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What np elastic scattering data are needed from 200 to 520 MeV? Bugg, D. V. (David Vernon) 1975

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T R I U M FWHAT NP ELASTIC SCATTERING DATA ARE NEEDED FROM 200 TO 520 MeV?D.V. Bugg*Queen Mary C o l le g e ,  London^P resen t add ress :  TRIUMFMESON F A C IL I T Y  OF:UN IVERS ITY  OF ALBERTA SIMON FRASER UN IVERS ITY  UN IVERS ITY  OF V IC TOR IA  UN IVERS ITY  OF BR IT ISH  COLUMBIA TR I-75 -5TRI-75 -5TR IUM FWHAT NP ELASTIC SCATTERING DATA ARE NEEDED FROM 200 TO 520 MeV?D.V. Bugg*Queen Mary Co l lege ,  London-'Present add ress :  TRIUMFPosta l  address :TRIUMFU n i v e r s i t y  o f  B r i t i s h  Columbia Vancouver,  B.C.Canada V6T 1W5 December 19751 . I n t r o d u c t  ionPresent  np e l a s t i c  s c a t t e r i n g  data in t h i s  energy range are r a t h e r  sparse .  They c o n s i s t 1 o f  severa l  measurements o f  da/df t  (which f r e q u e n t l y  d i f f e r  s y s t em a t i c a l l y  by severa l  t imes t h e i r  quoted e r r o r s ) ,  p o l a r i s a t i o n  data (mos t ly  f rom quasi  — e 1a s t i c  pn s c a t t e r i n g  in d e u te r i um ) ,  and i s o l a t e d  measurements o f  t r i p l e  s c a t t e r i n g  parameters (aga in  f r e q u e n t l y  f rom d eu te r ium ) .  A t temp ts  a t  phase s h i f t  ana lyses  have been made.2 However, w i t h o u t  the  s t r a i t  j a c k e t  imposed by ene rgy-dependen t  a n a l y s i s ,  t h e re  are am b ig u i t i e s  and la rg e  e r r o r s  in the  s o l u t i o n s .  In severa l  cases i t  is  c l e a r  t h a t  some e x i s t i n g  data must be in e r r o r ,  bu t  i t  is  hard t o  say wh i c h .The BASQUE expe r imen t  i s  in tended t o  r e c t i f y  t h i s  s o r r y  s t a t e  o f  a f f a i r s .  The f o l l o w i n g  measurements are p lanned in f r e e  np s c a t t e r i n g :WHAHTHWN HAN HTN (55-125 deg,  10 deg s t e p s ,  ± 0 .03)P (55-125 deg, 10 deg s t e p s ,  ± 0 .02 )da/df t ( 5-180 deg, 5 deg s te p s ,  ±1%  ) .Below 520 MeV, measurements o f  Dy, Ry, ar>8 Ay w i l l  n o t  ex tend  f u l l y  to  55 deg, because o f  a 110 MeV requ i remen t  on the  energy o f  the  r e c o i l  p ro ton  f o r  good a na ly s in g  power in ca rbon .  However, i t  is  p o s s i b l e  t o  ex tend  the Dy, Ry, and Ay measurements towards  180 deg i f  t h i s  is  necessary .The o b j e c t i v e  o f  t h i s  r e p o r t  is  to  assess q u a n t i t a t i v e l y  what  the impact w i l l  be o f  each measurement, so as t o  s e l e c t  the  most economical  and d e f i n i t i v e  s e t ,  and t o  assess whe the r f u r t h e r  measurements might  be necessary .  P resen t  u n c e r t a i n t i e s  are  such t h a t  the  conc lus ions  can o n l y  be t e n t a t i v e .2.  P resent  DataPresen t  pp and np da ta  are used in s i n g le - e n e r g y  phase s h i f t  ana­l yses  a t  210,  320, 425 and 520 MeV. A t  a l l  e n e rg ie s ,  1=0 phases a re  v a r i e d  up t o  and i n c l u d i n g  3G5 , and 1=1 phases up t o  3H6 . The va lue  o f  g2 is  f i x e d  a t  14 .4 .  The reasons f o r  r e l e a s i n g  a l l  1=0 G-waves are t h a t  ( i )  a t  210 and 425 MeV, where the  phase s h i f t  s o l u t i o n s  are  reasonab ly  s t a b l e ,3G3 is  s i g n i f i c a n t l y  d i f f e r e n t  f rom OPE, ( i i )  the  OPE va lue  o f  3G1+ is  la rge  (9 .2  deg a t  425 MeV), and ( i i i )  in pp s c a t t e r i n g ,  1Glt i s  known to  d ev ia te-  2 -s i g n i f i c a n t l y  f rom OPE. Table I  shows x 2 as success ive  G-waves a re  f i x e d  a t  OPE va lues  .Data f rom pd s c a t t e r i n g  have no t  been c o r r e c t e d  f o r  r e s c a t t e r i n g  e f f e c t s ;  these a re  expec ted  to  be a t  the  1 t o  10% l e v e l ,  depending on the geometry o f  the measurement. So the e r r o r s  quo ted  f o r  some p re sen t  da ta  may be o p t i m i s t i c .  Data a t  210 MeV f rom pd s c a t t e r i n g  above 160 deg have not  been used, because o f  the  la rge  s y s tem a t i c  e f f e c t  o f  the pp f i n a l  s t a t e  i n t e r a c t i o n . 3A t  210 MeV, the  phase s h i f t  s o l u t i o n  is  s t a b l e  enough t h a t  one has some con f idence  in p r e d i c t i o n s  f rom i t .  A t  320 MeV, the  s o l u t i o n  is  ve ry  p o o r l y  d e f i n e d ,  and the  v i c i n i t y  o f  the  x 2 minimum is  sha l low  and w r i n k l e d .  A t  425 MeV, the  s o l u t i o n  i s  j u s t  s t a b l e ,  bu t  im p re c i s e .  At  520 MeV, no s t a b l e  s o l u t i o n  is  found un less  one o f  the low 1=0 p a r t i a l  waves i s  f i x e d ;  a r b i t r a r i l y ,  3S1 has been f i x e d  a t  -12  deg in  o r d e r  to  f o r c e  a s o l u t i o n .The dcr/dft da ta  f rom P r i n c e t o n 4 pose a se r io u s  problem a t  320 MeV and above.  A ppa re n t l y  o f  h igh  accuracy  they  d i f f e r  s y s t e m a t i c a l l y  in  shape f rom L i v e r p o o l 5 (350 MeV) and Ca rneg ie6 (400 MeV) da ta  by many t imes  the  quoted e r r o r s .  I f  the l a t t e r  two se ts  are d i s c a rded ,  one s t i l l  cannot  ge t  a f i t  w i t h  a reasonab le  x 2 • At  320 MeV, f o r  example,  x 2 is  604 f o r  111 deg o f  f reedom, w h i l e  i f  the  L i v e rp o o l  data a re  used in s tead  x 2= 76 f o r  69 deg o f  f reedom. The e f f e c t s  o f  the  P r in ce to n  data are ( i )  t o  f o r c e  the  f i t t e d  va lues  o f  do/df i  t o  ve ry  h igh  va lues  near 0 deg and 180 deg,  ( i i )  t o  f o r c e  an unreasonab ly  h igh  va lue  o f  cry,  and ( i i i )  t o  r e q u i r e  a n o rm a l i z a t i o n  cons ta n t  o f  0 .6  t o  0 . 7 .  For these reasons the  P r in c e to n  data  have been om i t t e d  a t  a l l  e n e rg ie s .3.  The E f f e c t  o f  New DataWe assume t h a t  e x i s t i n g  da ta  w i l l  be supplemented by measurements o f  D, R ,  and R '  in  pp s c a t t e r i n g  in  the  range 10 t o  50 deg;  measurements are p lanned both  a t  TRIUMF and SIN.  These data w i l l  a c t  as an im po r ta n t  con­s t r a i n t  on h igh  p a r t i a l  waves in the 1=1 s t a t e  and on g2 . When h y p o t h e t i ­cal  new np data  a re  added,  one f i n d s  a remarkab ly  c o n s i s t e n t  p i c t u r e  a t  a l l  e n e rg ie s :  two d i r e c t  and t r a n s f e r  W o l f e n s te in  parameters  ( e . g .  D, R,  Dy ,Ry)  are  r e q u i r e d  f rom 55 deg t o  125 deg,  1% measurements o f  da/df i  o ve r  the-  3 -f u l l  a ngu la r  range in bo th  pp and np, and l i t t l e  e l s e .  Ins tead  o f  one o f  the  W o l f e n s te in  parameters one cou ld  s u b s t i t u t e  PEEH bu t  one can do w i t h ­ou t  i f  enough Wo l f e n s te in  parameters a re  measured.  In the angu la r  range 125 deg t o  180 deg, measurement o f  one o f  the  t r a n s f e r  parameters ( u s u a l l y  Dy) is  u se fu l  in  p in n in g  down r e s id ua l  u n c e r t a i n t i e s ,  bu t  doesno t  have the same d rama t i c  e f f e c t  as measurements near 90 deg.Tables I I ,  I I I  and IV  i l l u s t r a t e  t h i s  argument in d e t a i l  a t  f o u r  e n e rg ie s .  At  p re sen t ,  Cnn measurements a re  no t  p lanned in  np s c a t t e r i n g  in  t h i s  energy range,  so the t a b le s  c o ncen t r a te  on a se t  o f  measurements o m i t t i n g  C^n- I t  wou ld ,  however,  be a u se fu l  paramete r ,  and Table  I l l ( a )i l l u s t r a t e s  in  the  l a s t  f o u r  rows j u s t  how use fu l  a t  210 MeV. The t a b le sa re  s im p l i f i e d  by the assumpt ion  t h a t  d i r e c t  and t r a n s f e r  parameters ( e . g .  D and Dy) w i l l  be measured s im u l t a neous l y  where t h i s  is  k i n em a t i c a l -  1y poss i b l e .3.1 210 MeVI f  do/dSI cannot  be measured t o  1% accu racy ,  a l l  the  Wo l fens te in  parameters D, Dy,  R,  R y ,  A and Ay p la y  a v a lu a b le  r o l e .  Table I l ( c )  shows t h a t  s i z a b l e  e r r o r s  p e r s i s t  in p r e d i c t i o n s  c lo se  to  0 and 180 deg, many o f  them in  parameters e x p e r im e n t a l l y  i n a c c e s s ib l e ,  namely d i r e c t  parameters near 180 deg (s low r e c o i l  n eu t ron )  and t r a n s f e r  parameters near 0 deg (s low p r o t o n ) .  The most d e c i s i v e  way o f  e l im i n a t i n g  these u n c e r t a i n t i e s  i s  by 1% measurements o f  da/df t  o ve r  the f u l l  a ngu la r  range;  t h i s  is  a p a r ­t i c u l a r l y  d i f f i c u l t  measurement near 0 deg. i f  i t  is  f e a s i b l e ,  A and Ay (60-120 deg) become r a t h e r  redundant ;  however, in  v iew o f  the  d i f f i c u l t y  o f  np measurements,  one shou ld  perhaps regard  A and Ay as a va lu ab le  c ross -check  a g a in s t  s y s tem a t i c  e r r o r s .  From Tables I l ( d )  and I l l ( a )  one sees t h a t  Dy (130-170 deg) is  a l s o  a use fu l  though no t  c r u c i a l  measurement. F i n a l l y  A '  (13 deg) is  d e s i r a b l e ;  the  need f o r  i t  o r i g i n a t e s  f rom inade­quac ies  in p re sen t  pp data ( i . e .  u n c e r t a i n t i e s  in 1=1 phases) ,  and could  be removed by 1% measurements o f  da/df i  (5-20 deg) o r  2.5% measurements o f  A '  in  the  range 10 t o  50 deg in pp s c a t t e r i n g .I f  PEE  cou ld  be measured in np s c a t t e r i n g ,  i t  would be a powerfu l  measurement. In every  one o f  Tables I l ( a ) - ( d )  the  e r r o r  in  t h i s  q u a n t i t y  s tays  p e r s i s t e n t l y  h igh  compared w i t h  o t h e r  obse rvab le s .  I t  is  the-  4 -parameter  most s e n s i t i v e  to  3 S 1 . However, as one sees f rom l i n e  13 o f  Tab le  1 11 (a ) ,  Cnn i s  no t  e s s e n t i a l  i f  da/df t and enough W o l f e n s te in  param­e te r s  a re  measured t o  the r e q u i r e d  accu racy .A s u b s i d i a r y  b e n e f i t  o f  the  np measurements is  a n o t i c e a b l e  improve­ment in  the  e r r o r s  o f  1=1 phases [Tab le  V ( a ) ] ,  r o ugh ly  a f a c t o r  2 in ( e r r o r ) 2 . I t  o r i g i n a t e s  l a r g e l y  f rom D and R (symmetr ic  about  90 deg) .They a re  as e f f e c t i v e  as d i r e c t  measurements on the pp system in the  same a ngu la r  range,  and e l im i n a t e  the  need7 f o r  pp measurements o f  D and R near 90 deg .3.2  320 MeVAga in ,  measurements o f  PDRADyRyAy(55- 125 deg) p lu s  1% measurements o f  da/df tnp (5-180 deg) a lmost  comple te  the  ta s k  o f  reduc ing  e r r o r s  on a l lobse rvab les  t o  the  a r b i t r a r y  l i m i t s  s p e c i f i e d  in the I n t r o d u c t i o n .  At  t h i senergy A and Ay appear more u se fu l  than R and Ry.  A few r e s id u a l  e r r o r s  s u r v i v e  near 0 deg and 180 deg on obse rvab les  wh ich  a re  e x p e r im e n t a l l y  i n a c c e s s i b l e .  However, u n l i k e  the  s i t u a t i o n  a t  210 and 425 MeV, Dy,  Ry and Ay in  the  reg ion  130 t o  170 deg do no t  appear f a v o u ra b le  f o r  r e s o l v i n g  these e r r o r s  un less  an accuracy  o f  ±0.015 is  ach ieved .  Cnn (130-170 deg) does a much b e t t e r  j o b .  To e l im i n a t e  u n c e r t a i n t i e s  in  1=1 amp l i tudes  near 0 deg, one wou ld  l i k e  1% measurements o f  da/df t (5 - 20 deg) and 2.5% measure­ments o f  A and A '  in  the  range 10-50 deg in pp s c a t t e r i n g .3.3 425 MeVHere the  o n l y  pp measurement r e q u i r e d  is  da/df t  t o  0.8% accu racy .  At t h i s  energy Ay,  R y ' (140-170 deg) and t o  a l e s s e r  e x t e n t  Dy and Ry (140 to 170 deg) p la y  a use fu l  r o l e  in w h i t t l i n g  down the  f i n a l  u n c e r t a i n t i e s ,  more so than a t  325 MeV. Aga in Cnn wou ld be a v a lu ab le  measurement in np s c a t t e r i n g  f rom 30 t o  170 deg, bu t  one can manage w i t h o u t  i t .3 .4  520 MeVE x i s t i n g  da ta  a re  so l i m i t e d  t h a t  i t  is  hard t o  t e l l  j u s t  what  w i l lbe r e q u i r e d .  However, good da/df i  measurements in  bo th  pp and np s c a t t e r i n g ,p lus  D, Dy,  R ,  R y ,  A and Ay f rom 55-125 deg and Dy (135-170 deg ) ,  seem todo a good enough jo b  t h a t  one can manage w i t h o u t  PEE ' n nP s c a t t e r i n g .-  5 -A genera l  comment a p p l i c a b l e  a t  a l l  e ne rg ie s  is  t h a t  some Wo l fen ­s t e i n  parameters (bo th  d i r e c t  and t r a n s f e r )  va ry  ve ry  r a p i d l y  w i t h  ang le ,  and t h a t  i f  an accuracy  o f  ±0.03 is  t o  be ach ieved on eve ry  paramete r ,  s y s tema t i c  e r r o r s  on the s c a t t e r i n g  ang le  need t o  be kep t  down to  ±1 deg in the  cen t re  o f  mass system, o r  ±0 .5  deg lab .4. T r a n s fe r  Parameters Near 180 degThe BASQUE expe r imen t  i s  p lanned on the assumpt ion  t h a t  a n e a r l y  monoenerge t ic  neu t ron  beam o f  h igh  p o l a r i s a t i o n  can be made by s c a t t e r i n g  p o l a r i s e d  p ro tons  f rom deu te r ium  th rough an ang le  o f  about  9 deg lab (18 deg c en t re  o f  mass). Th is  t e chn iq ue ,  suggested by Folkmann and Measday,8 was based on an e a r l y  phase s h i f t  a n a l y s i s ,  wh ich  can now be up­da ted .  The p r e d i c t i o n s  f o r  Dy and Ry f rom the  l a t e s t  da ta  se ts  a re  shown in Table  V. P r e d i c t i o n s  f o r  Ry remain e ncou ra g in g l y  h igh  and s t a b l e .  Pre­d i c t i o n s  f o r  o t h e r  t r a n s f e r  parameters have changed q u i t e  s i g n i f i c a n t l y  f rom those g iven  by Folkmann and Measday, and t h e re  are s igns  t h a t  Dy cou ld  be a u se fu l  mechanism f o r  making a p o l a r i s e d  neu t ron  beam a t  the h ig he r  e n e rg ie s .5 . Conci us ionsThe most u rgen t  requ i remen t  is  f o r  comprehensive measurements o f  D, Dy, R, Ry, A and Ay f rom 55-125 deg in np s c a t t e r i n g ,  p lus  1% measurements o f  da/df t  in  bo th  np and pp s c a t t e r i n g  ove r  the f u l l  a ngu la r  range.  Measurements o f  Dy, Ry and Ay f rom 125-180 deg are less  c r u c i a l ,  bu t  f u l ­f i l l  a u se fu l  mopping-up o p e r a t i o n  in c o n s t r a i n i n g  the  f i n a l  e r r o r s .  Measurements o f  C^N ove r  the  f u l l  angu la r  range wou ld be a powerfu l  a d d i ­t i o n  to  these measurements,  bu t  one can manage w i t h o u t  i t ,  w i t h  s l i g h t l y  worsened e r r o r s  i f  necessary .  In pp s c a t t e r i n g ,  measurements o f  D, R and A' are  ve ry  power fu l  in the  a ngu la r  range 10-50 deg.-  6 -References1. J. B y s t r i c k y ,  F. Lehar and Z. Janout ,  CEA-N-15**7(E) (1972).2. M.H. M a c G r e g o r ,  R.A. Arndt and R.M. W r igh t ,  Phys. Rev. 173, 1272 (1968);P. S igne l l  and J. Holdeman, J r . ,  Phys. Rev. L e t t e rs  27., 1393 (1971);R.A. Arndt and L.D. Roper, Nuc l . Phys. B50, 285 (1972).3. N.W. Reay, E.H. Thornd ike,  D. Spalding and A.R. Thomas, Phys. Rev. 150,801 ( 1966).h. P.F. Shepard, T .J .  Dev l in ,  R.E. Mischke and J. Solomon, PPAR-10 Mar (1969).5.  A. Ashmore, W.H. Range, R.T. Tay lo r ,  B.M. Townes, L. C a s t i l l e j o  and R.F. P e ie r l s ,  Nucl .  Phys. 258 (1962).6.  A .J .  Hartzler ,  R.T. Siegel and W. Op i t z ,  Phys. Rev 95, 591 (195*0 •7. D.V. Bugg and C. Oram, 'Which pp parameters need measuring from 200 to525 MeV?' , TRI-75-** (1975) •8. F. Folkmann and D.F. Measday, CERN repo r t  MSC-C-17/675 (1968).Table I. Values of x? with various 1=0 G-waves fixed at OPE values.Variables 922 10Energy320(MeV)ft25 520A 1 1 G-waves free free 88.!t5 . 6it. 15 -Al 1 G-waves free llt.lt 8 8.6 6 7 6 .1 6it.it 8 2 . 53g 5 fixed at OPE 1 It . It 8 9 .2 1 77.it 65.6 85.5and !G5 fixed at OPE llt.lt 90.31 91.9 76.it no solutionAl 1 G-waves fixed at OPE llt.lt 102.3 153.8 8 6 .9 136.7Table Il(a). Predicted errors on common np observables at 210 MeV from the phase shift analysis of existing data. (g2 fixed at 1 ft. ft; phases varied up to 3 G5)Angle fio/a (SP <SD fiR 6A 6R iSA' (SCKP 2355 D,y tS Ry 2Ay SRj '(c.m. deg)10 0 051 0 012 0 029 0 030 0 018 0 026 0 116 0 010 0 036 0 036 0 0 15 0 036 0 03220 0 Oit 3 0 019 0 033 0 028 0 032 0 043 0 077 0 016 0 047 0 033 0 024 0 035 0 02530 0 OltO 0 016 0 031 0 022 0 035 0 042 0 032 0 016 0 058 0 036 0 039 0 025 0 026ItO 0 046 0 015 0 024 0 024 0 044 0 048 0 045 0 024 0 060 0 046 0 068 0 032 0 03050 0 043 0 0 1 7 0 024 0 027 0 059 0 065 0 056 0 047 0 080 0 064 0 092 0 031 0 03560 0 036 0 016 0 031 0 027 0 056 0 055 0 037 0 064 0 102 0 084 0 094 0 024 0 04170 0 027 0 015 0 050 0 040 0 040 0 038 0 031 0 057 0 098 0 091 0 084 0 029 0 04580 0 017 0 013 0 061 0 049 0 031 0 041 0 054 0 029 0 101 0 080 0 059 0 029 0 03890 0 015 0 009 0 051 0 044 0 026 0 033 0 057 0 012 0 117 0 070 0 027 0 041 0 028100 0 017 0 010 0 047 0 037 0 021 0 037 0 042 0 018 0 107 0 075 0 062 0 047 0 0361 10 0 015 0 009 0 050 0 029 0 032 0 056 0 032 0 023 0 094 0 081 0 083 0 050 0 042120 0 014 0 006 0 045 0 017 0 048 0 065 0 028 0 025 0 091 0 076 0 075 0 055 0 036130 0 012 0 006 0 039 0 01 1 0 056 0 057 0 020 0 029 0 079 0 059 0 057 0 055 0 0221 ItO 0 010 0 005 0 041 0 012 0 050 0 038 0 015 0 039 0 066 0 042 0 039 0 044 0 018150 0 010 0 006 0 038 0 022 0 037 0 016 0 023 0 039 0 083 0 045 0 017 0 033 0 026160 0 009 0 007 0 044 0 029 0 045 0 .020 0 030 0 .022 0 092 0 • 053 0 015 0 .023 0 .024170 0 012 0 004 0 065 0 019 0 047 0 .058 0 019 0 .005 0 .065 0 .043 0 .034 0 .011 0 .012Tab l e  I l ( b ) .  As T ab l e  I l ( a )  a f t e r  t h e  a d d i t i o n  t o  e x i s t i n g  da t a  o f  P and D measurements f r om  60 t o  120 deg a t  10 deg s t e p s  and Dy measurements f r om  90 t o  120 deg a t  10 deg s t e p s .Ang l e So /a 6P 6D 6R 6A 6R ' 6 A ' LPSI 6CNN 6 Dy S Ry 6 Ay 6 Ry '(c.m. deg)10 0 041 0 009 0 016 0 019 0 013 0 018 0 072 0 007 0 033 0 030 0 011 0 016 0 02620 0 035 0 014 0 019 0 018 0 024 0 030 0 052 0 011 0 037 0 029 0 017 0 017 0 01530 0 033 0 012 0 021 0 013 0 026 0 030 0 028 0 013 0 039 0 029 0 026 0 014 0 01240 0 037 0 012 0 017 0 013 0 024 0 026 0 027 0 014 0 033 0 030 0 042 0 022 0 01450 0 033 0 012 0 013 0 015 0 025 0 029 0 027 0 016 0 034 0 033 0 053 0 021 0 01460 0 027 0 010 0 013 0 020 0 022 0 023 0 021 0 021 0 042 0 037 0 046 0 012 0 01470 0 023 0 009 0 016 0 030 0 017 0 019 0 025 0 022 0 039 0 039 0 034 0 013 0 01980 0 016 0 007 0 017 0 031 0 017 0 018 0 025 0 016 0 038 0 032 0 030 0 011 0 02190 0 014 0 006 0 016 0 021 0 016 0 014 0 022 0 010 0 042 0 022 0 020 0 014 0 016100 0 016 0 006 0 016 0 017 0 013 0 018 0 018 0 014 0 039 0 017 0 019 0 016 0 017110 0 015 0 005 0 016 0 015 0 016 0 025 0 016 0 022 0 039 0 019 0 025 0 021 0 022120 0 013 0 005 0 017 0 009 0 027 0 028 0 015 0 021 0 040 0 019 0 029 0 028 0 021130 0 011 0 005 0 022 0 005 0 034 0 026 0 010 0 018 0 032 0 023 0 031 0 030 0 016140 0 010 0 005 0 025 0 008 0 032 0 020 0 007 0 025 0 033 0 031 0 026 0 027 0 017150 0 010 0 006 0 027 0 016 0 025 0 010 0 015 0 026 0 057 0 039 0 012 0 023 0 021160 0 009 0 006 0 028 0 021 0 037 0 014 0 021 0 015 0 066 0 038 0 010 0 017 0 018170 0 011 0 003 0 049 0 014 0 039 0 .042 0 .014 0 003 0 051 0 027 0 021 0 008 0 008Tab l e  1 1 ( c ) .  As T ab l e  11 (a )  a f t e r  t h e  a d d i t i o n  t o  e x i s t i n g  da t a  o f  D, R and A measure­ments f r om  60 t o  120 deg a t  10 deg s t e p s  and Dy, Ry and Ay measurements f r om  90 t o  120 deg a t  10 deg s t e p s .Ang 1 e .m. deg)So /o 6P 6D 6R 6A 6R ' 6 A ' 6CKP «CNN 6 Dy S Ry 6 Ay 6Ry '10 0 .033 0.007 0 .013 0 .016 0 .009 0 .012 0 .053 0.005 0 .027 0 .022 0 .008 0 .010 0 .01820 0 .030 0.012 0 .0 1 6 0 .0 1 5 0 .018 0 .022 0 .0 3 9 0 .009 0 .028 0 .0 2 3 0 . 0 ) 2 0 .012 0.01 130 0 .029 0.01 1 0 .017 0.011 0 .020 0 .023 0 .024 0 .012 0 .028 0 . 025 0 .018 0.013 0 .00940 0 .030 0 . 010 0 .014 0 .010 0.018 0.021 0 .022 0 .012 0 .024 0 .024 0.027 0 .016 0.01 150 0 .027 0 .009 0 .010 0.012 0 .017 0 .020 0 .019 0 .013 0 .024 0 .024 0 .032 0 .013 0.01 160 0 .024 0 .009 0 .008 0.013 0 .014 0 .015 0 .013 0 .016 0 .027 0.025 0 .029 0 .010 0.01170 0.021 0 .007 0.011 0 .016 0.011 0 .012 0 .015 0 .017 0 .027 0 .026 0 .025 0.011 0 .01280 0 .015 0 .006 0 .015 0 .016 0 .010 0 .013 0 .015 0 .013 0 .028 0 .023 0 .022 0 .009 0 .01290 0 .014 0 .006 0 .015 0 .012 0.011 0 .013 0 .015 0 .009 0 .029 0 .017 0 .015 0 .010 0 .010100 0 .015 0.006 0 .014 0.011 0 .010 0 .014 0 .013 0 .010 0 .026 0 .013 0 .012 0.01 1 0 .012110 0 .015 0.005 0 .015 0 .009 0.011 0 .017 0.011 0 .014 0 .025 0 .014 0 .014 0.012 0 .014120 0 .013 0 .004 0 .016 0 . 006 0 .015 0 .018 0 .010 0 .014 0 .025 0 .016 0 .015 0 .014 0 .014130 0.011 0 .004 0 .018 0 .004 0 .019 0 .016 0 .007 0 .014 0 .022 0 .020 0 .016 0 .017 0 .013140 0 .010 0 .004 0 .020 0 .006 0.019 0 .013 0 .005 0 .020 0 .024 0 .028 0 .015 0 .019 0 .016150 0 .009 0 .006 0 .023 0 .014 0 .020 0.008 0 .012 0.021 0 .039 0 .034 0 .008 0 .019 0 .018160 0 .009 0 .005 0 .030 0 .018 0 .029 0 .010 0.017 0 .012 0 .046 0 .033 0 .008 0 .014 0 .015170 0.011 0 .003 0 .035 0 .012 0.031 0 .029 0.012 0 .002 0.037 0 .022 0 .017 0 .007 0.007T ab le  I l ( d ) .  As T ab le  I l ( a )  a f t e r  th e  a d d i t i o n  t o  e x i s t i n g  da ta  o f  D, R, A measurements f rom  60 t o  120 deg in  10 deg s t e p s ,  Dy, Ry, Ay f rom  90 t o  120 deg in  10 deg s t e p s ,  and 1% do/dJ2 measurements f rom  5 t o  180 deg in  5 deg s te p s .Ang le 6 a / o 6P 6D 6R 6A 6R ' 6A ' 6CKp SCNN 6 Dy 6 Ry 6 Ay 6Ry '(c.m. deg]10 0 .005 0 005 0 008 0 009 0 .005 0 .008 0.041 0 .004 0 .010 0 .009 0 .005 0 .008 0 .00920 0 .004 0 .009 0 010 0 009 0 .010 0 .013 0 .029 0 .007 0 .011 0 .008 0 .008 0 .007 0 .00830 0 .004 0 009 0 012 0 007 0 . 012 0 .014 0 .016 0 .009 0 .015 0 .010 0 . 012 0 .008 0 .0084o 0 .005 0 007 0 010 0 008 0 013 0 .015 0 .015 0 .010 0 .015 0 012 0 .020 0 .012 0 00950 0 .004 0 007 0 007 0 010 0 014 0 .016 0 .016 0 012 0 .018 0 017 0 024 0 .010 0 01060 0 .005 0 007 0 007 0 012 0 013 0 .014 01012 0 015 0 024 0 022 0 024 0 008 0 01070 0 005 0 007 0 010 0 015 0 010 0 .012 0 .013 0 015 0 024 0 023 0 022 0 009 0 01 180 0 004 0 006 0 014 0 015 0 009 0 .013 0 .014 0 01 1 0 022 0 020 0 020 0 008 0 01 190 0 005 0 006 0 015 0 011 0 008 0 012 0.012 0 006 0 023 0 016 0 013 0 008 0 009100 0 004 0 005 0 014 0 009 0 008 0 013 0.011 0 008 0 023 0 013 0 012 0 009 0 010110 0 004 0 004 0 014 0 008 0 010 0 016 0.010 0 011 0 022 0 013 0 013 0 010 0 012120 0 004 0 003 0 015 0 005 0 011 0 017 0 .009 0 010 0 020 0 015 0 013 0 011 0 012130 0 004 0 003 0 017 0 003 0 013 0 014 0 .006 0 010 0 018 0 018 0 013 0 01 1 0 0101*40 0 004 0 003 0 018 0 004 0 014 0 009 0 .005 0 014 0 018 0 023 0 011 0 011 0 01 1150 0 004 0 004 0 015 0 008 0 013 0 003 0 .009 0 014 0 021 0 027 0 005 0 011 0 012160 0 004 0 003 0 013 0 01 1 0 014 0 006 0.01 1 0 008 0 022 0 026 0 005 0 009 0 010170 0 004 0 002 0 017 0 007 0 014 0 016 0 .007 0 002 0 016 0 017 0 012 0 004 0 005Tab le H ( e ) . P r e d ic te d  e r r o r s  on common np ob se rv a b le s a t  320 MeV f rom the phase s h i f tana 1ys i s o f  e x i s t i n g d a t a . (g 2 f i xed a t 14 4 ;  phases va r ed up t o  3G5)Ang le 6a /a 6P 6D 6R <5A 6R ' 6 A ' 6CKp fiCNN 6 Dy 6Ry 6 Ay 6 Ry '(c.m. deg)10 0 051 0 015 0 026 0 031 0 019 0 019 0 .055 0 017 0 071 0 118 0 014 0 075 0 11520 0 047 0 025 0 023 0 041 0 029 0 030 0.056 0 030 0 064 0 081 0 021 0 084 0 08630 0 054 0 022 0 035 0 038 0 032 0 035 0 .065 0 047 0 056 0 056 0 037 0 082 0 0704o 0 045 0 014 0 052 0 036 0 038 0 053 0 .065 0 067 0 056 0 056 0 059 0 072 0 05950 0 037 0 012 0 059 0 048 0 044 0 073 0 .053 0 082 0 067 0 060 0 071 0 055 0 04760 0 043 0 010 0. 047 0 053 0 046 0 08 0.036 0 083 0 091 0 084 0 074 0 041 0 03870 0 050 0 009 0 016 0 054 0 046 0 070 0 .027 0 064 0 130 0 131 0 083 0 034 0 03280 0 053 0 010 0 027 0 056 0 049 0 039 0.066 0 034 0 177 0 173 0 088 0 034 0 02990 0 053 0 009 0 048 0 049 0 068 0 025 0.110 0 036 0 205 0 163 0 080 0 048 0 023100 0 042 0 009 0 061 0 035 0 099 0 035 0 .116 0 037 0 196 0 103 0 066 0 067 0 015110 0 023 0 009 0 072 0 026 0 111 0 041 0 .083 0 040 0 158 0 077 0 061 0 078 0 022120 0 012 0 008 0 072 0 020 0 092 0 042 0 .044 0 040 0 120 0 100 0 065 0 073 0 024130 0 008 0 008 0 067 0 014 0 066 0 037 0.019 0 032 0 093 0 111 0 059 0 058 0 024140 0 007 0 007 0 053 0 015 0 051 0 035 0 .014 0 038 0 077 0 104 0 040 0 047 0 039150 0 006 0 007 0 041 0 022 0 054 0 036 0 .017 0 038 0 083 0 091 0 018 0 048 0 053160 0 004 0 008 0 069 0 031 0 067 0 063 0 .024 0 021 0 085 0 076 0 040 0 043 0 049170 0 005 0 004 0 105 0 023 0 066 0 101 0.019 0 006 0 054 0 055 0 051 0 020 0 023 1 1 ( e ) .          a l s   t .  i x e  4 . r i e sT ab l e  1 1 ( f ) .  P r e d i c t e d  e r r o r s  on common np o b s e r v a b l e s  a t  425 MeV f r om  t he  phase s h i f t  a n a l y s i s  o f  e x i s t i n g  d a t a .  ( g2 f i x e d  a t  1 4 . 4 ;  phases v a r i e d  up t o  3Gs)Ang le  (c.m. deg)6a/a 6P 6D 6R 6A SR' 6A' SCKP SCNN CWN C AN CTN RAN10 0 042 0 014 0 031 0 032 0 012 0 012 0 036 0 010 0 076 0 089 0 014 0 031 0 o CO -c-20 0 033 0 023 0 028 0 035 0 018 0 020 0 032 0 019 0 064 0 069 0 017 0 035 0 05230 0 031 0 022 0 026 0 032 0 018 0 023 0 032 0 019 0 051 0 052 0 017 0 037 0 03240 0 027 0 014 0 024 0 026 0 016 0 024 0 034 0 014 0 036 0 037 0 027 0 031 0 02750 0 023 0 008 0 022 0 021 0 014 0 022 0 036 0 021 0 026 0 030 0 037 0 025 0 04060 0 022 0 006 0 025 0 019 0 016 0 024 0 034 0 031 0 028 0 040 0 042 0 034 0 05070 0 021 0 006 0 025 0 019 0 017 0 025 0 027 0 035 0 031 0 046 0 041 0 038 0 04780 0 022 0 008 0 020 0 023 0 023 0 028 0 024 0 027 0 025 0 037 0 030 0 025 0 02990 0 023 0 009 0 018 0 024 0 027 0 030 0 025 0 008 0 022 0 022 0 011 0 013 0 016100 0 026 0 009 0 033 0 029 0 021 0 027 0 021 0 032 0 034 0 042 0 034 0 023 0 033110 0 029 0 009 0 052 0 043 0 020 0 038 0 022 0 050 0 044 0 066 0 060 0 022 0 044120 0 025 0 011 0 049 0 041 0 028 0 045 0 025 0 041 0 053 0 072 0 069 0 028 0 035130 0 022 0 010 0 032 0 021 0 032 0 034 0 020 0 024 0 044 0 061 0 064 0 027 0 022140 0 018 0 007 0 039 0 016 0 033 0 040 0 014 0 021 0 029 0 050 0 050 0 035 0 031150 0 016 0 005 0 053 0 019 0 039 0 070 0 012 0 021 0 056 0 060 0 041 0 048 0 044160 0 017 0 006 0 080 0 019 0 067 0 109 0 019 0 017 0 075 0 074 0 051 0 048 0 043170 0 020 0 003 0 117 0 013 0 077 0 130 0 017 0 010 0 071 0 058 0 051 0 022 0 020W P D R A DT Rt At Dt da/dft CNN 3SX ej 3Dj iPj 3D2 3D3 F3 3G3 !f3 3G4 3G5  60-120 deq 90-120 deg 130~170 deg 5~l80 deq 60-120 deqJ 2.58 0.58 2.05 6.23 3.17 0.74 0.51 0.34 0.90 1.27 0.49Ref 2-z,9 °-58 1.92 6.31 2.94 0.74 0.50 0.33 0.89 1.27 0.48Ref / / / 0.58 0.38 0.34 1.39 0.67 0.38 0.094 0.15 0.22 0.33 0.13 Ref / 7 J J 0.36 0.28 0.28 1.02 0.38 0.24 0.11 0.12 0.24 0.24 0.12Ref 7 / / 0.49 0.33 0.35 1.87 0.65 0.37 0.094 0.16 0.21 0.49 0.14 Ref / / / / y °-^2 °-29 °-28 1.10 0.46 0.23 0.080 0.12 0.15 O.36 0.11 Ref / / J  ^J / / °-29 0.25 0.21 0.67 0.30 0.21 0.065 0.093 0.12 0.17 0.084 Ref//|/ / '/'/'/ 'f 0.29 0.099 0.21 0.65 0.25 0.21 0.036 0.093 0.10 0.16 0.080Ref  ^ ^ ^ ^°-27 °-’8 °-25 0.76 0.24 0.077 0.046 0.055 0.098 0.11 0.075 Ref  ^ ^ ^ ^ ^ ^0,22 °-17 °-20 0.46 0.18 0.045 0.041 0.036 0.063 0.089 0.046 Ref/////// / 0.16 0.15 0.17 0.34 0.14 0.041 0.036 0.031 0.054 0.068 0.036 Ref/’///l‘/|//l / / 0.16 0.071 0.16 0.32 0.11 0.040 0.024 0.028 0.047 0.058 0.036Ditto + A'(13 deg)np   0.15 0.070 0.15 0.27 0.06 0.039 0.012 0.026 0.040 0.040 0.036Ref  ^°-51 °-45 0.27 3.24 0.62 0.43 0.11 0.16 0.36 O.36 0.11Ref / / / °-27 °-32 0.18 I.32 0.34 0.27 0.064 0.11 0.14 0.19 0.086 Ref/////// / 0.22 0.25 0.16 0.61 0.21 0.20 0.055 0.078 0.090 0.10 0.070Ref/////// / / 0.08 0.14 0.12 0.31 0.11 0.036 0.029 0.028 0.044 0.053 0.028Table Ill(a). Diagonal 1=0 elements of the error matrix (degrees2) at 210 MeV from existing data, W, and hypotheticaladditions. In the additions, 6P = ±0.02, 6a/0 = ±0.01, and the other errors = ±0.03; g2 is fixed at 14.4; da/dft is assumed at 5 deg steps, other data at 10 deg steps. Ref = W + PDR(13,33 53 deq)W W y pp•Table Ill(b). As Ill(a) at 320 MeV.Ref P55D A R - 125  degGN DN FN  75-125 degda/dS2 5 -180  deg3Si ^1 3Dl 3Pi 3D2 3»3 E 3 3G3 1 r 3 3 Git TRI/ 8 . 8 6 . it 5 -8 4.1 9 .8 1 .5 0 .4 0 2 .3 0 .32 1.5 0 .35/ / / / 0 . 86 0 . ^ 7 0.51 2 . 0 1.6 0 .47 0 .14 0 .65 0 .17 0 .62 0.21/ / /  / /  / 0 . 50 0 .39 0 .38 0 .93 0 .65 0 .42 0 .098 0 .43 0 .14 0 .16 0 .16/ / ✓ ✓ ✓ /  /  / 0 . 38 0 .33 0 .33 0 .59 0 .38 0 .33 0 .067 0 .24 0 .089 0 .12 0 .13/ / /  /  / /  /  / / 0 . 29 0 .16 0 .22 0.51 0 .23 0 .16 0 .020 0 .043 0 .047 0.11 0 .059Di t t o + da /dn  ( 5 -20  deg)pp 0 .28 0 .15 0 .20 0 .50 0 .22 0 .15 0 .019 0.042 0 .038 0.11 0 .055Di t t o + AA'  ( 33 , 53  d e g )DD 0 .23 0 .15 0 .17 0 .48 0 .22 0 .13 0 .018 0.041 0 .029 0 .097 0.051Di t t o + CNN ( 1 3 5 ,1 50 ,1 60 ,1 70  d e g ) np 0 .19 0.12 0 .16 0 .26 0.12 0.081 0 .017 0 .039 0 .023 0 .069  0 . 038Tab l e  I I l ( c ) .  As I I I ( a )  a t  425 MeV.Ref P55D-125R A deg°T r T aT 65-125  degf dal  [dnj np5-180f c*°l[dfljpp5-903Si El 3Di 3Pl 3D2 3d3 E3 TRT 1R3 3G„ TRI/ 5 . 50 2 .73 2 .60 5.51 3 .38 1.10 1.53 0 .67 1.11 1 .05 0 .46/ / / / 2 . 38 0 .98 1.15 2 .04 0 .89 0 .80 0 .37 0 .39 0 .19 0 .35 0 .24/ / / / /  / 1.72 0 .83 1.04 1.60 0 .69 0 .67 0 .22 0 .25 0 .16 0 .26 0 .20/ / / / ✓ /  /  / 1 .37 0 .70 0 .88 1 .26 0.52 0 .55 0 .16 0 .18 0 .13 0 .22 0 .16/ / / / / /  /  / / / 0 . 86 0 .2 6 0.31 0 .56 0 .29 0 .24 0 .06 0 .06 0 .05 0 .05 0 .05D i t t o  + aT r T ' D-r  AN ( 140-170 deg) np 0 .54 0 .18 0 .22 0 .48 0 .17 0 .070 .04 0 .03 0 .03 0 .04 0 .025T ab l e  I l l ( d ) .  As I l l ( a )  a t  520 MeV.Data 3Si e i OWM 3Pl 3D2 3d 3 e 3 3G3 1 r 3 O2 05 O2 RW 74 .2 100.8 27 .9 283 .7 94.1 74 .2 43 .4 69 .3 95 .9 26 .6 30 .4W + PDR(1 3 , 3 3 , 5 3  deg)DD + R ' ( 3 3 , 5 3 ) nD= Ref 59-9 94 .5 25 .2 266 .9 88.1 67 .9 41 .5 61 .5 93 -9 26 .5 29.1Ref  + eWATWNANTN V55~125 d e g ) np 2 .7 2 . 5 1.5 9 .4 1.0 1.7 0 .50 0 .45 0 .86 0 .50 0 .52D i t t o  + d o / d f l ( 5 - l  80 deg)np + da / d f l ( 5 - 9 0deg )pp 0 .48 0.31 0 .32 0 .22 0 .22 0 .16 0 .1 0 0 .09 0 .06 0 .06 0 .04D i t t o  + D j (  140-170 d e g ) np = X 0 .46 0 .13 0 .23 0 .22 0 .18 0 .16 0 .05 0 .08 0 .06 0 .04 0 .04X + Cj^p(90 deg )pp 0 .46 0 .13 0 .22 0.21 0 .18 0 .16 0 .05 0 .08 0 .06 0 .04 0 .04X + CNN(30 -90  d e g ) pp 0 .46 0 .13 0 .23 0 .22 0 .18 0 .16 0 .05 0 .08 0 .06 0 .04 0 .04Table IV(a). Diagonal 1-1 elements of the error matrix at 210 MeV from existing data, W, and hypothetical additions. Ref ? W + PDR(13,33,53 deg)pp.CO v O  r o  CT\  I A<£> — — — O  O  O31 O  O  O  O  O  Or o  . . . . . .O  O  O  O  O  OCO CM CO L A  Wi n  CM CM •—  •—  *— p—31 O  O  O  O  O  OCO • • « • • •W  W  W  W  W  WO  CO v O  i n  I A  L AH W  W  W  W  WA  W  W  W  W  W  WW  W  W  W  W  W—  ( A  CO  CO  v O  -■ t  - 4 -  ro» CM —  —  —■T N  W  W  W  W  Wco . . . . . .W  W  W  W  W  WP  NW NWELL LSL LIL EW NW WHA TN W  W  W  W  W  W1 to —  —  —  —  —  —W  W  W  W  W  WL O  CM —  CO CM —J -  CM CM CM —  —  e -U- O  O  O  O  O  OCO .................................................................O  O  O  O  O  O1—  CO v O  LO  CO COCO CO CM CM CM CM —U -  O  O  O  O  O  OCO .................................................................O  O  O  O  O  O( T l  N  CO v O  LO  —CM A" .  v O  CO CM CM CMO  O  O  O  O  O  OO  O  O  O  O  ONW H PE NW NPCM L O  L O  LO  CM CM —Li -  O  O  O  O  O  OCO . . . . . .O  O  O  O  O  O.B  co W  W  coCM —  OC0R W  W  W  W  W  WW  W  W  W  W  WCO MD LO  —  CO OOCM CM CM CM CM —  —. 08 O  O  O  O  O  Oco ................................................................O  O  O  O  O  OLO CO -3- O  f— vD-3- co CO CO CM CMQ- O  O  O  O  O  Oco . . . . . .O  O  O  O  O  OOO LO  L O  CO CM —O  CM CM >—  ■—  —  —CO .................................................................r-*  O  O  O  O  O  OCO v O  CM CO CO ■—O  CM CM CM —  —  —Q_ .................................................................co O  O  O  O  O  O^  iQ) “O O<1) CM O"O O  •— P-*CM I —O  —  O  ICM I CO O■—  O  '—  COI CO I—  —A  G  D CO I -  h -  f -— cd on c*ug *Q nQ arQ Q °  Q.2 + + +„CD3? “ ■ - F  SO  f -  r -  _~"CD T3S’ |  -  sF W G W  HO  CM IO  CM —  LOCM —  I  ------—  I O C ?1 O  v O  - OO  v O  \MD — '  C  t>'—  HA TT NPW  W  OQ. Q_ Q_ ++ + + o•MM- M - 4 _  l |_  4 J<I) Q) <1) <U —________________ ^  CC CC Od t£. Q  ^ 3p0 ^0 3Pl 3P2 3F2 1Dz 3F3 3p4 3Hi< lg4 3Hs 3h6”  2-6i* 1 - 36 0.80 0.28 0.14 0.29 0.15 0.36 0.044 0.065 0.090 0.065 0.26 0.026W + PDR(13,33,53 deg)pp = Ref 1.85 0.48 0.46 0.12 0.083 0.25 0.081 0.31 0.029 0.023 0.050 0.032 0.14 0.018Ref + PDDT(55-125 deg)np 0.55 0.40 0.28 0.10 0.043 0.076 0.064 0.13 0.025 0.013 0.029 0.028 0.085 0.015Ref + PDADtAt(55-125 deg)np 0.43 0.36 0.22 0.090 0.036 0.064 0.062 0.068 0.023 0.010 0.027 0.026 0.063 0.013Ref + PDARDTATRT(55-125 deg)np 0.33 0.24 0.18 0.078 0.033 0.051 0.052 0.054 0.020 0.009 0.022 0.023 0.047 0.012Ditto + do/dfi(5-l80 deg)np 0.30 0.18 0.16 0.070 0.029 0.044 0.039 0.050 0.018 0.005 0.016 0.017 0.037 0.011Ditto + do/dn(5-20 deg)pp 0.29 0.18 0.15 0.062 0.027 0.038 0.029 0.042 0.014 0.005 0.013 0.012 0.031 0.007Ditto + AA'(33,53 deg)pp 0.28 0.17 0.056 0.035 0.018 0.032 0.028 0.030 0.013 0.005 0.012 0.010 0.016 0.007Ditto + CNn(135,150-170 deg)np 0.27 0.16 0.055 0.033 0.017 0.030 0.028 0.030 0.013 0.005 0.012 0.010 0.016 0.007Table IV(c). As Table IV(a) at 425 MeV. °3ta  3p0 lSo 3Pl 3p2 Fz 3p2 l„2 3p3 3Fl+ Flt 3Hi+ lGlf 3^ 3HgRef = W + PDR(13,33,53 deg)pp + R'(33 deg)pp 0.65 0.36 0.26 0.13 0.10 0.091 0.092 0.052 0.033 0.033 0.048 0.032 0.073 0.027Ref + eWWNV55-125 deg)np 0.44 0.32 0.24 0.12 0.086 0.071 0.086 0.048 0.030 0.023 0.043 0.028 0.061 0.026Ref + PDRDjRj(55_125 deg)np 0.38 0.28 0.23 0.11 0.068 0.068 0.084 0.047 0.028 0.017 0.037 0.026 0.054 0.024Ref + PDRADtRtAt(55*125 deg)np 0.36 0.26 0.22 0.11 0.058 0.065 0.071 0.045 0.027 0.016 0.032 0.024 0.052 0.021Di tto + da/dfl(5-180 deg)np+ da/dfl(5-90deg)pp=X 0.26 0.17 0.11 0.064 0.040 0.026 0.036 0.016 0.008 0.009 0.014 0.011 0.016 0.008Ditto + AtRt'DtRt(140-170 deg)np__________________0.23 0.16 0.096 0.056 0.031 0.021 0.035 0.016 0.008 0.008 0.011 0.011 0.010 0.007x + Cnn(30-170 deg)np 0.24 0.15 0.082 0.050 0.032 0.023 0.029 0.014 0.008 0.008 0.014 0.010 0.010 0.007Table IV(b). As Table IV(a) at 320 MeVTable IV(d). As Table IV(a) at 520 MeVBEST-PRINTER CO LTD VANCOUVER. B CData 3P0 3Pi 3P2 e2 3F2 102 3f3 OyD eA 3h4 1gA 3h5 3h6W 16.5 29.2 8.6 1.25 3.45 1.71 12.7 2.9 0.50 2.0 1.03 3.85 1.19 0.36W + PDR(13,33,53 deg)DD + R'(33,53 deg)nn = Ref 6.6 6.8 1.8 0.50 0.70 0.43 1-55 0.42 0.15 0.63 0-25 1-14 0.27 0-16Ref + PDRADyRyAy(55-125 deg)np 0.68 1.23 0.45 0.14 0.17 0.13 0.57 0.26 0.094 0.048 0.063 0.11 0.12 0.062Ditto + da/dn(5-l80 deg)np +do/dn(5-90 deg)pp 0.35 0.53 0.17 0.049 0.056 0.029 0.074 0.036 0.010 0.017 0.022 0.015 0.015 0.013Ditto + DT(140-170 deg)np = X 0.33 0.53 0.17 0.048 0.051 0.027 0.071 0.035 0.010 0.015 0.022 0.013 0.015 0.013X + cKP(90 deg)pp 0.32 0.53 0.16 0.048 0.039 0.025 0.070 0.035 0.010 0.013 0.021 0.013 0.015 0.012X + cNN(3°-90 deg)pp 0.33 0.37 0.16 0.040 0.047 0.026 0.046 0.032 0.008 0.014 0.020 0.009 0.013 0.012Table V. Predictions for Dy and Ry in np scattering from the present energy-independent phase shift analysesEnergy (MeV) 210 320 425 520RT(140 deg) -0.631 ± 0.039 -0.555 ±0.027 -0.477 ± 0.050 -0.046 ±0.110 Ry(150 deg) -0.844 ± 0.017 -0.702 ± 0.014 -0.649 ± 0.041 -0.528 ± 0.073Ry(160 deg) -0.849 ± 0.015 -0.750 ± 0.037 -0.792 ± 0.051 -0.841 ± 0.042Ry(170 deg) -0.504 ± 0.034 -0.394 ± 0.045 -0.417 ± 0.051 -0.535 ± 0.047Dy(140 deg) 0.040 ± 0.042 0.063 + 0.093 0.522 ± 0.050 0.163 ± 0.107DX(150 deg) 0.110 ± 0.045 0.275 ± 0.081 O.685 ± 0.060 0.480 ± 0.107Dy(160 deg) 0.073 ± 0.053 0.405 ± 0.068 0.821 ± 0.074 0.579 ± 0.086Dy(170 deg) -0.144 ± 0.043 0.164 ± 0.049 0.434 ± 0.058 0.234 ± 0.053

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