in t  f ocus ing  h o r i z o n t a l l y  and po in t  to po in t  f ocus ing  v e r t i c a l l y  is used,  the r equ i red  quadrupole  f i e l d s  being obta ined  us ing  TRANSPORT.11 A s c i n t i l l a t i o n  counter  is located j u s t  a f t e r  the second bend.  Since the bends are in the v e r t i c a l  p l ane ,  the element ROTAT is used j u s t  before  the f i r s t  bending magnet.  The p a r t i c l e s  t r a v e r s i n g  the system are assumed to be p i ons ,  which decay in f l i g h t ,  w i t h  a l i f e t im e  o f  26.08  nsec.  Absorp t i on  and nuc l ea r  s c a t t e r i n g  can a l so  occu r .  T h i s  leads to f r a c t i o n a l  numbers of  par t icles o c c u r r i n g  in the o u t pu t ,  s i nce  whenever  an i n t e r a c t i o n  occurs  in the s c i n t i l l a t i o n  co un te r ,  a ca l cu l a t ed  f r a c t i o n  is assumed to be absorbed.. o2 .-  $k -1501-31+4@!0331+431+4@!0331+431+410:;<331+431+4:;<331+431+4+<+-1!<=0% =+>;=+>;PO0==40.64 23.0240.64 30.48173.9  50.0173.9L 0 .16  1 . 0  0.9157 150.0  73662497.3 . 00.1440.0841.090.13961 . 00.3177.62 0.36467.627.62 -0 .31937.62 15.2416.07.627.62 16.07.62 1 .03  6 . 07.622 .040 . 080.0  0 .0630.00.1055- 7 . 6 2- 7 . 6 2- 7 . 6 2- 7 . 6 2-15.2445.0  - 7 . 6 2  - 7 . 6 245.0  - 7 . 6 20.0843- 7 . 6 27.627.627.627.627.6215.2415.2415.241 . 015.240 . 026.08- 7 . 6 2- 7 . 6 2- 7 . 6 2- 7 . 6 2- 7 . 6 2- 1 5 . 2 4- 15 . 2 4- 15 . 2 4- 15 . 2 4;<34+<+MCNTE CARLO CALCULATION FOR COUNTER EXPERIMENTS   BEGIN CALCULATION NUMBER 1SYSTEM PARAMETERS CERIVEO FRCM INPUT — I L I K I J   11211211 E311311( 1-BETA )CMS= C • 8 1 Cl E —02 GAMMA — CM S= 0.7872E 01 P-C.MS= 0.69B0E-01 T3-CMS= 0.6980E-01 T4-CMS= 0.69BOF-01OECAY LENC-TP= C.61C9E 04 0.1C37E-03 0.0 0.0*1 ARC- *  SETTING UP fiEGICN 1 IDENTIFIER = 1CATAI 1 . J ) = 0.01000 0.317CO C.O 0.0 0.0u I i ) = o.oVACUUM IN THIS ELEMENTOEC.FRCBAE ILITY=G. 1C0CE 01 MCDL 1DEC.FFCEAEILITY=0.0 VOCE 2TOTAL INTERACTION LENGTH-0.1109E 04 ABS FRtJEAEILITY=0 . 0 3-OOOY DECAY PROBABILITY = 0.0 REGION 1♦DRIFT*   SETTING UF RtGICN 2   IDENTIFIER = 2CATAI 2 . J > - 100.00000 7.t2CC0 -7.E2C00 7.62000 -7.62000U( 2 ) = 0.0VACUUM IN THIS ELEMENTDEC.FRCEAEIL1TY=C.100CE 01 MODE 1DEC.FRCEAEILITY=0.0 MODE 2TOTAL INTERACTION LENGTH=0.6109E 04 ABS PRCEAEILITY=0.0 3-BODY DECAY PRQ8ABIL1TY=0.0 REGION 2♦ OUAT * SETTING UP RLCICN 3 IDENTIFIER = 3CATAI 3 . J > = 40.O4CG0 0.36460 0.0 0.0 0.0UI 3 ) = 0.0VACUUM IN THIS ELEMENTDEC.FfiCeAEILITY=0.1C0DE 01 MLDE 1DEC .FRCEAG ILITY=0.0 ML C E 2TOTAL INTERACTION LhNGTH = 0.fc1C9E U4 ABS FROG A 6ILITY = 0.0 3-BODY DECAY PRCJBA B IL I T Y = 0 . 0 ' REGION 3♦DRIFT*   SETTING UF RLGICN 4   IDENTIFIER = 4CATAI 4 . J ) = O.OIOCO 7.62 COO -7.62CC0 7.6 2 000 -7.620000(4) = 0.0VACUUM IN THIS ELEMENTDEC.PRCBAEILITY=C.1CC0E Cl MODE 1DEC.PRCEAEILITY=C.C MODE 2TCTAL INTERACTION L ENG T H = 0 . 6 1 09E 04 AHS RROt A E I L I T Y = 0 . 0 3-DODY OECAY PROB A FJIL I T Y= 0 . 0 REGION 456  -♦DRIFT*   SETTING !4 REGICN    IDENTIFIER  DA IA( 5 . J ) = 23.01999 7.62000 -7.o2000 7.62000 -7.62000U< 5 ) = 0.0VACUUM IN THIS ELEMENTDEC.FRCEAEILITY=0.1OOOE 01 MODE 1DEC.PRCEAEILITY=0 .C MCDE 2TOTAL INTERACT IC N LENGTH=C.6109E 04 AdS PRCGAEILITY = 0.0 3-BCDY DECAY PROBABILITY-0.0 REGION 5♦ OUAC * SETTING UP REGION 6 IDENTIFIER = 6DATA! 6 , J ) = 40.64000 -0.31930 0.0 0.0 0.0 U< 6 ) = 0.0VACLLM IN THIS ELEMENTOEC.FRCEAEILnY=0.1000F 01 MODE 1DEC.PRCBABILITY = 0 . 0 MCDE 2TOTAL INTERACTION LENGTP = L.6109E 04 ABS PROEAEILITY=0.0 3-BOOY DECAY PRGBABILITY—0.0 REGION 6♦DRIFT*   SETTING UP REGION 7   IDENTIFIER = 7DATA! 7 . J ) = O.OICOO 7.62COO -7.62000 7.62000 -7.62000UI 7 ) = C.OVACLLM IN THIS ELEMENTOEC.PRCEAEILITY=0.100CE 01 MCDE 1DEC.FRCBABILITY=0.0 MCDE 2TOTAL INTERACTION LENGTH=0.6109E 04 ABS PRCEAEILITY=0.0 3-BCDY DECAY PROBAHILITY=0.O REGION 7♦DRIFT*   SETTING UP REGICN 8   IDENTIFIER = 8CATAI 8 . J ) = 30.48000 lb.24000 -IS.24000 7.62000 -7.62000UI 8 > = 0.0VACLLM IN THIS ELEMENTOEC.FRCEAEILITY-0.1000E 01 MODE 1OEC.FRCEABILITY=0.0 MCDE 2TOTAL INTERACTION LENGTH=0.6109E 04 ABS PROeABI LITY=0.0 3-BCny DECAY PROBABILITY=0.0 REGION 8♦RCTAT*   SETTING UP REGICN 9   IDENTIFIER = 9DATAI S . J ) = 0.0 0.0 0.0 0.0 0.0 UI 9 I = 0.0. oa .ID+/ua.GV*OJco•0!"AzBUJajozzGZ!"zQaD-zHOJ!?G--O'O'O'•j» o   . . %7UJSiG  G< O•cX o c3 II IIa > >X X KD ►X ■_Cr G G'■C X CDC\i < <c cr Cc 3 o• rr DCin 0. a><uO><G3oil X o X' oG Q ■cr D <3-z cv CVJX > • > •□ G□IT O inX 3 1 CD IG 1 1n::G O oG o oz o o<1 'TCM•tf> CVJ>TVJ•UJX o O oX • • II • IIZ c o oo II cr II cr< > X o > X o2. XXoo»-XGoG II G X CVJ G MX CVJz X -4 X vO MX X ■0*-• G X z • X z •u 3 < X r** <. X p«-z Z X u 1 X u 1OJ < a X u <—a Xa 1crX 1X G 1 1G a uO 1 o U) 1 o3 z X 1 o a 1 GG — < 1 o < 1 GX • CVI CMX U) X X CVJ XX 2yop- °•> X z X zcx O' u O' Gu *-• CM o X C\J o MX *xX X G Gu G t : X XX Oj • a o • X o3 • X X 3 G X X G o G< N G u II X a G G II X GX CM U 3 X D — 3 U Q X G G  O UX CM 2 2 XG Go  •• 32 2 XG G3  • • o2G X •— Z Z O K —* z z 3 X X< z O X X Z O X MX S) z OX II X G x X G X XX X 2 X x 2 X X 2 XZ X X o Z X X G Z X X oX G G o u U) G O u UJ G GG X<X oaXX III II X OG 1II M G GX > I/) • • y 1 X Ul • . • G 1 x* X •a X -« o o < I — o 3 < 1 MX OX G X II ff x 1 3 X II II X 1 3 X IIG X > > X 1 H > > X 1 X >j) X x x 1 • h- » - X 1 » XX X z X —< Z 1 Z >-• MX z 1 z MXX w *~ J X X 1 — •-* G X >X 1 CM MX GM-* >—• 1 x  ^ —« •X 1 MX MX M-1UJ U) 2 X X G 1 2 X X G 1 2 X2 G G < < < x  x G <1 <. w  (\J G< M G X X x * ■1 x G X X X * <1 *X G Xa Q U G u □ X M- <J u u U X X G Gs <1 X X X X «!. w X X X X <1 « Xa X > u.•GXQa.•yXQXcr3*U  G > a•GXaX•GXacr*G  G > a•GXaIIC#C  D.3EaB@If)CUtO'oX  O  G  II-zoz#C l7 O' o  0 • • oEff il@zCDtCJ G-  -  -JJ UJ Q OB2G 21OPOGn BT b m,YMbp- Mbp:,mM9b3 MVb94yV 6,Y5fYy 12hKOPRAD IL £ CE CURVATURE- 227.2 CMS,INPUT ANGLE= 0.0 ANuL E£ OF BEND= 45.0026 OUTPUT ANGLE- -0.0026 DEGREESVACUUM IN THIS ELEMENT-  58  -*DRIET* SETTING GE RECICN 14 ICENT IF 1ER - 14DATA! 14 , J ) = 0.161.00 7.62CCC -7.62CC0 15.24000 -15.24000 0(141 = 0.01CC.COOO % OF AFERATUKE COVERED BY MATERIAL WITH DENSITY 1.0300 GM / CC CL MFCS ITIIN CF MATERIAL FELLOWS •Z FRCP CF MATERIALWITH ATOMIC NO Zt.0 C.91570C 1.0 0.C843C0 C.C C.C1/E SCATT.ANGLE = 0.6442E-0J 1/E DISPLACE MENT = 0.S34SE-04 THICKNESS IN RADIATION LENGTHS=0.3607F-0?ICNISATICN ENERGY ICES DISTRIBUTION IS CF LANDAU TYPE,AVERAGE=O.2823F-03 WIDTH=0.5975P—04 GEVINT.FRCEAEILITY=C.8290E 00 UN ATOM 1 RMS ANGLE=0.9647E-01INT.PRCEAEIL1TY=0.1524E 00 UN ATLM 2 RMS ANGLE=0.2212C 00INT .FRCEAEILITY-O.C ON ATCM 3 RMS ANGL E= 0.0DEC .PRCEAE ILI TY=C. ieCGE-01 MCDI 1DEC.PPLEAEILITY=0.C MODE. 2tut a l interaction lengtp = o.4597e C2 ags rrulae1l1ty = o.59550 00 3-scoy decay ppodao1l1ty = o.0♦ DRIFT* SETTING UP REGION 15 IDENTIFIER = 15DATA! 15 . J ) = 150.00000 7.62CC0 -7.(>2000 15.24000 -15.24000U < 15 ) - 0.0VACUUM IN THIS ELEMENTDEC.FRCEAEILITY=C.10C0E 01 VCC1 1OEC.PPCUAEILITY=C.C MCDI 2TOTAL INTERACT ILN L E N GT F = 0 . 6 1 C 9 E 04 ADS RRUE A P I L I T Y = 0 . C 3-BCDY DECAY °RHB A B I L I T Y = 0 . 0♦ 1 M T * SETTING UP RECICN 16 ICEN TI F I ER = ItRANCCM NUMEiER INITIALIZER = 73662497♦ GRCUF*  SETTING UP REGION 17  IDENTIFIER = 17CALCULATIONS TER 3 FLCCKS LE  ^THOUSAND h ACE NORMALIZATION EACTCR = 0. o/ .O  O • •o  o♦ NSPAC* SETTING UP REGION 16 IDENTIFIER = 18NSPACE = C NW =0♦ XSIZEA SETTING UP REGION 19 IDENTIFIER = 19XMAX = O.144C0 DXMAX - C.C400CXC = 0.0 CXMAXC = C.O♦ Y'S 12 E ♦  SETTING UP REGICN 20 IDENTIFIER = 20YMAX = C.C64C0 DYMAX = C.OaOCCYC = 0.0 DYMAXC = C.O♦ FU ♦  SETTING UP REGION 21 IDENTIFIER = 210m r eITQoTo 08px = o.oeccc zm = i.eooooT THR = 0.0♦ MASS ♦ SETTING UF REGION 22 IDENTIFIER = 22MASS = 0.1396 C SIGA = 30.C0000 SIGE = 20.00000TAEO = 0.2606E — 07 SCALE = l.COOOOCECAY MODES : ALF(l) - 1.00 A3III = 0.105E 2pSeC r oALF(2 ) = O.C A 31 2) = 0.0 A4(2) = 0-  60  -IN IRE FGLLGWING T ABUL A T IC N LF RESULTSINITIAL UR INITIALLY MEANS PARTICLES WERE TRACED THROUGH SYSTEM WITH NO DLCAY•SCATTERING,AGSGRPTIUN GR ENERGY LOSSFINAL UR FINALLY MEANS PARTICLES wLWE TRACED THROUGH SYSTEM wITH DECAY,SCATTLRING,AfaSC'RPTIUN AND ENERGY LOSSTCTAL NLMC-LR GF TRIAL FART I Cl ES TRACED THROUGH SYSTEM= 2000NUMbER UF PARTICLES ACCEPTED INITIALLY= 579NUMBER UF PARTICLES ACCEPTED FINALLY^ 528.0PARTICLES INITIALLY REJECTED FRCM TOTAL TRIALSOUTSIDE HORIZONTAL LIMITS OUTSICE VERTICAL LIMITS AT 1 TARG C.C 0.0AT 2 CRIFT 0.0 0.0AT 3 CLAC 0.0 0.0AT A GR IF T C.O C.OAT5CRIFT 0.0 %AT 6 CLAC O.C %AT 7 CFIFT 0.0 250.000AT E! 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Ml <3 II I 3 3 II 3 ZE 3 3 if) 3 a •M3 8f w 3 X Xz < Z 2. « □< 3 3 C/J <3. 3 U) C/iX GE X 3 •* X UJ X 3 oX • X X a; X • 3 o3 3 rj 3 3 oa 3 a 3 3 - o3 z X 3 t\j > □ z 3 Z o o O o O O O o O O o o o • O 2 X O • o O o o o** 3 • • • • • • • • • • • • • •M • 3 LL • CVJ • • • • • Z o O o o o o o o O o O o o O  O o o o o o7 3 O X CVJ >3 o   O <1X  X o wX X X  ? o > 3 3 3 3 3 3 3 3 3 3 > o u H- 3 3 M- o 3 z 3 X o X X %" X  < Q   G  X u o 3  u   u X3 o 3 •M  <1 ** .+ 7 > •-< Ml H — Ml 2 # O   ■— <17 o <  <  3  X 3   3 X X  X X   u . 3 «  3 X  3  *“* o > X 7 a o Q a 3 o G   - a  u a  CVJ O 7 u o - u CJ -3 ■0 M 7 .M XX •  7 cn • II  o < H CVJ ro vO 3 t X O' o CVJ n * X   > X Ml CVJ n U>  N%/ <n 3 .M «M •M 7 « 2II  tn 3 II 3 7s. • 7 H H H H z > H H > H H H H H H Ml •  U H H H H H H H ZX 3 3 Ml Ml *-< *-« i—« *•* »-* Ml Ml Ml Ml 7 7 u Ml Ml Ml M M Ml M7 7   I 7 < 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 * < > < 3 3 3 3 3 3 3 3  > H > H H > H  > H > H > > >  3 %" 3 Z H > > H > >C/J /5 ** "m m Ml IM Ml Ml cn 7 U mm ■M •M PM MW IM7 ■               X  7 •  3 X       < 7 3 3 3 7 7 3 3 7 7 7 7 7 7 3 7 < 3 1 7 3 7 3 7 3 37 7 7 7 3 3 3 3 3 7 7 3 7 7 3 3 3 P* 3 n 3 7 3 3 3 3 7u 3 7 7 7 3 3 3 3 7 3 3 3 3 7 3 3 u 7 3 3 3 3 3 3 37 > □ □ a O 3 U a □ a o □ □ □ U □ 3 2 Q 7 □ □ -  B. ta .o  o  o  oO O O  GO o  O GO O O Jo o o •• O • O O • o  u)$+ . J2 . . %o  o  o  oX ^ U X X U X u .X Q X X X X X XG X X Q Q X Q QJJ O' O -• v\j I*) <f 4) z z z z z z z zG G G O G G U Gx z z z z z z zu  33  3  □ □01u3oAoOJ• MW0  o  sII X X  N N  nI X CM X O' x  CVJ Cal t  Y< o  z3  II -  X3  Q  t  M< X X 3 M3<Zt  tU  d  >  3M  t  X  <1 X G XCXM3in o<r x0 o>1 rr, x O O' oJN -  Pw •^  oUJ• II I  X:II 3Y tV) <1UJ X  X• z2  Qt  r2  3Y tUJ UJ3  X  G  X  Z  U<1 uu 3MW <3  3N  t  cn 3-  68  -C1STRI6LTICNS CF ACCEPTED PARTICLES AS A FUNCTION OF STARTING CONDITIONS OF PARTICLE AT TARGETMCJMENTL M< CE V/C ) POSITION ALONG TARGET(CM)CEV/C INITIAL EEAM FINAL BEAM FINAL.NCTI INI 11AL) CM INITIAL BEAM FINAL BF A M FINAL.NOT(INITIAL1.C6150 37.0000 30.C0O0 O.C -0.475000E-02 55.0000 45.0000 0.01.CE450 27.CCC0 22.COOO 0.0 -0.425000E-02 61.0000 54.0000 2.000001.06750 43.0C00 38.0000 l.COOOO -0.37500OE-02 63.0000 57.0000 0.01.C7050 2 3.CO 00 29.0000 0.0 -0.3250OOE-02 49.0000 50.0000 1.000001.C7250 E9.0CCC 51.CC0C 0.0 -0.275000E-02 62.0000 59.0000 0.01.07650 66.C000 58.0000 0.0 -0.225000E-02 57.0000 52.0000 1.00000I.C795C 63.CCC0 58.0000 0.0 - 0.175C0OE—02 55.0000 53.0000 0.01.C8250 eC.COOO 72.CCCC 0. 0 - 0. 125000E-02 49.0000 41 .0000 1.000001.CE550 64.C0C0 57.COOC O.C —0•7500COE—03 59.0000 51.0000 0.0l.CEEEO 53.CC0C 49.0000 1 .00000 - 0.250000E-03 49.0000 45.0000 0.01.C9150 79.0000 76.C00C 2.C0000 0.250000E-03 55.0000 48.0000 1.000001.CS450 71.0000 65.000C 0.0 0.750000E-03 53.0000 55.0000 I.000001.C9750 75.CCCC 70.C0OC l.COOOO 0.125000E-02 65.0000 59.0000 0.01.10050 67.CC00 62.COCO l.COOOO 0.175000E-02 53.0000 49.0000 0.01.1C25C 57.CCC0 52.0000 0.0 0.225000E-02 57.0000 49.0000 0.01.10650 59.CC00 Se.COOC 0.0 0.275000E-02 65.0000 55.0000 0.01.1C950 63.CC00 55.CC00 0.0 0.325000E—02 49.0000 47.0000 1.000001.11250 44.0CCO 40.0000 0.0 0.375000E—02 63.0000 59.0000 0.01.1 1550 53.0 C 00 51 .0000 2.00000 0.425000E-02 57.0000 54.0000 1.000001.11850 27.0000 33.0000 0.0 0.475000E—02 59.0000 54.0000 0.0PCS IT IC N IN HORIZONTAL PLANE(CM) ANGLE IN HORIZONTAL PLANE I MR)CM INITIAL BEAM FINAL BEAM FINAL.NCT(INITIAL) MR INITIAL BEAM FINAL BEAM FINAL.NOT(INITIAL0.6E4COOE—01 51.0CC0 45.C00C C.C -19.0000 20.0000 13.0000 0.00.612CCCE-01 64.CCCC 54.0000 1.00000 —17.0000 70.0000 61.0000 0.0O.54C000E—01 47.CCCC 44.COOO O.C -15.0000 52.0000 46.0000 0.00.46ECCCE—01 72.0COO 69.C00C C.C -13.0000 64.0000 57.0000 0.00.3960COE—Cl 53.CC00 48.COOO 0.0 —11.0000 71.0000 67.0000 I.00000O.324CC0E-C1 5 2.0 C 00 46.C0CC C.C -9.00000 51 .0000 48.0000 1.000000.252CCCE—01 5I.OCOO 46.000C l.OOCOO -7.00000 51.0000 46.0000 0.0C.ieC000E-0 1 66.CC00 64.COCO 2.0OCOO -5.00000 60.0000 53.0000 0.0O.1C80C0E-01 55.0000 52.0000 2.COOOO -3.00000 61.0000 55.0000 0.0C.26C0CCE — 0 2 74.CCOO 67.COOO O.C —1.00000 59.0 0 00 54.0000 0.00.26CC00E-O2 66.COOO 61.COOC O.C 0.999999 50.0000 48.0000 1.000000.ICeOCOE-Ol 55.0000 50.0000 l.CCOOO 3.00000 73.0000 70.0000 0.0C.ieCOCCF—01 47.CCC0 43.0000 0.0 5.00000 54.0000 52.0000 1.000000.25 20 OCfc —01 51.CC00 45.0000 O.C 7.00000 62.0000 59.0000 1.000000.2240COE—01 S2.GC00 49.000C 0.0 9.00000 59.0000 51.0000 C.O0.396CC0E-01 69.CCC0 63.0000 1.00000 11.0000 69.0000 66.0000 0.00.46E0C0E—01 61.COOO 56.CC0C O.C 13.0000 64.0000 58.0000 0.00.54CCC0E — 01 54.0CC0 49.0000 l.COOOO 15.0000 70.0000 60.0000 0.00.612000E—01 45.CCC0 42.C0CC 0.0 17.0000 64.0000 58.0000 2.000000.6840006—01 55.0C00 42.00GC 0.0 19.0000 16.0000 14.0000 2.00000. t/ .6^POSITION IN VERTICAL PLANE(CM) ANGLE IN VF RTIC AL PLANE!MR)CM INITIAL C-EAM FINAL 6 E AM P IN AL . N G T ( IN I T I AL ) MR INITIAL BEAM FINAL BEAM F I N AL . NO T ( INIT I AL-0.299CGOE-G1 71.CCC0 El.COCO 0.0 -38.0000 0.0 0.0 0.0-O.257GCCE-01 64.CC0C EE.tCCC O.C -34.0000 0.0 0.0 0.0— O•315C C OE — 01 4 3.0 C 0 0 42.0000 l.OLOOO -30.0000 0 .0 0.0 0.0—0.273C00E—01 57.CCC0 54.CC0C O.C -26.0000 5.00000 4.00000 0.0-0.221CCOE-O1 65.CCC0 61.0000 C.C -22.0000 54.0000 48.0000' 0.0-0.1B9CCCE-01 57.CCC0 51.0000 0.0 -I8.000C 85.0000 78.0000 1.00000-0.I470C0E—01 49.0CC0 4E.C0CC 2.CO000 -14.0000 97.0000 91.0000 3.00000—0.1C5CCCE—01 41.0CC0 39.0000 l.OOCOO -10.0000 97.0000 90.0000 0.0$ 0.63CCCOE—02 61.C000 E4.CC00 l.CCOOO -6.00000 128.000  18.000 -0.210OOOE-02 50.CC00 39.C000 l.COCOO -2.00000 130.000 119.000 C.OC.21CCCCE—C2 55.CCC0 55.0000 2.C0C00 2.C0000 1 10.000 101.000 1.000000.629999E-02 58.CCC0 49.C00C O.C 6.00000 99.0000 86.0000 0.00.1C50C0E—01 65.0000 56.COCO C.C 9.99999 111.000 100.000 1.000000. 1470CCE — 01 66.C 000 61 .0000 0.0 14.0000 92.0000 83.0000 1.00000O.ie9CCCE-0I 51.CCC0 43.C00C O.C 18.0000 -32.0000 77.0000 0.00.2310OOE — 01 60.COCO 57.CC0C O.C 22.0000 45.0000 36.000 0 0.00.273CCCE — 01 59.CCCC 54.C00C O.C 26.0000 5.00000 5.00000 0.00.2150006-01 52.CC00 47.000C 0.0 30.0000 0.0 0.0 0.00.357CCCE-C1 S6.CCC0 55.0000 l.OOCOO 34.0000 0.0 C.C 0.00.3990006 — C1 6C.CC00 S2.CC00 0.0 38.0000 0 .0 0.0 0.0CENIRAL VALUES AND WIDTHS CF C I STRI ELTICNS IN STARTING MOMENTA ANC ANGLES (THESE RESLLTS ARE ROUGH ESTIMATES CNLY-FCR ACCURATE VALUES THE OISTRI8UTIONS SHOULD BE PLOTTED)INITIAL EE AM FINAL i3E AM CENT Rt WIDTH CENTRE WIDTHMEMENTUM(CEV/C ) 1 .09 0.465E-01 1. 39 0.422E-01 HCRIZCNTAL ANGLE < MP ) 0.189 42.5 0.320 41.4VERTICAL ANC-LE(MR) -0.347 27.5 -C.479 36.9. a- .IN INE FCLLCV ING TAEULATICN OF RESULTSINITIAL OF INITIALLY MEANS FAKTICLES WERE TRACED TFRUUGH SYSTEM WITH NO DECAY.SCATTERING*ABSGRPTICN CR ENERGY LOSSFINAL OR FINALLY MEANS PARTICLES WERE TRACED THROUGH SYSTEM wlTH OECAY * SCATTERING* ViSURPTION AND ENERGY LOSSTCTAL NLMEER OF TRIAL PARTICLES TRACED TFROUCF SYSTEM= 6000 NUMBER OF PARTICLES ACCEPTED INITIALLY^ 1714 NUMBtR UF PARTICLES ACCEPTED FINALLY= 1554.PARTICLE S INITIALLY REJECTED FRCM TOTAL TRIALSOUTSIDE PCRIZONTAL LIMITS OUTSICE VERTICAL LIMITS AT 1 TARC O.C 0.0AT 2 DRIFT O.C C.OAT 3 CLAC C.O 0.0AT 4 DR IFT C.C C.OA I 5 CRIFT 0.0 C.OAT t CLAC C.C C.OAT 7 CRIFT 0.0 1C42.00AT 6 CRIFT C.O 468.000AT 9 RCTAT C.C 0.0ATIOEENC 0.0 C.C AT 11 CRIFT 1429.00 0.0AT 12 CRIFT 202.000 0.0AT 12 EENC 0.0 C.OAT 14 CRIFT 636.000 0.0AT 15 DRIFT 296.COO 111.000PARTICLES FINALLY REJECTED FROM THOSE INITIALLY ACCEPTEDENERGY TCC LUW MULTIPLY SCATTERED OUT ABSORBED 3-ODDY DECAYS TOTAL NUMBER REJECTED AT 1 TARG O.C 0.0 0.0 0.0 0.0AT 2 CPIFT 0.0 O.C 0.0 0.0 0.0AT 3 CUAC 0.0 0.0 0.0 0.0 0.0AT 4 CRIFT C.C 0.0 0.0 0.0 0.0AT 5 CRIFT 0.0 0.0 C.O 0.0 1.00000AT 6 CLAC 0.0 0.0 0.0 0.0 0.0AT 7 CRIFT C.O 0.0 0.0 0.0 2.00000AT 8 CRIFT O.C O.C 0.0 0.0 5.00000AT 9 RCTAT 0.0 0.0 0.0 0.0 0.0AT 10 EENC 0.0 0.0 0.0 0.0 0.0AT 11 CRIFT C.O O.C 0.0 0.0 55.0000AT 12 DRIFT 0.0 0.0 0.0 0.0 11.0000AT 13 B E N C C.O 0.0 0.0 0.0 0.0AT14CRIFT 0.0 C.C 1.76645 0.0 42.0000 AT15DRIFT C.C 13.0000 0.0 0.0 55.213 5,cuo!"oooom.  ai .PARTICLES FINALLY ACCEPTED FRCM THCSE INITIALLY REJECTED BECAUSE OF INTERACTIONS OF THE FOLLOWING TYPESCATTERING FROM NUCLEUS 1 SCATTERING FROM NUCLEUS 2 SCATTERING FROM NUCLEUS 3 DECAY-MODE 1 DECAY-MODE 2OCCURING IN 1 TANG 0.0 0.0 0.0 0.0 T.OOCCUR ING IN 2 DRIFT 0.0 0.0 0.0 0.0 0.0OCCURING IN 3 CUAC 0.0 0.0 0.0 0.0 0.0OCCLRING IN A DRIFT 0.0 0.0 0.0 0.0 0.0OCCUR TNG IN E DRIFT 0.0 0.0 0.0 1 .00000 0.0OCCLRING IN 6 CLAC 0.0 0.0 O.C 0.0 0.0OCCURING IN 7 DRIFT 0.0 0.0 0.0 0.0 0.0CCCURING IN E DRIFT 0.0 0.0 0.0 1.00000 0.0CCCURING IN 9 RCTAT 0.0 0.0 0.0 0.0 0.0OCCLRING IN 1C BEND 0.0 0.0 0.0 0.0 0.0CCCURING IN 11 DRIFT 0.0 0.0 0.0 0.0 0.0OCCLRINC- IN 12 CRIFT 0.0 0.0 0.0 0.0 0.0OCCLRING IN 13 BEND 0.0 0.0 0.0 1.00000 0.0OCCLRING IN 14 DRIFT 0.0 C.O 0.0 0.0 0.0OCCLRING IN IE DRIFT 0.0 0.0 0.0 2.00000 0.0TCTAL EXTRA PARTICLES PL T INTO BE AM(SUMME D LVER ALL REGIONS)MULT.SCATT •— 0.8CCCCCE 01 NUC.SCATT= 0.0 OECAY MODE 1= 0.500000E 01 DECAY MODE 2= 0.0 TOTAL= 0.130CPARTICLES FINALLY REJECTED FRCM THOSE INITIALLY ACCEPTED BECAUSE OF INTERACTIONS OF THE FOLLOWING TYPESCATTERING FROM NUCLEUS 1 SCATTERING FROM NUCLEUS 2 SCATTERING FROM NUCLEUS 3 DECAY-MODE 1 DECAY-MODE 2OCCLRING IN 1 TARG 0.0 0.0 0.0 0.0 0.0OCCLRINC IN 2 CRIFT 0.0 C.O 0.0 30.0000 0.0OCCLRING IN 3 CLAD 0.0 0.0 0.0 14.0000 0.0OCCURING IN 4 DRIFT 0.0 0.0 0.0 0.0 0.0OCCLRINC- IN 5 DRIFT 0.0 0.0 0.0 3.00000 0.0OCCLRING IN t OU AO 0.0 0.0 0.0 5.00000 0.0OCCURING IN 7 DR IF T 0.0 0.0 0.0 ' 0.0 0.0 OCCLRINC- IN B DRIFT 0.0 0.0 0.0 1 1 .0000 0.0OCCLRING IN 9 RCTAT 0. 0 0.0 0.0 0.0 0.0CCCURING IN 10 BEND 0.0 0.0 0.0 36.0000 0.0OCCLRING IN 11 DRIFT 0.0 0.0 0.0 0.0 0.0OCCLRING IN 12 DRIFT 0.0 0.0 0.0 18.0000 0.0OCCLRING IN 13 BEND 0.0 C.O 0.0 29.0000 0.0OCCLRING IN 14 DRIFT 1.21354 0.0 0.0 0.0 0.0OCCURINC- IN 15 DRIFT 0.0 0.0 0.0 5.00000 0.0TCTAL PARTICLES REMOVED FROM B E A M(SUMME D OVER ALL REGIONS)MLLT.SCATT.= 0.19CCOOE 02 NUC.SCATT= 0.121354E 01 OECAY MODE 1- 0.151000E 03 DECAY MODE 2= 0.03-BCCY UECAY= C.C ABSC’RPTICN= 0.178645E 01 TCTAL- 0.173000F 03TCIAL NUMBER OF DECAY PRODUCTS FINALLY ACCEPTED FRCM DECAYS OCCURING IN 1 TARG 0.0OCCLRING IN 2 DRIFT 2.00000CCCURING IN 3 CUAD 0.0OCCLRINC IN 4 CRIFT 0.0OCCLRING IN 5 DRIFT 1.00000OCCURING IN 6 CUAC 0.0OCCLRINC- IN 7 CRIFT 0.0. ab .01UJro«in.Bi cu • —« o  o  III X  X  O0  NX Cvja c  4:  in ro-J •< ozB ff—  IX»- uU IX<  a.(X UJ LL-J<Z <j o  \  — > k-LU Uu <1 x B  '<IXUJ►- —  l/J o<r 4:o o o oO o o o 1 <7»<J o o o X CVIo J o o o oo o • • 00 <-*•o • o o CV! o m >a—• • CVJ • • • ro 00 •o o o o oU)• IIo Xu►- h- ►“ H- H* II H*x <a. CJ X X G X X • u•-* ►- z —•*■* z •m U) <a: u X) X X X X X X XQ X UJ y Q X G u X• z2 □cu O' o CVJ IO •a- X u-* ■"* •H 2 b# uz z z z z z z z X X*■*—< ►M»■* «—< 1^4 J XVJ Xo VJ CJ VJ VJ VJ VJ VJ z oz z z z z z z z «v VJ"■ •■* —•"M**X X X X X X X X u J3 J J D D -> J J <U u <J u u u u u -J h>m: VJ u VJ <J U w Vj □ o□ □ □ a o 3 □ u </) K. a2 .DIS7H IfeGTIONS LF ACCEPTED PARTICLES AS A EUNCTILN OF STARTING CONDITIONS OF P AH TI CL F AT TARGETMUMENTCM(CEV/CI POSITION ALONG T ARGET(CM)GEV/C INITIAL LEAN FINAL EF AM F INAL . NCT( INIT IAL ) CM INITIAL BEAM FINAL BEAM FINAL.NOT( INITIALI1.06150 ei.OCOO 52.CCOC 0.0 -0.475000E-02 7d.0000 gl.cooo 0.01.0645C 55.CC00 AS.0000 0.0 -0.A2500OE-02 94.0000 86.0000 3.000001.C £ 7 £ C £4.0000 57.C000 1 .00000 -0.375000E-02 91.0000 81 .0000 0.01.C70E0 £ 1 .C C C 0 55.00CC C.C -0.3250 0 0E-0 2 84.0000 80.0000 1.00000I.C725C S2.CC00 E3.C00C C.C - 0.275C0CE-02 88.0000 83.0000 0.01-C765C 98.COCO E7.C000 0.0 -0.225000E-02 78.0000 70.0000 1.000001.C7950 95.0000 84.CC0C 0.0 - 0. 175 0 0OE—02 78.0000 73.0000 0.01.CE250 113.000 101 .000 0.0 - 0. 12500OE—02 86.0000 73.0000 1. 000001.CES50 ICO.COO E6.CC0C 0.0 -0.75000OE-03 96.0000 86.0000 0.01 • C t 6 5 C E5.CCC0 EC.CCCC 2.CCOOO - 0.25000CE-03 83.0000 75.0000 0.01.C9150 1C6.CC0 9 8 .COCO 2.C0000 0.250000L-03 79.0000 70.0000 2. 000001.C9450 111.000 1C1.00C 0.0 0.750000E-03 88.0000 82.0000 1.000001.C975C 119.000 lll.GOC l.CCCOO 0.125000E-02 95.0000 86.0000 1.000001.10050 104.000 97.0000 2.CCC00 0.175000E-02 77.0000 70.0000 0.01.10250 82.0000 75.CCC0 O.C 0.225000E-02 82.0000 72.0000 0.01.1C65C 91.0000 E9.C000 2.C0C00 0.275000E—02 97.0000 81.0000 0.01.1C95C Ee.OCOC 7 6•C 0 0 C 0.0 0 .3250 0GE-02 79.0000 77.0000 1. 00 0001.11250 63.0CC0 58.COOC 0.0 0.37500CE-02 36.0000 80.0000 0.01.11550 C9.CCOO £5.0000 3.C0000 0.425000E-02 85.0000 82.0000 2.000001.11650 57.CCC0 5C.CC00 0.0 0.475000E-02 88.0000 82.0000 0.0PCSITICN IN HURIZONTAL FLANE(CM) ANGLE IN HORIZONTAL PLANE(MR)CM INITIAL EE AM FINAL 6 E AM FINAL.NOT( INITIAL) MR INITIAL BEAM FINAL BEAM FINAL.NOT( INIT IAL)— 0.6E4CCCE — 01 79.CC00 69.COCO 0.0 -19.0000 28.0000 20.0000 0.0— 0.612CC0E — 01 93.0000 EO.CCOO l.CCOOO -17.00 0 0 , 92.0000 83.0 000 0.0— 0.54CCC0E —01 74.CC00 69.0000 0.0 -1 5.0000 77.0000 68.0000 0.0-0.468CC0E-O1 98.0CC0 9C.CCC0 l.COCOO -13.0000 94.0000 87.0000 0.0-0•3960COE-O1 93.0CC0 fcj.COOO O.C —11.0000 106.000 96.0000 I.00000— 0.224CCCE-C1 77.CC00 70.0000 O.C —9.00000 88.0000 83.0000 1.00000i;i ;% 77.0000 F%% -7.00000 82.0000 75.0000 — 0.18C0CCE — 01 96.CC00 92.0 0 00 2.CCC00 -5.00C0C 87.0000 73.0000 0.0-0. 1 C8CC0E-01 E5.0CC0 82.COCO 3.COOOO -3.00000 80.0000 73.0000 0.0-O.36CCC0E-O2 91.CC00 E4.C00C 0.0 -I.00000 87.0000 81.0000 1.000000.36CCC0E—02 93.0000 67.COCO 1.00000 0.999999 82.0000 75.0000 1.00000O.ICeOOOE-Ol EC.CCCO 73.0CCC 1.00000 3.00000 102.000 94.0000 0.00.16COCOE-OI 77.CC00 69.CC0C O.C 5.00000 89.0000 87.0000 2.000000.252CCCE-01 9C.0CC0 79.0000 0.0 7.00000 99.0000 92.0000 2.000000.2240C0E-01 85.0CC0 79.CC0C 0.0 9.00000 84.0000 74.0000 0.00.296CC0 E —01 E7.C0CC 60.0000 l.CCOOO 1 1 .0000 102.000 95.0000 0.00.46EOCCE-01 93.0C00 65.0000 0.0 13.0000 100.000 90.0000 0.00.54CCC0 E —01 77.0000 £9.0000 2.C0000 15.0000 100.000 8e.OOOO 0.00.612CC0E—01 73.0000 66.0000 0.0 17.0000 101.000 92.0000 2.000000.6E4CCCE — 01 68.CCC0 69.COCO O.C 19.0000 34.0000 28.0000 3.00000. aL .© o o o o o o oz o o o o o o o© o o o o o o ow o o o o o o o© o o o o o o oo © o o o o • • o • o • • • • o o o o o oz • • • • • © © • CVJ • CVJ mrn cv cv • • • • • •9 o o o c o c o © c o o o oX<o c o c o o o o o c o o o o5. o o c o © o o o c o o o o o< o o o o o o c c c o c c o QL.’ o o • • • • • • • • • • o cA OO o • © sO n © mm IP o —1 © rv • oCL o c o • © ro n rv IP !T cv mm so • c o oz -J • • • If) N © © © © mm mm — © mm mm vp • • •< o o o o o oZ<Ja< <t o o o o o o o o o o o o o o© t : c c c o o o o o © o o c o o© 'R: o o o © o o o o o o o o o o© o o • • • • • • • • • • o oX J o • rnm o © ro © o o rv © ro • cUJ < o o o • ■tf cv in CO cc N Q SO W) cv N • o o o> © • • • CO CO © mm © mm mm rnm rnm © mm mm* s X • • •© o o o o o oxoz< ooo0 • CJro1o  o o o o o o o0  X C\JK  c\j )L1 I Io o o o o o o oo o o o o o o oa-IaUJccaXD0XinnzQm m m «3 «><I I0 0 ^ 5Cvi n  n  roX  X k- <if) X  © T <  Qcz<o X  I©  Uj Q © X © O •S  if) OuJa< CD D k- o mm ao mm— z J z • in mmk- mm < X — • • X© o o o o o o o o o H > u o o Xz o o o o o o c o o X 1 X© o o o o o o o o o < X Xo o o o o n © © © H H Dk- o CJ CJ CJ CJ © © o © </J < zu o o t • o o • • • • • o o o • o © © • o Cl —z • • © mm • • n cv mm mrn LV • • • • • • mm • z X © z• o o o o o o o o o © o mm © 1 uX V X X ©< ip < © M mm o ©z z < □ cv 9 • <— u X IJ —< cn © oo XX LL u X JC • n X© ►- X o ©W -P 1 X XUJ o o o o o o o CJ o o © o © o c o © © © o X > < <1z X o o u o o o o CJ o o o o o © o o o a o o X —* ©< < o o o o CJ o o a a o o o © o o o o © o o z k"X ill © © o o CJ o o CJ u a © o © © o © © u © o u ta- ©± X • • t • • • • • • • • • • • • • • • • • if) z zCT) cu IP cf cv mm cv so *■ P) ■«u V cu X 1*) lT) X mm >-m in «-* ©-J -I CO cu r^ . rv CU (V rv u rv O' fv UJ •u •0 •JJ X rv rv rv L) X JE< h- X O' r* mm uVJ z u. < LL o VU o ©© mm X z © • <r cv Xk- LL ta­ z —« • • QX cn k­ X o o XX X en © 1> K X Ds Q Xz < o o o o o o o o o o o o o o o o o © o © X X© LU a o o o o o o o o o o o o o © © o © o © o -* © X•X o o •Cj o CJ CJ CJ CJ © o © © o © © © o © o © X © a LL ©z • CJ o o o CJ CJ a © o © © • o o © o © o © u u N X X zu vv • • t • • • • • • • • mm • • • • • • • z IX > © W X—« < o cu rv CO CJ mm SO SO rv 7* VO ■0 © X X o CV n cv < X X X u u© © © O' rv rv J* UJ |V V LU (V s* CU mm O' rv Uw O' UJ X X X © X X © X© K m X w © © z ©V) X < z z z Xco 2; D D •a < za. © J © X ©mm © rnm mm mm mm Csi cv cv sV mm — •m mrn •m <1 cn z X X X Xo CJ o o CJ Q o o o o o o o o o o o o o o > H X < < © XI 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X i © © X XLU JJ UJ UJ UJ t : UJ UJ t : LU UJ UJ UJ UJ u UJ UJ UJ X X X X © z ta* © ©o CJ o CJ CJ o CJ o O o o J 1 © o o o © © © © in X © © Xo CJ CJ CJ o O CJ CJ © © o cr © o © © © © © © a X ’N LL X zVJ CJ o CJ o CJ CJ o © o o C7L© © J o a © © © k» a ta- X ©x O' rv If) mm O' rv UJ © © o O' UJ rv O' n UJ rv O' z X > Q© VT Ui wm |V I'i CJ V «• mm cv © mj rv mm UJ 0’ X X u z ©Hi 1') n CV cv mm mm VJ sv LV UJ m* mm mm cv ‘V t'J n © in i X X ©• • 9 t • 9 • • t • • • • 9 • • • • • • X u ©o o o o o o o Q o o © o © o © o o © o o i © X1 1 1 1 1 1 1 1 1 1 H in Xs- X. ao .ACKNOWLEDGEMENTSI would l i k e  to thank Dr.  G. St i nson  f o r  w r i t i n g  the data input  sub­rout i ne  READ. T h i s  is a g reat  improvement on my o r i g i n a l  ve r s ion  and makes the program much e as i e r  to use.  I am a l so  indebted to him f o r  many he lp fu l  d i scuss ions  and comments and f o r  h i s  ass i s tance  in debugging the f i na l  vers i o n .REFERENCES1 . R.W. W i l l i ams ,  Rev.  Mod. Phys.  36 (1964)  8152. See,  f o r  example,  H. Go ing ,  Z.  Na tu r fo r sch .  18a (1963)  1CMOO3. G. Mo l i e r e ,  Z.  Na tu r fo r sch .  2a (1947)  133,  3a (1948)  18,  Nuovo Cimento 7 (1958)  720;  Z.  Phys ik  156 (1959)  31810a (1955)  177;4. W.T .  S c o t t ,  Rev.  Mod. Phys.  35 (1963)  2315. U. Fano,  Ann.  Rev.  N u c l . Sci  . 13 (1963)  16. L.  Landau,  J .  Phys.  (USSR) 8 (1944)  2017. L . C . L .  Yuan and C. S.  Wu, Methods of Experimental Physios, Vol  5A p . 17,  (Academic P ress ,  New Yo rk ,  1961)8. R.M. S te rnhe imer ,  Phys.  Rev.  88 (1952)  8519- B. Ross i ,  High Energy Particles, Ch.  5 ( P r e n t i c e - H a l 1 , New York ,  1952)10. H. Bethe and W. H e i t l e r ,  Proc .  Roy.  Soc.  (London)  A 146 (1934)  8311 . K. L .  Brown and S .K .  Howry,  SLAC Report  No. 91 (1970)

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