Photodisintegration Reactions of 3He and 4He at TAGX,

7/28/2019 Photodisintegration Reactions of 3He and 4He at TAGX,

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Hadron and Nuc lear Physics w ith Electromagnet ic ProbesK. Maruyam a and H. Okuno (Editors)9 2 0 0 0 Elsev ier Sc ience B .V . A l l r ig ht s reserv ed . 155

P h o t o d i s i n t e g r a t i o n r e a c t i o n s o f a H e a n d 4 H e a t T A G XT . S u d a aa R I B e a m S c i e n c e , R I K E N1 - 2 H i r o s a w a , W a k o , S a i t a m a , J A P A N

1 . INTRODUCTIONT h e m e a s u r e m e n t o f t h e p h o t o d i s i n t e g r a t i o n c r o s s s e c t i o n s f o r f e w - n u c l e o n s y s t e m s ,

s u c h a s 3 H e a n d 4 H e , h a s b e e n o n e o f t h e m a i n e x p e r i m e n t a l p r o g r a m s o f t h e T A G Xp r o j e c t s i n c e t h e e n d o f 1 9 8 0 ' s . T h i s p r o g r a m a i m e d a t i n v e s t i g a t i n g r e a c t i o n m e c h a n i s m so f t h e n u c l e a r p h o t o d i s i n t e g r a t i o n i n t h e i n t e r m e d i a t e p h o t o n e n e r g y ( E ~ > _ I 0 0 M e V ) .I n a s e r i e s o f t h i s T A G X p r o g r a m , t h e m e a s u r e m e n t s o f t h e p h o t o d i s i n t e g r a t i o n r e a c t i o nc r o s s s e c t i o n f o r 3 H e a n d 4 H e c o v e r i n g a w i d e k i n e m a t i c a l r e g i o n h a v e b e e n a t t e m p t e di n a k i n e m a t i c a l l y c o m p l e t e w a y , w h i c h e n a b l e d o n e t o e x p l o r e t h e r e a c t i o n m e c h a n i s m si n d e t a i l . T h e d o m i n a n t r e a c t i o n m e c h a n i s m h a s b e e n r e v e a l e d t o b e p h o t o n a b s o r p t i o nb y t w o n u c l e o n s ( 2 N ) i n a n u c l e u s . I n t h e T A G X p r o g r a m , d i f f e r e n t p h o t o n a b s o r p t i o nm o d e s c o n t r i b u t i n g t h e p h o t o d i s i n t e g r a t i o n p r o c e s s e s h a v e b e e n s e p a r a t e l y i d e n t i f i e d , a n dw e h a v e s u c c e e d e d t o e x t r a c t t h e 2 N c r o s s s e c t i o n o v e r a w i d e E ~ r a n g e f o r t h e f i r s t t i m e .B y c o m p a r i n g t h e 2 N c r o s s s e c t i o n s w i t h m i c r o s c o p i c t h e o r i e s , o n e c a n s t u d y t h e t w o -n u c l e o n s y s t e m i n a n u c l e u s .

I n t h e c a s e o f 3 H e p h o t o d i s i n t e g r a t i o n , t h e c r o s s s e c t i o n s f o r p h o t o n a b s o r p t i o n b ya n p - a n d p p - p a i r ( a 2 N ( p n ) , r h a v e b e e n s e p a r a t e l y d e t e r m i n e d , a n d t h e a n a l y z i n gp o w e r f o r 2 N ( p p ) h a s b e e n a l s o m e a s u r e d . F o r 4 H e , t h e c r o s s s e c t i o n f o r 2 N ( p n ) h a s b e e ne x t r a c t e d , a n d c o m p a r e d w i t h t h a t o f 3 H e .

I n t h i s p a p e r , w e p r e s e n t m o s t o f t h e e x p e r i m e n t a l r e s u l t s o b t a i n e d b y t h e 3 H e a n d 4 H ep h o t o d i s i n t e g r a t i o n m e a s u r e m e n t s u s i n g t h e T A G X .O n e m a y c a l l t h e 2 N p r o c e s s ' p h o t o d i s i n t e g r a t i o n ' o f a t w o - n u c l e o n s y s t e m i n n u c l e u s .

A s t h e w a v e f u n c t i o n o f t h e d e u t e r o n a n d t h e n u c l e o n - n u c l e o n f o r c e h a v e b e e n e x t e n s i v e l ys t u d i e d f r o m t h e d e u t e r o n p h o t o d i s i n t e g r a t i o n [ I ] , w e m a y s t u d y t h e w a v e f u n c t i o n o f an u c l e o n p a i r a n d t h e n u c l e o n - n u c l e o n f o r c e s i n n u c l e a r m e d i u m f r o m ' p h o t o d i s i n t e g r a t i o n 'o f t h e t w o - n u c l e o n s y s t e m i n n u c l e i .

A b u i l d i n g b l o c k o f a n u c l e u s i s c o n s i d e r e d t o b e s u c c e s s i v e n u c l e o n - n u c l e o n c o l l i s i o n si n s i d e t h e n u c l e u s , b u t o u r u n d e r s t a n d i n g o n t h e t w o - n u c l e o n c o l l i s i o n s i n n u c l e a r m e d i u mi s s u r p r i s i n g l y p o o r . T h e b e s t m o d e l t o d e s c r i b e n u c l e i i s t h e m e a n - f i e l d t h e o r y b a s e d o nt h e i n d e p e n d e n t - s i n g l e - p a r t i c l e m o d e l , i n w h i c h a n u c l e o n i s a s s u m e d t o m o v e i n d e p e n -d e n t l y i n a n u c l e a r - m e a n - f i e l d p o t e n t i a l . I t a c c o u n t s f o r v a r i o u s p r o p e r t i e s o f n u c l e i a n dn u c l e a r r e a c t i o n w e l l , b u t t h i s m o d e l c a n n o t d e s c r i b e h o w t w o n u c l e o n s s c a t t e r e a c h o t h e ri n a n u c l e u s . T h e m e a s u r e m e n t s o f t h e ' p h o t o d i s i n t e g r a t i o n ' o f a n u c l e o n p a i r i n s i d e a


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

s t a t e , 3 S 1 . A s p i n - s i n g l e t n u c l e o n p a i r , 1 S 0 , c a n b e a l s o s t u d i e d w h e n o n e l o o k s a t an u c l e o n p a i r i n s i d e a n u c l e u s . F o r e x a m p l e , a p r o t o n - p r o t o n p a i r c a n b e a s s u m e d t ob e 1 S 0 s i n c e t h e i s o s p i n i s a l w a y s o n e . T h e n u c l e o n - n u c l e o n p o t e n t i a l f o r t h e 1 S 0 - p a i rb e c o m e s r e p u l s i v e w h e n t h e d i s t a n c e o f t w o n u c l e o n s b e c o m e s l e s s t h a n 0 . 5 f m . I t i s w e l lk n o w n t h a t t h i s r e p u l s i v e f o r c e p l a y s a n e s s e n t i a l r o l e f o r m a n y n u c l e a r p r o p e r t i e s s u c ha s t h e s a t u r a t i o n e f f e c t s , a l t h o u g h t h e o r i g i n h a s n o t b e e n y e t f u l l y u n d e r s t o o d . O n e c a ni n v e s t i g a t e t h i s u s i n g t h e p h o t o n a b s o r p t i o n p r o c e s s b y t w o p r o t o n s i n n u c l e i .

T h e i s o - s c a l e r n a t u r e o f t h e n u c l e o n - n u c l e o n f o r c e e n s u r e s t h e s i m i l a r i t y o f t h e w a v ef u n c t i o n o f t h e n p - a n d p p - p a i r s i n a n u c l e u s . T h e i n t e r a c t i o n w i t h t h e e l e c t r o m a g n e t i cf i e l d , h o w e v e r , i s q u i t e d i f f e r e n t d u e t o t h e d i f f e r e n c e s o f t h e c o n t r i b u t i n g e l e c t r o m a g n e t i cc u r r e n t s i n t h e 2 N ( p n ) a n d 2 N ( p p ) p r o c e s s . I n t h e c a s e o f 2 N ( p n ) , t h e m e s o n - e x c h a n g ec u r r e n t s ( M E C ) c a n c o n t r i b u t e i n a d d i t i o n t o n o r m a l o n e - b o d y c u r r e n t s ; t h e c o n v e c t i o na n d s p i n c u r r e n t s . I n t h e c a s e o f 2 N ( p p ) , h o w e v e r , n o c h a r g e d m e s o n c a n b e e x c h a n g e d .T h e r e f o r e o n l y t h e o n e - b o d y c u r r e n t p l a y s a r o l e . T h i s d i f f e r e n c e o f t h e e l e c t r o m a g n e t i cc u r r e n t s g i v e s s i g n i f i c a n t d i f f e r e n c e i n t h e a b s o l u t e m a g n i t u d e a n d E ~ - d e p e n d e n c e o f t h ec r o s s s e c t i o n f o r 2 N ( p n ) a n d 2 N ( p p ) .2 . E X P E R I M E N T A L D E T A I L S2 .1 . T h e T A G X s p e c t r o m e t e r

The TAGX spec t romete r was p laced in the tagged photon beam l ine a t the 1 .3 GeVelec t ron sy nchro t ron of the In s t i tu te for Nuc lear S tudy ( INS) , Unive r s i ty of Tokyo. (TheTA GX spec t rom ete r has been a l r eady moved f rom INS to LNS, Senda l in the f al l o f 1999 .)T A G X is a l a r ge - a cc e p ta nc e ma gne t i c - spe c t rome te r ha v ing a bou t ~ sr for charged par t ic leand 0 .8 sr for neutron. Deta i led descr ipt ion can be found e lsewhere [2] .

The t r a jec tor ie s o f cha rge pa r t ic le s photo-produced f rom the 3He or 4He ta rge ts , weret raced by s t r aw dr i f t chamb ers (SDC) and a se t o f cen t ra l d r i f t chambers (CDC ) p lacedin the d ipo le magn e t ic field . The ve loc ity was measured by the t ime-of - fl igh t (T OF )m etho d us ing two se t o f hodoscopes , Inne r Hodoscope ( IH) and O ute r So dosco pe (OH) .The f ligh t t ime b e tween IH and OH have been measured . Pa r t ic le iden ti f ica t ion for cha rgepar t ic le s was done us ing the m om entu m an d the ve loc ity. The ene rgy of the ne u t ron wasde te rmined by the t ime-of - f l igh t me thod .

S ince we a re in te res ted in photon absorp t ion by two nuc leons , two ene rge t ic nuc leonswere detec ted in coincidence , (7 , N N ) . The co inc idence s igna l s t robed the photon taggerto de te rmine the photon ene rgy .

D ue to f in i te m om e n tum th r e sho ld o f t he T A G X (300 Me V /c f o r p r o ton a n d 100 M e V /cfor neu t ron) , two d i f fe ren t t r igge r s were employed for the da ta acquis i t ion to make theTAGX spec t romete r have enough acceptance for d i f f e ren t photon absorp t ion processessuch as by two- and th ree -nuc leons . The f i r st one was lnp t - t r ig ge r for de tec t ing a nppa i r , and anothe r was ~ppt - t r igge r for de tec t ing two pro tons .2 .2 . P r o d u c t i o n o f p o l a r iz e d t a g g e d p h o t o n s a n d a p o l a r i m e t e r

In addi t ion to the measurement the photodis in tegra t ion c ross sec t ion for 3He and 4He ,the ana lyz ing power of the 3He(~, pp)n r e a c t ion ha s be e n me a su r e d to s tudy the 2N( pp)


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Figure 1. Exper imental setup for the aHe( '7, pp)n exper iment


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p r o c e s s . T o d o t h i s , t h e p h o t o n t a g g i n g s y s t e m h a s b e e n m o d i f i e d a n d a p o l a r i m e t e r h a sb e e n i n s t a l l e d i n t h e t a g g e d p h o t o n b e a m l i n e . W e d e s c r i b e t h i s n e w f a c i l i t y b r i e f l y .

F i g u r e 1 s h o w s th e e x p e r i m e n t a l s e t u p f o r t h e a n a l y z i n g p o w e r m e a s u r e m e n t o f t h e3H e(~ , pp)n r e a c ti o n . P o l a r iz e d t a g g e d p h o t o n s w e r e p r o d u c e d b y th e c o h e r e n t b r e m s s t r a h l u n go f a 1 . 1 6 - G e V e l e c t r o n b e a m i n a d i a m o n d c r y s t a l o f 1 . 1 - m m t h i c k n e s s i n s t a l l e d a t t h er a d i a t o r p o s i t i o n . T h e c r y s t a l w as m o u n t e d o n a th r e e - a x is g o n i o m e t e r a n d w a s p l a c e d a tt h e r a d i a t o r p o s i t i o n o f t h e t a g g e r . T h e a x i s w a s s e t s o t h a t t h e c o h e r e n t s p i k e a p p e a r sa t E~ = 290 MeV as show n in F ig . 2 .

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F i g u r e 2 . I n t e n s i t y a n d p o l a r i z a t i o n o f t h e c o h e r e n t b r e m s s t r a h l u n g f o r E e - 1 . 1 6 G e V .O p e n c i r c l e s s h o w t h e m e a s u r e d p h o t o n e n e r g y s p e c t r u m . T h e r e s u l t s o f a t h e o r e t i c a lc a l c u l a t i o n f o r t h e i n t e n s i t y a n d t h e p o l a r i z a t i o n a r e s h o w n t o g e t h e r b y t h e s o l i d - a n dd a s h e d - l i n e .

R e c o i l e d e l e c t r o n s w e r e d e t e c t e d b y t h e p h o t o n t a g g i n g s y s t e m , w h i c h c o v e r e d t h ep h o t o n e n e r g y r a n g e s o f 7 4 0 - 1 0 6 0 ( T a g g i n g H o d o s c o p e A ) a n d 2 0 0 - 6 0 0 M e V ( T a g g i n gH o d o s c o p e B ) w i t h A E ~ = - I - 5 a n d : l : 1 0 M e V r e s o l u t i o n , r e s p e c t i v e l y . T h e p h o t o n t a g g i n gd e t e c t o r s f o r E ~ - 2 0 0 - 6 0 0 M e V w e r e n e w l y e q u i p p e d f o r t h e p o l a r i z e d p h o t o n p r o j e c t .

I n t h e F i g . 2 , o p e n c i r c l e s s h o w t h e p h o t o n e n e r g y s p e c t r u m m e a s u r e d b y t h e t a g g i n gc o u n t e r s p l o t t e d w i t h t h e r e s u l t o f a t h e o r e t i c a l c a l c u l a t i o n w h i c h t a k e s t h e e x p e r i m e n t a lc o n d i t i o n s i n t o a c c o u n t . T h e t h e o r y r e p r o d u c e s t h e m e a s u r e d e n e r g y s p e c t r u m w e l l , a n dt h e m a x i m u m p o l a r i z a t i o n i s e x p e c t e d t o b e a b o u t 3 5 ~ 0 a t t h e c o h e r e n t s p i k e p o s i t i o n .

T h e p h o t o n p o l a r i z a t i o n h a s b e e n d e t e r m i n e d b y t w o w a y s . O n e i s b y a p a i r p o l a r i m e t e r ,w h i c h d e t e c t s a n e l e c t r o n - p o s i t r o n p a i r p r o d u c e d i n a c o n v e r t e r . T h e c o r r e l a t i o n b e t w e e nt h e m o m e n t u m v e c t o r s o f a p a i r h a s b e e n s h o w n t o b e s e n s i t i v e t o t h e p h o t o n p o l a r i z a t i o n[ 3 ] . T h e p a i r p o l a r i m e t e r c o n s i s t e d o f a n A l c o n v e r t e r , a p a i r m a g n e t , d r i f t c h a m b e r s a n dp l a s t i c s c i n t i l l a t o r s a s s h o w n i n F i g . i .A n o t h e r w a s t o u s e t h e q u a s i - f r e e n e g a t i v e p i o n p h o t o p r o d u c t i o n p r o c e s s , " ~ + ~ n ~ - - ~p + ~ r - , w h o s e a n a l y z i n g p o w e r h a s b e e n k n o w n t o b e l a r g e [ 4 ] . D u r i n g t h e 3 H e ( ~ , p p ) nm e a s u r e m e n t , t w o c h a r g e d p a r t i c l e s w e r e d e t e c t e d i n c o i n c i d e n c e , w h i c h e n a b l e d o n et o a c c u m u l a t e 3 H e ( ~ , p T r - ) p p e v e n t s s i m u l t a n e o u s l y . T h e p h o t o n p o l a r i z a t i o n w a s a l s o


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E7 (M eV)Figure 3 . P ho t on po la r iza t ion de te rmine d by the pa i r po la r imete r (open c i rc les ) and bythe 3He(7 , pTr-)pp reaction (solid circles).

d e t e rm i n e d b y u s in g t h e a s y m m e t ry o f t h e 3 He (~ , pzc-)pp events.Th e p h o t o n p o l a r i z a t i o n d e t e rm i n e d b y t h e p a i r p o l a r i m e t e r a n d t h e 3He('%pzr-)pp

reac t ion a re p lo t t ed toge ther in F ig . 3 , and the theore t i ca l ca lcu la t ion rep roduces theda ta wel l .3. D I S C U S S I O N S3 . 1 . T h e 2 N p r o c e s s3 . 1 . 1 . 3 H e

I n t h e 3 H e p h o t o d i s i n t e g r a t i o n p r o c e s s , t h r e e d i f f e r e n t p h o t o n a b s o r p t i o n m e c h a n i s m sm a y b e c o n s i d e r e d . T h e y a r e p h o t o n a b s o r p t i o n b y o n e n u c l e o n ( I N ) , b y t w o n u c l e o n s( 2 N ) a n d b y t h r e e n u c l e o n s ( 3 N ) . I n t h e c a s e o f I N , t h e o t h e r t w o n u c l e o n s i n 3 H e a r es p e c t a t o r s o f t h e r e a c t i o n , o n e n u c l e o n r e m a i n s a s a s p e c t a t o r i n 2 N , a n d n o s p e c t a t o rexis t s in 3N.

Considering the facts that the energet ic two nucleons were detected in the 3He(~/ , NN)m e a s u re m e n t s a n d a s p e c t a t o r n u c l e o n wa s h a rd l y d e t e c t e d d u e t o t h e TAGX d e t e c t i o nth resho ld , on ly the 2N and 3N p rocesses may con t r ibu te to the 3He(7 , NN) events. Sinceone nuc leon i s a spec ta to r in 2N, whereas no t in 3N, they can be iden t i f i ed by look ing a tthe u nde tec te d nuc leon d i s t r ibu t ion o f the 3He(3 , NN)N events.

F igure 4 shows typ ica l missing m om entu m d is t r ibu t ions o f the 3He(7 , pn)p and 3He(7 , pp)nevents for E~ = 280 M eV [6 ,7] . Th e resul ts of mo del calculat ions for (a) 2N(pn), (b)2N(pp) and (c) 3N tak ing the d e tec to r responses o f TA GX in to accoun t by the M onteCar lo m eth od a re shown toge ther . In the 2N(pp)(2N(pn)) model , a pair of pro tons (ap ro ton-neu t ron pa i r ) in 3He absorbs a pho ton , l eav ing neu t ron (p ro ton) as a spec ta to r ,whose momentum d is t r ibu t ion i s sampled f rom the s ing le -nuc leon momentum d is t r ibu t iond e t e rm i n e d b y t h e 3 He (e , e'p)d measuremen t [5 ] .

In the case o f the 3N model , the 3He nuc leus i s as sumed to be d i s in teg ra ted in to th reenuc leons whose momenta d i s t r ibu te accord ing to the th ree-body phase space .


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50

0 2 0 0 4 0 0 0 2 0 0 4 0 0P p ( M e V / c ) P n ( M e V / c )

Figure 4 . The unde tec ted -nuc leon mom entu m d is tr ibu t ions o f the 3He(v ,pn)p a n d(7, pp)n even ts for E~ = 280 MeV. Th e dashed- and do t ted - lines show the resu l t o f modelca lcu la t ions fo r 2N (a ,b ) and 3N (c) . T he so lid l ines a re the sum of 2N and 3 N.

T h e s u m o f 2N(pn)(2N(pp)) and 3N, whose s t reng ths a re de te rmined by the f i t t ing tothe da ta , rep roduces the m issing mo me ntum d is t r ibu t ion o f the 3He(7, pn)p(age (7, pp)n)events fairly well .3 . 1 . 2 . 4 H e

There are two different f inal s ta tes in the 4He(~/ , N N ) even ts , they a re th ree-body andfour-body b reakup channe ls .

9 t h r e e -b o d y b re a k u p 9 V +4 He ~ pnd9 f o u r -b o d y b re a k u p 9 V _ ~ _ 4 H e ~ pnpn

In th e case of 4He(7 , p n ) X , bo th th ree-body and four -body f ina l s t a tes con t r ibu te , i . e .X = d, np, whereas the 4He(7 , pp) always feeds the four-body f inal s ta te .Th e 4 He (v , pn)d even ts , where the deu te ron remains as a spec ta to r in the f ina l s t a te ,

could be considered as the 2N(pn) process . Since the energy resolut ion of the TA GXsys tem was no t good enough to reso lve the th ree- and four -body s ta tes , the 4He(7 , pn)dy ie ld was de te rm ined f rom the 4He(7, pn) even ts by sub t rac t ing the fou r -body co n t r ibu t ione s t i m a t e d f rom t h e 4 He (7 , pp)nn yield by correct ing for the detect ion eff ic iency [8] .

Figur e 5 shows the miss ing mass ( M x ) spec t ru m of the 4He(v , pn ) and 4He(v , pp )events . Th e resul ts of the calculated M x d i s t ri b u t io n o f t h e t h r e e -b o d y a n d fo u r -b o d ybreakup channe ls a re p lo t t ed toge ther , wh ich a re co r rec ted fo r the de tec t ion e f f i c iency o ft h e T A G X s p e c t r o m e t e r .

F igure 6 shows the miss ing mom entu m d is t r ibu t ion o f the ex t ra c ted 4He(y , pn)d events ,t h a t c o r r e s p o n d s t o t h e u n d e t e c t e d d e u t e ro n m o m e n t u m d i s t r i b u t i o n , Pd. During the4He(v , pp ) me asurem en t , severa l 4He(3, ,pd ) even ts w ere de tec ted and they a re iden t if i ed


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600

-, . . 400

200

01700

4He(~/,pn)X 9 4He(7,np)XO 4He(7,pp)

1800 1900 2000 2100 2200M x ( M e V / c 2)

F ig u r e 5 . M is s in g m a s s d i s t r i b u t io n o f t h e 4 H e ( 7 , pn) even ts . So l id - and o pen-c i r c les showth e 4 H e ( 7 , p n ) e v e n t s a n d t h e de t e c ti o n -e F f i ci e n c y- c o rr e c te d 4 H e ( 7 , p p ) e v e n t s . D o t t e d -a n d d a s h e d - l i n e s s h o w th e r e s u l t s o f m o d e l c a l c u l a t io n s f o r t h e t h r e e - b o d y a n d f o u r - b o d yb r e a k u p c h a n n e l s .

107

l o 5g~ 10 3

~ 101~ 10-1

0

9 4 H e ( 7 , n p ) d0 4 H e ( y , p d ) n

200 400 600 800 lOOO 12ooP d ( M e V / c )

F i g u r e 6 . U n d e t e c t e d - d e u t e r o n m o m e n t u m d i s t r ib u t i o n of t h e 4He(7,pn)d even ts . TheP d d i s t r i b u t io n d e t e r m in e d f r o m th e 4 H e ( 7 , pd)n even ts a r e a l so p lo t ted by open c i r c les .

a s t h e 4 H e ( 7 , pd)n e v e n t s. O n e c a n c o n s id er t h a t t h e s p e c t a to r d e u t e r o n s w e r e d e t e c t e di n t h e t h r e e - b o d y b r e a k u p c h a n n e l , 7 + 4 He ~ pnd. Open c i r c les in the f igu re show thed e u t e r o n m o m e n t u m d i s t r i b u t i o n o f t h e d e t e c t e d 4 H e( 7, pd)n even ts a f te r co r r ec t ing fo rthe de te c t io n eff ic iency. Th e ag reem en t in abso lu te m agn i tud e is sa t i s f ac to ry , a l tho ug ht h e c o m p a r i s o n w i t h t h e e x t r a c t e d 4 H e (7 , pn)d even ts i s poss ib le on ly h igher Pd region .T h i s f a c t j us t i fi e s o u r p r o c e d u r e t o e x t r a c t t h e 4 H e ( 7 , pn)d even ts f rom 4He(7 , pn) even ts .3 .2 . T o t a l c r o s s s e c t i o nT h e s t r e n g t h o f t h e p h o t o n a b s o r p t i o n p ro c es s; 2N(pn), 2N(pp) for 3He and 2N(pn) fo r4He, was ex t r ac ted f rom the da ta as shown in F ig . 4 and F ig . 5 , then the d i f f e ren t ia l andto t a l c r o ss s e c ti o n s w e re s e p a r a t e ly d e t e r m in e d o v e r a n e n t i re A - r e s o n a n c e r e g io n [ 6- 8] .

We wi l l d i scuss the to ta l c ross sec t ion o f 2N(pn) fo r 3He and 4He, and the to ta l c ross


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sect ion of 2N(pp) for aHe.3 . 2 . 1 . 2N(pn)

Figu re 7 , 8 shows the to ta l cross sect ion of the 2N(pn) process for 3He and 4He. In thef igu res , the deu te ron pho tod is in teg ra t ion c ross sec t ion (a.yd) i s p lo t ted together , which isscaled in magni tude with factors of 1 .24 and 6 .0 for 3He and 4He, respect ively .

1 5 0 , .L, ,= 9 I = 9 -o(3He(y,np)Psp)

5O

9 . . _ 9 |

1 0 0 2 0 0 3 0 0 4 0 0 5 0 0E y ( M e V )

Figure 7 . The 3He(-y ,pn)psp cross section.The sol id l ine is the deuteron photodis in-tegrat ion cross sect ion mult ip l ied by 1 .24.

8 0 0 . . . . . ,, .o ( 4 H e ( ' f , n p ) d sp )6 0 0

~. 4 0 02 0 0

II 9 9 9 1 =

1 0 0 2 0 0 3 0 0 4 0 0 5 0 0E y ( M e V )

Figure 8. The 4He(~/,pn)dsp cross section.The sol id l ine is the deuteron photodis in-tegrat ion cross sect ion mult ip l ied by 6 .0 .

The s imi la r i ty o f the E~ dependence o f the 2N(pn) cross sec tion and tha t o f the d eu te roncross sect ion over such a wide E~ range is remarkable for both 3He and 4He. How can weunders tand the scal ing factor of 1 .24 and 6 .0 for aHe and 4He ? P. Wilhelm, J . Niskanenand H. ArenhS vel have d iscussed th e d ifference of the np wave-func t ion in 3He f rom tha tof the de ute ron [9].

T h e 2N(pn) cross sect ion for 3He can be expressed in terms of the cross sect ion for thespin-s inglet (1S0) and spin-t r ip let (3S1) pairs taking in to account the spin-isospin weightsa S ~

1 1O ' 2 N ( p f t ) = ~ O ' 3 s 1 - ' [ - ~ 0 " 1 S o . (1 )

If one neglects the 1~ 0 cros s sect ion whose contr ibut ion is h indered by the spin-isospinweight of 1 /6 , one obtains ,Cr~s~ ~ 2a2N(p~). (2)

Th en one can com pare o-3s1 with aTd. Using the relat ion of (2) and the fac t th at 0"2N(pn)scales wi th t ha t of cr.rd one ob tains ,a~Sl ~ 2.5trod. (3)


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150

1 0 0

v*" 5o

l + l S 0 o ( 3 H e ( 7 , n p ) P s p )

, O:yd"%%..

O O . " " " " . . . . .0 ~ ' " ' ~1 0 0 2 0 0 3 0 0 4 0 0 5 0 0E7 (MeV)

F i g u r e 9 . T h e 2 N ( p n ) c r o s s s e c t i o n c o m p a r e d w i t h t h e c a l c u l a t i o n . T h e d e u t e r o n p h o t o -d i s i n t e g r a t i o n c r o s s s e c t i o n i s a l s o s h o w n t o g e t h e r [ 9 ].

I t i s c o n c l u d e d t h a t t h e ' p h o t o d i s i n t e g r a t i o n ' c r o s s s e c t i o n o f t h e s p i n - t r i p l e t n p - p a i r i sa b o u t 2 . 5 t i m e s l a r g e r t h a n a ~ d . T h i s e n h a n c e m e n t i s d u e t o t h e c o m p a c t w a v e f u n c t i o n o ft h e r i p - s y s t e m i n 3 H e [ 9 ] . T h i s w a s t h e f i r s t e x a m p l e t o d e m o n s t r a t e q u a n t i t a t i v e l y t h a tt h e t w o - n u c l e o n p h o t o d i s i n t e g r a t i o n p r o c e s s i s a g o o d t o o l t o i n v e s t i g a t e t h e t w o - n u c l e o nw a v e f u n c t i o n i n n u c l e i .

T h e M a i n z g r o u p h a s p e r f o r m e d a m i c r o s c o p i c c a l c u l a t i o n o f a 2 N ( p n ) [ 9 ] . T h e y a c c o u n t e df o r b o t h t h e 3 S 1 - a n d 1 S 0 _ p a i r , w h o s e w a v e f u n c t i o n s r e p r o d u c e t h e t w o - n u c l e o n c o r r e -l a t i o n f u n c t i o n o f 3 H e o b t a i n e d b y F a d d e e v m e t h o d . T h e r e s u l t s a r e s h o w n i n F i g . 9 w i t ht h e 2 N ( p n ) c r o s s s e c t i o n f o r 3 H e . I n t h e f i g u r e , t h e d a s h e d - a n d d o t t e d - l i n e r e p r e s e n t t h ec a l c u l a t e d p h o t o d i s i n t e g r a t i o n c r o s s s e c t i o n o f t h e 3 S t - a n d i S 0 - p a i r , r e s p e c t i v e l y . T h e 3 S Ic r o s s s e c t i o n s h o w s a b u m p c e n t e r e d a r o u n d 2 5 0 M e V c o m i n g f r o m t h e A - e x c i t a t i o n i nt h e i n t e r m e d i a t e s t a t e . T h i s i s d u e t o t h e M 1 t r a n s i t i o n , w h i c h i s t h e l e a d i n g t r a n s i t i o nm u l t i p l e i n t h i s e n e r g y r e g i o n .

I t i s n o t , h o w e v e r , t h e c a s e f o r t h e 1 S 0 c r o s s s e c t i o n b e c a u s e o f t h e l a c k o f t h e A -e x c i t a t i o n c o n t r i b u t i o n i n t h e i n t e r m e d i a t e s t a t e . I n a d d i t i o n t o t h e s m a l l n e s s o f t h eI S 0 c r o s s s e c t i o n , t h e c o n t r i b u t i o n o f t h e t S 0 _ p a i r i s h i n d e r e d f u r t h e r b y t h e s p i n - i s o s p i nw e i g h t s .

T h e s o l i d l i n e i s t h e s u m o f t h e m ; a 2 N ( p n ) . A l t h o u g h t h e r e i s s o m e d i s a g r e e m e n t i nE ~ d e p e n d e n c e a t l o w e r e n e r g y r e g i o n , t h e t h e o r y r e a s o n a b l y r e p r o d u c e s b o t h t h e E ~d e p e n d e n c e a n d t h e a b s o l u t e m a g n i t u d e o f t h e m e a s u r e d c r o s s s e c t i o n .3 . 2 . 2 . 2 N ( p p )

The smallness of the 2N(pp) cross section may be due to the wave function of a two-prot on s yst em in 3He. Since one can reasona bly assume th at two protons in 3He are in


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D

9 \ , \ . . . . .

9 l i P I l k . . , , . 9 " " - " " . . ' 2 ~ ' ~ , , , ' ,\ . - , ~ ,n , / . . . . "\ : - - " g i " N . . . o . ' i i .n I ~ = - = ~ I . n100 200 300 400 500

E ~ ( M e V )F i gure 10 . The 2N(pp) ross sect ion compared wi th the microscopic calculat ion [10 ,11] .

sp in - s ing le t s t a t e ( 1 ~ 0) , t h e d o m in a n t M 1 t r a n s i t i o n l e a d in g t h e 1 + fi n al s t a t e i s fo r b id d e nd u e t o t h e a n t i - s y m m e t r i z a t i o n o f t h e w a v e f u n c t i o n . S in ce th e p p - s y s t e m h a s n o e l ec t ri cd ip o l e m o m e n t , t h e E 1 t r a n s i t i o n i s a l s o s u p p r e s s e d , a n d o n ly t h e h ig h e r - o r d e r s p in - f l i pE 1 t r a n s i t i o n i s a l l o w e d .

T h e c r o ss s e c t io n d e c r e a se s m o n o to n i c a l l y a s a fu n c t i o n o f E ~ , a n d t h i s m a y b e t h er e s u l t f r o m th e l a c k o f t h e M 1 t r a n s i t i o n . T h e M a in z g r o u p h a s p e r f o r m e d a m ic r o s c o picca lcu la t ion a l so fo r a2N(pp) [10 ,11 ] . A r ea l i s t ic two-nuc leon wave func t ion fo r the in i t ia ls t a t e o f t h e p p - s y s t e m i s u s e d a n d a f in a l s t a t e w a v e f u n c t io n i s o b t a in e d b y a c o u p le d -c h a n n e l c a l c u l a t i o n i n o r d e r t o a c c o u n t f o r t h e A - N c o n f ig u r a ti o n in a d d i t i o n t o a p u r ep p - s t a t e . I n F ig u r e 1 0, t h e re s u l t s o f t h e c a lc u l a t i o n a r e p r e s e n t e d t o g e th e r w i th t h eT A G X d a t a , w h ic h t a k e s i n to a c c o u n t a l l p o s s ib l e t r a n s i t i o n m u l t i p o l e s u p to L = 3 , i.e .E l , E 2 , E 3 and M 2. ( In the f igures , the E 3 c ross sec t ion is no t p re sen te d s ince i t is sosmal l . )

T h e t h e o r y r e p r o d u c e s t h e m a g n i t u d e o f t h e s m a l l 2N(pp) cross sect ion . I t is not ,however , the case fo r the E~ dependence espec ia l ly a t h igher energy than 300 MeV,w h e r e th e t h e o r y p r e d i c ts t h a t t h e E 1 a n d M 2 m u l ti p o le s b e c o m e i m p o r t a n t . I n o r d e rto d e t e r m in e t h e l e a d in g t r a n s i t i o n m u l t i p l e a r o u n d 3 0 0 M e V , t h e a n a ly z in g p o w e r o f t h e2N(pp) p r o c e s se s h a s b e e n p r o p o s e d [ 11 ]. W e h a v e m e a s u r e d t h e a n a ly z in g p o w e r o f t h eaHe(ff , pp)n r e a c t i o n a n d t h e d a t a a n a ly s i s is u n d e r w a y . I n t h i s r e p o r t s o m e p r e l im in a r yresu l t s wi l l be p resen ted .

T h e a n a ly z in g p o w e r o f 2N(pp) h a s b e e n m e a s u r e d i n th e e n e r g y ra n g e o f E ~ = 2 4 0 -320 MeV . F ig u re 11 shows the p ro ton an gu la r d i s t r ibu t ion fo r the aHe(f f, pp)n even ts fo rPm 1 5 0 M e V /c r e g io nw h e r e t h e 3 N p r o c e s s d o m in a t e s . T h e o p e n a n d s o l id c ir cl e s i n t h e s e f ig u re s d e n o te s3He(if , pp)n e v e n t s b y v e r t i c a l l y a n d h o r i z o n t a l l y p o l a r i z e d p h o to n s .O n e m a y n o t i c e t h a t t h e p r o to n a n g u la r d i s t r i b u t io n s b y t h e v e r t i c a l l y a n d h o r i z o n t a l l yp o l a r i z e d p h o to n s a r e a lm o s t i d e n t i c a l a t h ig h e r P r n r e g io n , b u t n o t t h e c a s e f o r l o w e rP m r eg ion . Thre e nu c leons a re like ly to be invo lved a t the h igh er P m r eg ion , there fo ren o a s y m m e t r y i s e x p e c t e d t o b e o b s e r v e d .


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sp.N0i

i - i - i39 He(y.t.,pp)nsp3O He(Yii pp)nsp

P n _ < 1 5 0 M e W cm . m m m

4 0 8 0 1 2 0 1 6 0 0

3 ' ; -" '9 He(ya.,pp)n3(3 He(Yu pp)n

o gP n > 1 5 0 M e V / cl i I 9 I 9

4 0 8 0 1 2 0 1 6 00 p ( ~ 0 p ( ~

F i g u r e 1 1. T h e p r o t o n a n g u l a r d i s t r i b u t i o n o f t h e 3He(~,pp)n events for Pn _< 150 andP~ > 150 M eV /c . So l id and o pen c i r c l es a re for t he eve n t s due to ver t i ca l ly and ho r i zon -t a l l y p o l a r i z e d p h o t o n s .

0. 5

0-0.5

E y = 2 4 0 M eV" / -~ i :

11 . . z . . , , ' , \ i. . . . . [ ,,," " , ~'" " " * " I i . . . . . . . .. . . ! t

E y = 2 8 0 M eV- l - i - l - |

/ , , : , - - - , f ! , ". , . ' , ~ ' 7 " , .

E y = 3 2 0 M e V9 9 9 . 9 9 9 , 9 9 9 I . . . .

/ ~ '.

.... --,... ~ , ~ . r r ~ i I i . . - .

" , . . . .0 4 0 8 0 1 2 0 1 6 0 0 4 0 8 0 1 2 0 1 6 0 0 4 0 8 0 1 2 0 1 6 0

Op(~ Op(~ Op(~F i g u r e 12. P r e l i m i n a r y r e s u l t s o f t h e a n a l y z i n g p o w e r of 3He('%pp)n)for Pn _< 150M e V / c . T h e c u r ve s a re l a b el e d b y t h e r a t io o f t h e t r a n s it i o n s t r e n g t h o f E 1 a n d E 2 90 . 2 ( s o l i d ) , 0 . 5 ( l o n g - d a s h e d ) , 2 ( d a s h e d ) a n d o c ( d o t t e d ) .

F i g u r e 1 2 s h o w s p r e l i m i n a r y r e s u l t s o f t h e a n a l y z i n g p o w e r , E , w h i c h is d e f in e d a s ,

E = a - crtl (4)~ i + ~li

fo r E~ = 240 , 280 and 320 MeV in the 7 + , pp, c e n t e r - o f - m a s s s y s t e m .I n t h e s e f i gu r e s, t h e r e l a t i v e s t r e n g t h o f t h e E 1 a n d E 2 e x c i t a t i o n s a r e v a r i e d a n dp l o t t e d t o g e t h e r a s l in e s. T h e El~E2 r a t i o i s d e t e r m i n e d f o r t h r e e d i f f e r e n t p h o t o n

energ ies by f i tt i ng , a re p lo t t e d in F ig . 13 w i th the p red ic t ion o f t he M ainz g ro up [11 ].A t t h i s m o m e n t , d a t a is s t il l p r e l i m i n a r y a n d n o d e f in i te c o n c l u si o n c a n b e d r a w n . T h es y s t e m a t i c a l a s y m m e t r i e s a r e n o w c a r e f u l l y b e i n g e s t i m a t e d .


12/14

1 6 6

~ 2f q

9 T A G XP . W i l h e l m e t a l .

| ! ,2 0 0 3 0 0 4 0 0E~, (M eV )

F i g u r e 1 3 . T h e p r e l i m i n a r y El~E2 r a t i o c o m p a r e d w i t h a t h e o r y [ 1 1 ] .

3 H e ( ~ , p n ) p' O G o r b u n o v e t a l ."

- p n )3 * 1 . 2 4 A K o l b e t a l.1 [ ] B e r m a n e t a l.9 T A G X

:x. 102

1 0 1 - , . ' t . ,0 100 200 300 400

E y ( M e V )F i g u r e 1 4 . T h e 3 H e ( 7 , pn)pcross sect ion .T h e d a t a f o r l o w e r E ~ a r e p l o t t e d t o -g e t h e r . T h e s o l id li n e s h o w s t h e d e u t e r o ncross sec t ion w i th a sca l ing f ac to r o f 1 .24 .

800

600

400

200

4 H e ( y , p n ) d

o ( ~ , d - > p n ) * 6 . 0

9 T A G X9 M a i n z[ ] L e b d e v9 U k r a m a9 T o r i n o

0 100 200 300 400E ~, ( M e V )

Figure 15 . The 4He(~/ , pn)dcross sec t ion .T h e d a t a f o r l o w e r E ~ a r e p l o t t e d t o -g e t h e r . T h e s o li d l in e s h o w s th e d e u t e r o ncross sec t ion w i th a sca l ing f ac to r o f 6 .0 .

3 .3 . C o m p a r i s o n w i t h l o w e r E ~ d a t aT h e r e a r e s e v e r a l d a t a s e t s of 3 H e a n d 4 H e p h o t o d i s i n t e g r a t i o n a t l o w e r E ~ re g i o n, a n d

s o m e of t h e m d e t e r m i n e d t h e 2N(pn)cross sect ion .In Fig . 14 , the 2N(pn) c r o s s s e c t i o n f o r 3 H e b y T A G X i s p l o t t e d t o g e t h e r w i t h l o w e r

E ~ d a t a [ 1 2 , 1 3 ] . T h e d e u t e r o n p h o t o d i s i n t e g r a t i o n c r o s s s e c t i o n w i t h a s c a l i n g f a c t o r o f1 .24 i s a l so p lo t t ed . Th e s im i l a r i ty o f t he E ~ depe nden ce o f t he 2N(pn) cross sec t ion tot h a t o f t h e d e u t e r o n c r o ss s e c t io n o v e r s u c h a w i d e E ~ r a n g e f r o m t h r e s h o l d t o 5 0 0 M e Vi s r e m a r k a b l e . W e c a n c o n c l u d e t h a t t h e . p h o t o n a b s o r p t i o n c r o ss s e c t io n o f t h e r i p - p a i ri n 3H e s c a le s t o t h a t o f t h e d e u t e r o n p h o t o d i s i n t e g r a t i o n o v e r a w id e E ~ r a n g e .F igu re 15. show s 4H e(7 , pn)dcross sec t ion w i th low er E~ da t a [14-18] . In the f igu re , t hes c a l e d d e u t e r o n p h o t o d i s i n t e g r a t i o n c r o ss s e c ti o n w i t h a f a c t o r of 6 .0 i s p l o t t e d t o g e t h e r . I tis o u r s u r p r i s i n g t o f in d t h a t t h e r e i s a bi g d i s c r e p a n c y o r j u m p i n m a g n i t u d e a r o u n d E ~ =1 40 M e V , w h i c h is n o t o b s e r v e d i n t h e a H e c as e . T o c o n fi r m t h e a b s o l u t e m a g n i t u d e o f t h e


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c ros s s ec t ion by TA GX , we deduce th e inc lus ive 4He(7 , p ) c ros s s ec t ion by in tegr a t in g ove rt h e n e u t r o n m o m e n t u m v e c to r o f t h e 2N(pn) even ts . F ig ure 16 shows the 4He(7 , p ) c ros ssec t ion ob ta ined in th i s way . In the s ame f igure , the 4He(7 , p )X c r o s s s e c t i o n m e a s u r e d b yH o m m a et aI. [ 19 ] a r e p l o t t e d t o g e t h e r . T h e b u m p o b s e r v e d in H o m m a ' s d a t a a t a r o u n d7 0 0 M e V / c w a s a s s i g n e d d u e t o t h e 2N(pn) p r o c e ss . G o o d a g r e e m e n t o f t h e d e d u c e d(~/, p ) c r o s s s e ct i o n o f T A G X w i t h t h a t o f H o m m a ' s a t a r o u n d 7 0 0 M e V / c r e g i o n c o n f ir mt h a t t h e a b s o l u t e m a g n i t u d e o f t h e T A G X c r os s s e c ti o n s is c o r r e c t.

1.5

-~ 0.5of fr

030 0

. . . . i . . . . i . . . . u . . . r i m - - - - I , , - - -

0p = 30 ~~ ~ ~ ~ I , ~ " f 4 H e ( 7 ,P )X .

} ~ ~ ~ ~ ~ / 4He( 7 ,P~ d x .

400 500 600 700 800 900P p ( M e V / c )

Fig ure 16 . Th e doub le d i f fe ren t i a l c ros s s ec t ion fo r 4He(~ /,p ). O pen c i rc les show theinclu sive 4He(3, , p )X r e su l ts b y H o m m a et al. [19] . Sol id c i rc les show the different ia l c rosssec t ion fo r 4He(7 , p)nd d e t e r m i n e d f r o m t h e T A G X 4He(~/,pn)d c r o s s s e c t i o n i n t e g r a t e do v e r t h e n e u t r o n m o m e n t u m v e c t o r .

T h e r e f o r e t h e m e a s u r e m e n t s o f t h e 2N(pn) c r o s s s e c t i o n c o v e r i n g t h e p h o t o n e n e r g y o f1 4 0 M e V i s s t r o n g l y d e s i r e d t o u n d e r s t a n d w h a t i s g o i n g o n a t t h i s p h o t o n e n e r g y .4 . C O N C L U S I O N S

I n t h i s p a p e r , w e p r e s e n t t h e r e s u l t s o f t h e p h o t o d i s i n t e g r a t i o n e x p e r i m e n t s f o r 3 H ea n d 4 H e m e a s u r e d w i t h th e T A G X s p e c t r o m e t e r . L a r g e a c c e p t a n c e fo r b o t h p r o t o n a n dn e u t r o n o f T A G X e n a b l e d u s to c o v er a w id e k i n e m a t i c a l r a n g e , a n d t o p e r f o r m t h em e a s u r e m e n t s i n a k i n e m a t i c a l l y c o m p l e t e w a y . T h i s w a s e s s e n t i a l t o i d e n t i f y t h e p h o t o na b s o r p t i o n p r o c e s s b y tw o n u c l e o n s in t h e n u c le u s . T h e t o t a l c r o s s s e c t io n f o r p h o t o na b s o r p t i o n b y t h e n p - p a i r w a s d e t e r m i n e d f o r 3 H e a n d 4 H e, a n d t h e E ~ d e p e n d e n c e o f t h ec r o ss s e c ti o n w a s f o u n d t o b e q u i t e s im i l a r to t h a t o f t h e d e u t e r o n p h o t o d i s i n t e g r a t i o n .A m i c r o s c o p i c c a l c u l a t i o n s u c c e e d e d t o r e p r o d u c e t h e c r o s s s e c t i o n o v e r a w i d e E ~ r a n g e .P h o t o n a b s o r p t i o n b y t w o p r o t o n s i n a H e w a s a l s o o b s e r v e d a n d t h e c r o s s s e c t i o n w a se x t r a c t e d . T h e c r o ss se c t i o n w a s f o u n d t o b e a b o u t t w o o r d e r s m a l l e r t h a n t h a t o f t h enp c ros s s ec t ion , an d to have d if fe ren t E~ depen denc e . A mic roscop ic ca lcu la t ion us inga re a l i s ti c w a v e f u n c t i o n s u c c e e d e d t o r e p r o d u c e t h e m a g n i t u d e o f t h e c r o s s s e c ti o n , b u t


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fai led to account for the E~ dependence. The analyzing power for the photon absorptionby two protons was measured to study the photon absorption by two protons in detai l ,and the prel iminary resul ts are presented.R E F E R E N C E S

.

3.4.5.6.

.

.

.

10.11.12.13.14.15.16.17.18.19.

H.ArenhSvel and M. Sanzone, P h o t o d i s i n t e gr a ti o n o f D e u t e r o n , Few Body SystemsSuppl.3 (Springer-Verlag, Wien, 1991)M a r u y a m a et al . (TAGX Collab.): Nu cl . Instrum. Method s A376 (1996) 335.M.Kobayashi and K.Kondo, Nucl . Instrum. Methods, A376(1996)335.M.Vanderhaeghen et al . , Nucl. Phys. A5 95 (1995) 219.E . Jans et al . , Nucl. Phys. A4 75 (1987) 687.T . E m u r a et al . (TAG X Co llab.) : Phys. Rev. C 49 (1994) R597.S.Endo , P h.D. thesis , Journ. Sci . Hiroshima Univ. A57 , 1993.T . E m u a r et al . (TAG X Co llab.):Phy s. Rev. Lett. 73 (1994) 404.T . E m u r a et al . (TAG X Collab.) : Phys. Rev. Lett. 74 (1995 ) 1035.K . M a r u y a m a et a l . (TAGX Collab orat io n) : Phys. Lett . B393(1997)295.K.Niki, Ph .D. thesis, Jo urn. Sci. Hiroshim a Univ. A5 5, 1991.P. W ilhelm, J.A. N iskanen and H. ArenhSvel, Phys. Lett. B 33 5 (199 4) 109.P. W ilhelm, J.A. N iskanen and H. ArenhSvel, Phys. R ev. Lett. 74 (1995) 1034.P. W ilhelm, J.A. N iskanen and H. ArenhSvel, Phys. R ev. C51 (1995 ) 2841.B.L. Be rm an S.C. Fu ltz and P.F. Yergin, Phys. R ev. C10 (1974 ) 2221.V.N. F etisov, A.N. G orbu nov a nd A. T. Varfolomeev, Nucl. Phys. 71 (1965 ) 305.A.N. G orbun ov, So v. J. Nucl. Phys. 1 0(1969) 268Yu. M. Arkatov et al . , So v. J. Nucl. Phy s. 11(1970)639.F .Bales t ra et al . , Nuovo. Cim. 49(1979)575.F .Bales t ra et al . , Nuovo. Cim. 38(1977)145.S.M. Doran et al, Nucl. Phys. A559(1993)347.S . Homma et al . , Phys. Rev. C36 (198 7) 1623.

Photodisintegration Reactions of 3He and 4He at TAGX,

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