On the possible existence of hadron isomers

Volume 39B, number 3

ON

PHYSICS LETTERS

THE

POSSIBLE

EXISTENCE

OF

1May 1972

HADRON

ISOMERS

B. PONTECORVO Joint Insitute f o r 1Vuclear R e s e a r c h , Dubna, USSR Received 3 March 1972

In this note we a r e c o n c e r n e d with the a n g u l a r m o m e n t a of finite d i m e n s i o n m i c r o o b j e c t s e x c i t a b l e to many e n e r g y l e v e l s , such as m o l e c u l e s , a t o m s , a t o m i c nuclei and the s o - c a l l e d e l e m e n t a r y hadrons. In spite of the d i f f e r e n c e in t h e i r d i m e n s i o n s , t h e r e is s o m e analogy in these o b j e c t s . The a n g u l a r m o m e n t u m is the p r o d u c t of a m o m e n t u m P t i m e s the r a d i u s R. Now, b e c a u s e of the u n c e r t a i n t y r e l a t i o n , P ~ R -1, and as f a r as a n g u l a r m o m e n t a a r e c o n c e r n e d , we a r e faced with a s o r t of s i m i l a r i t y between quantum o b j e c t s widely d i f f e r i n g in the i r d i m e n s i o n s and in the s e p a r a t i o n s of t h e i r e n e r g y l e v e l s . This s i m i l a r i t y s u g g e s t s that we may i n q u i r e into what happens in the c a s e of o b j e c t s of known s t r u c t u r e , such as the a t o m i c nuclei, to get a hint of what might happen in the c a s e of o b j e c t s of unknown s t r u c t u r e , n a m e l y , the e l e m e n t a r y hadrons. The a s s u m p t i o n that h a d r o n s c o n s i s t of p a r t o n s may help to u n d e r s t a n d the analogy, but is not r e l e v a n t at p r e s e n t ; the main point is that hadrons have probably a v e r y c o m p l e x s t r u c t u r e , and that in spite of this t h e i r e n e r g y l e v e l s a r e well s e p a r a t e d ( r e s o n a n c e s ) . As it is well known, in n u c l e a r p h y s i c s m e t a s t a b l e n u c l e a r l e v e l s a r e often o b s e r v e d , i . e . t h e r e e x i s t c e r t a i n s t a t e s with l i f e t i m e s much l a r g e r than the l i f e t i m e s of " o r d i n a r y " s t a t e s of c o m p a r a b l e e x c i t a t i o n s . In g e n e r a l , this m e t a s t a b i l i t y is connected with the l a r g e a n g u l a r m o m e n t a of s t a t e s having r e l a t i v e l y low e x c i t a t i o n s ( n u c l e a r i s o m e r i s m ) . As the p r e s e n t time a l a r g e n u m b e r of n u c l e a r i s o m e r s is known, the m a x i m u m excitation e n e r g y of which r e a c h e s a few MeV. The m e a s u r e d l i f e t i m e s of stable n u c l e a r e x c it e d s t a t e s a r e in the i n t e r v a l of 10 -17 - 1011 sec. N u c l e a r i s o m e r s a r e known which have total a n g u l a r m o m e n t a g r e a t e r that J = 15. Why not c o n s i d e r v e r y l a r g e spin v a l u e s also in the c a s e of h a d r o n s ? Then the question a r i s e s as to w h e t h e r a m e t a s t a b i l i t y connected with l a r g e v a l u e s of J is p o s s i b l e also in hadron 346

p h y s i c s . In o t h e r w o r d s , do hadron i s o m e r s e x i s t ? H e r e hadron i s o m e r s a r e defined as l a r g e spin s t a t e s having r e l a t i v e l y low e x c i tation and ecaying, say, by e m i s s i o n of pions (or photons if the e x c i t a t i o n is v e r y low) with l i f e t i m e s v e r y long (because of the c e n t r i f u g a l barrier). It turns out that it is difficult to exclude such a p o s s i b i l i t y on the b a s i s of o u r knowledge of hadron p h y s i c s . Two c o n s i d e r a t i o n s a r e sufficient h e r e . 1) The fact that at p r e s e n t no e x a m p l e was o b s e r v e d of hadron i s o m e r i s m (connected with l a r g e J values) does not p r o v i d e a r g u m e n t s a g a i n s t its e x i s t e n c e . P r o b a b l y hadron i s o m e r s could not have been o b s e r v e d in e x p e r i m e n t s a l r e a d y p e r f o r m e d , as it will be seen l a t e r , and only s p e c i a l i n v e s t i g a t i o n s designed for the p u r p o s e can r e v e a l them. 2) N at u r al l y the l e v e l s of quantum o b j e c t s having l a r g e a n g u l a r m o m e n t a , g e n e r a l l y speaking, have high e x c i t a t i o n s . H o w e v e r , e x c e p t i o n s a r e p o s s i b l e . The a p p e a r a n c e of i s o m e r i s m j u s t r e q u i r e s , as a r u l e , that s o m e t i m e s t h e r e takes p l a c e a l e v e l " i n v e r s i o n " , i . e . that s o m e s t a t e s of v e r y high an g u l ar m o m e n t u m have r e l a t i v e low e x c i t a t i o n s . It is well known that in the c a s e of a t o m i c nuclei such " i n v e r s i o n " is a quite f r e q u e n t event: it is connected with the nuclear structure (orbits, magic numbers, form). It s e e m s that in the c a s e of hadrons nothing definite can be said f r o m a t h e o r e t i c a l point of view. T h e r e a r e v e r y few e m p i r i c a l data on hadron r e s o n a n c e s and it is i m p o s s i b l e to make on t h e i r b a s i s such a s t a t i s t i c a l a n a l y s i s which would exclude the p o s s i b i l i t y of l e v e l " i n v e r s i o n " . If such data do allow any conclusion to be drawn at all, they would r a t h e r s u g g e s t that " i n v e r s i o n " s o m e t i m e s may take p l a c e : for e x a m p l e , t h e r e a r e known four boson p a i r s ~ and ~? ', w and qS, no+(700 ) and Vo+(1070 , f(1260) and f'(1514), the two c o m p o nents of e a c h p a i r having, as f a r as we know, i d en t i cal quantum n u m b e r s , while the m a s s e s of the components in e a c h p a i r d i f f e r by a few

Volume 39B, number 3

PHYSICS

hundred MeV. In the c a s e of b a r i o n s it looks as if the " i n v e r s i o n " w e r e d i r e c t l y seen f o r N ( 1 6 8 8 ) J P = 5/2 + and N ( 1 7 8 0 ) J P = 1/2 +, N'(1670) J P = 5 / 2 - and S " ( 1 7 0 0 ) J P = 1 / 2 - , A ( 1 2 3 6 ) J P = 3/2 + and A ( 1 9 1 0 ) J P = 1/2 +, A ' ( 1 5 2 0 ) J P = 3 / 2 - and A'(1670) J P = 1 / 2 - . Of c o u r s e , t h e r e may be a n u m b e r of r e a s o n s e x plaining these data, f o r e x a m p l e , the e x i s t e n c e of additional quantum n u m b e r ( r e m i n d i n g of the a t o m i c p r i n c i p a l quantum n u m b e r n); b u t in any c a s e t h e r e a r e no data which would " a p r i o r i " indicate that the l e v e l i n v e r s i o n is i m possible. In connection with a p o s s i b l e e x p e r i m e n t a l s e a r c h f o r hadron i s o m e r s it is of i n t e r e s t to d i s c u s s t h e i r e x p e c t e d p r o p e r t i e s . As an e x a m p l e l et us c o n s i d e r the two p a r t i c l e decay of hadron i s o m e r s into p a r t i c l e s of m o m e n t u m K (the p o s s i b i l i t y that two p a r t i c l e s d e c a y s might often be l e s s p r o b a b l e than many p a r t i c l e d e c a y s is of no r e l e v a n c e here). If KR ~< 1, i . e . if the e x c i t a t i o n is sufficiently low (say < 1 C-eV) and if the i s o m e r a n g u l a r m o m e n t is sufficiently l a r g e , the l i f e t i m e ~ i of the i s o m e r can r e a c h v a l u e s s e v e r a l o r d e r s of magnitude l a r g e r than the l i f e t i m e s T of o r d i n a r y r e s o n a n c e s (say, T i >>7 ~< 1 0 - 2 1 s e c ) . B e c a u s e of the v e r y s m a l l width of hadron i s o m e r s , i t i s i m p o s s i b l e to d i s c o v e r them by i n v e s t i g a t i n g e l a s t i c c o l l i s i o n s of two p a r t i c l e s in analogy with what is being done, f o r e x a m p l e , in the i n v e s t i g a t i o n s of the b a r i o n s N and A. The hadron i s o m e r s m u s t be s e a r c h e d f o r by i n v e s tigating t h e i r d ecay p r o p e r t i e s . N a t u r a l l y the c r o s s s e c t io n f o r the i n c l u s i v e p r o c e s s e s in which a hadron i s o m e r is g e n e r a ted( i . e . the c r o s s s e c ti o n f o r the production of the i s o m e r t o g e t h e r with any o t h e r hadrons) is e x t r e m e l y s m a l l at low e n e r g i e s and can b e c o m e o b s e r v a b l e only at such high e n e r g i e s , that the contribution of w a v e s with l a r g e o r b i t a l m o m e n t s b e c o m e s c o n s i d e r a b l e . Even at sufficiently high e n e r g i e s the c r o s s s e c t i o n f o r the p r o d u c t i o n of hadron i s o m e r s is e x p e c t e d to be c o n s i d e r a bly s m a l l e r than the c r o s s s e c ti o n f o r the production of " n a r r o w " hadrons (such as kaons and hyperons) with s m a l l spin v a lu e s . Thus, it is u n d e r s t a n d a b l e why, even if h a dron i s o m e r s w e r e e x i s t i n g , no one would have not i c e d them until now: the decay lenght of the hadron i s o m e r s p r o d u c e d at e x i s t i n g a c c e l e r a t o r s is too s h o r t to be o b s e r v e d in a bubble c h a m b e r and the o b s e r v a t i o n of hadron i s o m e r s , f o r an e x p e r i m e n t a l point of v ie w , is than e q u i v a l e n t to the d i s c o v e r y of o r d i n a r y r e s o n a n c e s with s m a l l production c r o s s s e c t i o n ~ (it is v e r y

LETTERS

1 May 1972

difficult to find a new r e s o n a n c e if ~ ~ 10-30cm2). When the a c c e l e r a t o r e n e r g y i n c r e a s e s (Serpukhov, Batavia), the p r o b l e m of o b s e r v i n g hadron i s o m e r s stops being a c a d e m i c a l not only b e c a u s e of the contribution of high o r b i t a l w av es but mainly b e c a u s e the decay lenght can be o b s e r v e d . With L o r e n t z f a c t o r s of about 50 f o r hadron i s o m e r s , one could d e t e c t ~i ~ 10 -12 s e c in a bubble c h a m b e r and ~'i > 10-15 sec in p h o t o e m u l s i o n s . Thus in s e a r c h i n g f o r h adron i s o m e r s by m e a n s of t r a c k d e t e c t o r s one should pay attention to " c a s c a d e d e c a y s " ( o r connected " s t a r s " ) . Th ese s t a r s might have a v e r y s p e c i a l a p p e a r a n c e . F o r e x a m p l e , if the i s o m e r happens to be a hyperon its " s i g n a t u r e " might c o n s i s t of t h r e e o r m o r e connected e v e n t s (the i s o m e r p r o d u c t i o n , its decay with p r o d u c tion of a hyperon, the hyperon decay). R e t u r n i n g to the question as to w h e t h e r hadron i s o m e r s could have been o b s e r v e d b e f o r e , it may be stated that if c h a r g e d hadron i s o m e r s with m a s s e s ~ 2.2 GeV and l i f e t i m e s > 10 -9 s e c e x i s t e d , they would have been o b s e r v e d in the e x p e r i m e n t s a l r e a d y p e r f o r m e d at Serpukhov [2] p r o v i d e d the c r o s s s e c t i o n f o r t h e i r p r o duction by_ 70 GeV p r o t o n s w e r e l a r g e r than 10-31 cm 2. Not long ago e x p e r i m e n t s w e r e p r o p o s e d and i n i t i at ed [3], in which a s e a r c h is made f o r l o n g l i v ed p a r t i c l e s . In such e x p e r i m e n t s a new type of " r a d i o a c t i v i t y " of the p s e u d o - n u c l e i , in which the p a r t i c l e might be detained, is looked for. As the t i m e the m e t a s t a b i l i t y s e a r c h e d f o r w as not a s s u m e d to be connected with l a r g e J v a l u e s . In view of the i d e a s e x p r e s s e d above, it is n a t u r a l to put the question: what w i l l be the fate of a hadron i s o m e r captured inside a nucleus ? P r o bably an i s o m e r captured inside a n u cl eu s will decay by " i n t e r n a l c o n v e r s i o n " , a p r o c e s s s i m i l a r to the decay of h y p e r n u c l e i without pion e m i s s i o n . In such a p r o c e s s the e n e r g y t r a n s f e r f r o m the i s o m e r d i r e c t l y to the nucleons p r e d o m i n a t e s ~ and the mean life of the c a p t u r e d i s o m e r is g r e a t l y s h o r t e n e d with r e s p e c t to the m e a n life of the f r e e i s o m e r . This p r o b l e m was d i s c u s s e d m o r e than 15 y e a r s ago by K o b z a r e v and Okun [4] when the n a t u r e of the A p a r t i c l e m e t a s t a b i l i t y was not y e t c l e a r . A f t e r the idea about the p o s s i b l e e x i s t e n c e of hadron i s o m e r i s m has been a l r e a d y f o r m u lated, I was i n f o r m e d about a r e c e n t c o s m i c ray o b s e r v a t i o n [5] of a p a r t i c l e having a m a s s of about 2 GeV and a mean life of about 10 -14 sec. B e c a u s e the m a s s is so l a r g e , it s e e m s unlikely that such a p a r t i c l e would be the f i r s t e x a m p l e of hadron i s o m e r i s m , in the s e n s e of 347

Volume 39B, n u m b e r 3

PHYSICS

t h e w o r d u s e d in t h e p r e s e n t n o t e ( u n l e s s o n e w o u l d c o n s i d e r v a l u e s R << 1/m~). T h e q u e s t i o n a b o u t t h e e x i s t e n c e Of h a d r o n i s o m e r s is q u i t e f u n d a m e n t a l , a s t h e o b s e r v a t i o n of s u c h o b j e c t s w o u l d p r o v e t h e e x t r e m e c o m p l e x i t y of h a d r o n s . C o n s e q u e n t l y a s e a r c h for hadron isomerism at accelerator laborat o r i e s a n d in c o s m i c r a y i n v e s t i g a t i o n s s e e m s to b e of g r e a t i n t e r e s t .

In c o n c l u s i o n i t i s a p l e a s u r e f o r m e to t h a n k J . B j o r k e n a n d K. T o l s t o y w h o h a v e i n f o r m e d m e a b o u t t h e J a p a n e s e i n v e s t i g a t i o n s a n d D.

348

LETTERS

1 May 1972

B a r d i n , S. B i l e n k y , S. G e r s h t e i n , V. G r i s h i n , V. G r i b o v , L. Okun, S. P o l i k a n o v , V. S o l o v i e v , D. S h i r k o v f o r d i s c u s s i o n s .

References [1] "Review of P a r t i c l e P r o p e r t i e s " Rev. Mod..Apri[, 1971. [2] Yu. Bushnin et al., J a d e r n Phys. 10 (1969) 585. [3] B. Pontecorvo, J a d e r n Phys. 11 (1970) 846; A. Demianov e t a [ . , J a d e r n Phys. 13 (1971) 786. [4] Yu. Kobzarev and L. Okun, Zh. Eksp. i Teor. Fiz. 30 (1956) 798. [5] K. Niu and E. Mikumo, P r e p r i n t 1971.