HADRONIC ATOMS

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HADRONIC ATOMS

F. Scheck

To cite this version:

F. Scheck. HADRONIC ATOMS. Journal de Physique Colloques, 1972, 33 (C5), pp.C5-183-C5-193.

�10.1051/jphyscol:1972514�. �jpa-00215116�

JOURNAL

DE

PHYSIQUE Colloque C 5 , suppl6ment au no 8-9, Tome 33, Aoat-Septembre 1972, page C5-183

HADRONIC ATOMS

F .

Scheck

SIN and ETH Zurich

R6sum6

-

Nous mentionnons brisvement deux nouveaux rgsultats dans l'ktude des atomes muoniques concernant la mesure d e moments quadrupolaires spectro- scopiqueset l'etude d e corrections radiatives. A titre d'introduction au sujet on passe en revue quelques propri6tBs fondamentales des atomes hadroniques et les rnethodes d'analyse theorique. On discute p a r la suite quelques applications

2

l'btude du noyau (distributions d e neutrons, densitbs d e masse quadrupolairesl ainsi que d e nouvelles applications 3 l'etude des propriQt6s d e la particule capturee (effets d e polarisation) ou de l'amplitude d e diffusion particule-nucl6ons dans le noyau (extrapolation off-shell e t effets d e correlations).

Abstract - We mention briefly two new results in the study o f muonic atoms concerning the measurement of spectroscopi~quadrupole moments and the study of radiative corrections with muonic atoms. As an introduction to the sub- ject proper, we review shortly some o f the basic properties of hadronic atoms and their theoretical analysis. We then discuss some applications to the study of the nucleus [neutron distributions, quadrupole mass densities) as well a s novel applications to the investigation of properties of the captured particle fpolarizabilityl o r of the particle-nucleon scattering amplitude in the nucleus (off-shell extrapolation and correlation effectsf.

1. INTRODUCTION AND SURVEY

Since the recent discovery and first investigation of kaonic, p - and C - - -

atoms, the field of exotic atoms is re- ceiving increasing experimental and theo- retical interest [I]. The importance of these atoms lies in the fact that they have found applications in rather diffe- rent fields of physics ranging from solid- state physics and chemistry (cascade studies and muonium interactions] to nuclear structure (static electromagnetic densities, isomer shifts etc.1 and

particle physics (particle properties, particle-nucleon interactions,

OED

corrections). Our review is devoted to exotic atoms with strongly interacting particles. Among these w e concentrate primarily on pionic and kaonic atoms

which s o far are the best understood theoretically and which hopefully may serve a s a testing ground f o r the analysis of 5- and C--atoms. Although they fall somewhat outside the theme of this review, we start with a few remarks on muonic atoms discussing some recent progress in this field (Sec. 2 ) . In Sec. 3 we describe the basic properties of hadronic atoms and discuss briefly their theoretical d e s - cription in terms of equivalent optical potentials. Sec. 4 reviews nuclear structure studies with these atoms. Sec. 5, finally, is devoted to some new approaches to old problems of nuclear and particle properties as explored in hadronic atoms.

2 . A

"CLASSIC" IN THE FIELD: MUYNIC ATOMS Since the advent o f solid state y - r a y detectors of high resolution,muonic

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1972514

a t o m s h a v c become a p r e c i s i o n m e t h o d f o r t h e i n v e s t i g a t i o n o f e l e c t r o m a g n e t i c s t r u c t u r e o f t h e n u c l e u s . The m a i n a p p l i - c a t i o n s c o n c e r n n u c l e a r c h a , r g e d e n s i t i e s , n u c l e a r m a g n e t i z a t i o n d e n s i t i e s ( m a g n e t i c h y p e r f i n e s t r u c t u r e w i t h f i n i t e s i z e e f f e c t s ) a n d i s o m e r s h i f t s i n s p h e r i c a l a s w e l l a s d e f o r m c d n u c l e i . A l r i o , t h e p r o b l e m n f t h e p o l a r i z d b i l i t y o f t h e n u c l e u s a n d n o n - r a d i r ~ t i v e t r a r i s i t i o n ? o f t h e murln, w i t 1 1 n u c l e a r c x c i t o t i c ~ n , a r e r c - c e i v i n g i n c r e a s e d i n t e r c . ! s t . T h e s e m o r e c l a s s i c a l t o p i c s a r e c o v e r c : d i n r e c e n t r e - v i e w s o f t h e f i s l d p

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t o e x t r a c t : s p e c t r o - s c o p i c q u a d r u p o l e moments f r o m t h e q u a d r u - p o l e h y p e r . F l n e s p l i t t i n g o f h i g h e r s t a t e s i n t h e m u o n i c c a s c a d n f o r w h i c h t h e

s p l i t t i n g i s s t . i l l l a r g e e n o u g h t o b e o b s e r v a b l e b u t f o r whictr t h e p o i n t - n u c l e u s a p p r o x i n ! a t i o n i s a l r e s d y a g o o d o n e . The a d v a n t a g s s ? r e o b v i o u s : The f i e l d g r a d i e n t c r e a t e d by Lhu muon a t t h e s i t e o f t h e n u c l e u s i s p r e c i s e l y known; c o r r e c t i o n s f r o m f i n i t e s i z e , v r a g n e t i c h f s , d y n a m i c a l s t a t e m i x i n g a n d e l e c t r o n i c s c r e e n i n g a r e e i t h e r s m s 1 1 o r u n d e r r e ~ 3 s o n a b l e c o n t r o l .

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? s t i m a t a d ; t h e r e m a l r i i ng d i s c r e p a n c y t h u s i n d i c a t e s t h a t t h e r e i s s t i l l a s i z e a b l e 3 a r t o f t h e @ E C c o r r e c t i o n s m i s s i n g . ( N o t e t h a t w h i l e t h e e x n e r i m e n t a l r e s u l t s o f R e f s . 7 a n d

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3 .

IIADRONIC ATOPS, BASIC PROPERTIES A N D

TIIEORETICAL DESCRIPTION

3 . 1 . D c f i n i t i o n s a n d G r o s s F e a t u r e s o f t h e D a t a

S i n c e t h i s r e v i e w i s a d d r e s s e d t o

a n a u d i e n c e who may n o t b e t o o f a m i l i a r

w i t h t h i s b r a n c h o f i n t e r m e d i a t e e n e r g y

p h y s i c s , we s t a r t w i t h some d e f i n i t i o n s

a n d b a s i c o b s e r v a t i o n s i n h a d r o n i c a t o m s .

The a c c e s s t o h a d r o n i c a t o m s , c l e a r l y , i s

t h r o u g h t h e o b s e r v a t i o n o f e n e r g i e s a n d i n -

t e n s i t i e s o f c a s c a d e t r a n s i t i o n s . T h e r e f o r e ,

t i m e s c a l e s i n a n e x o t i c a t o m a r e s e t by

t h e ( i n v e r s e 1 r a d i a t i v e w i d t h s o f R o h r

HADRONIC ATOMS C5-185

o r b i t s . S p e c i f i c a l l y , o n l y t h o s e l e v e l s c a n s h i f t s ( i n I s - s t a t e s ) a n d p o s i t i v e s h i f t s b e s e e n f o r w h i c h t h e a b s o r p t i o n w i d t h b y

s t r o n g i n t e r a c t i o n i s a t m o s t c o m p a r a b l e t o t h e r a d i a t i v e w i d t h . T h i s i m p l i e s t h a t , i n p r a c t i c a l c a s e s we s h a l l b a v e t o a n a - l y z e , t h e C o u l o m b p o t e n t i a l s t i l l r e m a i n s t h e d o m i n a t i n g f e a t u r e ; t h e s t r o n g i n t e - r a c t i o n a p p e a r s a s n o t t o o v i o l e n t a p e r - t u r b a t i o n o f t h e e n e r g y s p e c t r u m p e r t a i n i n g t o t h e C o u l o m b p o t e n t i a l . One c a n e a s i l y e s t i m a t o ( f r o m t h e o v e r l a p o f t h e R o h r o r b i t s w i t h t h e n u c l e a r d e n s i t y ) t h a t t h e a b s o r p t i o n w i d t h

r A b S

d e p e n d s s t r o n g l y o n R, t h e o r b i t a l a n g u l a r mornentum o f t h e h a d r o n , b u t o n l y l i t t l e o n i t s m a i n q u a n t u m n u m b e r n . E . g . i n m e d i u m a n d h e a v y k a o n i c

r A b s

a t o m s , ( n , L ) i n c r e a s e s b y when g o i n g f r o m t h e c i r c u l a r o r b i t ( n , L = n ^{- 1 )} t o t h e n e x t i n n e r o r b i t ( n , i = n - 2 ) . F o r f i x e d 2 , o n t h e o t h e r h a n d , i t v a r i e s b y f a c t o r s o f t h e o r d e r o f t w o o n l y , when c h a n g i n g n b y o n e u n i t . E x c e p t f o r t h e v e r y l i g h t e s t n u c l e i , t h u s o n l y c i r c u l a r o r b i t s a r e i m p o r t a n t .

As c o m p a r e d t o t h e a h s o r p t i o n w i d t h , t h e r a d i a t i v e w i d t h v a r i e s v e r y s l o w l y f r o m o n e c i r c u l a r o r b i t t n t h e n e x t . I t i s t h e n u s e f u l t o d e f i n e t h e c r i t i c a l o r b i t as t h e o n e b e l o w w h i c h n o f u r t h e r t r a n s i t i o n c a n b e o b s e r v e d w i t h a s i z e a b l e i n t e n s i t y [ll]

.

I n g e n e r a l , o n e c a n m e a s u r e t h e w i d t h

r A b S

f o r t h e c r i t i c a l l e v e l a n d t h e o n e a b o v e , a s w e l l a s t h e s h i f t o f t h e c r i t i c a l l e v e l w h i c h i s d e f i n e d b y

€ ( n C , II

1

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c K G ( n c , k c ) - R e I E ( n c , I I c ) l e ( 1

1

H e r e E~~ i s t h e e n e r g y f o r t h e C o u l o m b p o t e n t i a l f r o m a p o i n t n u c l e u s , w i t h t h e K l e i n - G o r d o n e q u a t i o n , w h i l s t E i s t h e f u l l

( c o m p l e x ) e i g e n v a l u e w i t h f i n i t e n u c l e a r s i z e a n d s t r o n g i n t e r a c t i o n .

I n p i o n i c a t o m s , t h e a b s o r p t i o n i s o n l y m o d e r a t e l y s t r o n g a n d b o t h n e g a t i v e

( i n 2 p - s t a t e s a n d h i g h e r ) a r e o b s e r v e d . I n k a o n i c a t o m s . ( a n d p r o b a b l y a l s o i n

p-

a n d X - - a t o m s ) , t h e a b s o r p t i o n i s s t r o n g s o t h a t t h e s h i f t ~ (

,

n i ) i s a l w a y s n e g a t i v e , n o

C C

m a t t e r how s t r o n g l y a t t r a c t i v e t h e r e a l p a r t o f t h e o p t i c a l p o t e n t i a l i s . T h i s i s i l l u s t r a t e d b y F i g . 1 w i e r e we show t h e w i d t h a n d s h i f t o f t h e 3 d - l e v e l i n 3 2 r -

K a s a f u n c t i o n o f t h e r e a l p a r t F?c(A) o f t h e e f f e c t i v e s c a t t e r i n g a m p l i t u d c ( s e e b e l o w , e q . ( 5 ) ) a n d w i t h J m [ A ) a s p a r a m e t e r ( T . C . O . E r i c s o n a n d F . S c h e c k , ~ n p u b l i s h e d r e s u l t s . a n d R e f . 1 2 ) .

F i g . 1 : S h i f t a n d w i d t h o f t h e 3 d - l e v e l i n

3 2 ~ + ~a s a f u n c t i o n o f t h e e f f e c t i v e , i s n - -

s p i n a v e r a g e d

KN

s c a t t e r i n g a m p l i t u d e . R e [ A ) p o s i t i v e ( n e g a t i v e ) c o r r e s p o n d s t o a t t r a c t i o n ( r e p u l s i o n ) . F n r w e a k a b s o r p t i o n ( e . g . I n ( A ) = 0 . 1 f m ) t h e s h i f t E 3 d o s c i l - l a t e s b e t w e e n p o s i t i v e a n d n e g a t i v e v a l u e s a s R e ( A ) i s i n c r e a s e d . A t t h e same t i m e t h e w i d t h

r 3 d

s h o w s a n e a r l y p e r i o d i c r e s o n a n c e b e h a v i o u r . B e l o w e a c h r e s o n a n c e , i n p a r t i - c u l a r , E b e c o m e s i n c r e a s i n g l y p o s i t i v e . F o r s t r o n g a b s o r p t i o n ( e . g . I m ( A ) = 0.5 f m i n t h e f i g u r e ) , o n t h e o t h e r h a n d , t h e r e s o - n a n c e s i n

r

f l a t t e n o u t , w h i l s t t h e s h i f t

3 d

E 3 d r e m a i n s n e g a t i v e i n d e p e n d e n t l y o f I i o c s t r o n g l y a t t r a c t i v e R e ( A ) i s made. R e a -

C5-186 F. SCHECK

l i s t i c a l l y , f o r k a o n i c a t o m s o n e h a s I m ( A )

=

0 . 7 f m o r e v e n l a r g e r ; f o r

p

a n d

-

C

ImCA) i s p r o b a b l y o f t h e o r d e r o f 1 f m . T h e s e r e s u l t s a r e e a s i l y u n d e r - s t o o d a s a s a t u r a t i o n e f f e c t i n t h e p r e - s e n c e o f s t r o n g a b s o r p t i o n : An a b s o r p t i v e p o t e n t i a l r e p e l l s t h e C o u l o m b l e v e l . W h i l e i n c r e a s i n g t h e a t t r a c t i o n , o n e i n c r e a s e s t h e o v e r l a p o f t h e p a r t i c l e ' s wave f u n c t i o n w i t h t h e n u c l e u s , t h u s m a k i n g t h e a b s o r p t i o n e v e n m o r e e f f e c t i v e . ( T h e o s c i l l a t o r y b e - h a v i o u r i s f o u n d t o b e c a u s e d b y i n t e r - f e r e n c e o f " i n n e r " a n d " o u t e r " s t a t e s , s e e

[12], [13], a n d f u r t h e r d i s c u s s i o n i n

El41 1 .

3 . 2 . M u l t i p l e S c a t t e r i n g a n d O p t i c a l

P o t e n t i a l

H a d r o n i c a t o m s a r e a n a l y z e d i n t e r m s o f a n e q u i v a l e n t o p t i c a l p o t e n t i a l VOpT. T h i s o p t i c a l p o t e n t i a l i s u s u a l l y o b - t a i n e d f r o m a m u l t i p l e s c a t t e r i n g t h e o r y a d e q u a t e f o r l o w e n e r g i e s , u n d e r t h e f o l l o w i n g a s s u m p t i o n s : ( 1 1 t h e i n t e r a c t i o n o f t h e p i o n ( o r k a o n ) w i t h t h e n u c l e u s i s s h o r t - r a n g e d a s c o m p a r e d t o t y p i c a l i n t e r - n u c l e o n d i s t a n c e s ; ( 2 ) n u c l e a r e x c i t a t i o n s i n v i r t u a l i n t e r m e d i a t e s t a t e s c a n b e n e g - l e c t e d . The m u l t i p l e s c a t t e r i n g p r o b l e m c a n t h e n b e s o l v e d f i r s t w i t h t h e n u c l e o n s i n f i x e d p o s i t i o n s , t h e n a v e r a g i n g o v e r t h e n u c l e a r g r o u n d s t a t e wave f u n c t i o n b y i n - v o k i n g c l o s u r e . ( S e e h o w e v e r r e m a r k s b e l o w , S e c . 5 . 2 . ) .

( 3 )

t h e n u c l e a r d e n s i t y i s l o w s o t h a t l a l ~ ' ' ~ i s a s m a l l q u a n t i t y , w h e r e a i s a n a v e r a g e TN ( o r K ~ l s c a t t e r i n ~ a m p l i - -

t u d e . To f i r s t a p p r o x i m a t i o n V O p T i s f o u n d t o b e p r o p o r t i o n a l t o t h e c o h e r e n t sum o f t h e p i o n ( k a o n l - n u c l e o n s c a t t e r i n g a m p l i - t u d e s a n d t o t h e d e n s i t y p ( r ) . -+

"OPT in momentum s p a c e i s t h e n s i m p l y [151

.

w h e r e b o , b l a n d c o , c l a r e t h e a v e r a g e s - w a v e a n d p - w a v e s c a t t e r i n g l e n g t h s ( n o t e t h a t we a r e c l o s e t o t h r e s h o l d ) ; p i s t h e r e d u c e d mass, t a n d T a r e t h e p i o n ' s a n d n u c l e o n ' s i s o s p i n o p e r a t o r s , r e s p e c t i v e l y . S ( q ) i s t h e n u c l e a r f o r m f a c t o r w i t h

+

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q = k - k ' .

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The t h e o r y h a s r e c e n t l y b e e n r e - f o r m u l a t e d b y D o v e r , H f i f n e r a n d Lemmer, f o r p i o n i c a t o m s [16J. The a u t h o r s s t u d y t h e G r e e n ' s f u n c t i o n o f t h e p i o n embedded i n t h e n u c l e a r m e d i u m . T h e p i o n ' s s e l f - e n e r g y w h i c h i s i d e n t i f i e d w i t h t h e o p t i c a l p o t e n - t i a l , i s e x p a n d e d i n p o w e r s o f t h e n u c l e a r d e n s i t y . To f i r s t a n d s e c o n d o r d e r i n p t h e v a r i o u s t e r m s o f t h e E r i c s o n ' s p o t e n t i a l

[IS] a r e r e c o v e r e d . T h e r e a r e a d d i t i o n a l t e r m s i n v o l v i n g t h e n u c l e o n - n u c l e o n s c a t t e - r i n g a m p l i t u d e s o f f - s h e l l ( " q u e n c h i n g "

e f f e c t ) . To my o p i n i o n , t h e m e t h o d h a s a c l e a r a d v a n t a g e in so fm a s i t e x h i b i t s m o r e n e a t l y some o f t h e n e c e s s a r y a s s u m p t i o n s a s w e l l a s t h e u n d e r l y i n g e x p a n s i o n p a r a m e t e r s o f t h e m u l t i p l e s c a t t e r i n g s e r i e s .

F o r p i o n i c a t o m s t h e p i c t u r e i s n o t c o m p l e t e s i n c e t h e p o t e n t i a l ( 2 ) d o e s n o t a c c o u n t f o r a b s o r p t i o n o f t h e p i o n . I n - d e e d , t h e s c a t t e r i n g l e n g t h s i n e q . ( 2 1 a r e e s s e n t i a l l y r e a l . The a b s o r p t i o n w h i c h t a k e s p l a c e p r e d o m i n a n t l y o n t w o c o r r e l a t e d n u c - l e o n s , i s u s u a l l y i n t r o d u c e d p h e n o m e n o l o - g i c a l l y b y a d d i n g a n i m a g i n a r y t e r m p r o p o r - t i o n a l t o p 2 ( r ) t o VOpT. I n momentum s p a c e ,

A l t h o u g h i t seems h i g h l y d e s i r a b l e t h a t t h i s s i m p l e r e c i p e b e i m p r o v e d , i t a d -

m i t t e d l y i s f a i r l y s u c c e s s f u l i n a c c o u n t i n g o u t i n t h e p r e s e n c e o f s t r o n g a b s o r p t i o n f o r t h e d a t a . E x c e p t f o r t h e m e n t i o n a d

c o r r e c t i o n s w h o s e m a g n i t u d e i s s o m e w h a t u n - c e r t a i n , t h e p a r a m e t e r s a p p e a r i n g i n e q s .

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a n d c o u l d t h e n b e n e g l e c t e d . T h i s s t a t e - m e n t h a s h o w e v e r n o t b e e n p r o v e d f o r r e a -

l i s t i c o r b i t s o f t h e k a o n ( o t h e r t h a n s - s t a t e s ) . On t h e o t h e r h a n d . B a r d e e n a n d T o r i g o e [ZO] h a v e p r o p o s e d t o e x t r a p o l a t e t h e free KN a m p l i t u d e t o e n e r g i e s ( b e l o w t h r e s h o l d 1 a p p r o p r i a t e t o t h e k a o n i c o r b i t . s u b t r a c t i n g o f f t h e c e n t e r - o f - m a s s k i n e t i c e n e r g y o f t h e d e c a y p r o d u c t s

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F o r a l o n g t i m e k a o n i c a t o m s w e r e a g r e a t h o p e i n h u n t i n g f o r n e u t r o n d i s t r i - r i g h t a t t h r e s h o l d . ( T h e t w o - n u c l e o n a b -

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T h e p o l a r i z a t i o n o f t h e n u c l e u s b y t h e o r b i t i n g p a r t i c l e , i . e . t h e s e c o n d - o r d e r e l e c t r o m a g n e t i c i n t e r a c t i o n , i s a n i m p o r t a n t c o r r e c t i o n i n t h e s p e c t r a o f m u o n i c a t o m s . A l t h c u g h t h i s p o l a r i z a t i o n s h i f t is a w e l l - d e f i n e d q u a n t i t y t h e o r e - t i c a l l y , i t i s d i f f i c u l t t c c a l c u l a t e i n a r e l i a b l e m a n n e r f o r t h e l o w - l y i n g l e v e l s o f m u o n i c a t o m s . V a r i o u s m u l t i p o l e s d o i n g u n e - r a l c o n t r i b u t e a n d , i n t h e s u m o v e r i n t e r -

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9,)

s o m e w h a t a b o v e t h e critical level m u s t be chosen in o r d e r t o avoid t h e troubles f r o m strong interaction s h i f t s and line broadenings.

Also, electron s c r e e n i n g m u s t be u n d e r f a i r control. I f this i s a c h i e v e d , it s h o u l d b e p o s s i b l e , in f a v o u r a b l e cases, t o m e a s u r e the combined s h i f t (12) and t h u s t o d e t e r m i n e the h a d r o n i c polarizability

5.2. O f f - s h e l l T N S c a t t e r i n g A m p l i t u d e and Nucleon Correlations

The equivalent o p t i c a l potential in hadronic a t o m s involves t h e elementary hadron-nucleon s c a t t e r i n g amplitude o f f - shell. C l e a r l y , t h e f o r m o f the potential f o r p i o n i c a t o m s f o r instance, eq. (2). is by no m e a n s unique. F o r example, o n e could have t a k e n instead (omitting the isospin d e p e n d e n t terms f o r s i m p l i c i t y )

(13) w h i c h on the m a s s s h z l l i s i d e n t i c a l w i t h eq. (2). When t r a n s f ~ r m e d into c o n f i g u r a t i o n s p a c e , the f i r s t alternative, eq. ( 2 1 , g i v e s t h e v e l o c i t y - d e p e n d e q t K i s s l i n g e r potential

+ +

+ +

bo p(rl

-

co V p(r)V w h i l s t the latter g i v e s a local and energy dependent potential i n - volving the Laplacian n f the d e n s i t y p(r). + When s o l v i n g the K l e i n - G o r d o n equation with t h e s e t w o p o t e n t i a l s one f i n d s r a t h e r d i f f e - rent predictions f o r the s h i f t s and w i d t h s in p i o n i c atoms. Wilkin and I have r e c e n t l y t a k e n up t h i s p r o h l e m [ 2 9 ] . Recall t h a t o n e assumption (assumption

( 1 )

in SBC. 3.2.1 f o r t h e construction o f o p t i c a l p o t e n t i a l s w a s t h a t the elementary interaction should be short-ranged. When expressed in t e r m s o f potentials t h i s m e a n s t h a t the e l e m s n - tary n N p ~ t e n t i a ~ s h o u l d n o t overlap. I f t h i s is the case then it i s w e l l - k n o w n

_[30]

t h a t t h e d o u b l e s c a t t e r i n g a m p l i t u d e i s

e x p r e s s i b l e in t e r m s o f o n - s h e l l s i n g l e s c a t t e r i n g amplitudes. Now, calculating t h e d o u b l e s c a t t e r i n g a m p l i t u d e f r o m e i t h e r

( 2 1

o r (13) s h o w s that both the local and the K i s s l i n g e r o p t i c a l p o t e n t i a l s violate t h i s theorem. In o r d e r t o r e p a i r t h i s , o n e has t o add a c o u n t e r t e r m t o e i t h e r potential w h i c h , f o r t h e c a s e o f the K i s s l i n g e r p o - t e n t i a l , i s nothing but the f a m i l i a r L o r e n t z - L o r e n z term

[15].

I t a m o u n t s t o r e p lace

in the K i s s l i n g e r potential. An analogous term i s found in the c a s e o f t h e local potential.

O u r derivation s h o w s t h a t t h e L o r e n t z - L o r e n z t e r m i s a typical l o w - e n e r g y effect. Also, it i s little s e n s i t i v e t o t h e d e t a i l s of t h e nucleon s h o r t - r a n g e c o r r e - lations; a l l that has been used i s that t h e e l e m e n t a r y potentials should n o t o v e r - lap. F i n a l l y , a f t e r inclusion of t h e effect.

both potentials n o w g i v e very s i m i l a r p r e - d i c t i o n s f o r p i o n i c atoms. Remaining d i f f e - rences a r e d u e t o the d i f f e r e n t w a y s in w h i c h t h e Coulomb p o t e n t i a l i s introduced

in the two cases, ( t h e Coulomb p o t e n t i a l being long-ranged d o e s not obey the theorem), and to t e r m s o f h i g h e r o r d e r in the density.

6.

CONCLUDING R E M A R K S

In o u r previous d i s c u s s i o n w e have

s e e n t h a t s o m e progress has been m a d e r e -

cently in t h e understanding of hadronic

atoms. W e have concentrated on p i o n i c and

kaonic a t o m s in t h i s r e v i e w s i n c e they a r e

t h e best studied theoretically s o far. Also,

t h e elementary interaction is s u f f i c i e n t l y

w e l l - k n o w n s o t h a t t h e d a t a m a y be used t o

t e s t t h e reliability o f the theoretical

analysis. T h i s i s not s o f o r p- and C - -

a t o m s y e t in w h i c h c a s e s the s c a t t e r i n g

a m p l i t u d e s a t t h r e s h o l d a r e b a d l y k n o w n .

[ 2 ]

C . S . Wu, ' M u o n i c A t o m s " ; R e v i e w t a l k , H e r e v e r y l i t t l e h a s b e e n d o n e y e t t h e o - 4 t h I n t . C o n f . o n H i g h - E n e r g y P h y s i c s r e t i c a l l y . T h e h o p e i s o f c o u r s e , w i t h t h e a n d N u c l . S t r u c t u r e , D u b n a 1 9 7 1 . h e l p o f t h e m e t h o d s d e v e l o p e d f o r p j o n s

1 3 1 J . H i j f n e r a n d F . S c h e c k ; i n "Muon a n d k a o n s , t o a n a l y s e t h e d a t a f i n a l l y i n

P h y s i c s " , C.S. Wu a n d V . H u g h e s e d i t o r s , t e r m s o f FN a n d Z - N s c a t t e r i n g d a t a - w h i c h

A c a d e m i c P r e s s New Y o r k . a r e o f i n t e r e s t f o r article o h v s i c s .

, d

1 4 1 L. W i l e t s a n d C.S. Wu; Ann. R e v . N u c l . A s i m i l a r r e m a r k a p p l i e s t o i n f o r -

S c i . 19, 5 2 7 ( 1 9 6 9 ) . m a t i o n o n n u c l e a r s t r u c t u r e w h i c h c a n b e

e x t r a c t e d f r o m h a d r o n i c a t o m s . We s t i l l n e e d a m o r e d e t a i l e d u n d e r s t a n d i n g o f t h e o p t i c a l p o t e n t i a l b e f o r e t h e d a t a c a n b e f u l l y e x p l o i t e d i n t e r m s o f n u c l e a r s t r u c - t u r e . Up t o now t h e g r o s s f e a t u r e s o f t h e d a t a c a n b e e x p l a i n e d w i t h a f a i r l y n a i v e p i c t u r e o f t h e n u c l e a r g r o u n d s t a t e . A f e w o p e n p r o b l e m s a r e t h e f o l l o w i n g :

( a ) a p r o p e r m i c r o s c o p i c u n d e r s t a n d i n g o f p i o n a b s o r p t i o n o n c o r r e l a t e d n u c l e o n s

( i s o t o p i c v a r i a t i o n s ) ;

( b l t h e r o l e o f t h e Y b ( l 4 0 5 ) - r e s o n a n c e i n k a o n i c a t o m s ;

I c f i h e r e a s t h e e x p a n s i o n o f t h e o p t i c a l p o t e n t i a l i n t e r m s o f t h e n u c l e a r d e n s i t y s e e m s a d e q u a t e f o r p i o n i c a n d k a o n i c a t o m s , t h i s i s n o t s o c l e a r f o r ; - a t o m s , f o r i n - s t a n c e . H e r e t h e i n t e r a c t i o n i s n o t a s s h o r t - r a n g e d a s f o r p i o n s a n d k a o n s ; i t i s t h u s n o t c l e a r w h e t h e r t h e s a m e t y p e o f e x p a n s i o n i s m e a n i n g f u l .

A c k n o w l e d g e m e n t s : W e s h o u l d l i k e t o t h a n k G . F s l d t a n d 3 . H U f n e r , a s w e l l a s t h e m e m b e r s o f t h e SIN t h e o r y g r o u p f o r u s e - f u l d i s c u s s i o n s .

REFERENCES

[I] G . B a c k e n s t o s s , " H a d r o n i c A t o m s " ; T.E.O. E r i c s o n , " D y n a m i c s o f H a d r o n i c A t o m s " ; R e v i e w t a l k s a t t h e 4 t h I n k . C o n f . o n H i g h - E n e r g y P h y s i c s a n d N u c l . S t r u c t u r e , D u b n a 1 9 7 1

[5] S . D e v o n s a n d I . O u e r d o t h ; A d v a n c e s i n N u c l . P h y s . , V o l . 2. P l e n u m P r e s s (New Y o r k ) 1 9 6 3 .

[ I ]

W . Dey e t a l . H e l v e t i c a P h y s . A c t a , to b e p u b l i s h e d .

[7]

M S .

D i x i t e t a l .

Phys.

R e v . L e t t e r s 2 7 .

8 7 8

( 1 9 7 1 ) .

-

[8]

H . K . W a l t e r e t a l . P h y s . L e t t e r s ( t o b e p u b l i s h e d ) .

[9] J . B l o m q v i s t a n d L . T a u s c h e r , t o b e p u b l i s h e d . M . K . S u n d a r e s a n a n d P . J . S . W a t s o n ; p r e p r i n t C a r l e t o n U n i v e r s i t y , O t t a w a .

PO] ^{G .} B a c k e n s t o s s e t a l . P h y s . L e t t e r s 3 1 8 , 233 ( 1 9 7 0 ) .

-

[ I ? ] T.E.O. E r i c s o n a n d F. S c h e c k ; N u c l . P h y s . 819, 4 5 0 ( 1 9 7 0 ) .

[IZ] P . W o l f f , d i p l o m a t h e s i s ETH Z i j r i c h , u n p u b l i s h e d .

E l 3 3 M . K r e l l ; P h y s , R e v . L e t t e r s E, 584 ( 1 9 7 1 1 .

R .

S e k i ; P h y s . R e v . E, 1196

( 1 9 7 2 ) .

f 1 4 ) J . H . K o c h , M . M . S t e r n h e i m , a n d J . F .

W a l k e r ; P h y s . R e v . L e t t e r s 26, ? 4 6 5 ( 1 9 7 1 ) .

J . H . K o c h ; t h e s i s U n i v e r s i t y o f M a s s a c h u s e t t s , 1 9 7 2 .

[15] M . E r i c s o n a n d T.E.O. E r i c s o n ; Ann.

P h y s . ( N . Y . ) 36, 3 2 3 ( 1 9 6 6 ) a n d e a r l i e r r e f e r e n c e s t h e r e i n .

E l 6 1 C.B. D o v e r , 3 . H i i f n e r a n d R.H. Lemmer;

Ann. P h y s . ( N . Y . ) 66, 2 4 8 ( 1 9 7 1 ) .

[ 1 7 ] L. T a u s c h e r , 1 n t . S e m i n a r on P i o n Nucleus I n t e r a c t i o n s , S t r a s b o u r g (1971 ).

[ 1 8 ] B.R. M a r t i n and M . S a k i t t , Phys. Rev.

183

1345 and 1352 (1969).

[ 1 9 ] J. R e v a i , Phys. L e t t e r s

338,

587 (1970).

[ 2 0 ] W.A. Bardeen and E.W. T o r i g o e , Phys. Rev. C3, 1785 (1971) a n d CERN p r e p r i n t TH 1431 (1971).

[21 ] G. B a c k e n s t o s s e t a l . , Phys', L e t t e r s , t o b e p u b l i s h e d .

[ 2 2 ] D.H. W i l k i n s o n , Proc. I n t . Conf. on N u c l e a r S t r u c t u r e , Tokyo 1967, p.469 and e a r l i e r r e - f e r e n c e s t h e r e i n .

[ 2 3 ] ".E. Wiegand, Phys. Rev. L e t t e r s 22, 1235 (1969).

[24

1

^H.A. B e t h e and P. J. Siemens, Nucl. Phys. B L , 589 (1971); E r r a t u m Nucl. Phys.

E ,

641 ( 1 9 7 2 ) [ 2 5 ] F. Scheck, Nucl. Phys. ( i n p r e s s ) .

[ 2 6 ] T.E.O. E r i c s o n and J. Hiifner, CERN p r e p r i n t s TH1482 and 1496 ( 1 9 7 2 ) .

[ 2 7 ] F. I a c h e l l o and A. Lande, Phys. L e t t e r s

835,

205 (1971).

[28 ] U. E. S c h r a d e r

,

p r e p r i n t U n i v e r s i t y of F r a n k f u r t (1972).

[ 2 9 ] F. Scheck and C. W i l k i n , t o b e p u b l i s h e d . 1301 M.A. Beg, Ann. Phys.(N.Y.) l3, 110 (1961) ;

K. B r u e c k n e r , Phys. Rev. 89, 834 ( 1 9 5 3 ) and 90, 715 (1953).

-

DISCUSSION

K. BLEULER ( U n i v . ~ f Bonn)

1 . Concerning t h e vacuum p o l a r i z a t i o n : t h e r e might b e a n i n f i n i t y of v i r t u a l p a i r s o f d i f - f e r e n t t y p e s ( s m a l l i n each s i n g l e c a s e ) t o g i v e a f i n i t e c o n t r i b u t i o n ( s u g g e s t i o n of N i e l s Bohr)

2. The

NR

i n t e r a c t i o n shows up i n t h e " a n t i - p r o t o n i c atoms" (work of B a c k e n s t o s s e t a l l . The e f f e c t s of a n a t t r a c t i v e h a r d c o r e (from O-meson-exchange) might b e s e e n from c e r t a i n i r r e g u l a r i t i e s .

3. Weak i n t e r a c t i o n might b e s t u d i e d from t h e decay of p m e s i c atoms < i n t h e ground s t a t e s of l i g h t n u c l e i ) .

F. SCHECK ( Z u r i c h )

L e t me comment f i r s t on t h e q u e s t i o n c o n c e r - n i n g t h e

p

i n t e r a c t i o n w i t h t h e n u c l e u s . I d o n o t t h i n k t h e r e i s e v i d e n c e f o r any a n o m a l i e s from t h e CERN d a t a . Various v a l u e s f o r t h e

-

i s t h e o p t i c a l p o t e n t i a l p r o p o r t i o n a l t o t h e c o h e r e n t sum o f t h e s c a t t e r i n g a m p l i t u d e s . C o n c e r n i n g t h e vacuum p o l a r i z a t i o n due t o v i r - t u a l p a i r s o t h e r t h a n e l e c t r o n - p o s i t r o n p a i r s , p e o p l e h a v e c a l c u l a t e d t h e c o n t r i b u t i o n from (pL+p-) p a i r s and have f o u n d i t n e g l i g i b l y s m a l l . The c o n t r i b u t i o n s from h a d r o n i c s t a t e s ( x + <

p a i r , e t c . ) h a v e been e s t i m a t e d and seem t o b e v e r y s m a l l a s w e l l .

T. ERICSON (CERN)

T h e r e i s a b a r e p o s s i b i l i t y a s s u g g e s t e d by s e v e r a l p e o p l e , t h a t t h e anomaly i n muonic atoms i s due t o t h e p r e s e n c e of bound e l e c t r o n s . The vacuum p o l a r i z a t i o n p o t e n t i a l i s c a l c u l a t e d u- s i n g e l e c t r o n p a i r s i n t h e b a r e Coulomb f i e l d , w h i l e t h e r e s h o u l d b e a b l o c k i n g e f f e c t . J.W. NEGELE (M.I.T.)

A f t e r a s e m i n a r by Anderson on vacuum p o l a r i - z a t i o n a n o m a l i e s , Dr. F r i a r and I c a l c u l a t e d

SN

s c a t t e r i n g l e n g t h s have been p r o p o s e d i n

t h i s e f f e c t , and

i t

t u r n s o u t t o b e c o m p l e t e l y t h e l i t e r a t u r e ; some of t h e s e do f i t t h e d a t a ,

n e g l i g i b l e . o t h e r s do n o t . The q u e s t i o n r e a l l y - i s , . i n my

M. GOLDHABER (Brookhaven) o p i n i o n , whether one c a n u s e t h e same k i n d of

Some y e a r s a g o e m u l s i o n d a t a on

c+/c-

r a t i o s l o w - d e n s i t y a p p r o x i m a t i o n a s i n p i o n i c and

f o r K- c a p t u r e l e d t o c o n c l u s i o n s r e g a r d i n g n/p k a o n i c atoms. Onlv i n t h e

l i m i t

of low d e n s i t v

r a t i o s a t t h e e d g e of n u c l e u s . How d o t h e s e

HADWNIC AMMS

c o n c l u s i o n s l o o k now ?

F. SMECK ( Z u r i c h )

Here a g a i n t h e problem

i s

t h e p r e s e n c e of t h e

YE

resonance below t h r e s h o l d . C l e a r l y , n e i t h e r t h e kaonic atoms n o r t h e emulsion d a t a do ex- c l u d e any anomalies i n t h e n e u t r o n d i s t r i b u - t i o n s of heavy n u c l e i . On t h e o t h e r hand both s e t s of experimental r e s u l t s c a n be understood with t h e most c o n s e r v a t i v e assumption about t h e n u c l e u s , namely t h a t t h e n e u t r o n d e n s i t y b e p r o p o r t i o n a l t o t h e proton d e n s i t y . With t h i s assumption and t a k i n g t h e

YE

i n t o account Bloom, Johnson and T e l l e r , f o r i n s t a n c e , (Phys.

Rev. L e t t e r s 23 (1969) 28) c o u l d w e l l reprodu- c e t h e emulsion d a t a on K- c a p t u r e .

C.M. NEWSTEAD ( K a r l s r u h e )

What s o r t of s t r e n g t h does t h e i s o s p i n z e r o term have i n t h e o p t i c a l p o t e n t i a l you have been d i s c u s s i n g ?

F. SCHECK ( Z u r i c h )

A t y p i c a l v a l u e f o r t h e i s o s p i n z e r o s-wave s c a t t e r i n g l e n g t h i n

5 ,

a s given i n ~ e f . [IS],

i s

A

=

^(-1.66

+

i0.69) fm

.

The r e a l p a r t

0

i s t h u s s t r o n g l y r e p u l s i v e . The i s o s p i n one amplitude h a s a r e a l p a r t which

i s

c l o s e t o z e r o ; t h e a b s o r p t i v e p a r t o f both a r e rougnly t h e same.