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Nuclear polarizability of 7Li from Coulomb excitation
Volume 38B, n u m b e r 2
NUCLEAR
PHYSICS
POLARIZABILITY
OF
LETTERS
7
Li
FROM
24 J a n u a r y 1972
COULOMB
EXCITATION
O. H A U S S E R , A. B. M c D O N A L D , T. K. A L E X A N D E R $ , A. J. F E R G U S O N Chalk R i v e r Nuclear Laboratories, Atomic Energy of Canada Li~niled, Chalk River, O~zlario, Ca~mda and * :~ OberlDz Colh%w, Oberlin, Ohio, USA R. E . W A R N E R
Received 2 December 1972
Excitation of the f i r s t excited state in 7Li in the Coulomb and nuclear fields of 2O8pb was studied. BelowE(7Li) = 24 MeV the polarizability of 7Li was deduced to be oL= 0.32±0.07 fm 3. At higher e n e r g i e s a large backward c r o s s section for i f - p a r t i c l e production was observed reflecting the prominent (~-t c l u s t e r s t r u c t u r e of 'Li. In t h e l a s t d e c a d e a l a r g e n u m b e r of n u c l e a r static quadrupole moments have been determined f r o m s e c o n d o r d e r e f f e c t s in C o u l o m b e x c i t a t i o n [1]. T h e c r o s s s e c t i o n f o r e x c i t i n g l o w - l y i n g states contains both "reorientation" terms and off-energy shell contributions which provide a m e a n s of m e a s u r i n g m a t r i x e l e m e n t s to v i r t u a l l y e x c i t e d s t a t e s . In p a r t i c u l a r , t h e r e c a n b e v i r t u a l e x c i t a t i o n of s t a t e s of t h e g i a n t d i p o l e r e s o n a n c e , an effect, which can also be viewed as the induct i o n of a n E1 m o m e n t , o r p o l a r i z a t i o n , in t h e n u c l e u s b e i n g e x c i t e d . C a l c u l a t i o n s of t h e s i z e of this effect for rotational and vibrational nuclei by Winther [2] and by De Boer and EichLer [I] indicate that it is particularly large in light nuclei. Measurements of the polarizability of light nuclei by Coulomb excitation are significant because they complement photoabsorption measurements and will allow E i corrections to reorientation experiments in heavier nuclei to be made with more cozffidence. A strong indication of the E 1 polarization effect has recently been observed in the break-up of 6Li proceeding through the 2.18 MeV, J~ = 3 + state in the 208pb(6Li, ad)208Pb reaction [3]. In that case the small cross section and detection efficiency limited data taking to E(6Li) = 24 and 27 MeV. The present work was undertaken to confirm the effect in another reaction and over a wider energy range by making use of the more $ Research supported by the National Science Foundation through Grant No. GP-19269. Address during 1971-72: Department of Nuclear Physics, Oxford University, Oxford, England.
a c c e s s i b l e 0.48 M e V , j v = ½- s t a t e in 7Li. At e n e r g i e s b e l o w 24 MeV a r e a s o n a b l e v a l u e f o r t h e p o l a r i z a b i l i t y of 7 L i w a s d e d u c e d f r o m t h e a n g u l a r d e p e n d e n c e of t h e c r o s s s e c t i o n . A t h i g h e r e n e r g i e s b r e a k u p of 7 L i w a s o b s e r v e d with a strong preference for a-particle emission. A n 0.9 m g , / c m 2 t a r g e t e n r i c h e d to 9 9 . 1 % i n 2 0 8 p b w a s b o m b a r d e d w i t h a 60 nA 7 L i 3 + b e a m f r o m t h e C h a l k R i v e r M P T a n d e m a c c e l e r a t o r at s e v e n e n e r g i e s b e t w e e n 18 a n d 30 MeV. P a r t i c l e s w e r e d e t e c t e d c o n c u r r e n t l y a t ~ 173 ° in a n a n n u l a r 300 p m t h i c k s u r f a c e b a r r i e r d e t e c t o r a n d at v a r i a b l e a n g l e s in a c o u n t e r t e l e s c o p e c o n s i s t i n g of 33 a n d 2000 p m t h i c k d e t e c t o r s . A n e l e c t r o n i c p a r t i c l e i d e n t i f i e r [4] w a s u s e d w i t h t h e l a t t e r to s e p a r a t e c l e a n l y p, d, t, 3He, 4He, 6 L i a n d 7Li. G a m m a r a y s w e r e d e t e c t e d by f i v e 12.7 c m d i a m × 15.2 c m NaI(T1) d e t e c t o r s of w h i c h t h e e f f i c i e n c i e s w e r e m e a s u r e d to ± 6% w i t h c a l i b r a t e d r a d i o active sources**. When a y ray was coincident with a particle detected either in the annular d e t e c t o r o r in t h e t e l e s c o p e a t 90 o, p u l s e h e i g h t s a n d t i m e r e l a t i o n s h i p s w e r e r e c o r d e d on m a g netic tape. Singles spectra for the particle det e c t o r s w e r e r e c o r d e d c o n c u r r e n t l y to a l l o w n o r m a l i z a t i o n to R u t h e r f o r d c r o s s s e c t i o n s . T h e a p p a r a t u s h a s b e e n d e s c r i b e d p r e v i o u s l y in g r e a t e r d e t a i l [5]. T h e y i e l d of 0.48 M e V y r a y s w a s o b t a i n e d on p l a y b a c k of t h e m a g n e t i c t a p e s . D e v i a t i o n s of t h e y-ray angular distributions from isotropy res u l t i n g f r o m k i n e m a t i c e f f e c t s w e r e t a k e n into ** Supplied by International Atomic Energy Agency, Vienna, Austria.
75
Volume 38B. number 2
PHYSICS
a c c o u n t . In fig. l a the d o u b l e r a t i o f o r e l a s t i c scattering O
.
,
O
(d~el, d~Ruth)(90
(d~el/d~Kuth)(173)
)
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Fig. l(a) Double ratio (dffe 1/d~Ruth) (173°)/(d(rel/dCTRuth) (90 °) for elastic scattering of ~TLi on 208pb. (b) Ratio of excitation probabilities P(173°)/P(90°) for the 0.48 MeV state in 7Li. Dashed and solid lines are the result of Coulomb excitation calculations as explained in the text. (c) Excitation probabilities at 173 ° and 90 °. 76
LETTERS
24 January 1972
unity by m o r e than 1%. T h e r a t i o of e x c i t a t i o n p r o b a b i l i t i e s f o r the 0.48 MeV s t a t e , R -- P ( 1 7 3 ° ) / P ( 9 0 °) is shown in fig. lb and the individual excitation probabilities, P(0) z d o t 0 . 4 8 ) / d ~ R u t h ( 0 ) i n fig. l c . T h e d a s h e d c u r v e s a r e the r e s u l t of a C o u l o m b e x c i t a t i o n c a l c u l a t i o n [6] in which the p o l a r i z a t i o n of the 7 L i p r o j e c t i l e is i g n o r e d . H o w e v e r , we do inc l u d e the e f f e c t s of g r o u n d - s t a t e q u a d r u p o l e r e o r i e n t a t i o n (Qs = -0.045 eb f r o m ref. [7]), w h i c h i n c r e a s e the c a l c u l a t e d r a t i o R by about 2.8%. A l s o i n c l u d e d a r e c o n t r i b u t i o n s f r o m M1 e x c i t a t i o n ( B ( M I : ~- -. ½-) = 2.5 p2 f r o m ref. [7]) w h i c h a m o u n t to only 0.6% of P(90o) and a r e c o m p l e t e l y n e g l i g i b l e at 173 ° . T h e e x p e r i m e n t a l r a t i o s b e l o w 24 MeV a r e 6% l o w e r than p r e d i c t e d by t h i s c a l c u l a t i o n , a d i f f e r e n c e which is a s c r i b e d to the p o l a r i z a t i o n of 7Li d u r i n g the e x c i t a t i o n p r o c e s s . In d e r i v i n g the p o l a r i z a b i l i t y of 7 L i we f o l l o w the r e c e n t w o r k of N a k a i and W i n t h e r [8]. A s s u m i n g that the n u c l e a r p o l a r i z a b i l i t y is a d i a g o n a l t e n s o r in the i n t r i n s i c f r a m e with p o l a r i z a b i l i t i e s p r o p o r t i o n a l to the s q u a r e of the r a d i i in the p r i n c i p a l d i r e c t i o n s , we m a y w r i t e the e f f e c t i v e q u a d r u p o l e i n t e r a c t i o n as [8] y(2) = V(2)(1 _ 0.0056 kEAa/Z2r) eff In t h i s e x p r e s s i o n A, Z a r e the m a s s and c h a r g e n u m b e r s of the n u c l e u s b e i n g e x c i t e d , E is the CM e n e r g y in MeV, a is the d i s t a n c e of c l o s e s t a p p r o a c h , r is the t a r g e t - p r o j e c t i l e d i s t a n c e . T h e p a r a m e t e r k is r e l a t e d to the (-2) m o m e n t of the n u c l e a r p h o t o a b s o r p t i o n c r o s s s e c t i o n by the f o r m u l a [9] ~-2 = f o r ( % )E;2d% = 3.5 #A 5/3 p b / M e V . 0 In t u r n , or_ 2 i s r e l a t e d [9] to the p o l a r i z a b i l i t y a by 2~2a=ficcr_ 2. T h e l o w - e n e r g y d a t a can be f i t t e d ( s o l i d c u r v e s ) by a s s u m i n g k= 3.5 4- 0.7, w h i c h c o r r e s p o n d s to a m o m e n t ~-2 = 3154-65~b/MeV and a p o l n r i z a b i l i t y a = 0.32 4- 0.0-7 fm 3. T h i s v a l u e of k a p p e a r s r e a s o n a b l e in v i e w of s y s t e m a t i c s in l i g h t n u c l e i [9]. P h o t o a b s o r p t i o n m e a s u r e m e n t s [10, 11] in 6Li y i e l d k b e t w e e n 3.2 and 3.9. M e a s u r e m e n t s of the p h o t o n e u t r o n c r o s s s e c t i o n s in 7 L i [12] y i e l d a l o w e r l i m i t , ~ - 2 > 160 p b / M e V c o n s i s t e n t with the p r e s e n t r e s u l t . F r o m the m e a s u r e d e x c i t a t i o n p r o b a b i l i t i e s a v a l u e B ( E 2 : ½- ~ ½-) = 8.3 4- 0.7 e 2 f m 4 w a s d e r i v e d . U n c e r t a i n t i e s in k and in the NaI(T1) d e t e c t o r e f f i c i e n c y c o n t r i b u t e about e q u a l l y to t h i s u n c e r t a i n t y . T h e d a t a in fig. 1 i n d i c a t e that n u c l e a r r e a c tions become increasingly important above E(TLi)= = 24 MeV. E v e n s t r o n g e r e v i d e n c e c o m e s f r o m a and t c r o s s s e c t i o n s w h i c h i n c r e a s e s h a r p l y f r o m
Volume 38B, n u m b e r 2
i
PHYSICS
= :30 M e V F E r u "[-r ELASTIC
I.o
SCATTERING
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a= b
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• ALPHA • TRITON
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LETTERS
24 J a n u a r y 1972
t r i t o n e n e r g y e x c e e d s t h e C o u l o m b b a r r i e r (calcul a t e d w i t h a o = 1.25 f m a n d a n a d d i t i o n a l d i s t a n c e of 3 f m b e t w e e n s u r f a c e s ) by v 3.1 M e V w h e r e a s t h e a - p a r t i c l e e n e r g y is v 2.3 M e V b e l o w t h e barrier. The tritons correlated with baekscattered a particles have therefore a large probability of f o r m i n g a c o m p o u n d n u c l e u s w i t h 2 0 8 p b . This interpretation has been confirmed at this l a b o r a t o r y [14]. W i t h G e ( L i ) c o u n t e r s f o r d e t e c t ing known 7 rays which can only result from (TLi, axn) r e a c t i o n s , l i f e t i m e s of s o m e s i n g l e p a r t i c l e a n d c o l l e c t i v e s t a t e s in n u c l e i n e a r t h e 208pb closed shell have already been obtained [14]. S i n c e t h e r e c o i l n u c l e u s i s p r e p a r e d w i t h a h i g h v e l o c i t y ( v / c ~ 0.5%) t h e (TLi, axn) r e a c t i o n m a y w e l l p r o v i d e a g e n e r a l l y u s e f u l tool f o r d e t e r m i n i n g l i f e t i m e s in h e a v y n u c l e i . The authors are indebted to A. Winther and K. Nakai for communicating their calculation of the El polarization effect to us prior to publication.
Rcfc~'cnccs
O,I
L
30 °
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A__I
60 °
90 °
120°
I 150 °
180 °
OLAB Fig. 2(a) E l a s t i c s c a t t e r i n g c r o s s s e c t i o n s f o r 30 MeV 7Li on 2 0 8 p b . (b} A n g u l a r d i s t r i b u t i o n s of t r i t o n s and c~ p a r t i c l e s o b s e r v e d with 30 MeV 7Li on 2 0 8 p b .
24 u ~ to 30 MeV. A n g u l a r d i s t r i b u t i o n s of i d e n t i fied'Li, a a n d t, m e a s u r e d a t 30 M e V w i t h t h e t e l e s c o p e a n d a m o n i t o r d e t e c t o r f i x e d at 90 o, a r e s h o w n i n f i g s . 2 a a n d 2b. T h e a - p a r t i c l e c r o s s s e c t i o n s a m o u n t to a b o u t 30% of t r u t h at b a c k w a r d a n g l e s a n d a r e o r d e r s of m a g n i t u d e larger than would be expected from Coulomb b r e a k u p of 7 L i t h r o u g h t h e c o n t i n u u m o r t h r o u g h p a r t i c l e u n b o u n d s t a t e s [13]. T h e s t r o n g d i f f e r e n c e s in t h e c r o s s s e c t i o n s a n d a n g u l a r d i s t r i b u tions for a and t are also incompatible with a Coulomb breakup process. A qualitative unders t a n d i n g of t h e s e d i f f e r e n c e s i s o b t a i n e d b y i n v o k i n g t h e c~ot c l u s t e r s t r u c t u r e of 7Li. N e g l e c t ing the small binding energy as well as the rotat i o n a l en*ergy of t h e c~-t s y s t e m o n e f i n d s t h a t t h e
[1] J. De Boer and J. Eiehler, in Advances in nuclear physics, eds. M. B a r a n g e r and E. Vogt (Plenum P r e s s , Inc., New York. 1968) Vol. ]. [2] A. Winther, in P r e c . Intern. Syrup. on Nuclear physics with tandems, Heidelberg (1966). [3] D.L. Disdier, G.C. BaII, O. HRusser and R.A. Warner, Phys. Rev. Lett. 27 (1971) 1391. [4] P.S. F i s h e r and D.K. Seott, Nucl. Instr. 49 (1967) 301. [5] O. H~usser et al., Can. J. P h y s . . i 8 (1970) 35. [61 A. Winther and J. De Boer. in Coulomb excitation, eds. K. Aider and A. Winther (Academic P r e s s , Inc., New York, 1966) p. 303. [71 T. L a u r i t s e n and F, Ajzenberg-Selove, Nucl. Phys. 78 (1966) 1. [8] K. Nakai and A. Winther, p r e p r i n t and private communication. [9] J.S. Levinger, Phys. Rev. 107 (1957) 554. [101 V. P. Denisov, A . P . K o m a r , L.A. Kul'ehitskii and g . D . Makhnowskii, a. Nucl. Phys. (USSR) 5 (1967) 498.
[11] E. B. Bazhonov, A . P . Komar, A.V. Kulikov and E.D. Makhnovsky, Nucl. Phys. 68 (1965) 191. [12] E. B. Bazhanov, A. P. Komar and A. V. Kulikov, Soy. Phys. Dokl. 11 (196'7) 953. [lal H. A. Weidenmtiller and A. Winther. Annals of Physics 66 (1971) 218. [14] D. Ward and O. H~iusser, Atomic Energ3, of Canada Ltd. r e p o r t s AECL-3865:-3996: O. HRusser. D. Ward, A. Olin and D.L. Disdier. AECL-4068.
77
NUCLEAR
PHYSICS
POLARIZABILITY
OF
LETTERS
7
Li
FROM
24 J a n u a r y 1972
COULOMB
EXCITATION
O. H A U S S E R , A. B. M c D O N A L D , T. K. A L E X A N D E R $ , A. J. F E R G U S O N Chalk R i v e r Nuclear Laboratories, Atomic Energy of Canada Li~niled, Chalk River, O~zlario, Ca~mda and * :~ OberlDz Colh%w, Oberlin, Ohio, USA R. E . W A R N E R
Received 2 December 1972
Excitation of the f i r s t excited state in 7Li in the Coulomb and nuclear fields of 2O8pb was studied. BelowE(7Li) = 24 MeV the polarizability of 7Li was deduced to be oL= 0.32±0.07 fm 3. At higher e n e r g i e s a large backward c r o s s section for i f - p a r t i c l e production was observed reflecting the prominent (~-t c l u s t e r s t r u c t u r e of 'Li. In t h e l a s t d e c a d e a l a r g e n u m b e r of n u c l e a r static quadrupole moments have been determined f r o m s e c o n d o r d e r e f f e c t s in C o u l o m b e x c i t a t i o n [1]. T h e c r o s s s e c t i o n f o r e x c i t i n g l o w - l y i n g states contains both "reorientation" terms and off-energy shell contributions which provide a m e a n s of m e a s u r i n g m a t r i x e l e m e n t s to v i r t u a l l y e x c i t e d s t a t e s . In p a r t i c u l a r , t h e r e c a n b e v i r t u a l e x c i t a t i o n of s t a t e s of t h e g i a n t d i p o l e r e s o n a n c e , an effect, which can also be viewed as the induct i o n of a n E1 m o m e n t , o r p o l a r i z a t i o n , in t h e n u c l e u s b e i n g e x c i t e d . C a l c u l a t i o n s of t h e s i z e of this effect for rotational and vibrational nuclei by Winther [2] and by De Boer and EichLer [I] indicate that it is particularly large in light nuclei. Measurements of the polarizability of light nuclei by Coulomb excitation are significant because they complement photoabsorption measurements and will allow E i corrections to reorientation experiments in heavier nuclei to be made with more cozffidence. A strong indication of the E 1 polarization effect has recently been observed in the break-up of 6Li proceeding through the 2.18 MeV, J~ = 3 + state in the 208pb(6Li, ad)208Pb reaction [3]. In that case the small cross section and detection efficiency limited data taking to E(6Li) = 24 and 27 MeV. The present work was undertaken to confirm the effect in another reaction and over a wider energy range by making use of the more $ Research supported by the National Science Foundation through Grant No. GP-19269. Address during 1971-72: Department of Nuclear Physics, Oxford University, Oxford, England.
a c c e s s i b l e 0.48 M e V , j v = ½- s t a t e in 7Li. At e n e r g i e s b e l o w 24 MeV a r e a s o n a b l e v a l u e f o r t h e p o l a r i z a b i l i t y of 7 L i w a s d e d u c e d f r o m t h e a n g u l a r d e p e n d e n c e of t h e c r o s s s e c t i o n . A t h i g h e r e n e r g i e s b r e a k u p of 7 L i w a s o b s e r v e d with a strong preference for a-particle emission. A n 0.9 m g , / c m 2 t a r g e t e n r i c h e d to 9 9 . 1 % i n 2 0 8 p b w a s b o m b a r d e d w i t h a 60 nA 7 L i 3 + b e a m f r o m t h e C h a l k R i v e r M P T a n d e m a c c e l e r a t o r at s e v e n e n e r g i e s b e t w e e n 18 a n d 30 MeV. P a r t i c l e s w e r e d e t e c t e d c o n c u r r e n t l y a t ~ 173 ° in a n a n n u l a r 300 p m t h i c k s u r f a c e b a r r i e r d e t e c t o r a n d at v a r i a b l e a n g l e s in a c o u n t e r t e l e s c o p e c o n s i s t i n g of 33 a n d 2000 p m t h i c k d e t e c t o r s . A n e l e c t r o n i c p a r t i c l e i d e n t i f i e r [4] w a s u s e d w i t h t h e l a t t e r to s e p a r a t e c l e a n l y p, d, t, 3He, 4He, 6 L i a n d 7Li. G a m m a r a y s w e r e d e t e c t e d by f i v e 12.7 c m d i a m × 15.2 c m NaI(T1) d e t e c t o r s of w h i c h t h e e f f i c i e n c i e s w e r e m e a s u r e d to ± 6% w i t h c a l i b r a t e d r a d i o active sources**. When a y ray was coincident with a particle detected either in the annular d e t e c t o r o r in t h e t e l e s c o p e a t 90 o, p u l s e h e i g h t s a n d t i m e r e l a t i o n s h i p s w e r e r e c o r d e d on m a g netic tape. Singles spectra for the particle det e c t o r s w e r e r e c o r d e d c o n c u r r e n t l y to a l l o w n o r m a l i z a t i o n to R u t h e r f o r d c r o s s s e c t i o n s . T h e a p p a r a t u s h a s b e e n d e s c r i b e d p r e v i o u s l y in g r e a t e r d e t a i l [5]. T h e y i e l d of 0.48 M e V y r a y s w a s o b t a i n e d on p l a y b a c k of t h e m a g n e t i c t a p e s . D e v i a t i o n s of t h e y-ray angular distributions from isotropy res u l t i n g f r o m k i n e m a t i c e f f e c t s w e r e t a k e n into ** Supplied by International Atomic Energy Agency, Vienna, Austria.
75
Volume 38B. number 2
PHYSICS
a c c o u n t . In fig. l a the d o u b l e r a t i o f o r e l a s t i c scattering O
.
,
O
(d~el, d~Ruth)(90
(d~el/d~Kuth)(173)
)
is shown as a function of incident energy. At 24 MeV and above the double ratio deviates from
I
I
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ELA s ( M eV )
Fig. l(a) Double ratio (dffe 1/d~Ruth) (173°)/(d(rel/dCTRuth) (90 °) for elastic scattering of ~TLi on 208pb. (b) Ratio of excitation probabilities P(173°)/P(90°) for the 0.48 MeV state in 7Li. Dashed and solid lines are the result of Coulomb excitation calculations as explained in the text. (c) Excitation probabilities at 173 ° and 90 °. 76
LETTERS
24 January 1972
unity by m o r e than 1%. T h e r a t i o of e x c i t a t i o n p r o b a b i l i t i e s f o r the 0.48 MeV s t a t e , R -- P ( 1 7 3 ° ) / P ( 9 0 °) is shown in fig. lb and the individual excitation probabilities, P(0) z d o t 0 . 4 8 ) / d ~ R u t h ( 0 ) i n fig. l c . T h e d a s h e d c u r v e s a r e the r e s u l t of a C o u l o m b e x c i t a t i o n c a l c u l a t i o n [6] in which the p o l a r i z a t i o n of the 7 L i p r o j e c t i l e is i g n o r e d . H o w e v e r , we do inc l u d e the e f f e c t s of g r o u n d - s t a t e q u a d r u p o l e r e o r i e n t a t i o n (Qs = -0.045 eb f r o m ref. [7]), w h i c h i n c r e a s e the c a l c u l a t e d r a t i o R by about 2.8%. A l s o i n c l u d e d a r e c o n t r i b u t i o n s f r o m M1 e x c i t a t i o n ( B ( M I : ~- -. ½-) = 2.5 p2 f r o m ref. [7]) w h i c h a m o u n t to only 0.6% of P(90o) and a r e c o m p l e t e l y n e g l i g i b l e at 173 ° . T h e e x p e r i m e n t a l r a t i o s b e l o w 24 MeV a r e 6% l o w e r than p r e d i c t e d by t h i s c a l c u l a t i o n , a d i f f e r e n c e which is a s c r i b e d to the p o l a r i z a t i o n of 7Li d u r i n g the e x c i t a t i o n p r o c e s s . In d e r i v i n g the p o l a r i z a b i l i t y of 7 L i we f o l l o w the r e c e n t w o r k of N a k a i and W i n t h e r [8]. A s s u m i n g that the n u c l e a r p o l a r i z a b i l i t y is a d i a g o n a l t e n s o r in the i n t r i n s i c f r a m e with p o l a r i z a b i l i t i e s p r o p o r t i o n a l to the s q u a r e of the r a d i i in the p r i n c i p a l d i r e c t i o n s , we m a y w r i t e the e f f e c t i v e q u a d r u p o l e i n t e r a c t i o n as [8] y(2) = V(2)(1 _ 0.0056 kEAa/Z2r) eff In t h i s e x p r e s s i o n A, Z a r e the m a s s and c h a r g e n u m b e r s of the n u c l e u s b e i n g e x c i t e d , E is the CM e n e r g y in MeV, a is the d i s t a n c e of c l o s e s t a p p r o a c h , r is the t a r g e t - p r o j e c t i l e d i s t a n c e . T h e p a r a m e t e r k is r e l a t e d to the (-2) m o m e n t of the n u c l e a r p h o t o a b s o r p t i o n c r o s s s e c t i o n by the f o r m u l a [9] ~-2 = f o r ( % )E;2d% = 3.5 #A 5/3 p b / M e V . 0 In t u r n , or_ 2 i s r e l a t e d [9] to the p o l a r i z a b i l i t y a by 2~2a=ficcr_ 2. T h e l o w - e n e r g y d a t a can be f i t t e d ( s o l i d c u r v e s ) by a s s u m i n g k= 3.5 4- 0.7, w h i c h c o r r e s p o n d s to a m o m e n t ~-2 = 3154-65~b/MeV and a p o l n r i z a b i l i t y a = 0.32 4- 0.0-7 fm 3. T h i s v a l u e of k a p p e a r s r e a s o n a b l e in v i e w of s y s t e m a t i c s in l i g h t n u c l e i [9]. P h o t o a b s o r p t i o n m e a s u r e m e n t s [10, 11] in 6Li y i e l d k b e t w e e n 3.2 and 3.9. M e a s u r e m e n t s of the p h o t o n e u t r o n c r o s s s e c t i o n s in 7 L i [12] y i e l d a l o w e r l i m i t , ~ - 2 > 160 p b / M e V c o n s i s t e n t with the p r e s e n t r e s u l t . F r o m the m e a s u r e d e x c i t a t i o n p r o b a b i l i t i e s a v a l u e B ( E 2 : ½- ~ ½-) = 8.3 4- 0.7 e 2 f m 4 w a s d e r i v e d . U n c e r t a i n t i e s in k and in the NaI(T1) d e t e c t o r e f f i c i e n c y c o n t r i b u t e about e q u a l l y to t h i s u n c e r t a i n t y . T h e d a t a in fig. 1 i n d i c a t e that n u c l e a r r e a c tions become increasingly important above E(TLi)= = 24 MeV. E v e n s t r o n g e r e v i d e n c e c o m e s f r o m a and t c r o s s s e c t i o n s w h i c h i n c r e a s e s h a r p l y f r o m
Volume 38B, n u m b e r 2
i
PHYSICS
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LETTERS
24 J a n u a r y 1972
t r i t o n e n e r g y e x c e e d s t h e C o u l o m b b a r r i e r (calcul a t e d w i t h a o = 1.25 f m a n d a n a d d i t i o n a l d i s t a n c e of 3 f m b e t w e e n s u r f a c e s ) by v 3.1 M e V w h e r e a s t h e a - p a r t i c l e e n e r g y is v 2.3 M e V b e l o w t h e barrier. The tritons correlated with baekscattered a particles have therefore a large probability of f o r m i n g a c o m p o u n d n u c l e u s w i t h 2 0 8 p b . This interpretation has been confirmed at this l a b o r a t o r y [14]. W i t h G e ( L i ) c o u n t e r s f o r d e t e c t ing known 7 rays which can only result from (TLi, axn) r e a c t i o n s , l i f e t i m e s of s o m e s i n g l e p a r t i c l e a n d c o l l e c t i v e s t a t e s in n u c l e i n e a r t h e 208pb closed shell have already been obtained [14]. S i n c e t h e r e c o i l n u c l e u s i s p r e p a r e d w i t h a h i g h v e l o c i t y ( v / c ~ 0.5%) t h e (TLi, axn) r e a c t i o n m a y w e l l p r o v i d e a g e n e r a l l y u s e f u l tool f o r d e t e r m i n i n g l i f e t i m e s in h e a v y n u c l e i . The authors are indebted to A. Winther and K. Nakai for communicating their calculation of the El polarization effect to us prior to publication.
Rcfc~'cnccs
O,I
L
30 °
J
A__I
60 °
90 °
120°
I 150 °
180 °
OLAB Fig. 2(a) E l a s t i c s c a t t e r i n g c r o s s s e c t i o n s f o r 30 MeV 7Li on 2 0 8 p b . (b} A n g u l a r d i s t r i b u t i o n s of t r i t o n s and c~ p a r t i c l e s o b s e r v e d with 30 MeV 7Li on 2 0 8 p b .
24 u ~ to 30 MeV. A n g u l a r d i s t r i b u t i o n s of i d e n t i fied'Li, a a n d t, m e a s u r e d a t 30 M e V w i t h t h e t e l e s c o p e a n d a m o n i t o r d e t e c t o r f i x e d at 90 o, a r e s h o w n i n f i g s . 2 a a n d 2b. T h e a - p a r t i c l e c r o s s s e c t i o n s a m o u n t to a b o u t 30% of t r u t h at b a c k w a r d a n g l e s a n d a r e o r d e r s of m a g n i t u d e larger than would be expected from Coulomb b r e a k u p of 7 L i t h r o u g h t h e c o n t i n u u m o r t h r o u g h p a r t i c l e u n b o u n d s t a t e s [13]. T h e s t r o n g d i f f e r e n c e s in t h e c r o s s s e c t i o n s a n d a n g u l a r d i s t r i b u tions for a and t are also incompatible with a Coulomb breakup process. A qualitative unders t a n d i n g of t h e s e d i f f e r e n c e s i s o b t a i n e d b y i n v o k i n g t h e c~ot c l u s t e r s t r u c t u r e of 7Li. N e g l e c t ing the small binding energy as well as the rotat i o n a l en*ergy of t h e c~-t s y s t e m o n e f i n d s t h a t t h e
[1] J. De Boer and J. Eiehler, in Advances in nuclear physics, eds. M. B a r a n g e r and E. Vogt (Plenum P r e s s , Inc., New York. 1968) Vol. ]. [2] A. Winther, in P r e c . Intern. Syrup. on Nuclear physics with tandems, Heidelberg (1966). [3] D.L. Disdier, G.C. BaII, O. HRusser and R.A. Warner, Phys. Rev. Lett. 27 (1971) 1391. [4] P.S. F i s h e r and D.K. Seott, Nucl. Instr. 49 (1967) 301. [5] O. H~usser et al., Can. J. P h y s . . i 8 (1970) 35. [61 A. Winther and J. De Boer. in Coulomb excitation, eds. K. Aider and A. Winther (Academic P r e s s , Inc., New York, 1966) p. 303. [71 T. L a u r i t s e n and F, Ajzenberg-Selove, Nucl. Phys. 78 (1966) 1. [8] K. Nakai and A. Winther, p r e p r i n t and private communication. [9] J.S. Levinger, Phys. Rev. 107 (1957) 554. [101 V. P. Denisov, A . P . K o m a r , L.A. Kul'ehitskii and g . D . Makhnowskii, a. Nucl. Phys. (USSR) 5 (1967) 498.
[11] E. B. Bazhonov, A . P . Komar, A.V. Kulikov and E.D. Makhnovsky, Nucl. Phys. 68 (1965) 191. [12] E. B. Bazhanov, A. P. Komar and A. V. Kulikov, Soy. Phys. Dokl. 11 (196'7) 953. [lal H. A. Weidenmtiller and A. Winther. Annals of Physics 66 (1971) 218. [14] D. Ward and O. H~iusser, Atomic Energ3, of Canada Ltd. r e p o r t s AECL-3865:-3996: O. HRusser. D. Ward, A. Olin and D.L. Disdier. AECL-4068.
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