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Even parity states of 38Ar
Volume 31B. number 7
PHYSICS
EVEN
PARITY
LETTERS
STATES
30 March 1970
OF
38Ar
L. D. SKOURAS Schuster LaboratoKv, University of Manchester, UK Received 25 January 1970
An extended model allowingfor the mixing between 2 hole and 2 particle - 4 hole configurations is introduced for the interpretation of the even parity spectrum of 3BAr. The theoretical results are in good agreement with experiment on both energy levels and transition rates.
Recently several theoretical calculations have b e e n r e p o r t e d [1-3] on t h e l o w - e n e r g y e v e n p a r i ty s p e c t r a of m a s s 18 a n d m a s s 42 n u c l e i . T h e m a i n f e a t u r e of t h e s e c a l c u l a t i o n s i s t h a t t h e y e m p l o y an e x t e n d e d m o d e l w h i c h a l l o w s f o r m i x ing between 2 p a r t i c l e and 4 p a r t i c l e - 2 hole conf i g u r a t i o n s . T h e good a g r e e m e n t b e t w e e n e x p e r iment and theory, found in these calculations. c l e a r l y s u g g e s t s t h a t t h e s a m e m o d e l can a l s o b e a p p l i e d to o t h e r n u c l e i w i t h s i m i l a r p r o p e r t i e s to t h o s e of m a s s 18 and 42 n u c l e i . S u c h a n u c l e u s is 38Ar. In the simple shell-model picture the even parity s p e c t r u m of 3 8 A r c a n b e d e s c r i b e d in t e r m s of two p r o t o n h o l e s in t h e d o u b l y c l o s e d
4~8 4.71 4.~ 4.s7 4.48
3(r.2) 4" +
3.~ 3.o,
2* 3-
40Ca
3.3~
core.
However,
shell-model
calculations
[5, 7] e m p l o y i n g t h i s s i m p l e m o d e l h a v e f a i l e d to r e p r o d u c e t h e e x p e r i m e n t a l s p e c t r u m of 3 8 A r (fig. 1) a n d in p a r t i c u l a r to e x p l a i n t h e p r e s e n c e of a 0 + s t a t e at 3.38 M e V . In a n a l o g y to t h e 180 a n d 42Ca c a s e s t h i s a d d i t i o n a l 0 + s t a t e c a n b e interpreted as arising mainly from 2p-4h configurations. Experimental evidence supporting this idea is provided by the results of the 39K(d, 3He) 3BAr reaction [5.6]. The fact that the 0+ level of 3BAr at 3.38 MeV is not excited in this experiment indicates that it a r i s e s mainly from 2p-4h configurations and that the ground state of 39K contains very small 2p-3h components. Furthermore this reaction shows that there a r e more states of 3BAr with Ip = 0 c h a r a c t e r i s t i c s than can be accounted for by two hole configurations. In our extended model these Fig. 1. The experimental s p e c t r u m of 38Ar as given in ref. 4. The assignment of (1, 2) ~ to the 4.57 MeV level is suggested in ref. 5. Also shown are the positions of the even parity levels as obtained from the p r e s e n t calculation.
o:
s.n ~ 5,51 sas s.,s
11, +2S1 -
~ 5~7
4+
(,,a}*
5.,3
2+
4.73
4.63
:;+
~61
2+ +
o*
O
3.3~
2* 2.~7
2+
2.16
0,00
0
Experiment
+
O+
0,00,
Theory
439
Volume 31B, number 7
PHYSICS LETTERS
states can be interpreted as arising from the strong mixing between 2 hole and 2p-4h configurations. Full details of the procedure followed in the calculation a r e given in refs. 2 and 3. The 4hole intrinsic wave function was constructed by placing 2 proton and 2 neutron holes in the highest available Nilsson orbital in the s - d shell i+ which, for oblate deformations, has ]e = 2 • States of good angular momentum were projected from this intrinsic state and coupled to all p o s sible configurations of 2 neutrons in the f-p shell to obtain 2p-4h states of given angular momentum. The single particle energies and the exchange p a r a m e t e r s of the residual interaction were the same as those used in ref. 3 but the strength of the interaction was reduced to 47 MeV. Harmonic oscillator wave functions were used and the oscillator p a r a m e t e r was taken to be 1.9 fm. In table I we give the values
30 March 1970 Table 1 Deformation parameters.
j 7~
c 3/2
c I/2
c 5/2
O: 2~ 4~
-0.80 -0.75 -0.75
-0.30 -0.40 -0.40
0.52 0.53 0.53
of t h e d e f o r m a t i o n p a r a m e t e r s which were obtained from the variation procedure. The two other parameters u s e d in t h e c a l c u l a t i o n of t h e m a s s 42 s p e c t r a , n a m e l y t h e fT/2-d3/2 g a p a n d the overlap between deformed and spherical 40Ca c o r e s w e r e f i t t e d h e r e to h a v e v a l u e s of 6 , 7 M e V and 1 respectively. T h e e v e n p a r i t y s p e c t r u m of 3 8 A t o b t a i n e d from this calculation is shown in fig. 1 while the c a l c u l a t e d w a v e f u n c t i o n s a r e g i v e n i n t a b l e 2. As seen from fig. 1 the model reproduces satis-
Table 2 Wave f u n c t i o n s for e v e n p a r i t y s t a t e s of 38Ar *.
Config. (d3/2) 2 (sl/2) ~ (d5/2) z 0.0.(f;/2) 2 0.0.(p3/~) 2
01
02
03
0,87 0.31 0.20 0.17 0 . 0 6 -0.98 0.22 0 . 0 7 -0.04 0.35 - 0 . 7 7 0.00 0.13 - 0 . 1 7 0.0O
Config. (d3/2) 2 d3/2svz d3/2d~/2
21
22
23
24
25
Config.
-0.04 0.01 0.61 0.ii 0.07
0.38 -0.06 0.41 0.17 0.08
(d5/2) 2 0.2,(f7/2) 2 0, 2. fT/zp3/2 0. 2, fT/2f5/2 0.2. (P3/2)2 0.2.P3Apv2
0.07 0.02 0.01 0.00 0.00
-0.52 -0.12 -0.06 -0.04 -0.04
-0.32 -0.36 -0.02 -0.06 -0.06
0.19 -0.63 -0.02 -0.I0 -0.07
O, 4. fT/2fs/2 0,4.p3/2fs/2 2.2,(f7/2)2 2.2, fT/2P3/2 2.2.fT/2fs/2
0.00 0.00 0.35 0.12 0.06
-0.02 -0.02 -0.04 -0.03 -0.03 - 0 . 0 5 - 0 . 6 0 0.13 0.37 -0.12 0.07 0 . 0 5 -0.06 0.03 0.02
-0.06 -0.08 -0.22 -0.11 -0.03
2,2.pi/~/2 0 . 0 6 -0.01 2.2. (f5/2)2 0.05 -0.03 2.3.fl/2P3/2 0.08 0.10 2.4,(f7/2)'- - 0 . 2 7 -0.05 2. 4. f7/~3/2 0.03 O.lO
0.0.(pi/2)-' O.O. (fs/~) 2 2.2. (f:/:)2 2.2.f:/~3/2 2, 2, fT/:f~,/~
0.07 0.ii -0.01 -0.02 -0.01
-0.08 -0.12 -0.45 -0.12 -0.06
O.O0 0.O0 0.00 0.00 0.00
2.2.(f5/2) 2 4 . 4 , (f7/~)2 4.4. f~/2fs/2
-0.03 O.O1 O.Ol
-0.05 0.13 0.05
0.00 0,2.P3/2fs/2 O.O0 0.2.Pl/2fs/2 0.00 2.0. (f7/2) 2 2.0.(P3/2) 2 2.O.(pl/2) 2
-0.02 d3/2ds/2 0.19 (d5/2) 2 0.00 0,4,(f7/2) 2 - 0 . 0 4 O,4.fT/2P3/2 -O.Ol 0,4,fT/apt/2
42
-0.84 0.31 0.13 -0.14 -0.ii
sl/zdMz
-0.38 0.34 - 0 . 0 5 -0.11 0.71 - 0 . 4 9 0.01 0.05 -0.03 0 . 0 2 - 0 . 1 8 0.ii -0.02 -0.02 0.02
41
-0.42 -0.14 -0.03 -0.04 -0.04
0.07 0.05 0.04 0.05 0.63 -0.28 0.16 -0.02 0.04 -0.05
2.0.(f5/2) z 2.2.(f7/2) 2 2.2.fl/2p3/2 2,2.(P3/2)2 2.2.P3/~1/2
0.10 -0.04 0.00 0.00 0.00
-0.09 0.34 0.02 0.01 0.02
0.05 0.13 -0.11 -0.01 -0.01
0.05 -0.16 -0.32 -0.05 -0.05
-0.03 -0.35 -0.33 -0.06 -0.05
2.6,(f7/2) 2 4.0,(f7/2) 2 4.0.(!o3/2) 2 4.0.(Pi/2) ~ 4.0.(f5/2) 2
0.14 0.17 0.05 0.02 0.03
0.17 -0.64 -0.16 -0.07 -0.12
2. 2. P3/2f5/o 2.2.Pl/~5/2 2. 3. f~/2p3/,. 2. 4. (f7/~2)2 2. 4. fT/2P3/2
0.00 0.00 0.00 -0,01 0.00
O.O0 0.02 0.00 -0.12 -0.02
-0.01 -0.01 0,01 -0.29 -0.01
-0.04 -0.05 0.06 -0.38 -0.02
-0.05 -0.05 0.12 0.29 -0.05
4.2.(f7/2) 2 4.2.fT/zp3/2 4.4. (f7/2) 2 4.6.(fl/2) 2
-0.13 0.05 0.14 -0.06
0.17 0.04 0.09 -0.08
2. 4. fT/zfs/_o 4.2.(f7/2) 2 4.2.fT/2p3/2 4.4.(f/2) 2 4 . 6 . (f7//2)2
0.00 0.00 -0.01 0.01 -0.01
-0.01 -0.14 -0.04 0.00 0.02
-0.04 0.07 0.00 0.05 -0.04
-0.05 0.25 0.03 0.04 -0,08
-0.03 -0.21 -0.07 -0.19 0.07
* T h e 2p-4h c o m p o n e n t s a r e g i v e n in the o r d e r J 1 . J 2 - ( J l , J2) w h e r e J 1 is the a n g u l a r m o m e n t u m of t h e 4 h o l e s while J2. ( ] 1 . ) 2 ) r e f e r s to the c o n f i g u r a t i o n of the two p a r t i c l e s .
440
Volume 31B, number 7
PHYSICS
f a c t o r i l y t h e known e v e n p a r i t y s t a t e s of 3 8 A t up to 3.94 M e V e x c i t a t i o n . T h e r e c e n t s t u d y of t h e 39K(d, 3He) 38Ar r e a c t i o n b y W i l d e n t h a l a n d N e w m a n [5] s h o w s t h a t t h e r e a r e t h r e e m o r e e v e n p a r i t y s t a t e s at 4.57, 5.15 a n d 5 . 5 5 M e V w i t h p r o b a b l e s p i n s 1+ o r 2 + ( l p = 0). T h e s e l e v e l s a r e w e l l u n d e r s t o o d in t e r m s of o u r m o d e l p r o v i d e d t h a t t h e i r s p i n s a r e 2 + ( s e e fig. 1); no 1+ s t a t e a p p e a r s in o u r r e s u l t s b e l o w 6.7 M e V excitation. One of t h e m a i n f e a t u r e s in t h e t h e o r e t i c a l s p e c t r u m i s t h e a p p e a r a n c e of two 4 + s t a t e s at a b o u t 4.73 a n d 5.47 M e V e x c i t a t i o n e n e r g y . A s s e e n f r o m t a b l e 2 t h e s e two s t a t e s a r i s e p r e dominantly f r o m 2p-4h c o n f i g u r a t i o n s ; the 4+ -1 - I c o n f i g u r a t i o n l e v e l c o r r e s p o n d i n g to t h e da/2ds/2 a p p e a r s in o u r r e s u l t s a t a b o u t 6.9 M e V c o m p a r e d w i t h t h e e x p e r i m e n t a l e s t i m a t e of 7.11 M e V [ 5]. R e g a r d i n g t h e s e c o n d 4 + l e v e l at a b o u t 5.47 M e V t h e r e a r e s e v e r a l e x p e r i m e n t a l l e v e l s at a b o u t t h e s a m e e n e r g y w i t h u n i d e n t i f i e d s p i n s . On t h e o t h e r h a n d t h e o n l y e x p e r i m e n t a l l e v e l w i t h no d e f i n i t e s p i n a s s i g n m e n t , w h i c h i s c l o s e to o u r f i r s t 4 + l e v e l , i s a t 4.71 M e V . A g a i n s t t h e i d e a of a s s i g n i n g s p i n 4 + to t h e 4.71 M e V l e v e l a r e t h e r e s u l t s of t h e 39K(d, 3 H e ) 3 8 A r r e a c t i o n , s t u d i e d by Wei et al. [6], t h a t s h o w l p = 0 w h i c h e x c l u d e s a 4 + a s s i g n m e n t to t h a t l e v e l . H o w e v e r , a m o r e r e c e n t s t u d y of t h e s a m e e x p e r i m e n t [5] did not r e p r o d u c e a n y e x c i t a t i o n of t h e 4.71 M e V l e v e l . A l s o t h e 4.71 l e v e l h a s n o t b e e n e x c i t e d in t h e 39K(t, a) 38Ar r e a c t i o n [8] w h i c h one s h o u l d e x Table 3 Comparison between m e a s u r e d and calculated lifetimes of 38At states. T m (fs) E x (MeV) ref. 9 2.17 3.38 3.94 4.57
540 7000 46 25
~' 65 -+ 4000 ~: 18 ± 25
ref. 10
theory
1300 ~- 100 > 3200 < 40 74 ± 9
840 4500 68 45
• Calculated on the assumption that this level has spin 2 ~ .
*
LE T T E RS
30 March 1970
p e c t to g i v e t h e s a m e r e s u l t s a s 39K(d, 3He) 3BAr [5 I. U n d e r t h e s e c i r c u m s t a n c e s w e can t e n t a t i v e l y i d e n t i f y o u r f i r s t 4 + l e v e l w i t h t h e e x p e r i m e n t a l o n e at 4.71 M e V but we i n t e n d to r e - e x a m i n e t h e p r o b l e m in a l a t e r p a p e r , w h e r e we shall also study the o d d - p a r i t y s p e c t r u m of 3BAr. In t h e m e a n t i m e it i s h o p e d t h a t m o r e detailed e x p e r i m e n t a l i n f o r m a t i o n will b e come available. In t a b l e 3 w e c o m p a r e t h e e x p e r i m e n t a l l y k n o w n l i f e t i m e s of t h e e v e n p a r i t y s t a t e s of 38Ar w i t h t h o s e c a l c u l a t e d with t h e w a v e f u n c t i o n s of t a b l e 2. In c a l c u l a t i n g E2 m a t r i x e l e m e n t s an e f f e c t i v e c h a r g e of 0 . B e h a s b e e n u s e d . A s s e e n f r o m table 3 t h e r e is an e n c o u r a g i n g a g r e e m e n t between our initial r e s u l t s and the c u r r e n t exp e r i m e n t a l i n f o r m a t i o n . It i s o b v i o u s , h o w e v e r , t h a t to c h e c k t h e v a l i d i t y of o u r m o d e l m u c h more detailed experimental information is required. I w o u l d l i k e to t h a n k P r o f e s s o r S i r B r i a n F l o w e r s for suggesting this p r o b l e m and Dr. J . M. I r v i n e f o r m a n y h e l p f u l d i s c u s s i o n s . C o m puting f a c i l i t i e s w e r e p r o v i d e d by the ATLAS C o m p u t i n g L a b o r a t o r y of t h e U n i v e r s i t y of M a n chester.
References 1. B.H. Flowers and L.D. Skouras. Nucl, Phys. All(; (1968) 529. 2. H.G. Benson and B.H. Flowers. Nucl. Ph3s. A126 (1969) 332. 3. B.H. Flowers and L.D. Skouras. Nucl. Phys. A136 (1969) 353. 4. P . M . Endt and C.Van der L(,un. Nucl. Phys. A105 (1967) 1. 5. B.H. Wildenthal and E.Ne\~man. Nucl. Phys. At 18 (1968) 347. 6. T.Wei. W.S. Gray. J. Janecke and R.M. Polichar. Bull. Am. Phys. Soc. 12 (1967) 681. 7. P . W . M . Glaudemans. G. Wiechers and P . J . B r u s s a a r d . Nucl. Phys. 56 (1964) 529. 548. 8. I . J . Taylor. Nucl. Phys. 41 (1963) 227. 9. G . A . P . E n g e l b e r t i n k and G. Van Middelkoop. Nucl. Phys. A138 (1969) 588. 10. P . R . Alderson. University oI Liverpool. private communication.
441
PHYSICS
EVEN
PARITY
LETTERS
STATES
30 March 1970
OF
38Ar
L. D. SKOURAS Schuster LaboratoKv, University of Manchester, UK Received 25 January 1970
An extended model allowingfor the mixing between 2 hole and 2 particle - 4 hole configurations is introduced for the interpretation of the even parity spectrum of 3BAr. The theoretical results are in good agreement with experiment on both energy levels and transition rates.
Recently several theoretical calculations have b e e n r e p o r t e d [1-3] on t h e l o w - e n e r g y e v e n p a r i ty s p e c t r a of m a s s 18 a n d m a s s 42 n u c l e i . T h e m a i n f e a t u r e of t h e s e c a l c u l a t i o n s i s t h a t t h e y e m p l o y an e x t e n d e d m o d e l w h i c h a l l o w s f o r m i x ing between 2 p a r t i c l e and 4 p a r t i c l e - 2 hole conf i g u r a t i o n s . T h e good a g r e e m e n t b e t w e e n e x p e r iment and theory, found in these calculations. c l e a r l y s u g g e s t s t h a t t h e s a m e m o d e l can a l s o b e a p p l i e d to o t h e r n u c l e i w i t h s i m i l a r p r o p e r t i e s to t h o s e of m a s s 18 and 42 n u c l e i . S u c h a n u c l e u s is 38Ar. In the simple shell-model picture the even parity s p e c t r u m of 3 8 A r c a n b e d e s c r i b e d in t e r m s of two p r o t o n h o l e s in t h e d o u b l y c l o s e d
4~8 4.71 4.~ 4.s7 4.48
3(r.2) 4" +
3.~ 3.o,
2* 3-
40Ca
3.3~
core.
However,
shell-model
calculations
[5, 7] e m p l o y i n g t h i s s i m p l e m o d e l h a v e f a i l e d to r e p r o d u c e t h e e x p e r i m e n t a l s p e c t r u m of 3 8 A r (fig. 1) a n d in p a r t i c u l a r to e x p l a i n t h e p r e s e n c e of a 0 + s t a t e at 3.38 M e V . In a n a l o g y to t h e 180 a n d 42Ca c a s e s t h i s a d d i t i o n a l 0 + s t a t e c a n b e interpreted as arising mainly from 2p-4h configurations. Experimental evidence supporting this idea is provided by the results of the 39K(d, 3He) 3BAr reaction [5.6]. The fact that the 0+ level of 3BAr at 3.38 MeV is not excited in this experiment indicates that it a r i s e s mainly from 2p-4h configurations and that the ground state of 39K contains very small 2p-3h components. Furthermore this reaction shows that there a r e more states of 3BAr with Ip = 0 c h a r a c t e r i s t i c s than can be accounted for by two hole configurations. In our extended model these Fig. 1. The experimental s p e c t r u m of 38Ar as given in ref. 4. The assignment of (1, 2) ~ to the 4.57 MeV level is suggested in ref. 5. Also shown are the positions of the even parity levels as obtained from the p r e s e n t calculation.
o:
s.n ~ 5,51 sas s.,s
11, +2S1 -
~ 5~7
4+
(,,a}*
5.,3
2+
4.73
4.63
:;+
~61
2+ +
o*
O
3.3~
2* 2.~7
2+
2.16
0,00
0
Experiment
+
O+
0,00,
Theory
439
Volume 31B, number 7
PHYSICS LETTERS
states can be interpreted as arising from the strong mixing between 2 hole and 2p-4h configurations. Full details of the procedure followed in the calculation a r e given in refs. 2 and 3. The 4hole intrinsic wave function was constructed by placing 2 proton and 2 neutron holes in the highest available Nilsson orbital in the s - d shell i+ which, for oblate deformations, has ]e = 2 • States of good angular momentum were projected from this intrinsic state and coupled to all p o s sible configurations of 2 neutrons in the f-p shell to obtain 2p-4h states of given angular momentum. The single particle energies and the exchange p a r a m e t e r s of the residual interaction were the same as those used in ref. 3 but the strength of the interaction was reduced to 47 MeV. Harmonic oscillator wave functions were used and the oscillator p a r a m e t e r was taken to be 1.9 fm. In table I we give the values
30 March 1970 Table 1 Deformation parameters.
j 7~
c 3/2
c I/2
c 5/2
O: 2~ 4~
-0.80 -0.75 -0.75
-0.30 -0.40 -0.40
0.52 0.53 0.53
of t h e d e f o r m a t i o n p a r a m e t e r s which were obtained from the variation procedure. The two other parameters u s e d in t h e c a l c u l a t i o n of t h e m a s s 42 s p e c t r a , n a m e l y t h e fT/2-d3/2 g a p a n d the overlap between deformed and spherical 40Ca c o r e s w e r e f i t t e d h e r e to h a v e v a l u e s of 6 , 7 M e V and 1 respectively. T h e e v e n p a r i t y s p e c t r u m of 3 8 A t o b t a i n e d from this calculation is shown in fig. 1 while the c a l c u l a t e d w a v e f u n c t i o n s a r e g i v e n i n t a b l e 2. As seen from fig. 1 the model reproduces satis-
Table 2 Wave f u n c t i o n s for e v e n p a r i t y s t a t e s of 38Ar *.
Config. (d3/2) 2 (sl/2) ~ (d5/2) z 0.0.(f;/2) 2 0.0.(p3/~) 2
01
02
03
0,87 0.31 0.20 0.17 0 . 0 6 -0.98 0.22 0 . 0 7 -0.04 0.35 - 0 . 7 7 0.00 0.13 - 0 . 1 7 0.0O
Config. (d3/2) 2 d3/2svz d3/2d~/2
21
22
23
24
25
Config.
-0.04 0.01 0.61 0.ii 0.07
0.38 -0.06 0.41 0.17 0.08
(d5/2) 2 0.2,(f7/2) 2 0, 2. fT/zp3/2 0. 2, fT/2f5/2 0.2. (P3/2)2 0.2.P3Apv2
0.07 0.02 0.01 0.00 0.00
-0.52 -0.12 -0.06 -0.04 -0.04
-0.32 -0.36 -0.02 -0.06 -0.06
0.19 -0.63 -0.02 -0.I0 -0.07
O, 4. fT/2fs/2 0,4.p3/2fs/2 2.2,(f7/2)2 2.2, fT/2P3/2 2.2.fT/2fs/2
0.00 0.00 0.35 0.12 0.06
-0.02 -0.02 -0.04 -0.03 -0.03 - 0 . 0 5 - 0 . 6 0 0.13 0.37 -0.12 0.07 0 . 0 5 -0.06 0.03 0.02
-0.06 -0.08 -0.22 -0.11 -0.03
2,2.pi/~/2 0 . 0 6 -0.01 2.2. (f5/2)2 0.05 -0.03 2.3.fl/2P3/2 0.08 0.10 2.4,(f7/2)'- - 0 . 2 7 -0.05 2. 4. f7/~3/2 0.03 O.lO
0.0.(pi/2)-' O.O. (fs/~) 2 2.2. (f:/:)2 2.2.f:/~3/2 2, 2, fT/:f~,/~
0.07 0.ii -0.01 -0.02 -0.01
-0.08 -0.12 -0.45 -0.12 -0.06
O.O0 0.O0 0.00 0.00 0.00
2.2.(f5/2) 2 4 . 4 , (f7/~)2 4.4. f~/2fs/2
-0.03 O.O1 O.Ol
-0.05 0.13 0.05
0.00 0,2.P3/2fs/2 O.O0 0.2.Pl/2fs/2 0.00 2.0. (f7/2) 2 2.0.(P3/2) 2 2.O.(pl/2) 2
-0.02 d3/2ds/2 0.19 (d5/2) 2 0.00 0,4,(f7/2) 2 - 0 . 0 4 O,4.fT/2P3/2 -O.Ol 0,4,fT/apt/2
42
-0.84 0.31 0.13 -0.14 -0.ii
sl/zdMz
-0.38 0.34 - 0 . 0 5 -0.11 0.71 - 0 . 4 9 0.01 0.05 -0.03 0 . 0 2 - 0 . 1 8 0.ii -0.02 -0.02 0.02
41
-0.42 -0.14 -0.03 -0.04 -0.04
0.07 0.05 0.04 0.05 0.63 -0.28 0.16 -0.02 0.04 -0.05
2.0.(f5/2) z 2.2.(f7/2) 2 2.2.fl/2p3/2 2,2.(P3/2)2 2.2.P3/~1/2
0.10 -0.04 0.00 0.00 0.00
-0.09 0.34 0.02 0.01 0.02
0.05 0.13 -0.11 -0.01 -0.01
0.05 -0.16 -0.32 -0.05 -0.05
-0.03 -0.35 -0.33 -0.06 -0.05
2.6,(f7/2) 2 4.0,(f7/2) 2 4.0.(!o3/2) 2 4.0.(Pi/2) ~ 4.0.(f5/2) 2
0.14 0.17 0.05 0.02 0.03
0.17 -0.64 -0.16 -0.07 -0.12
2. 2. P3/2f5/o 2.2.Pl/~5/2 2. 3. f~/2p3/,. 2. 4. (f7/~2)2 2. 4. fT/2P3/2
0.00 0.00 0.00 -0,01 0.00
O.O0 0.02 0.00 -0.12 -0.02
-0.01 -0.01 0,01 -0.29 -0.01
-0.04 -0.05 0.06 -0.38 -0.02
-0.05 -0.05 0.12 0.29 -0.05
4.2.(f7/2) 2 4.2.fT/zp3/2 4.4. (f7/2) 2 4.6.(fl/2) 2
-0.13 0.05 0.14 -0.06
0.17 0.04 0.09 -0.08
2. 4. fT/zfs/_o 4.2.(f7/2) 2 4.2.fT/2p3/2 4.4.(f/2) 2 4 . 6 . (f7//2)2
0.00 0.00 -0.01 0.01 -0.01
-0.01 -0.14 -0.04 0.00 0.02
-0.04 0.07 0.00 0.05 -0.04
-0.05 0.25 0.03 0.04 -0,08
-0.03 -0.21 -0.07 -0.19 0.07
* T h e 2p-4h c o m p o n e n t s a r e g i v e n in the o r d e r J 1 . J 2 - ( J l , J2) w h e r e J 1 is the a n g u l a r m o m e n t u m of t h e 4 h o l e s while J2. ( ] 1 . ) 2 ) r e f e r s to the c o n f i g u r a t i o n of the two p a r t i c l e s .
440
Volume 31B, number 7
PHYSICS
f a c t o r i l y t h e known e v e n p a r i t y s t a t e s of 3 8 A t up to 3.94 M e V e x c i t a t i o n . T h e r e c e n t s t u d y of t h e 39K(d, 3He) 38Ar r e a c t i o n b y W i l d e n t h a l a n d N e w m a n [5] s h o w s t h a t t h e r e a r e t h r e e m o r e e v e n p a r i t y s t a t e s at 4.57, 5.15 a n d 5 . 5 5 M e V w i t h p r o b a b l e s p i n s 1+ o r 2 + ( l p = 0). T h e s e l e v e l s a r e w e l l u n d e r s t o o d in t e r m s of o u r m o d e l p r o v i d e d t h a t t h e i r s p i n s a r e 2 + ( s e e fig. 1); no 1+ s t a t e a p p e a r s in o u r r e s u l t s b e l o w 6.7 M e V excitation. One of t h e m a i n f e a t u r e s in t h e t h e o r e t i c a l s p e c t r u m i s t h e a p p e a r a n c e of two 4 + s t a t e s at a b o u t 4.73 a n d 5.47 M e V e x c i t a t i o n e n e r g y . A s s e e n f r o m t a b l e 2 t h e s e two s t a t e s a r i s e p r e dominantly f r o m 2p-4h c o n f i g u r a t i o n s ; the 4+ -1 - I c o n f i g u r a t i o n l e v e l c o r r e s p o n d i n g to t h e da/2ds/2 a p p e a r s in o u r r e s u l t s a t a b o u t 6.9 M e V c o m p a r e d w i t h t h e e x p e r i m e n t a l e s t i m a t e of 7.11 M e V [ 5]. R e g a r d i n g t h e s e c o n d 4 + l e v e l at a b o u t 5.47 M e V t h e r e a r e s e v e r a l e x p e r i m e n t a l l e v e l s at a b o u t t h e s a m e e n e r g y w i t h u n i d e n t i f i e d s p i n s . On t h e o t h e r h a n d t h e o n l y e x p e r i m e n t a l l e v e l w i t h no d e f i n i t e s p i n a s s i g n m e n t , w h i c h i s c l o s e to o u r f i r s t 4 + l e v e l , i s a t 4.71 M e V . A g a i n s t t h e i d e a of a s s i g n i n g s p i n 4 + to t h e 4.71 M e V l e v e l a r e t h e r e s u l t s of t h e 39K(d, 3 H e ) 3 8 A r r e a c t i o n , s t u d i e d by Wei et al. [6], t h a t s h o w l p = 0 w h i c h e x c l u d e s a 4 + a s s i g n m e n t to t h a t l e v e l . H o w e v e r , a m o r e r e c e n t s t u d y of t h e s a m e e x p e r i m e n t [5] did not r e p r o d u c e a n y e x c i t a t i o n of t h e 4.71 M e V l e v e l . A l s o t h e 4.71 l e v e l h a s n o t b e e n e x c i t e d in t h e 39K(t, a) 38Ar r e a c t i o n [8] w h i c h one s h o u l d e x Table 3 Comparison between m e a s u r e d and calculated lifetimes of 38At states. T m (fs) E x (MeV) ref. 9 2.17 3.38 3.94 4.57
540 7000 46 25
~' 65 -+ 4000 ~: 18 ± 25
ref. 10
theory
1300 ~- 100 > 3200 < 40 74 ± 9
840 4500 68 45
• Calculated on the assumption that this level has spin 2 ~ .
*
LE T T E RS
30 March 1970
p e c t to g i v e t h e s a m e r e s u l t s a s 39K(d, 3He) 3BAr [5 I. U n d e r t h e s e c i r c u m s t a n c e s w e can t e n t a t i v e l y i d e n t i f y o u r f i r s t 4 + l e v e l w i t h t h e e x p e r i m e n t a l o n e at 4.71 M e V but we i n t e n d to r e - e x a m i n e t h e p r o b l e m in a l a t e r p a p e r , w h e r e we shall also study the o d d - p a r i t y s p e c t r u m of 3BAr. In t h e m e a n t i m e it i s h o p e d t h a t m o r e detailed e x p e r i m e n t a l i n f o r m a t i o n will b e come available. In t a b l e 3 w e c o m p a r e t h e e x p e r i m e n t a l l y k n o w n l i f e t i m e s of t h e e v e n p a r i t y s t a t e s of 38Ar w i t h t h o s e c a l c u l a t e d with t h e w a v e f u n c t i o n s of t a b l e 2. In c a l c u l a t i n g E2 m a t r i x e l e m e n t s an e f f e c t i v e c h a r g e of 0 . B e h a s b e e n u s e d . A s s e e n f r o m table 3 t h e r e is an e n c o u r a g i n g a g r e e m e n t between our initial r e s u l t s and the c u r r e n t exp e r i m e n t a l i n f o r m a t i o n . It i s o b v i o u s , h o w e v e r , t h a t to c h e c k t h e v a l i d i t y of o u r m o d e l m u c h more detailed experimental information is required. I w o u l d l i k e to t h a n k P r o f e s s o r S i r B r i a n F l o w e r s for suggesting this p r o b l e m and Dr. J . M. I r v i n e f o r m a n y h e l p f u l d i s c u s s i o n s . C o m puting f a c i l i t i e s w e r e p r o v i d e d by the ATLAS C o m p u t i n g L a b o r a t o r y of t h e U n i v e r s i t y of M a n chester.
References 1. B.H. Flowers and L.D. Skouras. Nucl, Phys. All(; (1968) 529. 2. H.G. Benson and B.H. Flowers. Nucl. Ph3s. A126 (1969) 332. 3. B.H. Flowers and L.D. Skouras. Nucl. Phys. A136 (1969) 353. 4. P . M . Endt and C.Van der L(,un. Nucl. Phys. A105 (1967) 1. 5. B.H. Wildenthal and E.Ne\~man. Nucl. Phys. At 18 (1968) 347. 6. T.Wei. W.S. Gray. J. Janecke and R.M. Polichar. Bull. Am. Phys. Soc. 12 (1967) 681. 7. P . W . M . Glaudemans. G. Wiechers and P . J . B r u s s a a r d . Nucl. Phys. 56 (1964) 529. 548. 8. I . J . Taylor. Nucl. Phys. 41 (1963) 227. 9. G . A . P . E n g e l b e r t i n k and G. Van Middelkoop. Nucl. Phys. A138 (1969) 588. 10. P . R . Alderson. University oI Liverpool. private communication.
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