Schopper, H.

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J A N U A R  1962 K F K  80 I N S T I T U T  F U R  E X P E R I M E N T E L L E  K E R N P H Y S I K  D O E S  T H E  R O S E N B L U T H  F O R M U L A  B R E A K  D O W N ?  H E R W I G  S C H O P P E R  KERNREAKTOR Biuc. und Bc:;-lcto-Ocacllsc:h m. b.W. Ve**ung der ZonfrslbUchemi KERNFORSCHUNGSZENTRUM KARLSRUHE January 1962 I n s t i t u t  f ü r  Experiinentelle Kernphysik Does t h e  Rosenbluth formula break down? Herwig Schopper - KERN REAKTOR Bau- und Eck i, ::n-Gcec!lnt:i:~ft lYl. b. H. Verwaiiur,~ dor ZcnOra;btlcherel Kernreaktor Bau und Be t r i ebs  Gese l l scha f t  mbH Karlsruhe I n  t h e i r  r e c c n t l y  published peper Hof s t a d t e r  e t  a1, point, oiit t h a t  c r ; n s i r , i g  tlici.1 d a t a  f0P tkie e l ez t ron -  protoll so2 t te r i r .g  a'; a sca t tey i r ig  angle 0f 1115~ a d  e l e a t r o c  encygy of 975 ivle\i wi th  Corne l l  d a t a 2 )  a t  112' a ~ d  1050 KeV a mial l  ~i lcoi ls is -¿ency has s o s s i b l y  beeil -mvorere6. Z i i - s  con j ec t w e  has Geen c o r r o b o r a t e ~  b;r Coyiei? r c su i t s3 '  at i ' 1 5 ~  2-d an enO??g'J of  1120 MeV P:_-ich gave a  scaJ;terlng c ~ o s s  s e c t i o n  about  2,5 t imes lu:>f;eil t h sn  what oon ~would c;::pect f ~ 0 t ~  ai?. e x t r a p o l a t i o n  of t:le fcym Z a c t c s  determiried a t  lower e n e r g i e s .  A t  t h e  Aix-en-Provence Canrerence on E l e m e n t ~ r y  Par- t i c l e s  ( ~ e p t e m b e i  1961) i t  ha,s k e n  discusseci  whether these r e s u l t s  irnply a brealcdown o f  t k e  Rose:~bluth f o r -  mula o r  !vhe¿her8 e more o r  lcss sudden change of t h e  forrn f ' ac to rs  at Ligh q-v21at?s c o ~ ~ l d  exp la i r ,  t h e  l a r g e  0 c r o s s  s ~ c t i o i ? . ~  2.t 145 . I'ü :rzs t n c  ~ e n e - a l  op ln ion  C t,::at -- ons of ( c h e s ~  tlr;o p a r , s i b l l l t l e s  could  o n l y  j e  s ing l ed  , - cus 27 rr:a~.~urcri:er_~;s zt c e r g i r c ;  abo-re *: 200 i"4eT,T. It i s  Jhe PLZ;-PGS;? OT t h i s  ?ote., hcrr:u::-i., :D s501v t'lst, t h e  F . s Q c . o . 7 ~ -  k r L  !~n0?2~2 r e ~ u y i t ~  erc  i n  prFncipLe s u t i i c i e n t  t o  pi-ave a  L;?ecni;iSüwfi of  the R o s E ~ ? ~ ~ . L ! ~ ~  forrnula I"or q > 30 .- j fe;2yi I n  o rder  t o  t e u t  the F ~ s e n b l u - t h  t o ~ m u l e  i t  i s  c o m e n i e n t  t o  w r i t e  i t  i n  +he fol lorving form G, 2.n3 G, e r e  the slsc",ic Li 1.1 an2 inagnkU2c Term f c c t o r s  i n -  .:-.-7d,, -.- -..czC by Sachs et 3.1. I ) 2r.d t = (55/ '2~c !  2 .  The o t h e r  f.=l'¿atir>rj S. L- 5 1;2r.G?.3'i: , 2  P l o t t i n g  R a s  a funct ion  of t a n  @/2 one ob ta ins  a  s t r a i g h t  l i n e  i f  t h e  formula i s  c o r r e c t .  However, i t  can be shown t h a t  n o t  a l l  s t r a i g h t  - l i n e s  drawn through experimental po in t s  ---  a r e  cbmpatible with the  ---- formula. It i s  easy t o  prove t h a t  the  s l o p e d o f  a  s t r a i g h t  l i n e  drawn through a p a r t i c u l a r  point  R a  a t  tan2 0 / 2  = a i s  r e s t r i c t e d  t o  values This impl ies  i n  p a r t i c u l a r  t h a t  t a n d c a n n o t  exceed 2  a  c e r t a i n  maximum value which i s  r e a l i z e d  i f  G E = 0.  I n  the  enclosed f i g u r e  t h e  experimental values of R a r e  displayed f o r  t h r e e  values of the  r e c o i l  momentum q. The broken l i n e s  i n d i c a t e  t h e  l a r g e s t  s lope compa- t i b l e  with t h e  experimental po in t s  a t  90' o r  112O, r e -  spec t ive ly .  Only po in t s  below t h i s  broken l i n e  a re  i n  agreement with t h e  Rosenbluth formula. The measure- ments f o r  q2 = 24,8 f - 2  a r e  represented by the  f u l l  l i n e  which i s  well  below t h e  Limiting l i n e .  For q2 = 30 f" a  s l i g h t  discrepancy appears and f o r  q2 = 37 f-2 t h e  h ighes t  point  i s  f a r  above the  l i n e  compatible with the  point  a t  1 1 ~ ~ .  I f  t h e r e  a r e  no systematic  e r r o r s  i n  the  experiments (and t h i s  cannot y e t  be excluded d e f i n i t e l y )  t h i s  con- s i d e r a t i o n  s t rong ly  i n d i c a t e s  t h a t  the  Rosenbluth formula brealcs down f o r  q2 > 30 f -2  a t  backward angles .  The Rosenbluth formula has  been derived On t h e  assumption of one photon exchange between e l e c t r o n  and nucbson (Born epproximation). A breakdown of t h i s  formula suggests  therefore  t h a t  t h i s  approximation i s  n o t  v a l i d  any langer, D r e l l  and Fiuderman5) and D r e l l  arid Fubini6) estirnated th, cont r ibut ion  of the  two photon exchange and found t h a t  i t  i s  < I $  f o r  energies  below 1  GeV. However, i n  these ca lcu la t ions  the  nucleon was t r e a t e d  n o n - r e l a t i v i s t i -  c a l l y  and i t  was assumed t h a t  the  Compton Cross sec t ion  f o r  a  v i r t u a l  photon i s  the  same a s  t h a t  f o r  a r e a l  one if the  frequencies  a r e  the  same. I n  view of t h e  new experimental r e s u l t s  a  more r igorous  c a l c u l a t i o n  of these e f f e c t s  would be des i rab le .  Qua l i t a t ive ly  i t  i s  p laus ib le  a t  l e a s t  t h a t  dev ia t ions  show up f i r s t  a t  l a r g e  angles as t h e  s c a t t e r i n g  Cross sec t ion  drops of f  r ap id ly  with inc reas ing  angle  where- a s  the  higher cor rec t ion  terms do not  depend s t rong ly  on the  angle.  Hence t h e i r  r e l a t i v e  c o n t r i b u t i o n  be- Comes l a r g e r  a t  backward angles.  1) Bumiller, Croissiaux, Dally and Hofstadter ,  Phys. Rev. 124, 1623, 1961 41 2 )  Olson, Schopper and Wilson, Phys. Rev. L e t t .  6, 286, 1961 3 )  Li t t aue r ,  Schopper and Wilson, Phys. Rev. L e t t .  7, 141 and 144, 1961 Wilson, Aix-en-Provence Conference on Elementary P a r t i c l e s ,  September 1961 4) Ernst ,  Sachs and Wali, Phys. Rev. 119, 1105, 1960 5) Dre l l  and Ruderman, Phys. Rev. 106, 561, 1957 6) Dre l l  and h i b i n i ,  Phys. Rev. 113, 741, 1959 

Does the Rosenbluth formula break down?

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Does the Rosenbluth formula break down?

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