SPIN DEPENDENT NN AND N[MATH] INTERACTION FROM THE PARIS POTENTIAL

HAL Id: jpa-00224554

https://hal.archives-ouvertes.fr/jpa-00224554

Submitted on 1 Jan 1985

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of

sci-entific research documents, whether they are

pub-lished or not. The documents may come from

teaching and research institutions in France or

abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est

destinée au dépôt et à la diffusion de documents

scientifiques de niveau recherche, publiés ou non,

émanant des établissements d’enseignement et de

recherche français ou étrangers, des laboratoires

publics ou privés.

SPIN DEPENDENT NN AND N[MATH]

INTERACTION FROM THE PARIS POTENTIAL

B. Loiseau

To cite this version:

JOURNAL DE PHYSIQUE

Colloque C2, supplement au n°2, Tome 46, fevrier 1985

page C2-339

SPIN DEPENDENT NN AND NN INTERACTION FROM THE PARIS POTENTIAL

B. Loiseau

Division de Physique Théorique*, Institut de Physique Nucléaire,

91406 Orsay, France

and

LPTPE, Université Pierre et Marie Curie, 75230 Paris Cedex OS, France

Résumé — Dans cet exposé nous voulons illustrer ce qui est compris pour les interactions Nucléon-Nucléon (NN) et Nucléon-antinucléon (NN) - leur dépen-dance en spin en particulier - en termes d'échange de mésons et éventuelle-ment de résonances pion-Nucléon (nN) à l'aide de l'exemple du Potentiel de Paris.

Abstract - In this talk we would like to illustrate what is understood in low and medium energy NN and NN interactions - their spin dependence in par-ticular - in terms of meson exchanges and eventually irN resonances through the example of the Paris potential.

I - INTRODUCTION

In the experimental study of the NN interaction at low and medium energy it was early realized /!/ that the observed non-zero values for NN polarization and depolarization parameters were a signal to the existence of the spin dependence of the NN interac-tion. Besides a central force not only a long ranged tensor but also a medium ranged spin-orbit force were necessary. After the discovery of the ir-meson, postulated by Yukawa /2/ as being the mediator of the NN force, one has found that the long ranged one-pion-exchange (OPE) force, which is of spin-spin and tensor type,did not generate the needed amount of spin-orbit force. Such a component was then thought to be gene-rated by 2ir-exchange, in particular 2ir correlated in P-wave i.e. the vector-isovector p-meson (760 MeV) considered in the one-boson-exchange (OBE) models. The relatively large size of the differential cross section, doYdn, indicates an intermediate range attraction not explained by the pion exchange but again by 2ir exchange, specially correlated in S-wave (the non-observed scalar-isoscalar "e" (^550 MeV) introduced in OBE potential models). When the existence of the excited states of the Nucleon was demonstrated in the TTN scattering experiments, mainly that of the spin 3/2, isospin 3/2,A(1232 MeV), it became evident that any theoretical approach to the low and intermediate energy NN interaction should take into account this supplementary degree of freedom. The 27T-exchange box diagram with a nucleon and a A and that with two-A intermediate states contribute to the medium range attraction and to the non-locality (energy dependence in particular) of the NN force. Part of the short range repulsion has been then accounted for by the u (783 MeV)-exchange. Furthermore the finite size of the nucleon and its structure in term of quarks, proven in deep elas-tic scattering experiments, lead to think that the short range NN force arising from quark interactions (quark-gluon exchanges) is of complicated nature.

The most appropriate tool to derive the long and medium ranged NN force taking into account the pionic and isobaric degree of freedom is that of the use of dispersion relations /3/. After the pioneering works of ref.(4), there has been several attempts trying to explain and reproduce the complexity of the NN interaction in these terms /5,6,7/. In this talk, to illustrate what is theoretically known on the long and intermediate range NN force at medium energy, we shall restrict ourselves to the

*

Laboratoire Associe au C.N.R.S.

C2-340

JOURNAL

DE

PHYSIQUE

approach t o t h e problem by t h e P a r i s group

171.

It i s n o t t h e o n l y group which h a s s t u d i e d t h i s , i n p a r t i c u l a r t h e r e h a s been a l a r g e amount of work performed by t h e Stony-Brook group / 6 / .

T h i s t a l k , n o t b e i n g a r e v i e w , we a p o l o g i z e t o a u t h o r s who h a v e devoted some of t h e i r t i m e t o t h e s t u d y of t h e NN/N i n t e r a c t i o n and who w i l l n o t b e quoted h e r e . We r e f e r , f o r c o m p l e t n e s s , t o t h e r e c e n t NN and NN r e v i e w s of r e f . (8) and ( 9 ) r e s p e c t i v e l y . A f t e r a b r i e f r e c a l l i n s e c t i o n I1 o f how was b u i l t t h e P a r i s NN p o t e n t i a l we s h a l l

i l l u s t r a t e , i n s e c t i o n 111, t h e s p i n dependence of t h e NN i n t e r a c t i o n by summarising t h e e f f e c t of t h e d i f f e r e n t components of t h e f o r c e on d i f f e r e n t

NN

o b s e r v a b l e s

a t

low e n e r g y i . e . f o r TL ( l a b o r a t o r y k i n e t i c e n e ~ g y ) le s s t h a n .35 GeV o r ~ ~ 4 . 8 8 GeV/c. S e c t i o n I V w i l l d e m o n s t r a t e how o n e c a n u s e t h e d i s p e r s i o n r e l a t i o n a p p r o a c h t o d e r i - v e t h e o r e t i c a l c o n s t r a i n t s on t h e NN i n e l a s t i c i t y p a r a m e t e r s i n t h e one- and two

-

p i o n p r o d u c t i o n r e g i o n , .35 GeV 4 TL 6 2.5 GeV o r .8R_ GeV/c d pL 6 3.3 GeV/c. S e c t i o n V w i l l i l l u s t r a t e t h e s p i n dependence of t h e P a r i s NN i n t e r a c t i o n b u i l t up from c o n s t r a i n e d phenomenology and t h r o u g h G p a r i t y t r a n s f o r m a t i o n from t h e P a r i s Poten- t i a l . Some c o n c l u d i n g remarks and o u t l o o k w i l l b e drawn i n t h e l a s t s e c t i o n . I1

-

RECALL ON THE PARIS POTENTIAL

L e t u s h e r e r e c a l l b r i e f l y some f o r m u l a e showing how was b u i l t t h e P a r i s P o t e n t i a l

171.

The s p i n - i s o s p i n dependence of t h e NN s c a t t e r i n g m a t r i x c a n b e w r i t t e n a s

5

+I +2

M(w,t) = [3p:(w,t) + 2p-(w,t) i t .T

I

Pi (2.1) i= 1

where w and t a r e t h e u s u a l Mandelstam va- r i a b l e s ( s e e F i g . 1)

F i g . 1

-

L a b e l l i n g of t h e n u c l e o n s and Pi t h e 5 f o l l o w i n g p e r t u r b a t i v e inva- r i a n t s ,

i i

The T and y a r e t h e i s o t o p i c s p i n P a u l i and D i r a c m a t r i c e s of t h e n u c l e o n i ( i = 1 , 2 ) r e s p e c t i v e l y and

The l o n g r a n g e OPE a m p l i t u d e ( p i o n p o l e ) w i t h p s e u d o s c a l a r c o u p l i n g i s t h e n

2

where g i s t h e nN c o u p l i n g c o n s t a n t , gIrN,41r = 1'4.43 and t h e p i o n mass. IrN

s i o n r e l a t i o n s and u n i t a r i t y . One can b a s i c a l l y w r i t e

The u n i t a r i t y of t h e S m a t r i x , SS+=I, w i t h S = l + i M , when s a t u r a t e d by t-channel exchanges l e a d s t o

T h i s e q u a t i o n g i v e s I m M i n t e r m s of t h e -+ 2n a m p l i t u d e i t s e l f r e l a t e d t o t h e nN amplitude. T h i s a l l o w s t o w r i t e f o r t h e p;(w,t) s u b t r a c t e d d i s p e r s i o n r e l a t i o n s of t h e t y p e / 7 / (we s u p p r e s s t h e i and

+

o r

-

dependence f o r s i m p l i c i t y ) :

2

m b e i n g t h e nucleon mass, w = 2m2

-

t / 2 t h e s u b t r a c t i o n p o i n t and

t

= 4m

-

w

-

t. The S ( t ) and S l ( t ) s u b t r a c t i o n s c o r r e s p o n d t o t h e exchange of 2n c o r r e l a t e d i n a S- and

PO

wave r e s p e c t i v e l y and a r e c a l c u l a t e d i n terms of t h e NN -+ 2 r S- and P- wave h e l i c i t y a m p l i t u d e s / l o / . The S- wave exchange, r e s p o n s a b l e of t h e needed medium r a n g e a t t r a c t i o n , i s r e p l a c e d i n t h e OBE models by a f i c t i t i o u s s c a l a r , i s o s c a l a r E

o r 0 meson. The P- wave exchange, r e p l a c e d by t h e v e c t o r , i s o v e c t o r ~ ( 7 7 0 MeV) meson i n OBE models, is t h e a g e n t of t h e medium r a n g e s p i n - o r b i t f o r c e and i t a l s o 'diminishes t h e s t r o n g t e n s o r f o r c e a r i s i n g from t h e n-exchange. The d o u b l e s p e c t r a l f u n c t i o n s y ( w ' , t l ) a r e c a l c u l a t e d i n terms of t h e a b s o r p t i v e p a r t s I m and I m B " ~ of t h e nN s c a t t e r i n g a m p l i t u d e a s s' max st' max nN nN y ( w ' , t l )

=/

d s '

J

d s 9 * R ( w ' , t ' , s ' , s l * ) I m A ( s r , t ' ) I m B ( s f l , t ' ) (2.9) (m+d (m+v)

s' and s" b e i n g t h e mN sub e n e r g i e s ( s e e F i g . 2 ) . The term w i t h w r e p l a c e d by

t

c o r - respond t o t h e c r o s s e d diagram ( F i g . 2b). K ( w ' , t ' , s l , s " ) i s t h e Mandelstam Kernel which d e f i n e s t h e domain of i n t e g r a t i o n ( s t m a x and st' _max

1.

a

>

b

F i g . 2

-

Diagrams r e p r e s e n t i n g t h e u n c o r r e l a t e d 2n exchanges. The b l o b s r e p r e s e n t t h e

r N i n t e r a c t i o n w i t h s u b e n e r g i e s s ' and s", i n c l u d i n g t h e n u c l e o n p o l e term.

C2-342 JOURNAL

DE PHYSIQUE

I n t h e P a r i s p o t e n t i a l u s e was made of t h e Glasgow 70, nN

-

PSA / I I / . ~ h e s e should be r e p l a c e d by more up t o d a t e TN -PSA a s t h a t of Karlsruhe-Helsinki 78, /12/,although t h e dominant e f f e c t , a s i t w i l l b e show l a t e r ( s e e s e c t i o n I V ) , a r i s e s from t h e w e l l known BN, E = 1 , s p i n - i s o s p i n 312 wave i . e . t h e A resonance which dominates t h e low

energy BN s c a t t e r i n g .

A t low energy and when t h e one-pion p r o d u c t i o n i s s t i l l s m a l l i . e . f o r T L \ < 3 . 5 GeV t h e u s e of t h e Schrgdinger e q u a t i o n with a NN p o t e n t i a l i s v e r y adequate t o d e s c r i b e t h e NN i n t e r a c t i o n . The NN a m p l i t u d e s p r e v i o u s l y d e s c r i b e d l e a d i n c o n f i g u r a t i o n space and f o r a g i v e n i s o s p i n 1=0 o r 1 , t o a p o t e n t i a l of t h e t y p e :

w i t h t h e f o l l o w i n g c e n t r a l , s p i n - s p i n , t e n s o r , s p i n - o r b i t and q u a d r a t i c s p i n - o r b i t terms

.

I n eq.(2.12) t h e i s o s p i n s u p e r s c r i p t s have been dropped o u t f o r s i m p l i c i t y . I t can be s e e n t h a t t h e n o n - l o c a l i t y h a s been c a s t i n t o a v e l o c i t y dependent term i n t h e c e n t r a l and s p i n - s p i n components. The phenomenological s h o r t r a n g e p a r t

r

<

.8 fm added t o t h e t h e o r e t i c a l long and medium r a n g e p a r t a r i s i n g from one-pion-, two-pion- exchanges, a s d e s c r i b e d above and u-and A1-exchanges, a s p a r t of t h e 3n-exchanges,

i s t h e n f i t t e d i n such a way t h a t t h e f u l l p o t e n t i a l reproduces w e l l t h e NN d a t a 1131. 111

-

SPIN DEPENDENCE OF THE NN INTERACTION

The s t u d y of t h e c o r r e l a t i o n s between t h e s p i n components of t h e P a r i s P o t e n t i a l and

NN o b s e r v a b l e s h a s been f u l l y d e s c r i b e d i n r e f . (14) t o which we r e f e r t h e i n t e r e s - t e d r e a d e r f o r d e t a i l s . We h e r e g i v e a summary of t h e main c o n c l u s i o n s . The v e l o c i t y dependent component, a t t r a c t i v e a t low energy and r e p u l s i v e a t h i g h energy p l a y s a r o l e a t a l l e n e r g i e s . The p o l a r i s a t i o n P, t h e d e p o l a r i s a t i o n D and t h e parameters D t , A, R, CKP and

Cm

a r e good t e s t s f o r t h e t e n s o r , s p i n o r b i t and, t o a s m a l l e r e x t e n t , q u a d r a t i c s p i n - o r b i t f o r c e s . The i s o v e c t o r t e n s o r f o r c e c o n t r i b u t i o n i s important a t low energy and t h a t of t h e i s o v e c t o r s p i n - o r b i t a t h i g h energy. The i s o s c a l a r t e n s o r f o r c e e f f e c t i s l a r g e a t a l l e n e r g i e s and t h a t of t h e i s o s c a l a r s p i n - o r b i t f o r c e r a t h e r s m a l l . The p o t e n t i a l without q u a d r a t i c s p i n - o r b i t term reproduces w e l l t h e experimental d a t a f o r TL - 1 5 GeV.

and f o r coupled s t a t e s a s 'i'L= j T 1 x T = C O S 2 € T l

s

=

(" ")

w i t h e . g

1

J L = J ~ I ~ i('L,J-l + 'L=J+l + a) i Y X+ Y = s i n 2 ~ J t h e t o t a l i n e l a s t i c c r o s s s e c t i o n i s

The c o e f f i c i e n t 2J+1 enhances t h e p e r i p h e r a l p a r t i a l wave ( l a r g e J ) c o n t r i b u t i o n t o '1ne1. On t h e o t h e r hand, t h e u s e o f u n i t a r i t y t e l l u s

" ~ n e l =

C

B I < N N I T I B > I ~ =

~ r n

< N N I T ' ~ ~ ' ~ N N >

I n e l a s t i c c h a n n e l

and f o r .4 GeV

<

TL 4 1 GeV, B = NNn and rid and f o r 1 GeV < TL 6 2.5 GeV,

B

= N N s and NNriv. We a r e n o t g o i n g t o c o n s i d e r h e r e t h e s d c h a n n e l , t h e c r o s s s e c t i o n of which peaks a t TL % .65 GeV w i t h a v a l u e o f 3.2 mb. The p e r i p h e r a l p a r t of TIne1 i s

g i v e n by IT-exchange and t h e h i g h p a r t i a l wave c o n t r i b u t i o n t o 0

t h e n b e c a l c u l a t e d from t h e imaginary p a r t s of t h e diagrams of I n e l

::::

;e4) can

s",

a ) lnN b l o b b) 2sN b l o b s F i g . 3

-

ZIT-exchange d i a g r a m s , t h e i m a g i n a r y p a r t s of which c o n t r i b u t e t o a I n e l ' The n u c l e o n p o l e

i s

excluded from t h e s N b l o b s . where t h e b l o b s r e p r e s e n t t h e s N i n t e r a c t i o n w i t h o u t t h e nucleon-pole c o n t r i b u t i o n . One o b t a i n s ( s e e eq. 2.8) I ~ T I ~ ~ ' ( W , ~ ) = - - (4.5) 4112

The d o u b l e s p e c t r a l f u n c t i o n s y ( w , t f ) a r e g i v e n by eq. ( 2 . 9 ) . P r o j e c t i n g eq. ( 4 . 5 ) on p a r t i a l wave, one o b t a i n s f o r t h e i n e l a s t i c i t y p a r a m e t e r s i n Born a p p r o x i m a t i o n

w i t h _CO

C2-344

JOURNAL

DE

PHYSIQUE

2 2

For

a

g i v e n energy, w = 4(m + k ), and a g i v e n J , t h e Legendre f u n c t i o n of t h e second kind QJ a c t s l i k e a damping f a c t o r a t h i g h t ' , s u p p r e s s i n g t h e unknown s h o r t r a n g e , heavy meson exchanges o r q u a r k s f o r c e s , c o n t r i b u t i o n s t o y ( w , t S ) . N e v e r t h e l e s s depen- d i n g on J and on t h e e n e r g y o u r r e s u l t s w i l l show some s e n s i t i v i t y t o t h e maximum v a l u e of t ' , tAax, up t o which we s h a l l p e r f o r m t h e i n t e g r a t i o n .

Following r e f . (16) o n e c a n a l s o u n i t a r i z e v i a a K-matrix p r o c e d u r e . One w r i t e s t h e f u l l p a r t i a l wave S-matrix a s t h e r e a l K m a t r i x b e i n g J I f one n e g l e c t s t h e K + t r a n s i t i o n s one c a n show t h a t w i t h U S N ' J ) =

,

m ( J ) + i I m hJ The K m + N N ( J ) b e i n g r e l a t e d t o t h e NN p h a s e s of t h e P a r i s p o t e n t i a l e x t r a p o l a t e d a t h i g h e n e r g y , e . g . f o r uncoupled waves we h a v e

The imaginary p a r t I m hJ ( s e e eq. 4.7) is t h e n c a l c u l a t e d from t h e 1-and 2-rrN b l o b diagrams ( F i g . 3 ) .

We

h e r e c o n s i d e r e d o n l y t h e S (R=O) and P (R=l) wave of t h e K a r l s r u h e - H e l s i n k i 78 a n a l y s i s / 1 2 / . We u s e d f o r t h e 1-blob diagram a t ' c u t - o f f of 4 @ 2 . Such a v a l u e was chosen h e r e t o s i m u l a t e t h e c a n c e l l a t i o n of t h e rr exchange by t h a t of t h e P which was demonstrated i n t h e work of r e f . (16) and a l s o t o ' r e p r o d u c e 0!gel around 1 GeV 1171. The ttmaX c u t o f f f o r t h e 2-blob diagram was chosen t o b e

70u2 i n s u c h

a

way t h a t a;:el b e c l o s e d t o t h e e x p e r i m e n t a l v a l u e a t 1.5 GeV / I S / .

The r e s u l t s f o r t h e 1-blob and 1+2-blob diagrams a r e compared t o t h e e x p e r i - m e n t a l p o i n t s /17,18/ and t o t h e f i t of r e f . (19) i n F i g . 4. It c a n b e s e e n t h a t below 1 GeV t h e 2-blob c o n t r i b u t i o n i s n e g l i g i b l e . We found t h a t t h e P ₃₃

*N

F i g . 4

-

I n e l a s t i c pp c r o s s - s e c t i o n F i g . 5

-

P a r t i a l wave c o n t r i b u t i o n s t o from t h e 1- and 1+2

-

b l o b diagrams t h e i n e l a s t i c pp c r o s s - s e c t i o n

112 (1.1) 1 BLOB

.S

1.0

1.5

2.0

2.5

F i g . 6

-

I n e l a s t i c np c r o s s - s e c t i o n Fig. 7

-

I s o s p i n 0 p a r t i a l wave c o n t r i - from t h e 1- and 1+2

-

b l o b diagrams b u t i o n s t o t h e i n e l a s t i c np c r o s s - s e c t i o n S i m i l a r c u r v e s f o r a r e p l o t t e d i n Figs: 6 and 7. R e c a l l

As expected from t h e f a c t t h a t t h e 1- b l o b diagram w i t h t h e P33 does n o t c o n t r i b u t e

- -

t o t h e i s o s p i n I = O c r o s s - s e c t i o n t h i s c r o s s - s e c t i o n i s v e r y s m a l l below 1 GeV. Above 1 GeV t h e 1- b l o b c o n t r i b u t i o n t o t h e 1=0 c r o s s - s e c t i o n a r i s e s mainly from t h e 1-

b l o b diagram w i t h t h e S and P, i s o s p i n 1 / 2 , nN waves, t h e 2-blob c o n t r i b u t i o n which

i s

l a r g e comes h e r e a l s o mainly from 2 P (2A) exchanges. Here ( F i g . 7) t h e r e a r e

3 3

₃

i m p o r t a n t c o n t r i b u t i o n s t o u;Kel from t h e 3~ and D i n e l a s t i c i t i e s . T t should b e

C2-346

JOURNAL

DE

PHYSIQUE

noted t h a t t h e 1 b l o b diagram w i t h t h e PI1 c o n t r i b u t e s weakly t o a l l i n e l a s t i c i t i e s except t o t h e ' G ~ one t o which it i s t h e main c o n t r i b u t i o n . Let u s remark t h a t , t o our knowledge, t h i s i s t h e f i r s t work t o u s e d i s p e r s i o n r e l a t i o n s t o c a l c u l a t e high p a r t i a l wave NN i n e l a s t i c i t i e s . Such an approach has been however r e c e n t l y a p p l i e d t o t h e nN s c a t t e r i n g c a s e 1201.

Before c l o s i n g t h i s s e c t i o n we g i v e i n r e f . (21) a l i s t of a u t h o r s who have a l s o s t u d i e d t h e NN i n e l a s t i c i t i e s from t h e n and A (and e v e n t u a l l y P l l ) d e g r e e s of f r e e - dom. Furthermore Kloet and Tjon 1221 have r e c e n t l y s t u d i e d t h e model dependence of t h e NN i n e l a s t i c i t i e s of some of t h e s e c a l c u l a t i o n s .

V

-

SPIN DEPENDENCE OF THE PARIS

fi

INTERACTIONS

A t low energy f o r TL .4 GeV o r p L < . 9 6 GeV/c t h e u s e of t h e Schrijdinger e q u a t i o n f o r NN i s a s adequate a s i n t h e NN c a s e , however one h a s t o t a k e i n t o account t h e a n n i h i l a t i o n . One c a n u s e coupled channel e q u a t i o n 1231 o r e q u i v a l e n t l y i n t r o d u c e an o p t i c a l p o t e n t i a l 1241. The P a r i s i n t e r a c t i o n 1251 u s e s a n o p t i c a l p o t e n t i a l

The long and i n t e r m e d i a t e range r e a l p o t e n t i a l U* is g i v e n by t h e G-parity t r a n s f o r m of t h e P a r i s NN p o t e n t i a l

U t h e o r e t i c a l

(G,

nn exchange) = (-1)"

vtheoretical

(NN, nn exchange) ( 5 . 2 ) The OPE

,

w and A1 exchange p o t e n t i a l s change t h e i r s i g n , one t h e n o b t a i n s a s t r o n g l y a t t r a c t i v e p o t e n t i a l which could g i v e r i s e t o bound s t a t e s and resonances 1261. The s h o r t r a n g e part,which could b e i n p r i n c i p l e c a l c u l a t e d i n terms of quark forces, i s determined phenomenologically i n t h e P a r i s p o t e n t i a l .

The imaginary p a r t of t h e p o t e n t i a l , W

-

i s r e l a t e d v i a t h e u n i t a r i t y t o t h e modulus

NN

s q u a r e of t h e NN a n n i h i l a t i o n i n t o mesons 125,271. I t i s expected .to be of s h o r t range, t h e lowest mass of t h e t exchange being t h a t of 2m, and t h e range w i l l be

It i s a l s o expected t o b e non-local and s t a t e dependent. I n t h e P a r i s

NG p o t e n t i a l ,

W

-

was parametrized, f o r both i s o s p i n , a s

NN

The modified B e s s e l f u n c t i o n K (2mr) a r i s e s - f r o m t h e c a l c u l a t i o n of t h e imaginary p a r t of a box diagram with 2noand a N and N exchanges. The unknown s h o r t range p a r t of U - and t h e parameters g NN C ,

_-

f C , gSS e t c . . . were a d j u s t e d t o f i t t h e e x i s t i n g d a t a

_-

doPP + nn ( P F ) . a t o t ( p i ) , apP + n i of - dcl and ~ ( p p ) , 1251

The s e n s i t i v i t y of some

NN

o b s e r v a b l e s t o d i f f e r e n t s p i n components of U NN

-

and W

-

and t o t h e energy dependence

NN

of W

-

a r e i l l u s t r a t e d i n F i g s . 9 t o 11. NN F i g . 9 shows t h a t t h e backward = .34 GeVlc do/dCl,which compares w e l l t o t h e mea-

surements of r e f . (30), i s v e r y s e n s i t i - v e t o t h e t e n s o r component UT of U

-

NN

l o 2

Coro (1973)

and t o a l e s s e r e x t e n t t o t h a t of t h e s p i n - o r b i t ULS. I t i s a l s o v e r y s e n s i - t i v e t o t h e energy dependence of W

-

NN b u t much l e s s s e n s i t i v e t o t h e sum, LS T

10"

-

W NN

-

+

W NN

-,

of t h e s p i n - o r b i t and t e n s o r p o t e n t i a l of WNi. T h i s s t r o n g energy dependence i s e x p e c t e d a s t h e p r e s e n c e of a n imaginary p a r t of V e r e p l a c e s a

11

I

( ~ e ~ / c ) ~

coupled c h a n n e l problem where t h e aper-

I - , L t u r e of new a n n i h i l a t i o n c h a n n e l s i s

0

0.5

energy dependent. T h i s s t u d y on t h e p o l a r i s a t i o n a t T, = 230 MeV, compared ,., F i g . 8

-

P r e d i c t i o n of t h e P a r i s

f

poten- t o t h e measurement of r e f . (31) i n F i g . t i a l f o r d a / d t of pn + pn a t P =.94 ~ e V / c _10, shows a s i m i l a r p a t e r n . I t c a n b e (TL = '39 GeV).

L

f u r t h e r m o r e s e e n t h a t below 9 0 ° , t h e p o l a r i s a t i o n i s m a i n l y g i v e n by t h e

da/dn (mb/

sr)

+

_{Alston Garnjost et al.}

JOURNAL

DE

PHYSIQUE

F i g . 10

-

The same a s i n Fig.9 b u t f o r t h e pp P o l a r i s a t i o n a t TL = .230 GeV.

8

(degrees)

C

M

. ~ ~ ' ~ . . ' . . ~ l ' . ' l ' . ' l " ~ l ' ~ " " ' l ~ . '

0

20

40

60

80

100

120

140 160

180

F i g . 11

-

A s i n F i g . 9 b u t f o r t h e p i D e p o l a r i s a t i o n a t TL = .230 GeV. The r e s u l t s LS T

w i t h

W e

+ WNfi = 0 and s t a t i c W

-,

v e r y c l o s e t o t h a t w i t h t h e complete p o t e n t i a l ,

NN

a r e n o t p l o t t e d .

t e n s o r f o r c e UT. The d e p o l a r i s a t i o n p a r a m e t e r (Fig.

111,

i n s e n s i t i v e t o t h e energy

LS T I ,

dependence of W

-

and t o W

-

+

W

-,

i s a l s o m a i n l y g i v e n by t h e t e n s o r f o r c e UT. T h i s

NN NN NN

i m p o r t a n t t e n s o r component of U

-

i s due h e r e t o t h e c o h e r e n t a d d i t i o n of t h e t e n s o r

f o r c e s of t h e n-, 2n- ( i n p a r t i c u l a r 2n c o r r e l a t e d i n P wave i . e . t h e p meson) and

w- exchanges. The s p i n - o r b i t f o r c e p l a y s a l e s s i m p o r t a n t r o l e . T h i s i s t h e r e v e r s e s i t u a t i o n of t h e NN c a s e a s h a s been r e c a l l e d i n s e c t i o n I11 and i l l u s t r a t e d i n r e f . (14) and i s a consequence of t h e G-Parity t r a n s f o r m a t i o n . Such a f a c t h a s been a l s o found and shown i n r e f . ( 3 2 ) .

VI

-

SOME CONCLUDING REMARKS

AND

OUTLOOK

A t low e n e r g y , TL

<

.35 GeV o r pL 6 .88 ~ e V / c t h e l o n g and i n t e r m e d i a t e r a n g e NN f o r - c e f s w e l l u n d e r s t o b d i n t e r m s of meson exchanges. The s p i n e f f e c t s (P,D,A,

...

) a r e w e l l e x p l a i n e d by a l o n g r a n g e t e n s o r f o r c e a r i s i n g from n- and 2n- ( c o r r e l a t e d i n P- wave i . e . t h e p) exchange p l u s a n i n t e r m e d i a t e r a n g e s p i n - o r b i t f o r c e (exchange of 2n c o r r e l a t e d i n P- wave i . e . t h e p ) . I n t h e P a r i s p o t e n t i a l t h e s h o r t r a n g e p a r t was t r e a t e d phenomenologically, however o n e should b e a b l e t o e x p l a i n it i f t h e t h e o r y of s t r o n g i n t e r a c t i o n was f u l l y u n d e r s t o o d .

Some a t t e m p s t o d e r i v e s h o r t r a n g e f o r c e s h a v e been made w i t h i n t h e Quantum Chromo- dynamic framework. These m i c r o s c o p i c a p p r o a c h e s 133,341 depend on t h e quark-quark f o r c e s , t h e q u a r k confinement mechanism and t h e wave f u n c t i o n of o v e r l a p p i n g n u c l e o n s and t h e i r dynamics. T h e r e h a s been a l s o h y b r i d quark-nucleon models where a n i n n e r r e g i o n of q u a r k s j o i n s i n a smooth way t o a n o u t e r r e g i o n of n u c l e o n s 1351. It h a s been s u g g e s t e d by Skyrme 1361 t h a t t h e n u c l e o n c o u l d b e a s o l i t o n i n t h e n and o f i e l d . R e c e n t l y Adkins, Nappi and W i t t e n 1371 have q u a t i z e d t h e Skyrme s o l i t o n and f i t t i n g t h e N and A masses, t h e y were a b l e t o d e s c r i b e t h e s t a t i c p r o p e r t i e s of t h e n u c l e o n w i t h i n 30%. A baryon-baryon f o r c e c a n t h e n b e c a l c u l a t e d a s r e s u l t i n g from a s o l i t o n - s o l i t o n i n t e r a c t i o n . A s t a t i c NN p o t e n t i a l h a s been r e c e n t l y d e r i v e d i n r e f s . (38) and (39) w i t h t h e a p p r o x i m a t i o n t h a t t h e f i e l d c o n f i g u r a t i o n f o r two s o l i t o n s i s a p r o d u c t of two s i n g l e s o l i t o n f i e l d s . I n r e f . ( 3 9 ) i t was found t h a t t h i s s o l i t o n - s o l i t o n i n t e r a c t i o n g i v e s r i s e t o a l o n g r a n g e t e n s o r p o t e n t i a l v e r y c l o s e t o t h a t of a r exchange of z e r o mass. A t s h o r t r a n g e a c e n t r a l r e p u l s i o n i s o b t a i n e d . Furthermore n o t o n l y NN -t NN b u t a l s o NN -t NA and NA + NA s t a t i c p o t e n t i a l s were d e r i v e d . Some non s t a t i c f o r c e t e r m s h a s been a l s o c o n s i d e r e d i n r e f . ( 4 0 ) . T h e o r e t i c a l h i g h p a r t i a l wave i n e l a s t i c i t i e s a r i s i n g from n and A d e g r e e s o f freedom, s h o u l d b e u s e d a s c o n s t r a i n t s , w i t h some model dependent e r r o r s , i n PSA, i n p a r t i c u l a r waves w i t h L >, 4 f o r TL ,<

1

GeV (pL \< 1.7 GeVlc) and L 5 f o r 1 GeV < TL ,< 2.5 GeV

(1.7 GeV/c < p L 4 3 . 3 GeV/c).

The u s e of G - p a r i t y t r a n s f o r m a t i o n t o b u i l t up t h e l o n g and i n t e r m e d i a t e r a n g e

%

f o r c e from t h e NN f o r c e t e s t s c o h e r e n c e s between meson exchanges. The s t u d y of s p i n e f f e c t s w i t h t h e P a r i s NN p o t e n t i a l h a s shown t h e importance of a s t r o n g t e n s o r f o r - c e , h e r e t h e n

+

2 r ( p )

+

w exchange t e n s o r f o r c e s add c o h e r e n t l y , t h e r o l e of t h e s p i n - o r b i t f o r c e b e i n g weaker. The phenomenological a n n i h i l a t i o n , c o n s t r a i n e d t o b e s h o r t ranged i n t h e P a r i s p o t e n t i a l , a s p r e d i c t e d by meson t h e o r y , shows a weak s p i n dependence b u t a s t r o n g energy-dependence. There h a s been d i f f e r e n t t r i a l s t o d e r i v e t h e a n n i h i l a t i o n i n t e r m s of qq f o r c e s e i t h e r i n t e r m s of q u a r k rearangement models a n d / o r i n t e r m s o f a n n i h i l a t i o n diagrams / 4 1 / . I t should b e n o t e d t h a t o n l y few p o l a r i - s a t i o n measurements around 230 MeV and 379 MeV e x i s t s o f a r . More d a t a on s p i n o b s e r - v a b l e ~ (P,D,D

,...

) a r e needed t o f u l l y e x p l a i n t h e s p i n dependence of t h e NN i n t e r - a c t i o n . Some 8 a t a w i l l b e h o p e f u l l y soon a v a i l a b l e from LEAR 1421.

ACKNOWLEDGEMENTS

C2-350

JOURNAL DE PHYSIQUE

REFERENCES

1

-

B.P. Nigam, Rev. Mod. Phys.

35

(1963) 117 ; and r e f s . c i t e d t h e r e i n . 2

-

H. Yukawa, P r o c . Phys. Math. Soc. J a p a n 17 (1935) 48.

3

-

S. Mandelstam, Phys. Rev.

112

(1958) 1344.

4

-

D. A m a t i , E. Leader and B. V i t a l e , Nuovo Cimento (1960) 68 ;

18

(1960) 409 ;

Phys. Rev. (1963) 750;W.N. Cottingham, R. Vinh Mau, Phys. Rev.

130

(1963)735. 5

-

S. F u r u i c h i , Supplement P r o g r e s s of Theor. P h y s i c s 39 (1967) 190.

6

-

G.E. Brown, Comments Nucl. P a r t . Phys. 4 (1970) 140; M. Chemtob, J . W . Durso and D.O. R i s k a , Nucl. Phys.

g

(1972) i 4 1 ; J . W . Durso, M. S a a r e l a , G.E. Brown and A.D. J a c k s o n , Nucl. Phys.

A278

(1977) 445 ; G.E. Brown and A.D. J a c k s o n , The Nucleon-Nucleon I n t e r a c t i o n , (North-Holland, Amsterdam, 1976).

7

-

W.N. Cottingham, M. Lacombe, B. L o i s e a u , J . M . Richard and R. Vinh Mau, Phys. Rev.

5

(1973) 800 ; R. Vinh Mau, "The P a r i s N-N P o t e n t i a l " i n Mesons i n N u c l e i , e d i t e d by M. Rho and D. W i l k i n s o n (North-Holland, Amsterdam, 1979) p.179 ; W.N. Cottingham,"Mesons and t h e two-nucleon p o t e n t i a l " , R e p . Prog. Phys.

5

(1979)1509. 8

-

J.J. d e Swart, W.A. van d e r Sanden, W. Derks, Nucl. Phys.

A416

(1984) 299c. 9

-

C.B. Dover, Nucl. Phys.

A416

(1984) 313c.

10

-

G. HShler and E. P i e t a r i n e n , Nucl. Phys.

B95

(1975) 210. E. P i e t a r i n e n , H e l s i n - k i r e p o r t (1978) ; P. Gauron, P a r i s r e p o r t , IPNO/TH 78-07 (1978) ; B . Bonnier and P. Gauron, Nuovo Cimento

57A

(1980) 261.

11

-

P a r t i c l e Data Group, UCRL r e p o r t

N o 20030 (1970).

12

-

G. HGhler, F. K a i s e r , R. Koch and E. P i e t a r i n e n , Handbook of P i o n Nucleon S c a t - t e r i n g , P h y s i c s Data 12-1, K a r l s r u h e (1979).

13

-

M. Lacombe, B. L o i s e a u , J . M . R i c h a r d , R. Vinh Mau, J . CBt6, P. P i r S s and R. d e T o u r r e i l , Phys. Rev.

C21

(1980) 861 ; M. Lacombe, B. L o i s e a u , R. Vinh Mau, J. Cbt6, P. P i r S s and R. d e T o u r r e i l , Phys. Rev.

3

(1981) 2405.

14

-

F. P a u s s , L. M a t h e l i t s c h , J . CbtC, M. Lacombe, B. L o i s e a u and R. Vinh Mau, Nucl. Phys.

A365

(1981) 392.

15

-

M. Lacombe, B. L o i s e a u , S. Morioka and R. Vinh Mau, Few Body Problems i n P h y s i c s Vol. I1 c o n t r i b u t e d p a p e r s , B. Z e i t n i t z ( e d i t o r ) , E l s e v i e r 1984, p. 151 ; P a r i s r e p o r t , IPNo/TH 84-12 ; P a r t i c l e s and N u c l e i Tenth I n t e r n a t i o n a l Conference, Book of A b s t r a c t s , Vol. 1 , H e i d e l b e r g 1984, F. G i i t t n e r , B. Pooh, G. zu P u t l i t z E d i t o r s , S p r i n g e r - V e r l a g , C10.

16

-

J. CbtL, M. Lacombe, B. L o i s e a u and W.N. Cottingham, Nucl. phys.

A379

(1982)349. 17

-

F. Shimizu, Y Kubota, H. Koiso, F. S a i , S. Sakamoto and S.S. Yamanoto, Nucl.

Phys.

A386

(1982) 571.

18

-

J. B y s t r i c k y and F. Lehar, P h y s i c s D a t a 11-1, K a r l s r u h e (1978). 19 - B . J . Verwest and R.A. A r n d t , Phys. Rev.

C25

(1982) 1979.

20

-

G. HShler, D. G r e t h e r , M. H u t t and I. Sabba-Stefanescu, K a r l s r u h e r e p o r t , TPK 83-24 (1983).

21

-

A.M. Green, J.N. Niskanen, J . Phys. (1978) 1055 ;A.M. Green,M.E. S a i n i o , J. Phys.

65

(1979) 503 ; i b i d G8 (1982) 1337 ; W.M. K l o e t and R.R. S i l b a r

,

Nucl. Phys.

A338

(1980) 281; Nucl. Phys. A338 (1980) 317 ; Nucl. Phys.

2

(1981) 346 ; Phys. Rev. L e t t .

45

(1980)

~ ~ T J . H .

Gruben and B . J . Verwest, Phys. Rev.

C28

(1983) 836.

22

-

W.M. K l o e t and J.A. Tjon, R u t g e r s U n i v e r s i t y r e p o r t , RU-84-26 (1984).

23

-

P.H. Timmers, W.A. van d e r Sanden and J.J. d e Swart, Phys. Rev. (1984) 1928. 24

-

R. Bryan and R. P h i l l i p s , Nucl. Phys. (1968) 201 ; C. Dover and J . M . R i c h a r d ,

Phys. Rev.

g

(1980) 1466.

25

-

J. C B t C , M. Lacombe, B. L o i s e a u , B. Moussallam and R. Vinh Mau, Phys. Rev. L e t t . 48 (1982) 1319.

26

-

Lacombe, B. L o i s e a u , B. Moussallam and R. Vinh Mau, Phys. Rev.

C29

(1984)1800. 27

-

R. Vinh Mau, "NN f o r c e s and a n n i h i l a t i o n i n t h e p o t e n t i a l a p p r o a c h M i n P h y s i c s

a t LEAR w i t h low-energy c o o l e d a n t i p r o t o n s

,

e d i t e d by U. G a s t a l d i and R. Kla- p i s h , Plenum P u b l i s h i n g C o r p o r a t i o n , 1984, p. 395 ; B. L o i s e a u , " P o t e n t i a l approach t o Antinucleon-Nucleon i n t e r a c t i o n " , P r o c e e d i n g s of t h e T h i r d LAMPF I1

Workshop L.A.N.L., Los Alamos, N.M., 1983, LA-9933-C Vol.1 p. 366. 28

-

K. Nakamura e t a l . , Phys. Rev. L e t t .

12

(1984) 885.

29

-

D.E. Caro e t a l . , Nucl. Phys.

B52

(1973) 301.

30

-

M. A l s t o n - G a r n j o s t e t a l . , Phys. Rev. L e t t .

43

(1979) 1901.

32

-

C. Dover and J.M. R i c h a r d , Phys. Rev.

g

(1922) 1952.

33

-

D.A. Liberman, Phys. Rev. Jig (1977) 1542 ; C. d e T a r , Phys. Rev.

D17

( 1 9 7 8 ) 3 2 3 ; i b i d

19

(1979) 1451 ; M. Harvey, Nucl. Phys.

A35P

(1981) 301, 326 ; A . F a e s s l e r ,

F. Fernandez, G. Liibeck and K. Shimizu, Phys. L e t t . (1982) 201 ; M. Oka and

K. Yazaki, Nucl. Phys.

A402

(1983) 477 ; S. F u r u i and A . F a e s s l e r , Nucl. Phys. A397 (1983) 413.

34

-

C.W. Wong, "Yukawa, Skyrme and QCD", Tenth I n t e r n a t i o n a l Conference on P a r t i c l e and N u c l e i , H e i d e l b e r g 1984, Nucl. Phys.

A,

t o b e p u b l i s h e d .

35

-

E. Lomon, i n Hadron S u b s r t u c t u r e i n Nuclear P h y s i c s , e d i t e d by W.Y.P. Hwang and

M.H. M a c f a r l a n e , AIP P r o c e e d i n g s Nol10 (1984) 117 ; L.S. K i s s l i n g e r ,

p. 271 ; E. Lomon, t h e s e p r o c e e d i n g s ; P . J . Mulders, Nucl. Phys.

A416

( 1 9 8 4 1 9 9 ~ . 36

-

T. Skyrme, P r o c . Roy. Soc. London

260

(1961) 127 ; Nucl. Phys.

31

(1962) 556. 37

-

G.S. Adkins, C.R. Nappi and E. W i t t e n , Nucl. Phys.

B228

(1983) 552.

38

-

A . J a c k s o n and V. P a s q u i e r , Stony Brook p r e p r i n t , t o b e p u b l i s h e d i n Nucl. Phys.

39

-

R. Vinh Mau, M. Lacombe, B. L o i s e a u , W.N. Cottingham, P. L i s b o a , IPNO/TH p r e - p r i n t N084-66, t o b e p u b l i s h e d i n Phys. L e t t . B.

40

-

Z . Hlousek, Brown U n i v e r s i t y P r e p r i n t , HET 526 (1984).

41 - M. Maruyama and T. Ueda, Phys. L e t t .

124B

(1983) 121 ; A.M. Green, J . Niskanen,

J.M. R i c h a r d , Phys. L e t t . 121B (1983) 101.