NUCLEON-NUCLEON SCATTERING DATA IN LIGHT OF RECENT PHASE SHIFT ANALYSES

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NUCLEON-NUCLEON SCATTERING DATA IN LIGHT OF RECENT PHASE SHIFT ANALYSES

J. Bystricky

To cite this version:

J. Bystricky. NUCLEON-NUCLEON SCATTERING DATA IN LIGHT OF RECENT PHASE SHIFT ANALYSES. Journal de Physique Colloques, 1985, 46 (C2), pp.C2-487-C2-491.

�10.1051/jphyscol:1985263�. �jpa-00224580�

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Colloque C2, supplément a u n02, Tome 46, f é v r i e r 1985 page C2-487

NUCLEON-NUCLEON SCATTERING DATA IN LIGHT OF RECENT PHASE S H I F T ANALYSES

J . B y s t r i c k y

DPhPE, CEN-Saclay, F r a n c e

Resumé

-

Nous d i s c u t o n s l e s données d e l a d i f f u s i o n nucléon-nucléon j u s q u ' à l ' é n e r g i e d e 1 GeV. La comparaison d e s a n a l y s e s e n d é p h a s a g e s r é c e n t e s permet d e d é t e r m i n e r l e s é n é r g i e s où l e s m e s u r e s d e v r a i e n t ê t r e c o m p l é t é e s .

A b s t r a c t

-

A v a i l a b l e nucleon-nucleon e l a s t i c s c a t t e r i n g d a t a up t o 1 GeV a r e d i s c u s s e d . Comparison of r e c e n t p h a s e s h i f t a n a l y s e s shows what a r e t h e e n e r g y r e g i o n s where measurements should b e p e r f ormed.

Comparison of r e c e n t l y a p p e a r i n g p h a s e - s h i f t a n a l y s e s ( 1 y 2 y 3 y 4 ) g i v e s a n i d e a a b o u t t h e c o m p l e t e n e s s of t h e p r e s e n t l y a v a i l a b l A e N

-

^N d a t a and t h e g a p s which s h o u l d b e f i l l e d i n . An i n s t r u c t i v e g r a p h i c a l r e p r e s e n t a t i o n of t h e d a t a measured up t o 1 GeV i s g i v e n i n r e f . 2. T h i s i s t h e energy r e g i o n we w i l l l i m i t o u r s e l v e s t o .

Looking f i r s t o n t h e pp measurements, t h e f o l l o w i n g e n e r g y i n t e r v a l s a r e remarkable.

Between 145 and 300 MeV o n l y d i f f e r e n t i a l c r o s s s e c t i o n s , a n a l y z i n g powers and a few p o i n t s of t h e W o l f e n s t e i n p a r a m e t e r s ( a t 209 and 213 MeV) were measured. The d a t a between 600 and 800 MeV, which a r e s t i l l i n s u f f i c i e n t , w i l l b e completed by e x t e n s i v e measurements a t LAMPF a number of which a r e n o t y e t a n a l y z e d . The r e g i o n from 800 t o

950 MeV h a s a l m o s t no two-index ~ a r a m e t e r m e a s u r e d . Recent e x p e r i m e n t s a t SATURNE II a r e expected t o improve c o n s i d e r a b l y t h e s i t u a t i o n even above 1 GeV.

E x i s t i n g i n c o m p a t i b i l i t i e s between . d a t a sets f rom d i f f e r e n t e x p e r i m e n t s c a n i n g e n e r a l be overcome by a p p r o p r i a t e n o r m a l i z a t i o n . T h i s i s t h e c a s e of

AuL

d a t a which i s d i s - c u s s e d i n r e f

.

^{1 .}

From t h e t o t a l number of a b o u t 6000 pp d a t a p o i n t s below 1 GeV 42% a r e spin-indepen- d e n t measurements, 26% a r e p o l a r i z a t i o n s a n d a n a l y z i n g powers and 32% a r e two and t h r e e - i n d e x p a r a m e t e r s .

I n t h e np (pn) s c a t t e r i n g t h e s i t u a t i o n i s much l e s s s a t i s f a c t o r y . From t h e t o t a l num- b e r of 6100 p o i n t s below 800 MeV t h e c o r - r e s p o n d i n g p e r c e n t a g e s a r e 8 1 % , 13% and 6%, r e s p e c t i v e l y . The energy r e g i o n s w i t h r e l a t i v e l y lower number of np d a t a c o i n - c i d e w i t h t h o s e o f t h e pp s c a t t e r i n g . Moreover f ew np d i f f e r e n t i a l cross-sec-

t i o n s above 400 MeV a r e measured i n t h e forward d i r e c t i o n . I n t h e l i t t l e number of t h e s p i n dependent np e x p e r i m e n t s t h e c o r r e l a t i o n s a r e a l m o s t a b s e n t .

I n c o m p a t i b i l i t i e s between d i f f e r e n t d a t a s e t s a r e more d i f f i c u l t t o b e d e a l t w i t h . The c a s e of np t o t a l c r o s s - s e c t i o n measu- r e m e n t s i s w e l l known. The s e r i e s of LAMPF d a t a ( 5 ) i s i n c o m p a t i b l e w i t h t h e o l d e r d a t a even i f normalized. The r e c e n t FREIBURG experiment a t SIN(^) between 120 and 580 MeV s u p p o r t s t h e LAMPF d a t a .

180 a 4

0 3 a 2

a i

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ecw deo. F i g . 1

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Aoono and A a t 425 MeV.

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, 1 1 8 r 1 '

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l L m P F %oon

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O TRIUMF Aoono

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O

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90

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985263

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Another example of t h e experimental discrepancy i s i l l u s t r a t e d b t h e Fig. 1. The an- g u l a r dependenees of

bon0

from IRTUM.(~) and Aooon from LAMPF(BY a t 1 2 5 MeV show qui- t e d i f f e r e n t shapes. The v a l u e s a r e c o n s i s t e n t below 80' and above 120' CM b u t a r e l a - t i v e d i f f e r e n c e a s l a r g e a s 30% o c c u r e s around 100" CM. The i n c o n s i s t e n c y p e r s i s t s between Aoono a t 495 MN(') and A,,,,, a t 475 M ~ v @ ) .

-100

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T (

MeV 1

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PSA symbols:

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r e f . 1 , - - - + - r e f . 2 , r e f . 3 , r e f . 4 , 0 , 0 , A ,V f o u r so- l u t i o n s a t l GeV, r e f . l .

L e t u s s e e p a r t i c u l a r f e a t u r e s of s e v e r a l r e c e n t p h a s e - s h i f t a n a l y s e s (PSA).

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I l I I I 1 I

400 600 800 1000

The Saclay-Geneva PSA") i s a n energy dependent a n a l y s i s . Each e n e r g y i n t e r v a l was cho- s e n s m a l l enough t o a l l o w a d e s c r i p t i o n o f t h e s h a p e o f each p h a s e - s h i f t i n t h e i n t e r - v a l by a c u b i c e n e r g y f u n c t i o n . The p r o c e d u r e r e s u l t s i n f o u r m u t u a l l y independent pp and n p a n a l y s e s i n t h e i n t e r v a l s 10-220 MeV, 140-450 MeV, 380-610 MeV and 520-800 MeV.

No i n p u t from d i s p e r s i o n r e l a t i o n o r p o t e n t i a l c a l c u l a t i o n s supplemented expezimental d a t a . The s o l u t i o n s a r e f a i r l y smooth from o n e i n t e r v a l t o t h e o t h e r f o r t h e pp analy- ses ( s e e f u l l l i n e s w i t h e r r o r c o r r i d o r s i n F i g s 2 and 3 ) . Dashed lines i n Fig. 3 are p r e d i c t i o n s from t h e P a r i s p o t e n t i a l ( 9 ) . A v e r y ood agreement w i t h t h e a n a l y s i s i s found f o r Im

.

The s h a p e s of h t h ïm d e p e n d e n c i e s a r e s i m i l a r even though t h e p o t e n t i a l was i n t e n d e d o n l y f o r h i g h e r waves. The bad c o n t i n u i t y of t h e i s o s p i n 1=0 p h a s e s h i f ts ( s e e Fig. 4) r e f l e c t s 10, t h e i n s u f f i c i e n c y of t h e n p d a t a . A s i n g l e e n e r g y

pp a n a l y s i s a t 1 GeV was performed r e s u l t i n g i n f o u r d i f f e r e n t s o l u t i o n s ( F i g . 2 , 3 ) .

The a n a l y s i s of Arndt e t i s ar, e n e r g y de- pendent one performed i n t h e l a r g e i n t e r v a l from ZOO 400 600 800 1000 O t o 1050 MeV. D i s p e r s i o n - t h e o r y q u a n t i t i e s weak-

l y c o n s t r a i n i n g t h e f o r w a r d d i r e c t i o n a m p l i t u d e s 30

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3p3 and 1 ~ 4 200 400 600 800 1000

In 3P, -

s h i f t s a r e p r e s e n t e d i n F i g s 2 , 3 , 4 a s dot-and- 3 dashed l i n e s . For t h e pp s c a t t e r i n g b o t h a n a l y s e s

..-

( r e f s 1 and 2) d i f f e r s l i g h t l y below 300 MeV (e.g.

E2 p a r a m e t e r ) and t h e n c o i n c i d e up t o -500 MeV.

A b t h e n t h e d i f f e r m e n i n s u c h impor- t a n t p h a s e s h i f t s a s l Ç O o r ( s e e F i g . 2) r e -

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i n - d e g r e e s .

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----pre- f l e c t i n g t h u s i n c o m p l e t n e s s of t h e a n a l y z e d d a t a . At 1 GeV o f t e n n e i t h e r of t h e f o u r s o l u t i o n s of r e f . 1 c o r r e s p o n d s t o t h a t of r e f . 2 . The d i f f e- r e n c e between t h e i n e l a s t i c i t i e s i n r e f . 1 and 2

200 400 600 800 1000

d i c t i o n s of r e f . 9.

I n r e f . 3 and 4 imagi- n a r y p a r t s were n o t de- termined a t a l 1 e n e r g i e s .

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( s e e F i g . 3 ) i s a t l e a s t p a r t l y d u e t o t h e d i f f e r e n t t r e a t e m e n t of 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 s . Both a u t h o r s u s e a s a n i n p u t t o t h e a n a l y s i s a sum of i n e l a s t i c r e a c - t i o n c r o s s - s e c t i o n s , which a r e f i t t e c t t o e x p e r i m e n t a l d a t a by f u n c t i o n s of energy.

Whereas in r e f

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¹ a l 1 a v a i l a b l e r e a c t i o n s a r e c o n s i d e r e d and t h e i r f i t s a r e m u t u a l l y i n d e p e n d e n t , i n r e f

.

2 t h e i s o s p i n decomposition of t h e one-pion p r o d u c t i o n is impo- sed and t h e two-pion p r o d u c t i o n i s n e g l e c t e d . The d i f f e r e n c e between t h e two approa- c h e s becomes s i g n i f i c a n t above 750 MeV and r e a c h e s f o r t h e pp t o t a l i n e l a s t i c c r o s s -

T M e V

I I I I ~ l l I l I

O 200 400 600 800 1000

---.-._._

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T M e V

( I I l I I I I I I

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3 1

F i g . 4 - R e a l p a r t s of SI

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3 ~ 3 and l ~ 3 . Symbols a s i n F i g . 2

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s e c t i o n a b o u t 2 mb a t 1 GeV. For t h e np s c a t t e r i n g t h e d i f f e r e n c e i s even l a r g e r . The d i s a g r e e m e n t of b o t h a n a l y s e s i s more s t r i k i n g f o r 1=0 p h a s e s h i f t s ( s e e F i g . 4 ) . Smooth energy dependences of r e f . 2 c o n t r a s t w i t h broken l i n e s of r e f . 1 o f t e n ambigu- o u s i n t h e e n e r g y - i n t e r v a l o v e r l a p s . These d i s c o n t i n u i t i e s show o n c e more t h e i n s u f - f i c i e n c y of t h e d a t a which c a n p r e s e n t l y o n l y be overcome by imposing a c o n s t r a i n i n g energy dependence.

A s i n g l e energy a n a l y s i s of t h e pp and np s c a t t e r i n g a t 142, 210, 325, 425 and 515 MeV and o n l y t h e pp o n e a t 580, 650 and 800 MeV was performed by Dubois e t

W i t h i n one s o l u t i o n t h e i r p h a s e s h i f t s were l i n e a r l y dependent o n energy. The s l o p e s were t a k e n i t e r a t i v e l y from smooth c u r v e s t h r o u g h s o l u t i o n s o v e r t h e complete energy r a n g e . D i s p e r s i o n r e l a t i o n s and heavy boson exchange p r e d i c t i o n s were used t o supple- ment t h e e x p e r i m e n t a l i n p u t d a t a . Some h i g h e r - l p h a s e s h i f t s , b o t h r e a l and imaginary, were t a k e n from OBE + HBE p r e d i c t i o n s . The s o l u t i o n s of r e f . 3 a r e p r e s e n t e d i n F i g s 2 , 3 , 4 a s open boxes. The r e a l pp p h a s e s h i f t s a g r e e up t o 515 MeV w i t h t h o s e of r e f s 1 and 2, t h e n t h e y f o l l o w b e t t e r t h e dependences of r e f . 1 e x c e p t f o r some p h a s e s h i f t s a t 800 MeV. The agreement of imaginary p a r t s of r e f . 1 and 3 i s good e x c e p t i n g I m 3 ~ 0 (Fig

.

^{3 ) .}

The l a t e s t ~ o s h i z a k i ' s pp a n a l y s i s ( 4 ) was donne a t 26 e n e r g i e s f rom 400 t o 3170 MeV.

The a n a l y s i s makes u s e of f o r w a r d - s c a t t e r i n g d i s p e r s i o n - r e l a t i o n p r e d i c t i o n s a s i n - p u t d a t a . The r e s u l t s of 16 a n a l y s e s below 1050 MeV a r e p l o t t e d i n F i g s 2 , 3 a s f u l l c i r c l e s . They show more d i s p e r s i o n t h a n o t h e r t h r e e a n a l y s e s , e s p e c i a l l y i n t h e imagi- n a r y p h a s e s h i f t s , m a n i f e s t i n g t h u s t h e l i m i t s imposed by p r e s e n t e x p e r i m e n t a l d a t a t o s i n g l e energy a n a l y s e s even i n pp s c a t t e r i n g .

We c a n c o n c l u d e t h a t t h e e x i s t i n g pp d a t a should b e completed by s p i n dependent expe- r i m e n t s . From l o w e s t e n e r g i e s up t o 300 MeV t h e y would improve c o n s i d e r a b l y t h e known s o l u t i o n . Above 500 MeV t h e y w i l l a l l o w d e t e r m i n a t i o n of imaginary p a r t s of p h a s e s h i f t s w i t h o u t any mode1 i n p u t . The l a s t measurements a r e e x p e c t e d t o be soon a v a i l a b - l e from SIN, LAMPF and SATURNE II e x p e r i m e n t s .

I n t h e n-p s c a t t e r i n g t h e d a t a should be completed i n t h e e n t i r e e n e r g y r a n g e . A t v e r y low e n e r g i e s t h e t h r e s h o l d b e h a v i o u r of t h e mixing p a r a m e t e r i s s t i l l n o t c o r r e c t - l y determined ( s e e F i g . 4 ) . The l a c k of spin-dependent measurements r e f l e c t s a n i n - suf f i c i e n t q u a l i t y of e x i s t i n g p o l a r i z e d n e u t r o n beams. The s p i n c o r r e l a t i o n parame- t e r s and s p i n dependent t o t a l c r o s s s e c t i o n s a r e p r a c t i c a l l y i n e x i s t a n t and d i s c r e - p a n c i e s i n t h e a n a l y z i n g power measurements throw s e r i o u s d o u b t s on t h e q u a l i t y of t h e np s c a t t e r i n g e x p e r i m e n t s . The imaginary p a r t s of t h e i s o s p i n 1=0 p h a s e s h i f t s a r e e x t r e m e l y u n c e r t a i n s i n c e t h e i n e l a s t i c c r o s s s e c t i o n s a r e p r a c t i c a l l y unknown above 650 MeV. T h i s problem c a n b e s e t t l e d by measurements of t h e n p - + n p r o t o t a l c r o s s s e c t i o n .

On t h e o t h e r hand, a c o n s i d e r a b l e improvment was a c h i e v e d i n t h e measurements of s p i n lndependent p a r a m e t e r s (atof du/dR). The LAMPF and FREIBURG n p t o t a l c r o s s s e c t i o n d a t a seems t o e s t a b l i s h d e f ~ n ~ t e l y t n e e n e r g y dependence of atot(np) below 800 MeV.

I t i s d e ç i r a b l e t o r a n e a s u r e utot(np) a b o v e 800 MeV, s i n c e t h e R u t h e r f o r d data(''), w i t h s m a l l e r r o r s , d e t e r m i n e d from q u a s i - e l a s t i c pn(d) s c a t t e r i n g , d e s a g r e e w i t h t h e d a t a measured w i t h f r e e n e u t r o n s . S e v e r a l s e r i e s of t h e do/dR d a t a a t m a l 1 a n g l e s , measured a t SATURNE II, w i l l soon be a v a i l a b l e and w i l l c o n s i d e r a b l y c o n t r i b u t e t o d e t e r m i n e t h e e n t i r e a n g u l a r dependence of t h e d i f f e r e n t i a l c r o s s s e c t i o n s . REFERENCES

(1) J . B y s t r i c k y e t a l , P r e p r i n t DPhPE 82-12, r e v i s e d Feb. 1984, t o b e p u b l i s h e d (2) R.A.Arndt e t a l , Phys.Rev. D28 (1983) 97

(3) R.Dubois e t a l , Nucl.Phys. A377 (1982) 554

(4) N.Hoshizaki, Seminar a t Dubna, June 1984 and p r i v a t e communication of A.Masaike (5) P.W.Lisowski e t a l , Phys.Rev.Letts 49 (1983) 225

(6) V.Grundiers e t a l , 1 0 t h I n t . Conf

.,

H e i d e l b e r g 1984 and priv.comm. of E.Rossle.

( 7 ) A.S.Clough e t a l , Phys.Rev. C21 (1980) 988

(8) C .R.Newsom e t a l , r e f

.

^/N-39

^/

i n "NUCLEON-NuCLEON SCATTERING DATA", K F Z K a r l s r u h e , P h y s i c s d a t a , Vols. 11-2, 11-3 (1981) H.Behrens and G.Ebe1, e d i t o r s

(9) J.CÔtè e t a l , Nucl.Phys. A379 (1982) 349 and M.Lacombe e t a l , Phys.Rev. C21 (1980) 861 (10) D.V.Bugg e t a l , Phys.Rev. 146 0 6 6 ) 980