Spin-orbit splitting of 13ΛC

7/28/2019 Spin-orbit splitting of 13C

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Hadron and Nuclear Physics with ElectromagneticProbesK. Maruyamaand H. Okuno (Editors)9 2000 Elsevier Science B.V. All rights reserved. 147

Sp in-orbit spl i t t ing of k3CH. K ohr i a , S . A j im ura ~, R . E . Ch r ien b , P . M. Eug enio c , G. F ran kl in c , J . F ran z d ,T . F u k u d a e, L . G a n f, H . H a y a k a w a ~, P . K h a u s t o v c, T . K i s h i m o t @ , K . M a t s u o k a ~,M. M ay b , S . M ina m i ~, Y. M iyake ~, T . M orP , K. M or iku bo ~, J . N akan o g , H. No um i ~,H. O u ta e , K. Pas ch ke c , P . P i le b , B. Q ui nn c , A. R use k b, E . Saj i a , A. Sak agu chi a ,R . S a w a f t a h , Y . S h i m i z u ~, M . S u m i h a m a a , R . S u t t e r b , T . T a m a g a w a g , H . T a m u ra i,K . T a n i d a g , L . T a n g f a n d L . Y u a n fa O s a k a U n i v e r s i t y , M a c h i k a n e y a m a I - I , T o y o n a k a 5 6 0 - 0 0 4 3 , J a p a nb B r o o k h a v e n N a t i o n a l L a b o r a t o r y , U p t o n , N e w Y o r k 1 1 9 7 3 , U S Ac C a rn e g i e M e l l o n U n i v e r s i t y , P i t t s b u rg h , P A 1 5 2 1 3 , U S Ad U n i v e r s i ty o f F r e i b u rg , H e rm a n n -H e rd e r -S t r . 3 , D 7 9 1 0 4 F re i b u rg , G e rm a n ye H i g h E n e r g y A c c e l e r a t o r R e s e a r c h O r g a n i z a t i o n , T s u k u b a , I b a r a g i , 3 0 5 - 0 8 0 1 , J a p a nf H a m p t o n U n i v e r s i t y , H a m p t o n , V A 2 3 6 6 8 , U S AgU nivers i ty o f Tokyo , Tok yo 113-0033, J ap anh N o r t h C a ro l i n a A T S t a t e U n i v e r s i t y , G re e n s b o ro , N C 2 7 4 1 1 , U S Ai T o h o k u U n i v e r s i t y , S e n d a i 9 8 0 -8 5 7 8 , J a p a n

T h e 7 - r a y s fr o m th e 1 / 2 - a n d 3 / 2 - d o u b l e t st a t e s a t ~ 1 1 M e V t o t h e g r o u n d s t a t e i n~3C w e re s u c c e ss fu l ly m e a s u re d b y u s i n g 7 2 N a I d e t e c t o r s t o o b t a i n t h e s p i n -o rb i t s p l i t t i n ge n e rg y w i t h h i g h p r e c i s i o n . T h e (K - , 7 r - ) r e a c t i o n o n a n e n r i c h e d l a C t a rg e t w a s u s e d a tt h e B r o o k h a v e n A l t e r n a t e G r a d i e n t S y n c h r o t r o n . T h e e n e r g y r e s o lu t i o n fo r t h e 1 1 M e V" ,/- ra ys i s 3 4 0 k e V F W H M w h i c h i s m u c h b e t t e r t h a n t h o s e o b t a i n e d b y u s i n g m a g n e t i cs p e c t r o m e t e r s ( ~ 2 M e V F W H M ) . T h e o b t a i n e d s m a l l s p l i tt i n g e n e r g y o f t h e 1 / 2 - a n d3 / 2 - d o u b l e t s t a t e s i n k3 C i s a b o u t 1 50 k e V (p re l i m i n a ry ) .


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1. I N T R O D U C T I O NSince AN scat ter ing data are extremely l imited due to experimental d i ff icul t ies , the (Tr+,

K +) reac t ion da ta have clar i fied the gross s t ructu re of the A -nucleus in terac t ion [1][2].The phenom eno log ica l ana lyses wi th the use o f Wo ods-saxon po ten t ia l s ind ica ted t ha t thedom inan t cen t ra l par t o f the A-nuc leus in te rac t ion was rough ly 2 /3 (~28 MeV ) o f tha tof the nucleon. W hile , the spin dep end ent par ts were found to be surpris ingly smal l . Forexample , the sp in -o rb i t in te rac t ion was rough ly one o rder of ma gn i tude smal le r than tha to f the nuc leon [3 ]. I t can be na ive ly exp la ined tha t the s t range quark con t r ibu tes l i tt l eto the nuclea r force. T he sm al l A-nucleus spin-orbi t in teract ion has been one of the m ostin te res t ing sub jec t s in the hypernuc lear phys ics fo r more than 20 years .

Ex perim ental ly , th e f irs t indicat ion of the smal l A-nucleus spin-orbi t in tera ct ion w asg iven by the 160(K- , 7 r - ) ) t60 exper imen t per fo rmed a t CERN [ 3 ] . The sp l i t t ing o f ob -served peaks wi th the conf igura t ions o f [ (p l /2 )g l (p l /2 )A]0+ and [ (p3 /2 )~ l (p3 /2 )A]0+ wasabo u t 6 MeV. The sp l i t t ing i s very close to the sp l i t ting o f the n eu t ron pl/2 a n d p3/2 holes tates in 150 (6 .176 M eV). T he sp l i t t ing of p-s ta te A is es t im ated to be less th an 0 .3 MeV.In the 13C(/(- , 7r-)~3C experiment a t BNL, the A spl i t t ing energy in ~aC was obtainedas O.36 + o.3 MeV [ 4 ] . The 9Be(K- , 7 r - 7 )~Be exper imen t a t BNL a l so ind ica ted thesmall A spin-orbi t sp l i t t ing [5] . O bserved s ingle -) ,- ray peak suggests tha t the exci teddoub le t s t a tes o f [ g B e ( 2 + ) | 5 / 2 + are a lmos t degenera te . The sp l i t t ing energyhas to be less than 0 .1 MeV. On the o ther hand, a large spl i t t ing was indicated by the89y(Tr+ , K+)89y exper imen t a t KEK [6 ] . The sp l i t t ing energy o f a few MeV fo r f - s ta teA was observed . Th ey per fo rm ed a new exper imen t us ing the same reac t ion in o rder toconf irm the sp l i tt ing . The re -ana lys is o f the emuls ion exper im en ta l d a ta co l lec ted by theEu rop ean K - co l labora t ion a l so ind ica ted a re la t ive ly la rge sp l i t t ing [7 ]. The observedsp l i t t ing o f two s ta tes wi th the conf igura tions of [ (p l / 2 )~ l (p l /2 )A ] and [ (p l /2 )~ l (p 3 /2 )A ]in ~60 was 1.56 + 0.12 MeV.

There a re a l so d i sc repanc ies be tween theore t i ca l p red ic t ions on the sp in -o rb i t sp l i t t ing .One b oson e xchan ge (O BE ) models pred ict sp l i t t ings of 0 .75 ~ 0 .96 MeV for ~aC [8].Th e c alculat ions are perfo rm ed in the fram ewo rk of microscopic 3c~ + A model by us ingNi jmegen model D, F and NSC97f . On the o ther hand , quark models p red ic t a lmos t ze rospl i t t ings for the A-nucleus spin-orbi t in teract ion [9][10].

A new e xper im en t wi th h igh reso lu t ion and h igh s ta t i s t ics is necessary to conc lude thesed isc repanc ies descr ibed above. We per fo rme d the exper imen t w i th an e lec t romag net icp robe in 1998 . Our exper imen t has g rea t advan tages over p rev ious exper imen ts .2 . E X P E R I M E N T

T h e 1 3 C ( K - , ~ - ")')~3C exper im en t was per fo rmed a t B NL -AG S-D 6LIN E to m easurethe sp in -o rb i t sp l i t t ing o f ~3C wi th h igh p reci sion. The K - bea m m om entu m w as 0 .93Ge V /c , and sca t te red 7 r- par t i c les a t 0 to 16 degrees were de tec ted by 48D48 spec t rometer .Th e (Tr- , p - , e - ) / K - r a t i o of t h e b e a m l in e wa s a b o u t 0 .3 . Ty p i c a l b e a m i n t e n s it y wa s 5 104 K -s /s pi l l ( 4 . 5 s) . T he 13C benz ene targ et was an act ive targ et of 6 .0 cm wide, 1 .5cm high and 12.0 cm th ick . The act ive target is a useful device to detect the weak decayof ~3C and to suppress the backgrou nd due to the in -f light decay o f K - . In the (K - ,7 r -) expe r imen t , the in - fl igh t decay o f K - is a main background . Espec ia l ly , we mea sure


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v - r a y s , t h e r e f o r e t h e K - ~ 7 r- zr~ d e c a y p r o d u c i n g t w o 7 - r a y s m u s t b e s u p p r e s se d . I nt h e o f f - l i n e a n a l y s i s , t h e a c t i v e t a r g e t p l a y e d a n i m p o r t a n t r o l e i n i d e n t i f y i n g t h e l a C ( K - ,7 r- )~ 3 C r e a c t i o n a n d i n r e d u c i n g b a c k g r o u n d . 7 2 N a I d e t e c t o r s o f 6 .4 cm x 6 .4 cm x3 0 . 5 c m w e r e l o c a t e d a t 1 0 . 5 c m f r o m t h e t a r g e t c e n t e r t o m e a s u r e t h e v - r a y s f r o m t h e1 / 2 - a n d 3 / 2 - d o u b l e t s t a t e s a t ~ 1 1 M e V t o t h e g r o u n d s t a t e in [ aC . C o n f i g u ra t io n s o ft h e t w o s t a t e s a r e m a i n l y [ 1 2 C ( 0 + ) | B y v i r t u e o f t h e 0 + s p i n o ft h e 12C c o re , a p u r e r s p i n - o r b i t s p l i t t i n g c a n b e o b s e r v e d i n ka C . T h e e n e r g y c a l i b r a t i o no f t h e N a I d e t e c t o r s i n t h e h i g h e n e r g y r e g i o n is p a r t i c u l a r l y i m p o r t a n t . W e u s e d t h e8 .999 MeV v- rays f rom the 5SNi(n , 7 ) reac t ion because the ene rgy i s c lose to 11 MeV.T h e s e g m e n t a t i o n o f t h e N a I d e t e c t o r i s a ls o i m p o r t a n t f or t h e e n e r g y c o r r e c t i o n o f t h eD o p p l e r s h i ft , a n d i t is n e c e s s a r y to e n d u r e h i g h c o u n t i n g r a t e n e a r t h e t a r g e t . T y p i c a le n e r g y r e s o l u t i o n o f t h e N a I d e t e c t o r i s e x p e c t e d t o b e 3 40 k e V F W H M f o r t h e d e t e c t i o no f t h e 11 M e V 7 - r a y . I t is r o u g h l y o n e o r d e r o f m a g n i t u d e b e t t e r t h a n t h o s e o b t a i n e d b yu s in g t h e m a g n e t i c s p e c t r o m e t e r s ( ~ 2 M e V F W H M ) . T h e b e t t e r e n e r g y r e s o lu t i o n e n a b le su s t o m e a s u r e e n e r g i es o f t h e d o u b l e t s t a t e s w i t h p r e c i si o n o f a fe w te n s k e V . A c c o r d i n gt o t h e o r e t i c a l c a l c u l a t i o n o n t h e c r o s s - s e c t i o n s b y T . M o t o b a e t a l . , t h e 1 / 2 - s t a t e i sd o m i n a n t l y e x c i t ed a t t h e f o r w a rd s c a t t e r in g a n g l es , w h il e t h e 3 / 2 - s t a t e is d o m i n a n t l ye x c i t e d a t t h e l a r g e r a n g l e s o f ~ 1 3 ~ T h e a n g u l a r d i s t r i b u t i o n o f t h e ( K - , 7 r - ) r e a c t i o ne n a b l e s u s t o s e p a r a t e t h e d o u b l e t s t a t e s , w h i c h i s o n e of t h e m o s t i m p o r t a n t a d v a n t a g e s .D a t a w e r e c o ll e c t e d w i t h 2 . 1 x 109 K - s o n th e t a r g e t , a n d t h e d a t a c o l l ec t e d s t a b l y w i t h1 .4 x 109 K - s w e r e a n a l y z e d .

3 . P R E L I M I N A L Y R E S U L T3 . 1. Q u a s i - f r e e r e g i o n

I n t h e q u a s i - fr e e r e g i o n of t h e 1 3 C ( K - , 7 r -) r e a c t io n , t w o p e a k s a r e d o m i n a n t l y o b s e r v e d .O n e p e a k i s 7 - r a y s f r o m t h e 2 + s t a t e a t 4 . 4 39 M e V t o t h e g r o u n d s t a t e i n 1 2 C . F i g . l ( a )s h o w s a n e n e r g y s p e c t r u m o f 7 - r a y s i n t h e q u a s i -f r e e re g i on , w h e r e t h e 7 r- s c a t t e r i n gang les o f 0 to 7 degrees a re s e lec ted . A f i t t ing to the h i s tog ram in the re g ion o f 3 .0 to5 .6 M e V is p e r f o r m e d w i t h t h e f u n c t i o n o f t w o g a u s s ia n s a d d e d t o t h e l i n e a r fu n c t i o n .The h ighe r gauss ian i s fo r the fu l l ene rgy peak , and the lower gauss ian i s fo r the s ing lee s c a p e p e a k . T h e m e a s u r e d e n e r g y o f t h e f u ll e n e r g y p e a k i s 4 .4 4 4 + 0 .0 0 8 M e V , a n dt h e e n e r g y r e s o l u t i o n i s 2 2 0 1 8 k e V F W H M . T h e e n e r g y is a l m o s t t h e s a m e a s 4 . 43 9M e V w i t h i n t h e s t a t i s t ic a l e r ro r . A s s u m i n g t h e r e l a ti o n , A E c~ ~ / ~ f o r t h e e n e r g yd e p e n d e n c e , a n e s t i m a t e d e n e r g y r e s o l u t i o n f o r t h e 1 1 M e V v - r a y i s 3 4 0 k e V F W H M .u -T h e e n e r g y r e s o l u t i o n i s t h e s a m e a s w h a t w e p l a n n e d t o a c h i e v e b e f o r e t h e e x p e r i m e n t .O b s e r v e d p e a k s t r u c t u r e s a t 2 . 2 M e V a n d 6 . 2 M e V a r e t h o u g h t t o c o r r e s p o n d t o " , / - r a y sf r o m t h e 7 //2 + s t a t e a t 2 .1 6 4 M e V t o t h e g r o u n d s t a t e i n 27 S i a n d 7 - r a y s f r o m t h e 3 / 2 -s t a t e a t 6 . 1 7 6 M e V t o t h e g r o u n d s t a t e i n 1 5 0 . T h e 2 s S i a n d 1 6 0 n u c l e i a r e t h e m o s td o m i n a n t c o m p o s i t i o n s o f t h e t a r g e t c e l l m a d e o f q u a r t z w i t h t o t a l t h i c k n e s s o f 8 r a m .T h e o t h e r p e a k i s v - r a y s f r o m t h e I + s t a t e ( T = I ) a t 1 5 . 1 1 0 M e V t o t h e g r o u n d s t a t e i n1 2 C . F i g . l ( b ) s h o w s a n e n e r g y s p e c t r u m o f v - r a y s i n t h e q u a s i - f r e e r e g i o n , w h e r e t h e ~ -s c a t t e r i n g a n g l e s o f 0 t o 1 6 d e g r e e s a r e s e l e c t e d . A c l e a r p e a k a t 1 5 M e V i s d o m i n a n t l yo b s e r v e d . T h e a m o u n t o f t h e b a c k g r o u n d a r o u n d 1 5 M e V i s m u c h l e s s t h a n t h a t a r o u n d4 . 4 M e V .


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F i g u r e 1. E n e r g y s p e c t r a o f " ),- ra ys i n th e q u a s i - f r e e r e g i o n a t t h e s c a t t e r i n g a n g l e s o f 0t o 7 d e g r e e s ( a ) a n d a t t h e s c a t t e r i n g a n g l e s o f 0 t o 1 6 d e g r e e s ( b ) .

3 .2 . B o u n d r e g i o nA n e n e r g y s p e c t r u m o f v - r a y s i n t h e A b o u n d r e g i on o f )t3 C is s h o w n i n F i g . 2 , w h e r e t h e

7 r- s c a t t e r i n g a n g l e s o f 0 t o 9 d e g r e e s ( u p p e r ) a n d 9 t o 1 6 d e g r e e s ( lo w e r ) a r e s e l e c t e d .T h e o r e t ic a l l y, e s t i m a t e d p o p u l a t i o n r a t i o s b e t w e e n th e 1 / 2 - a n d 3 / 2 - s t a t e s a re a b o u t8 :2 i n t h e u p p e r s p e c t r u m a n d 2 :8 i n t h e l ow e r s p e c t r u m . T h e o b s e r v e d p e a k s i n t h eb o t h s p e c t r a a r e l o c a t e d c l o s el y t o e a c h o t h e r . S t r e n g t h s o f t h e s i n gl e e s c a p e p e a k s a r ea b o u t 5 0 % of t h e f u ll e n e r g y p e a k s , w h i c h i s c o n s i s t e n t w i t h t h e r e s u l t s o f t h e M o n t eC a r l o s i m u l a t i o n . F i t t i n g s a r e p e r f o r m e d w i t h t h e f u n c t i o n o f t w o g a u s s i a n s a d d e d t o t h ee x p o n e n t i a l . T h e h i g h e r g a u s s i a n i s f or t h e f ul l e n e r g y p e a k , a n d t h e l o w e r g a u s s i a n i sf o r t h e s i n g l e e s c a p e p e a k . P o s i t i o n o f t h e l o w e r g a u s s i a n i s f i xe d a t 0 .5 1 1 M e V l o w e rt h a n t h a t o f t h e h i g h e r g a u s s i a n . W i d t h s o f t h e g a u s s i a n s a r e al so f ix e d t o th e e s t i m a t e dw i d t h o f 3 4 0 k e V F W H M . S t a t i s t i c a l e r r o r s a r e a b o u t 2 0 k e V f or t h e m e a n s o f t h e h i g h e rg a u s s i a n s . T h e e r r o r s a r e a l m o s t t h e s a m e a s t h a t w e e x p e c t e d . T h e e n e r g y d i ff e re n c eo f t h e t w o p e a k s i s ~ 9 0 k e V ( p r e l im i n a r y ) . T h e s p l i t ti n g o f t h e 1 / 2 - a n d 3 / 2 - d o u b l e ts t a t e s i s e s t i m a t e d t o b e ~ 1 5 0 k e V b y c o n s i d e ri n g t h e m i x i n g o f t h e t w o s t a t e s .I n t h e p r e s e n t p r e l i m i n a r y r e s u l t, s y s t e m a t i c e r r o rs h a v e n o t b e e n e s t i m a t e d , y e t . As y s t e m a t i c e r r o r i n t h e e n e r g y c a l i b r a t i o n o f t h e N a I d e t e c t o r i s t h o u g h t t o b e s m a l l ino b t a i n i n g t h e s p l i t t i n g e n e r g y b e c a u s e s a m e e n e r g y c a l i b r a t i o n i s u s e d f o r a ll t h e s c a t t e r i n ga n g le s . T h e r e f o r e , s y s t e m a t i c e r r o r s i n t h e f it t in g s a n d i n t h e e n e r g y c o r r e c t i o n o f t h eD o p p l e r s h i ft a r e e x p e c t e d t o m a i n l y c o n t r i b u t e t o t h e s p l i tt i n g . F o r t h e e s t i m a t i o n o ft h e s y s t e m a t i c e r r o r i n t h e f i t t i n g s , v a r i o u s f u n c t i o n s s u c h a s a f u n c t i o n m o r e s i m i l a r t ot h e e n e r g y s p e c t r u m o b t a i n e d w i t h t h e s i m u l a t i o n s h o u l d b e a p p l i e d . T h e s i m u l a t i o n w i l la l so h e l p t o e s t i m a t e t h e s y s t e m a t i c e r r o r i n t h e e n e r g y c o r r e c t i o n o f t h e D o p p l e r s h i ft .


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F i g u r e 2 . E n e r g y s p e c t r a o f " ),- ra y s i n t h e A b o u n d r e g io n . T h e e n e r g y c o r r e c t io n o f t h eD o p p l e r s h i ft i s p e r fo r m e d . T h e s c a t t e r i n g a n g l e s o f 0 ~ t o 9 ~ i n t h e u p p e r s p e c t r u m a n d9 ~ t o 1 6 ~ i n t h e l o w e r s p e c t r u m a r e s e l e c t e d .

R E F E R E N C E S.

2 .3 .4.5 .6 .

.

8 .9 .10 .11 .

P . H. Pi le e t a l . , P h y s . R e v . L e t t . 6 6 ( 1 9 9 1 ) 2 5 8 5 .T . H a s e g a w a e t a l . , P h y s . R e v . L e t t . 7 4 ( 1 9 9 5 ) 2 2 4 .W . B r u c k n e r e t a l . , P h y s . L e t t . 7 9 B ( 1 9 7 8 ) 1 5 7 .M . M a y e t a l . , P h y s . R e v . L e t t . 4 7 ( 1 9 8 1 ) 1 1 0 6 .M . M a y e t a l . , P h y s . R e v . L e t t . 5 1 ( 1 9 8 3 ) 2 0 8 5 .T . N a g a e e t a l . , I n t . I N S s y m p . o n N u c l e a r a n d P a r t i c l e P h y s i c s w i t h m e s o n b e a m s i nt h e 1 G e V / c r e g i o n , e d s . S. S u g i m o t o a n d O . H a s h i m o t o ( U n i v e rs a l A c a d e m i c P r e s s ,T o k y o , 1 9 9 5 ) 1 7 5 .R . H . D a l i t z e t a l . , N u cl . P h y s . A 6 2 5 ( 1 9 9 7 ) 7 1 .E . H i y a m a e t a l . , t o b e p u b l i s h e d .O . M o r i m a t s u e t a l . , N u cl . P h y s . A 4 2 0 ( 1 9 8 4 ) 5 7 3 .H . J . P i r n e r e t a l . , P h y s . L e t t . 1 1 4 B ( 1 9 8 2 ) 3 0 8 .T . M o t o b a e t a l , p r i v a t e c o m m u n i c a t i o n .

Spin-orbit splitting of 13ΛC

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