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Proton elastic scattering at 61.4 MeV
Volume 24B number 10
PHYSICS
LETTERS
c o r r e s p o n d to an e x c i t e d s t a t e in 28Si a n d / o r to the 28Sl(p,2p) r e a c t i o n w h i c h h a s a Q v a l u e of -11.6 M e V . T h e e f f i c i e n c y of t h i s d e t e c t o r f o r d e t e c t i n g a full e n e r g y e v e n t was d e t e r m i n e d to be g r e a t e r than 97%. It was a l s o o b s e r v e d that 0.71% of the e v e n t s a r e l o c a t e d m the w e l l - i d e n t i f i e d t a l l p e a k s . T h i s l o s s of i n f o r m a t i o n i s s o m e w h a t l a r g e r than we would e x p e c t on the b a s i s of simple calculatmns assuming a geometric cross s e c t i o n f o r the r e a c t i o n .
PROTON
ELASTIC
15 Ma.~ 1967
T h e s e m e t h o d s can be u s e f u l m the e l i m i n a t i o n of b a c k g r o u n d , but b e c a u s e of the p u l s e - h e i g h t d e f e c t o b s e r v e d , the p u l s e h e i g h t s of the t a i l p e a k s m a y be d e p e n d e n t upon the p a s t h i s t o r y of the d e t e c t o r (the m e t h o d of c o n s t r u c t i o n , s t o r a g e e n v i r o n m e n t , and r a d i a t i o n d a m a g e ) .
References 1. R . C . A x t m a n n a n d D . K e d e m , 32 (1965) 7O.
SCATTERING
AT
61.4
Nue[. Inst. andMeth.
MeV*
C. B. F U L M E R , J . B. B A L L and A. S C O T T * * Oak Ridge Natzonal Labo~'atory and M. L. W H I T E N Unwerszty of Georgia USA Received 17 Apml 1967
DffferentmI cross sections for elastic scattering of 61.4 MeV protons by 27A1, 58N1, 90Zr, ll6sn and 208pb were measured at 2 ° mtc~ vals between 20 ° and 112 °. Some results of optical model analysis of these data are discussed. T h e r e is c o n s i d e r a b l e i n t e r e s t in the study of e l a s t i c s c a t t e r i n g of p r o t o n s , w~th e m p h a s i s on finding s y s t e m a t i c t r e n d s m o p t i c a l m o d e l p a r a m e t e r s a s f u n c h o n s of b o m b a r d i n g e n e r g y and m a s s of the t a r g e t n u c l e u s . E x t e n s i v e e x p e r i m e n tal s t u d i e s and o p t i c a l m o d e l a n a l y s e s h a v e b e e n r e p o r t e d f o r b o m b a r d i n g e n e r g i e s of 9 to 22 MeV [1-2], 30 MeV [3-4], 40 MeV [5-6], and 45 MeV [7]. In t h i s n o t e p r e l i m i n a r y r e s u l t s of a s t u d y of 61.4 M e V p r o t o n s c a t t e r i n g a r e r e p o r t e d . D a t a w e r e o b t a i n e d with a p r o t o n b e a m f r o m the Oak R i d g e I s o c h r o n o u s C y c l o t r o n . A NaI(T1) s c i n t i l l a t i o n d e t e c t o r was u s e d ; the o v e r a l l e n e r g y r e s o l u t i o n w a s 0.9%. C r o s s s e c t m n s w e r e m e a s u r e d at 2° i n t e r v a l s b e t w e e n 20 ° and 112 ° f o r 27A1, 58Nl, 9 0 Z r , l l 6 S n and 208pb t a r g e t s . Optical model calculations were performed * Research sponsored by the U,S. Atomic Energy Comm~ssmn under contract w~th the Umon Carbide C o r poration. ** 1966 Oak Ridge Assoemted U m v e r s l t m s Summer Research Participant from the Umvers~ty of Georgm.
with the O R N L a u t o m a t i c s e a r c h c o m p u t e r code H U N T E R [8], which m i n i m i z e s the u s u a l X2 c r i t e r ion [3]. T h e c a l c u l a t i o n s u s e d a l o c a l p o t e n t i a l of the s a m e f o r m a s that u s e d in r e f s . 3, 4, 5 and 6. F o r s t a r t i n g v a l u e s of the p a r a m e t e r s we u s e d the r e s u l t s of the 40 MeV w o r k of F r l c k e e t a [ . [6]. A C o u l o m b r a d i u s p a r a m e t e r of 1.25 fm was u s e d t h r o u g h o u t . T h e v a r i a b l e p a r a m e t e r s in the a n a l y s i s of the 61.4 MeV p r o t o n s c a t t e r i n g data a r e : V, t o , a, W, WD, t o , a ~ d e f i n e d a s in r e f . 3. In fig. 1 the e x p e r i m e n t a l e l a s t i c s c a t t e r i n g d a t a a r e c o m p a r e d with o p t i c a l m o d e l p r e d i c t i o n s that were obtained from a seven-parameter s e a r c h . T h e s e q u e n c e of p a r a m e t e r s e a r c h e s w a s : t o , a, r ~ , a ' ; V, WD; V, W; and f i n a l l y V, W, WD, t o , a, r ~ , a ' . The final p a r a m e t e r s o b t a i n e d f r o m t h e s e s e a r c h e s a r e l i s t e d in t a b l e 1 a l o n g with the crA (total r e a c t i o n c r o s s s e c t i o n ) and X 2 / ( N - M ) v a l u e s , w h e r e N is the n u m b e r of data p o i n t s and M is the n u m b e r of v a r i a b l e p a r a m e t e r s . The e r r o r s of the d a t a p o i n t s a r e ~ 5% f o r d a t a p o i n t s b e t w e e n 20 ° and 60 ° and ~ 10% for 505
Volume 24B number 10
PHYSICS LETTERS
of l a r g e m a s s f av o r a potential with w e a k e r v o l u m e a b s o r p t i o n and s t r o n g e r s u r f a c e a b s o r p tion. The p r e s e n c e of a n u c l e a r s y m m e t r y dependence of the optical m o d e l potential was s u g g e s t e d by G r e e n and Sood [9] and by Lane [10]. T h i s dependence has usually been a s c m b e d to the r e a l well depth and has been d e m o n s t r a t e d s e v e r a l h m e s to be c o n s i s t e n t with the r e s u l t s of proton s c a t t e r i n g st u d i es m the e n e r g y r an g e of 10 to 40 MeV [111. It has m o r e r e c e n t l y been pointed out [3] that if the s y m m e t r y dependence of the n u c l e a r potential ~s a s s u m e d to be r e s p o n s i b l e for (p,n) r e a c t i o n s o b s e r v e d between analog s t a t e s ~t could be i n t e r p r e t e d as a dependence of the r a d i u s p a r a m e t e r on (N-Z)/A. A s t r a i g h t - l i n e l e a s t - s q u a r e s fit to a plot of the r o v a l u e s (from table 1) v e r s u s (N-Z)/A gives
t0
5
I
5
4
2
I
-T--T-
o5
15 May 1967
~
r o = [1.16 + 0.3 (N-Z)/A]fm. ~05
;
O5
i
: r °'i
i , i I0
20
~
i
k
!V oo,
t ~las'n
50
40
- @
::
r.! . ; t
! I
:\/
i
j
1
I
1
',
I
i 70
80
90
~00
5o
60
...4,
llrl
, 110
~ZO
Oc~ (deg)
Ftg. i . Expemmental data compared with optical model predmtmns from best fit seven-parameter s e a r c h e s . data points at l a r g e r a n g l e s . A few obvmusly poor data points have e r r o r s of 20-25%. The s e a r c h s e q u e n c e r e s u l t e d in a d l u s t m e n t s in the g e o m e t r i c a l p a r a m e t e r s , p a r t i c u l a r l y re, for the i n i t m l fitting. This a d j u s t m e n t of r e r e s u l ted in a r e l a t i v e l y s m a l l s p r e a d in r e a l well depths for the s e v e r a l t a r g e t n u c l e i . The l i g h t e r t a r g e t s a p p e a r to f a v o r a potential in Whleh v o l u m e absorption p r e d o m i n a t e s while the t a r g e t s 506
The c o e f f i m e n t of (N-Z)/A thus obtained a g r e e s r e a s o n a b l y well with the value of 0 . 2 5 f m f r o m 30 MeV proton s c a t t e r i n g r e s u l t s [3] and the value of ~0.3 fm f r o m the a n a l y s i s of (p,n) r e a c tions by S a t c h l e r et al. [12]. To t e s t our 61.4 MeV proton e l a s t i c s c a t t e r i n g data for evidence of the n u c l e a r s y m m e t r y d e p e n dence of the r e a l well depth, V, optical model c a l c u l a t m n s w e r e done m which the 40 MeV a c e r age g e o m e t r y p a r a m e t e r s of r e f . 6 w e r e used as h x e d g e o m e t r y p a r a m e t e r s , and X2 was m i n i m i zed by s e a r c h i n g the ~ eal and n n a g l n a r y well depths only. T h i s y i e l d e d v a l u e s of V = 38.0, 40.3, 42.9, 45.8 and 47.1 r e s p e c t i v e l y for 27A1, 58N1, 90Zr, 116Sn and 208pb. When t h ese v a l u e s of V (w~th the conventional [1] Coulomb c o r r e c t i o n s ) for the even t a r g e t s w e r e plotted as a functmn of (N-Z)/A, a s t r a i g h t h n e l e a s t - s q u a r e s h t y~elded a n u c l e a r s y m m e t r y p a r a m e t e r of 27.2 MeV. T h i s v al u e of the n u c l e a r s y m m e t r y p a r a m e t e r is in good a g r e e m e n t with the v al u e of 26.4 MeV f r o m the 40 MeV work of F r i c k e et al. [6], 26 MeV f r o m the 30 MeV work of S a t e h l e r [3], 27.8 MeV f r o m the 22 MeV work of Ball e t a l . [13] and 26.4 MeV f r o m the s u r v e y of P e r e y [1]. In the 61.4 MeV work r e p o r t e d h e r e , optical m o d e l s e a r c h e s wtth the s a m e a v e r a g e g e o m e t r y p a r a m e t e r s as used by F r i c k e et al. [6] y i el d a r e a l well depth d e s c m b e d by 1
-(V-O.4Z/A~) = [36.7 + 27.2 ( N - Z ) / A ] M e V . A c o m p a r i s o n with the r e s u l t s of ref. 6, m a p h e s the e n e r g y dependence of V m the r an g e f r o m 40 to 61 MeV to be dV/dE = -0.21, m good a g r e e m e n t with t h e i r value of -0.22 obtained f o r p r o tons in the energ27 r a n g e of 30 to 40 MeV.
Volume 24B
n u m b e r 10
PHYSICS
LETTERS
15 May 1967
Table I " B e s t h t " optwal model p a r a m e t e r s obtained f r o m s e v e n p a r a m e t e r s e a r c h e s . Spin orbit p a r a m e t e r s taken f r o m table 2 of ref. 6 were used. Target
t
!/I/D (MeV)
ro (fro)
a (fm)
W (MeV)
27A1
36.8
1.17
0.66
6.36
0.33
1 45
0.63
545
2.31
58N~
41.1
1.16
0 73
6.66
2 32
1.33
0.50
891
2 16
90Zr
39.5
1.20
0.69
5.12
2.54
1.40
0.53
1239
2 12
116Sn
42.4
1.21
0.66
1.64
6.34
1.26
0.69
1463
0.99
208pb
41.4
1.22
0.58
2.01
7.81
1.32
0 67
2162
1.75
T h e a s s i s t a n c e of T . H. J e o n g , D . P . C a u f f m a n , M a v i s G e o r g e a n d A. E . P u g h on t h e i n i t m l p h a s e s of t h i s w o r k i s g r a t e f u l l y a c k n o w l e d g e d . W e a r e i n d e b t e d to G. R . S a t c h l e r f o r h e l p f u l dlSCUSmOns.
R@TPgnccs 1. F . G . P e r e y , P h y s , Rev. 131 (1963) 745. 2. L . R o s e n J . G . B e e r y A . S . G o l d h a b e r and E . H . A u e r bach, Ann. P h y s . N.Y. 34 (1965) 96. 3. G . I t . S a t e h l e r Nuel. P h y s . A92 (1967) 273. 4. G . W . G r e e n l e e s and G . J . Pyle, P h y s . Rev. 149 (1966) 149. 5. M . P . F m e k e and G . R . S a t c h l e r P h y s . Rev. 139 (1965) B 567. 6. M . P . F m e k e , E . E . G r o s s , B . J . M o r t o n a n d A Z u e k e r , (ONRL) P h y s . Rev., to be p u b h s h e d . 7. H . W l l h a m s , U m v . of C a h i . Los A n g e l e s T e c h m c a l Report P - 7 1 (1965). 8. R . M . D m s k o , (Oak Ridge National L a b o r a t o r y , u n pubhshed) 9. A . E . S . ( h e e n a n d P . C . S o o d , P h y s . Hey. 111 (1958~ 1147
ro (fm)
a, (fro)
X2/(N-M)
V (MeV)
crA (rob)
10. A . M . L a n e , P r e c . Intern. Conf. on Nuclear p h y s ics, Paros 1958 (Dunod Paros 1959), p. 32 P h y s . Rev. L e t t e r s 8 (1962) 171 Nucl. P h y s . 35 (1962) 676. 11 P . E . I l o d g s o n , P r e c . Congr. Intern. de Physique nueldaire, Paros, 1964, ed, P . G u n g e n b e r g e r (Centre Natlonale de R e c h e r c h e Selentff~que, Paros, 1964) p. 258. 12, G R , S a t e h l e r R . M . D m s k o and R . H . B a s s c l , P h y s . Rev. 136 (1964) B637. 13. J . B . B a l l , C . B . F u l m e r a n d R . H . B a s s e l P h y s . Rev 135 (1964) B 706, 14. B . W . R l d l e y and J . F . T u r n e r , NucI. P h y s . 58 (1964) 497. 15. R . M . C r a l g J C.Dore, G . W . G r e e n l e e s J.S Lflley, J. L o w e a n d P , C . R o w e Nuel. Phys. 58 (1964) 515, 16. d F T u r n e r B . W . R l d l e y , P . F . C a ~ a n a g h , G . A . Gard and A . G H a r d a c r e , Nuel, P h y s . 58 (1964) 509.
.#~**
THE
ENERGY,
LIFETIME,
AND
SPIN
OF
THE
1611
keV
LEVEL
IN
37Ar*
D. R . G O O S M A N a n d R . W . K A V A N A G H
Cahfornza Institute of Technology, Pasadena, Cahforn~a Received 18 ApmI 1967
The e n e r g y of the second excited s t a t e of 3 7 A r h a s been m e a s u r e d to be 1611 • 1 keV The h a l f - h f e h a s been d e t e r m i n e d by a r e c o i l - D o p p l e r - s h i f t method to be 5.15 ± 0.7 ns, c o n f i r m i n g the spin and pamty of this level as } - . R o s n e r a n d S c h n e i d [1] h a v e s h o w n t h a t t h e 3 6 A r ( d , p ) 3 7 A r r e a c t i o n p o p u l a t e s t h e 1.60 M e V 7level v i a In = 3 s t r i p p i n g , ~ m p l y i n g jTr = 5 - o r ~ . * Supported m p a r t by the Offme of Naval R e s e a r c h Nonr-220(47).
They assigned jr = ~- using shell-model argum e n t s . S i n c e t h i s l e v e l d e c a y s b y 7 r a d i a t i o n to t h e j n = ~+ g r o u n d s t a t e , t h e h a l f - h v e s w o u l d be v a s t l y d i f f e r e n t f o r t h e two c a s e s , 4 - to 3 + by E1 a n d } - to T3+ by M 2 - E 3 . T h i s r e p o r t d e s c m b e s a m e a s u r e m e n t of t h i s h a l f - l i f e , b y a m e t h o d r e p o r 507
PHYSICS
LETTERS
c o r r e s p o n d to an e x c i t e d s t a t e in 28Si a n d / o r to the 28Sl(p,2p) r e a c t i o n w h i c h h a s a Q v a l u e of -11.6 M e V . T h e e f f i c i e n c y of t h i s d e t e c t o r f o r d e t e c t i n g a full e n e r g y e v e n t was d e t e r m i n e d to be g r e a t e r than 97%. It was a l s o o b s e r v e d that 0.71% of the e v e n t s a r e l o c a t e d m the w e l l - i d e n t i f i e d t a l l p e a k s . T h i s l o s s of i n f o r m a t i o n i s s o m e w h a t l a r g e r than we would e x p e c t on the b a s i s of simple calculatmns assuming a geometric cross s e c t i o n f o r the r e a c t i o n .
PROTON
ELASTIC
15 Ma.~ 1967
T h e s e m e t h o d s can be u s e f u l m the e l i m i n a t i o n of b a c k g r o u n d , but b e c a u s e of the p u l s e - h e i g h t d e f e c t o b s e r v e d , the p u l s e h e i g h t s of the t a i l p e a k s m a y be d e p e n d e n t upon the p a s t h i s t o r y of the d e t e c t o r (the m e t h o d of c o n s t r u c t i o n , s t o r a g e e n v i r o n m e n t , and r a d i a t i o n d a m a g e ) .
References 1. R . C . A x t m a n n a n d D . K e d e m , 32 (1965) 7O.
SCATTERING
AT
61.4
Nue[. Inst. andMeth.
MeV*
C. B. F U L M E R , J . B. B A L L and A. S C O T T * * Oak Ridge Natzonal Labo~'atory and M. L. W H I T E N Unwerszty of Georgia USA Received 17 Apml 1967
DffferentmI cross sections for elastic scattering of 61.4 MeV protons by 27A1, 58N1, 90Zr, ll6sn and 208pb were measured at 2 ° mtc~ vals between 20 ° and 112 °. Some results of optical model analysis of these data are discussed. T h e r e is c o n s i d e r a b l e i n t e r e s t in the study of e l a s t i c s c a t t e r i n g of p r o t o n s , w~th e m p h a s i s on finding s y s t e m a t i c t r e n d s m o p t i c a l m o d e l p a r a m e t e r s a s f u n c h o n s of b o m b a r d i n g e n e r g y and m a s s of the t a r g e t n u c l e u s . E x t e n s i v e e x p e r i m e n tal s t u d i e s and o p t i c a l m o d e l a n a l y s e s h a v e b e e n r e p o r t e d f o r b o m b a r d i n g e n e r g i e s of 9 to 22 MeV [1-2], 30 MeV [3-4], 40 MeV [5-6], and 45 MeV [7]. In t h i s n o t e p r e l i m i n a r y r e s u l t s of a s t u d y of 61.4 M e V p r o t o n s c a t t e r i n g a r e r e p o r t e d . D a t a w e r e o b t a i n e d with a p r o t o n b e a m f r o m the Oak R i d g e I s o c h r o n o u s C y c l o t r o n . A NaI(T1) s c i n t i l l a t i o n d e t e c t o r was u s e d ; the o v e r a l l e n e r g y r e s o l u t i o n w a s 0.9%. C r o s s s e c t m n s w e r e m e a s u r e d at 2° i n t e r v a l s b e t w e e n 20 ° and 112 ° f o r 27A1, 58Nl, 9 0 Z r , l l 6 S n and 208pb t a r g e t s . Optical model calculations were performed * Research sponsored by the U,S. Atomic Energy Comm~ssmn under contract w~th the Umon Carbide C o r poration. ** 1966 Oak Ridge Assoemted U m v e r s l t m s Summer Research Participant from the Umvers~ty of Georgm.
with the O R N L a u t o m a t i c s e a r c h c o m p u t e r code H U N T E R [8], which m i n i m i z e s the u s u a l X2 c r i t e r ion [3]. T h e c a l c u l a t i o n s u s e d a l o c a l p o t e n t i a l of the s a m e f o r m a s that u s e d in r e f s . 3, 4, 5 and 6. F o r s t a r t i n g v a l u e s of the p a r a m e t e r s we u s e d the r e s u l t s of the 40 MeV w o r k of F r l c k e e t a [ . [6]. A C o u l o m b r a d i u s p a r a m e t e r of 1.25 fm was u s e d t h r o u g h o u t . T h e v a r i a b l e p a r a m e t e r s in the a n a l y s i s of the 61.4 MeV p r o t o n s c a t t e r i n g data a r e : V, t o , a, W, WD, t o , a ~ d e f i n e d a s in r e f . 3. In fig. 1 the e x p e r i m e n t a l e l a s t i c s c a t t e r i n g d a t a a r e c o m p a r e d with o p t i c a l m o d e l p r e d i c t i o n s that were obtained from a seven-parameter s e a r c h . T h e s e q u e n c e of p a r a m e t e r s e a r c h e s w a s : t o , a, r ~ , a ' ; V, WD; V, W; and f i n a l l y V, W, WD, t o , a, r ~ , a ' . The final p a r a m e t e r s o b t a i n e d f r o m t h e s e s e a r c h e s a r e l i s t e d in t a b l e 1 a l o n g with the crA (total r e a c t i o n c r o s s s e c t i o n ) and X 2 / ( N - M ) v a l u e s , w h e r e N is the n u m b e r of data p o i n t s and M is the n u m b e r of v a r i a b l e p a r a m e t e r s . The e r r o r s of the d a t a p o i n t s a r e ~ 5% f o r d a t a p o i n t s b e t w e e n 20 ° and 60 ° and ~ 10% for 505
Volume 24B number 10
PHYSICS LETTERS
of l a r g e m a s s f av o r a potential with w e a k e r v o l u m e a b s o r p t i o n and s t r o n g e r s u r f a c e a b s o r p tion. The p r e s e n c e of a n u c l e a r s y m m e t r y dependence of the optical m o d e l potential was s u g g e s t e d by G r e e n and Sood [9] and by Lane [10]. T h i s dependence has usually been a s c m b e d to the r e a l well depth and has been d e m o n s t r a t e d s e v e r a l h m e s to be c o n s i s t e n t with the r e s u l t s of proton s c a t t e r i n g st u d i es m the e n e r g y r an g e of 10 to 40 MeV [111. It has m o r e r e c e n t l y been pointed out [3] that if the s y m m e t r y dependence of the n u c l e a r potential ~s a s s u m e d to be r e s p o n s i b l e for (p,n) r e a c t i o n s o b s e r v e d between analog s t a t e s ~t could be i n t e r p r e t e d as a dependence of the r a d i u s p a r a m e t e r on (N-Z)/A. A s t r a i g h t - l i n e l e a s t - s q u a r e s fit to a plot of the r o v a l u e s (from table 1) v e r s u s (N-Z)/A gives
t0
5
I
5
4
2
I
-T--T-
o5
15 May 1967
~
r o = [1.16 + 0.3 (N-Z)/A]fm. ~05
;
O5
i
: r °'i
i , i I0
20
~
i
k
!V oo,
t ~las'n
50
40
- @
::
r.! . ; t
! I
:\/
i
j
1
I
1
',
I
i 70
80
90
~00
5o
60
...4,
llrl
, 110
~ZO
Oc~ (deg)
Ftg. i . Expemmental data compared with optical model predmtmns from best fit seven-parameter s e a r c h e s . data points at l a r g e r a n g l e s . A few obvmusly poor data points have e r r o r s of 20-25%. The s e a r c h s e q u e n c e r e s u l t e d in a d l u s t m e n t s in the g e o m e t r i c a l p a r a m e t e r s , p a r t i c u l a r l y re, for the i n i t m l fitting. This a d j u s t m e n t of r e r e s u l ted in a r e l a t i v e l y s m a l l s p r e a d in r e a l well depths for the s e v e r a l t a r g e t n u c l e i . The l i g h t e r t a r g e t s a p p e a r to f a v o r a potential in Whleh v o l u m e absorption p r e d o m i n a t e s while the t a r g e t s 506
The c o e f f i m e n t of (N-Z)/A thus obtained a g r e e s r e a s o n a b l y well with the value of 0 . 2 5 f m f r o m 30 MeV proton s c a t t e r i n g r e s u l t s [3] and the value of ~0.3 fm f r o m the a n a l y s i s of (p,n) r e a c tions by S a t c h l e r et al. [12]. To t e s t our 61.4 MeV proton e l a s t i c s c a t t e r i n g data for evidence of the n u c l e a r s y m m e t r y d e p e n dence of the r e a l well depth, V, optical model c a l c u l a t m n s w e r e done m which the 40 MeV a c e r age g e o m e t r y p a r a m e t e r s of r e f . 6 w e r e used as h x e d g e o m e t r y p a r a m e t e r s , and X2 was m i n i m i zed by s e a r c h i n g the ~ eal and n n a g l n a r y well depths only. T h i s y i e l d e d v a l u e s of V = 38.0, 40.3, 42.9, 45.8 and 47.1 r e s p e c t i v e l y for 27A1, 58N1, 90Zr, 116Sn and 208pb. When t h ese v a l u e s of V (w~th the conventional [1] Coulomb c o r r e c t i o n s ) for the even t a r g e t s w e r e plotted as a functmn of (N-Z)/A, a s t r a i g h t h n e l e a s t - s q u a r e s h t y~elded a n u c l e a r s y m m e t r y p a r a m e t e r of 27.2 MeV. T h i s v al u e of the n u c l e a r s y m m e t r y p a r a m e t e r is in good a g r e e m e n t with the v al u e of 26.4 MeV f r o m the 40 MeV work of F r i c k e et al. [6], 26 MeV f r o m the 30 MeV work of S a t e h l e r [3], 27.8 MeV f r o m the 22 MeV work of Ball e t a l . [13] and 26.4 MeV f r o m the s u r v e y of P e r e y [1]. In the 61.4 MeV work r e p o r t e d h e r e , optical m o d e l s e a r c h e s wtth the s a m e a v e r a g e g e o m e t r y p a r a m e t e r s as used by F r i c k e et al. [6] y i el d a r e a l well depth d e s c m b e d by 1
-(V-O.4Z/A~) = [36.7 + 27.2 ( N - Z ) / A ] M e V . A c o m p a r i s o n with the r e s u l t s of ref. 6, m a p h e s the e n e r g y dependence of V m the r an g e f r o m 40 to 61 MeV to be dV/dE = -0.21, m good a g r e e m e n t with t h e i r value of -0.22 obtained f o r p r o tons in the energ27 r a n g e of 30 to 40 MeV.
Volume 24B
n u m b e r 10
PHYSICS
LETTERS
15 May 1967
Table I " B e s t h t " optwal model p a r a m e t e r s obtained f r o m s e v e n p a r a m e t e r s e a r c h e s . Spin orbit p a r a m e t e r s taken f r o m table 2 of ref. 6 were used. Target
t
!/I/D (MeV)
ro (fro)
a (fm)
W (MeV)
27A1
36.8
1.17
0.66
6.36
0.33
1 45
0.63
545
2.31
58N~
41.1
1.16
0 73
6.66
2 32
1.33
0.50
891
2 16
90Zr
39.5
1.20
0.69
5.12
2.54
1.40
0.53
1239
2 12
116Sn
42.4
1.21
0.66
1.64
6.34
1.26
0.69
1463
0.99
208pb
41.4
1.22
0.58
2.01
7.81
1.32
0 67
2162
1.75
T h e a s s i s t a n c e of T . H. J e o n g , D . P . C a u f f m a n , M a v i s G e o r g e a n d A. E . P u g h on t h e i n i t m l p h a s e s of t h i s w o r k i s g r a t e f u l l y a c k n o w l e d g e d . W e a r e i n d e b t e d to G. R . S a t c h l e r f o r h e l p f u l dlSCUSmOns.
R@TPgnccs 1. F . G . P e r e y , P h y s , Rev. 131 (1963) 745. 2. L . R o s e n J . G . B e e r y A . S . G o l d h a b e r and E . H . A u e r bach, Ann. P h y s . N.Y. 34 (1965) 96. 3. G . I t . S a t e h l e r Nuel. P h y s . A92 (1967) 273. 4. G . W . G r e e n l e e s and G . J . Pyle, P h y s . Rev. 149 (1966) 149. 5. M . P . F m e k e and G . R . S a t c h l e r P h y s . Rev. 139 (1965) B 567. 6. M . P . F m e k e , E . E . G r o s s , B . J . M o r t o n a n d A Z u e k e r , (ONRL) P h y s . Rev., to be p u b h s h e d . 7. H . W l l h a m s , U m v . of C a h i . Los A n g e l e s T e c h m c a l Report P - 7 1 (1965). 8. R . M . D m s k o , (Oak Ridge National L a b o r a t o r y , u n pubhshed) 9. A . E . S . ( h e e n a n d P . C . S o o d , P h y s . Hey. 111 (1958~ 1147
ro (fm)
a, (fro)
X2/(N-M)
V (MeV)
crA (rob)
10. A . M . L a n e , P r e c . Intern. Conf. on Nuclear p h y s ics, Paros 1958 (Dunod Paros 1959), p. 32 P h y s . Rev. L e t t e r s 8 (1962) 171 Nucl. P h y s . 35 (1962) 676. 11 P . E . I l o d g s o n , P r e c . Congr. Intern. de Physique nueldaire, Paros, 1964, ed, P . G u n g e n b e r g e r (Centre Natlonale de R e c h e r c h e Selentff~que, Paros, 1964) p. 258. 12, G R , S a t e h l e r R . M . D m s k o and R . H . B a s s c l , P h y s . Rev. 136 (1964) B637. 13. J . B . B a l l , C . B . F u l m e r a n d R . H . B a s s e l P h y s . Rev 135 (1964) B 706, 14. B . W . R l d l e y and J . F . T u r n e r , NucI. P h y s . 58 (1964) 497. 15. R . M . C r a l g J C.Dore, G . W . G r e e n l e e s J.S Lflley, J. L o w e a n d P , C . R o w e Nuel. Phys. 58 (1964) 515, 16. d F T u r n e r B . W . R l d l e y , P . F . C a ~ a n a g h , G . A . Gard and A . G H a r d a c r e , Nuel, P h y s . 58 (1964) 509.
.#~**
THE
ENERGY,
LIFETIME,
AND
SPIN
OF
THE
1611
keV
LEVEL
IN
37Ar*
D. R . G O O S M A N a n d R . W . K A V A N A G H
Cahfornza Institute of Technology, Pasadena, Cahforn~a Received 18 ApmI 1967
The e n e r g y of the second excited s t a t e of 3 7 A r h a s been m e a s u r e d to be 1611 • 1 keV The h a l f - h f e h a s been d e t e r m i n e d by a r e c o i l - D o p p l e r - s h i f t method to be 5.15 ± 0.7 ns, c o n f i r m i n g the spin and pamty of this level as } - . R o s n e r a n d S c h n e i d [1] h a v e s h o w n t h a t t h e 3 6 A r ( d , p ) 3 7 A r r e a c t i o n p o p u l a t e s t h e 1.60 M e V 7level v i a In = 3 s t r i p p i n g , ~ m p l y i n g jTr = 5 - o r ~ . * Supported m p a r t by the Offme of Naval R e s e a r c h Nonr-220(47).
They assigned jr = ~- using shell-model argum e n t s . S i n c e t h i s l e v e l d e c a y s b y 7 r a d i a t i o n to t h e j n = ~+ g r o u n d s t a t e , t h e h a l f - h v e s w o u l d be v a s t l y d i f f e r e n t f o r t h e two c a s e s , 4 - to 3 + by E1 a n d } - to T3+ by M 2 - E 3 . T h i s r e p o r t d e s c m b e s a m e a s u r e m e n t of t h i s h a l f - l i f e , b y a m e t h o d r e p o r 507