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Observation of target ground state correlations in the (d,n) reactions on even argon isotopes
Volume31B, number 1
PHYSICS
OBSERVATION (d,n)
OF TARGET REACTIONS
LETTERS
5January1970
GROUND STATE CORRELATIONS ON EVEN ARGON ISOTOPES
IN
THE
H, FUCHS, M. HAGEN, U. JANETZKI and K.-H. MAIER Hahn-Meitner-lnstitu! flit Kernforschung Berlin, Sektor Kernphysik, Berlin-West, Germany Received 1 D e c e m b e r 1969
The (d,n) reactions on 36'38'40Ar have been studied with the t i m e - o f - f l i g h t technique at E d = 5.6 MeV. The extracted spectroscopic factors indicate shell-model impurities of the o r d e r of 10% in the Ar ground states, and s e v e r e splitting of the f~ and p~ proton s i n g l e - p a r t i c l e states in the K fina[ nuclei. T h e d a t a on p r o t o n t r a n s f e r o n a r g o n i s o t o p e s a r e e x t r e m e l y s c a r c e . Only 3 6 A r ( % d ) h a s b e e n s t u d i e d t h u s f a r [1], but no s p e c t r o s c o p i c f a c t o r s w e r e given. T h e r e f o r e we have i n v e s t i g a t e d the
38Ar(d.n neutron
6000 °
flight
0 c
1
3SAr (d.n)39K
0.5 I~
\
Ex=0 0 MeV. 3/2 + 1=2 ---cutoff 3fro
Ed=5 6MeV
~
)39 K
path:7 50m
01 /f
D,!
~" Ed=56MeV ::r
OO5
o
4000 ~
I=1
++i
~"
®Lo.b = 3 0 °
"
++
i lI1~ /
time-of-flight spectrum
+ Ex=3 0 2 M e V . 3 / 2 -
%
"o O no
0.1 5
°
" .°
;-~
.:
-
• .
..
.~ "
•
..
2000
.
~'-..~,,,.,p,/"~
.',. :.. :' <.,.
i
1'75
200
Ex=2 82MeV.7/2 l=3
~:.,
+÷*
I
l
~
225 250 t , m e - o f . - f l i g h t [ns] ~ o
~
,~o~Q
'-~'~'-":
I
II111
I111
Ex=4.0 1
"-.
i
o
j . j "
0.05
**..
*
05
/
39K
l
[ co.t0m c~
HI
~o
Fig. I. Time-of-flight spectrum of neutrons from the 5.6 MeV deuteron bombardment of an 38Ar target. The calculated peak positions are based on the excitation energies E x given in ref. 2. Accumulation time about 3 h.
14
_
L
30
6LO
L0
9
I
120
I
150
,o
,'o
' 120
150
ec.rn
Fig. 2. Differential cross sections for 38Ar(d,n)39K transitions. Relative e r r o r s , where not indicated, are smaller than the size of the points. The uncertainty of the absolute normalization is about 15%. Solid lines are DWBAfits (see text).
Volume31B, number 1
PHYSICS
LETTERS
5 January 1970
Table 1. Absolute spectroscopic factors Slj from the 36,38,40Ar(d,n) 37,39,41K reactions in comparison wit5 the shell-model (SM) values. 37 K j~a) l
Ex(MeV ) a)
39 K (2Jf+l)C
2Sl]
exp.
SM
Ex(MeV ) a)
41 K (2Jr+l)
C2Slj
exp.
SM
Ex(MeV ) a)
(2Jf+
1)C2Slj
exp.
SM
~+
2
0.0
2.0
2
0.0
1.8
2
0.0
1.6
2
½~
0
1.368
0.2
0
0
1.380
4.6
8
0 5.33
0.16
3
0.08 2.0
0.98
~-
2.53 2.82
~-
1
2.169
1.6
4
3.02 4.08 b)
0.05 0.58
2.67
1.23 1.65 b)
2.0 0.32
6.4 3.2
a) F r o m ref. 2, b) Unresolved multiplet. p r o t o n t r a n s f e r to t h e t h r e e s t a b l e e v e n a r g o n i s o t o p e s by m e a n s of t h e (d,n) r e a c t i o n . T h e m o t i v a t i o n of t h e p r e s e n t study w a s m a i n l y to o b s e r v e s y s t e m a t i c s in t h e s h e l l - m o d e l f o r b i d d e n l = 0 t r a n s i t i o n s to 2s± s t a t e s . F r o m t h e i r s t r e n g t h s one m a y e s t i m a t e t h e a m o u n t of s h e l l m o d e l i m p u r i t i e s ( g r o u n d - s t a t e c o r r e l a t i o n s ) in t h e a r g o n n u c l e i . T h e s e d a t a a r e of i n t e r e s t in connection with similar comprehensive studies of s t r i p p i n g and p i c k - u p on t h e e v e n c a l c i u m i s o t o p e s [2]. T h e r e , g r o u n d - s t a t e c o r r e l a t i o n s a r e found to b e i m p o r t e n t and to v a r y s y s t e m a t i c a l l y with the neutron number. The experiment was performed with the neut r o n t i m e - o f - f l i g h t s y s t e m [3] at t h e V a n de G r a a f f of t h e H a h n - M e i t n e r - I n s t i t u t . T h e d e u t e r o n b e a m of 5.8 MeV p r i m a r y e n e r g y p e n e t r a t e d t h r o u g h a 3.3 m g / c m 2 m o l y b d e n u m window into a gas c e l l c o n t a i n i n g t h e s e p e r a t e d a r g o n * at a p r e s s u r e of about 100 T o r r . A r e p r e s e n t a t i v e t i m e - o f - f l i g h t s p e c t r u m and t h e e x t r a c t e d a n g u l a r d i s t r i b u t i o n s a r e shown in f i g s . 1 and 2 f o r one of t h e t a r g e t s . A t r i p l e t of s t a t e s a r o u n d 4.08 MeV in39K w a s not resolved. Their common angular distribution (fig. 2) s h o w s that at l e a s t one c o m p o n e n t h a s a s t r o n g l = 1 c h a r a c t e r . Fig. 2 i n c l u d e s t h e r e s u l t s of D W B A c a l c u l a t i o n s p e r f o r m e d in t h e s a m e way and w i t h t h e s a m e p o t e n t i a l p a r a m e t e r s a s in a r e c e n t study [ 4 ] of th e 39 K ( d, n ) r e a c t i o n , with t h e e x c e p t i o n that no c o m p o u n d - n u c l e u s c o n t r i b u t i o n s to t h e r e a c t i o n w e r e t a k e n along. T h e o b t a i n e d s t r e n g t h s Glj = C2(2/f+/)Slj of t h e l o w e s t s t a t e s p o p u l a t e d w i t h e a c h of t h e ! - v a l u e s 0,1,2,3 a r e s h o w n in t a b l e 1 t o g e t h e r w i t h t h e p r e d i c t i o n s of * Isotopic enrichment of the 36Ar and 38Ar samples: 99.9%.
t h e s h e l l - m o d e l f o r t r a n s f e r into t h e l d ~ , 2s½, lf_~ and 2p~ o r b i t s , r e s p e c t i v e l y . T h e g e n e r a l t r e n d s d i s p l a y e d by t h e d a t a m a y b e d e s c r i b e d a s f o l l o w s . 1. W i t h i n t h e u n c e r t a i n t y of t h e a b s o l u t e d e t e r m i n a t i o n (about 30%) t h e g r o u n d - s t a t e t r a n s i tion strength exhaust the shell-model value. The s l i g h t d e c r e a s e of s t r e n g t h , and, t h e r e f o r e , i n c r e a s e of t h e d e v i a t i o n f r o m t h e s h e l l - m o d e l v a l u e in t h e h e a v i e r i s o t o p e s , m i g h t b e s i g n i f i c a n t , s i n c e r e l a t i v e v a l u e s a r e s u b j e c t to s m a l l e r e r r o r s t h a n a b s o l u t e m a g n i t u d e s . 2. T h e s h e l l m o d e l f o r b i d d e n l = 0 t r a n s i t i o n s , p o s s i b l e only b e c a u s e of c o m p o n e n t s of t h e t a r g e t g r o u n d s t a t e s with p r o t o n p a i r s e x c i t e d f r o m t h e 2s½ into s o m e h i g h e r s h e l l , h a v e s t r e n g t h s in t h e o r d e r of 10% of t h e d~ s t r e n g t h s . T h e y i n d i c a t e , t h e r e f o r e , t h e p r e s e n c e of s u c h c o m p o n e n t s ( g r o u n d - s t a t e c o r r e l a t i o n s ) to about t h e s a m e o r d e r . Only l o w e r l i m i t s f o r t h e a m o u n t of g r o u n d - s t a t e c o r r e l a t i o n s m a y b e d e r i v e d b o t h b e c a u s e of t h e p o s s i b l e e x i s t e n c e of n o n - o b s e r v e d 1 = 0 t r a n s i t i o n s to h i g h e r !+ 2 s t a t e s and t h e g e n e r a l p r o b l e m s in e x t r a c t i n g spectroscopic factors from shell-model forbidden t r a n s i t i o n s [5]. 3. T h e l o w e s t f_~ and P~2 s t a t e s c o n t a i n l e s s t han about 50% of t h e s i n g l e - D a r t i c ] . e s t r e n g t h . T h i s f r a c t i o n d e c r e a s e s f r o m 37K to 41K~ t h u s i n d i c a t i n g an i n c r e a s e d s p l i t t i n g of t h e s i n g l e p a r t i c l e s t a t e s . T h i s b e h a v i o u r i s s i m i l a r to that of t h e 38,40Ar(d,p) r e a c t i o n s as o b s e r v e d by F i t z et al. [6], but c o n t r a s t s w i t h s t r i p p i n g on t h e Ca i s o t o p e s [1]. T h e r e only t h e p~ s t r e n g t h is s t r o n g ly s p l i t , w h e r e a s t h e f_~ s t r e n g t h is c o n c e n t r a t e d in t h e g r o u n d - s t a t e t r a n s i t i o n s . 4. T h e m o s t s u r prising result is, that the neutron shell closure in 3 8 A r d o e s not m a n i f e s t i t s e l f , e x c e p t m a y b e in t h e s m a l l s t r e n g t h of t h e 1 = 0 t r a n s i t i o n on 38Ar. 15
Volume 31B, number 1
PHYSICS
LETTERS
Thus we a r e c o n f r o n t e d with a c o n t r a s t i n g c h a r a c t e r of t h e g r o u n d s t a t e s of t h e s t u d i e d A r a n d K n u c l e i on t h e o n e h a n d and t h e e x c i t e d K s t a t e s on t h e o t h e r . In t h e g r o u n d s t a t e s , n o t a b l y of t h e A r nuclei, shell-model-impurities have been det e c t e d , but a p p e a r t o b e m i n o r c o r r e c t i o n s , whereas severe deviations from the simple shellm o d e l s h o w up in t h e t r a n s i t i o n s t o e x c i t e d f i n a l s t a t e s . It w o u l d b e of i n t e r e s t t o c o m p a r e t h e i r s t r e n g t h s to t h e o r e t i c a l s p e c t r o s c o p i c f a c t o r s o b t a i n e d f r o m t h e e i g e n f u n c t i o n s of r e c e n t c a l c u l a t i o n s w i t h an e x t e n d e d s h e l l - m o d e l b a s i s [7]. W e a r e i n d e b t e d to P r o f . K. H. L i n d e n b e r g e r f o r continuous i n t e r e s t and s u p p o r t , and to our colleagues B o m m e r , G r a b i s c h and R b s c h e r t for h e l p d u r i n g t h e m e a s u r e m e n t s . T h e DWBA c a l * * * * *
16
5 J a n u a r y 1970
c u l a t i o n s w e r e p e r f o r m e d at t h e D e u t s c h e s Rechenzentrum, Darmstadt.
References 1. D. R. Goosman and R. W. Kavanagh, Phys. Rev. 161 (1967) 1156. 2. see refs. in P. M. Endt and C. Van der Leun, Nucl. Phys. A105 (1967) 1. 3. H. Fuchs, K. Grabisch, P. Kraaz and G. Rbschert, Nucl. Phys. A105 (1967) 590. 4. H. Fuchs, K. Grabisch and G. R~schert, Nucl. Phys. A129 (1969) 545. 5. R . J . Philpott, W.T. Pinkston and G. R. Satchler, Nucl. Phys. Al19 (1968) 241. 6. W. Fitz, R. J a h r and R. Santo, Nucl. Phys. Al14 (1968) 392. 7. A . E . C . Dieperink and J. P. B r u s s a a r d , Nucl. Phys. A128 (1968) 34.
PHYSICS
OBSERVATION (d,n)
OF TARGET REACTIONS
LETTERS
5January1970
GROUND STATE CORRELATIONS ON EVEN ARGON ISOTOPES
IN
THE
H, FUCHS, M. HAGEN, U. JANETZKI and K.-H. MAIER Hahn-Meitner-lnstitu! flit Kernforschung Berlin, Sektor Kernphysik, Berlin-West, Germany Received 1 D e c e m b e r 1969
The (d,n) reactions on 36'38'40Ar have been studied with the t i m e - o f - f l i g h t technique at E d = 5.6 MeV. The extracted spectroscopic factors indicate shell-model impurities of the o r d e r of 10% in the Ar ground states, and s e v e r e splitting of the f~ and p~ proton s i n g l e - p a r t i c l e states in the K fina[ nuclei. T h e d a t a on p r o t o n t r a n s f e r o n a r g o n i s o t o p e s a r e e x t r e m e l y s c a r c e . Only 3 6 A r ( % d ) h a s b e e n s t u d i e d t h u s f a r [1], but no s p e c t r o s c o p i c f a c t o r s w e r e given. T h e r e f o r e we have i n v e s t i g a t e d the
38Ar(d.n neutron
6000 °
flight
0 c
1
3SAr (d.n)39K
0.5 I~
\
Ex=0 0 MeV. 3/2 + 1=2 ---cutoff 3fro
Ed=5 6MeV
~
)39 K
path:7 50m
01 /f
D,!
~" Ed=56MeV ::r
OO5
o
4000 ~
I=1
++i
~"
®Lo.b = 3 0 °
"
++
i lI1~ /
time-of-flight spectrum
+ Ex=3 0 2 M e V . 3 / 2 -
%
"o O no
0.1 5
°
" .°
;-~
.:
-
• .
..
.~ "
•
..
2000
.
~'-..~,,,.,p,/"~
.',. :.. :' <.,.
i
1'75
200
Ex=2 82MeV.7/2 l=3
~:.,
+÷*
I
l
~
225 250 t , m e - o f . - f l i g h t [ns] ~ o
~
,~o~Q
'-~'~'-":
I
II111
I111
Ex=4.0 1
"-.
i
o
j . j "
0.05
**..
*
05
/
39K
l
[ co.t0m c~
HI
~o
Fig. I. Time-of-flight spectrum of neutrons from the 5.6 MeV deuteron bombardment of an 38Ar target. The calculated peak positions are based on the excitation energies E x given in ref. 2. Accumulation time about 3 h.
14
_
L
30
6LO
L0
9
I
120
I
150
,o
,'o
' 120
150
ec.rn
Fig. 2. Differential cross sections for 38Ar(d,n)39K transitions. Relative e r r o r s , where not indicated, are smaller than the size of the points. The uncertainty of the absolute normalization is about 15%. Solid lines are DWBAfits (see text).
Volume31B, number 1
PHYSICS
LETTERS
5 January 1970
Table 1. Absolute spectroscopic factors Slj from the 36,38,40Ar(d,n) 37,39,41K reactions in comparison wit5 the shell-model (SM) values. 37 K j~a) l
Ex(MeV ) a)
39 K (2Jf+l)C
2Sl]
exp.
SM
Ex(MeV ) a)
41 K (2Jr+l)
C2Slj
exp.
SM
Ex(MeV ) a)
(2Jf+
1)C2Slj
exp.
SM
~+
2
0.0
2.0
2
0.0
1.8
2
0.0
1.6
2
½~
0
1.368
0.2
0
0
1.380
4.6
8
0 5.33
0.16
3
0.08 2.0
0.98
~-
2.53 2.82
~-
1
2.169
1.6
4
3.02 4.08 b)
0.05 0.58
2.67
1.23 1.65 b)
2.0 0.32
6.4 3.2
a) F r o m ref. 2, b) Unresolved multiplet. p r o t o n t r a n s f e r to t h e t h r e e s t a b l e e v e n a r g o n i s o t o p e s by m e a n s of t h e (d,n) r e a c t i o n . T h e m o t i v a t i o n of t h e p r e s e n t study w a s m a i n l y to o b s e r v e s y s t e m a t i c s in t h e s h e l l - m o d e l f o r b i d d e n l = 0 t r a n s i t i o n s to 2s± s t a t e s . F r o m t h e i r s t r e n g t h s one m a y e s t i m a t e t h e a m o u n t of s h e l l m o d e l i m p u r i t i e s ( g r o u n d - s t a t e c o r r e l a t i o n s ) in t h e a r g o n n u c l e i . T h e s e d a t a a r e of i n t e r e s t in connection with similar comprehensive studies of s t r i p p i n g and p i c k - u p on t h e e v e n c a l c i u m i s o t o p e s [2]. T h e r e , g r o u n d - s t a t e c o r r e l a t i o n s a r e found to b e i m p o r t e n t and to v a r y s y s t e m a t i c a l l y with the neutron number. The experiment was performed with the neut r o n t i m e - o f - f l i g h t s y s t e m [3] at t h e V a n de G r a a f f of t h e H a h n - M e i t n e r - I n s t i t u t . T h e d e u t e r o n b e a m of 5.8 MeV p r i m a r y e n e r g y p e n e t r a t e d t h r o u g h a 3.3 m g / c m 2 m o l y b d e n u m window into a gas c e l l c o n t a i n i n g t h e s e p e r a t e d a r g o n * at a p r e s s u r e of about 100 T o r r . A r e p r e s e n t a t i v e t i m e - o f - f l i g h t s p e c t r u m and t h e e x t r a c t e d a n g u l a r d i s t r i b u t i o n s a r e shown in f i g s . 1 and 2 f o r one of t h e t a r g e t s . A t r i p l e t of s t a t e s a r o u n d 4.08 MeV in39K w a s not resolved. Their common angular distribution (fig. 2) s h o w s that at l e a s t one c o m p o n e n t h a s a s t r o n g l = 1 c h a r a c t e r . Fig. 2 i n c l u d e s t h e r e s u l t s of D W B A c a l c u l a t i o n s p e r f o r m e d in t h e s a m e way and w i t h t h e s a m e p o t e n t i a l p a r a m e t e r s a s in a r e c e n t study [ 4 ] of th e 39 K ( d, n ) r e a c t i o n , with t h e e x c e p t i o n that no c o m p o u n d - n u c l e u s c o n t r i b u t i o n s to t h e r e a c t i o n w e r e t a k e n along. T h e o b t a i n e d s t r e n g t h s Glj = C2(2/f+/)Slj of t h e l o w e s t s t a t e s p o p u l a t e d w i t h e a c h of t h e ! - v a l u e s 0,1,2,3 a r e s h o w n in t a b l e 1 t o g e t h e r w i t h t h e p r e d i c t i o n s of * Isotopic enrichment of the 36Ar and 38Ar samples: 99.9%.
t h e s h e l l - m o d e l f o r t r a n s f e r into t h e l d ~ , 2s½, lf_~ and 2p~ o r b i t s , r e s p e c t i v e l y . T h e g e n e r a l t r e n d s d i s p l a y e d by t h e d a t a m a y b e d e s c r i b e d a s f o l l o w s . 1. W i t h i n t h e u n c e r t a i n t y of t h e a b s o l u t e d e t e r m i n a t i o n (about 30%) t h e g r o u n d - s t a t e t r a n s i tion strength exhaust the shell-model value. The s l i g h t d e c r e a s e of s t r e n g t h , and, t h e r e f o r e , i n c r e a s e of t h e d e v i a t i o n f r o m t h e s h e l l - m o d e l v a l u e in t h e h e a v i e r i s o t o p e s , m i g h t b e s i g n i f i c a n t , s i n c e r e l a t i v e v a l u e s a r e s u b j e c t to s m a l l e r e r r o r s t h a n a b s o l u t e m a g n i t u d e s . 2. T h e s h e l l m o d e l f o r b i d d e n l = 0 t r a n s i t i o n s , p o s s i b l e only b e c a u s e of c o m p o n e n t s of t h e t a r g e t g r o u n d s t a t e s with p r o t o n p a i r s e x c i t e d f r o m t h e 2s½ into s o m e h i g h e r s h e l l , h a v e s t r e n g t h s in t h e o r d e r of 10% of t h e d~ s t r e n g t h s . T h e y i n d i c a t e , t h e r e f o r e , t h e p r e s e n c e of s u c h c o m p o n e n t s ( g r o u n d - s t a t e c o r r e l a t i o n s ) to about t h e s a m e o r d e r . Only l o w e r l i m i t s f o r t h e a m o u n t of g r o u n d - s t a t e c o r r e l a t i o n s m a y b e d e r i v e d b o t h b e c a u s e of t h e p o s s i b l e e x i s t e n c e of n o n - o b s e r v e d 1 = 0 t r a n s i t i o n s to h i g h e r !+ 2 s t a t e s and t h e g e n e r a l p r o b l e m s in e x t r a c t i n g spectroscopic factors from shell-model forbidden t r a n s i t i o n s [5]. 3. T h e l o w e s t f_~ and P~2 s t a t e s c o n t a i n l e s s t han about 50% of t h e s i n g l e - D a r t i c ] . e s t r e n g t h . T h i s f r a c t i o n d e c r e a s e s f r o m 37K to 41K~ t h u s i n d i c a t i n g an i n c r e a s e d s p l i t t i n g of t h e s i n g l e p a r t i c l e s t a t e s . T h i s b e h a v i o u r i s s i m i l a r to that of t h e 38,40Ar(d,p) r e a c t i o n s as o b s e r v e d by F i t z et al. [6], but c o n t r a s t s w i t h s t r i p p i n g on t h e Ca i s o t o p e s [1]. T h e r e only t h e p~ s t r e n g t h is s t r o n g ly s p l i t , w h e r e a s t h e f_~ s t r e n g t h is c o n c e n t r a t e d in t h e g r o u n d - s t a t e t r a n s i t i o n s . 4. T h e m o s t s u r prising result is, that the neutron shell closure in 3 8 A r d o e s not m a n i f e s t i t s e l f , e x c e p t m a y b e in t h e s m a l l s t r e n g t h of t h e 1 = 0 t r a n s i t i o n on 38Ar. 15
Volume 31B, number 1
PHYSICS
LETTERS
Thus we a r e c o n f r o n t e d with a c o n t r a s t i n g c h a r a c t e r of t h e g r o u n d s t a t e s of t h e s t u d i e d A r a n d K n u c l e i on t h e o n e h a n d and t h e e x c i t e d K s t a t e s on t h e o t h e r . In t h e g r o u n d s t a t e s , n o t a b l y of t h e A r nuclei, shell-model-impurities have been det e c t e d , but a p p e a r t o b e m i n o r c o r r e c t i o n s , whereas severe deviations from the simple shellm o d e l s h o w up in t h e t r a n s i t i o n s t o e x c i t e d f i n a l s t a t e s . It w o u l d b e of i n t e r e s t t o c o m p a r e t h e i r s t r e n g t h s to t h e o r e t i c a l s p e c t r o s c o p i c f a c t o r s o b t a i n e d f r o m t h e e i g e n f u n c t i o n s of r e c e n t c a l c u l a t i o n s w i t h an e x t e n d e d s h e l l - m o d e l b a s i s [7]. W e a r e i n d e b t e d to P r o f . K. H. L i n d e n b e r g e r f o r continuous i n t e r e s t and s u p p o r t , and to our colleagues B o m m e r , G r a b i s c h and R b s c h e r t for h e l p d u r i n g t h e m e a s u r e m e n t s . T h e DWBA c a l * * * * *
16
5 J a n u a r y 1970
c u l a t i o n s w e r e p e r f o r m e d at t h e D e u t s c h e s Rechenzentrum, Darmstadt.
References 1. D. R. Goosman and R. W. Kavanagh, Phys. Rev. 161 (1967) 1156. 2. see refs. in P. M. Endt and C. Van der Leun, Nucl. Phys. A105 (1967) 1. 3. H. Fuchs, K. Grabisch, P. Kraaz and G. Rbschert, Nucl. Phys. A105 (1967) 590. 4. H. Fuchs, K. Grabisch and G. R~schert, Nucl. Phys. A129 (1969) 545. 5. R . J . Philpott, W.T. Pinkston and G. R. Satchler, Nucl. Phys. Al19 (1968) 241. 6. W. Fitz, R. J a h r and R. Santo, Nucl. Phys. Al14 (1968) 392. 7. A . E . C . Dieperink and J. P. B r u s s a a r d , Nucl. Phys. A128 (1968) 34.