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On (γ, p) and (γ, n) reactions mechanism in the medium and heavy nuclei region
Volume 22, number 4
t e d by two o r d e r s . H o w e v e r , it h a s to be taken into c o n s i d e r a t i o n that the n e u t r o n r e d u c e d - w i d t h v a l u e s , c h a r a c t e r i z i n g the d e g r e e of i s o s p i n p u r i t y v i o l a t i o n , a r e e x t r e m e l y s e n s i t i v e to a lot of v a r i o u s p a r a m e t e r s of the c a l c u l a t i o n . It i s s u f f i c i e n t to note that the b a c k g r o u n d of the s t a t e s with T = T o i s v e r y n o n u n i f o r m a c c o r d i n g to the c a l c u l a t i o n , t h e r e a r e a g r e a t n u m b e r of r e s o n a n c e s with T = T o in the r e g i o n 12.0 - 17.0 MeV: 12.49; 13.67; 14.08; 14.35; 14.47; 15.95 MeV etc.
A d e t a i l e d ru n of the c a l c u l a t i o n p a r a m e t e r s will be c a r r i e d out e l s e w h e r e . T h e a n a l y s i s of the analogue r e s o n a n c e s of 90Zr with o t h e r spin v a l u e s (0-, 1-, 3-) and a d i s c u s s i o n of the c o r r e s p o n d i n g s t a t e s of 9 0 y will be r e p o r t e d t h e r e a s well.
ON
(y,p)
1 September 1966
P H Y SI C S L E T T E R S
AND
In any c a s e , the r e s u l t s obtained by now on the nucleon widths m ay be c o n s i d e r e d a s a convincing a r g u m e n t f o r a high validity of i s o s p i n in the r e gion of n u c l e i width A ~ 100.
References 1. V.V.Balashov, P. Doleshal, G. Ya. Korotkih and V. N. Fetisov, Yadernaja Physika 2 (1965) 643. 2. J. Sehr~ler, Nuovo Cim. 60 (1959) 512. 3. V.A.Kravtsov, Massy atomov (Atomizdat 1965). 4. J.D. Fox et al,, Phys. Lett. 12 (1964) 198. 5. V.V. Batashov, K.A. Tumanov and Yu. M. Shirokov, Yaderniye reaktsiyi pri malih i srednih energiyah. (Moscow, 1958) p.548. 6. L.A. Sliv and Yu. T. Kharitonov, Ydernaya Physika 1 (1965) 1129. 7. G.S.Mani, G.C.Dutt, Phys. Letters 16 (1965) 50.
(y,n) REACTIONS MECHANISM IN AND HEAVY NUCLEI REGION
THE
MEDIUM
V. V. BALASHOV and E. L. YADROVSKY Research Institute of Nuclear Physics of Moscow State University, Moscow, USSR Received 20 July 1966
Coupling in additional configurations necessary to obtain levels of good isospin pushes the (y,p) cross section to higher energies than the (y,n) one. m6 M~,'b
R e c e n t l y , F a l l i e r o s e t al. [1] s u g g e s t e d that the known u p w a r d s shift of the c r o s s s e c t i o n m a x i m u m of the r e a c t i o n (y,p) with r e s p e c t to the (7,n) c r o s s s e c t i o n m a x i m u m i s c o n n e c te d with the i s o t o p i c s p l i t t i n g of the dipole giant r e s o n a n ce. The c a l c u l a t i o n of M a i l i n g et al. [2] f o r Ni have shown that in the l ig h t n u c l e i r e g i o n t h i s a s s u m p t i o n i s valid. How f a r t h i s e f f e c t p e r s i s t s when we go o v e r to the m e d i u m - w e i g h t and h e a v y n u c l e i depends on i s o t o p i c spin a c c u r a c y in t h i s n u c l e i r e g i o n and on the way of f o r m a t i o n of a c o l l e c t i v e state in e a c h of the two t r a n s i t i o n gr oups : T = ½ (N-Z); T = ½ (N-Z) + 1. In a p r e v i o u s work of the a u t h o r s [3] an a n a l y s i s of n u cl eo n widths of i s o b a r i c - analogue s t a t e s was c a r r i e d out, which d e m o n s t r a t e d high p u r i t y of i s o t o p i c spin in n u c l e i with N - Z >> 1. In the p r e s e n t p a p e r , in the f r a m e work of the m e t h o d d e s c r i b e d in r e f . 3 we c o n s i d e r e d the
r-] - - T~5
- - TJ,6
1604
,,otl $0-
~10-
0
8
~2
f6
2O
2~
E¢ (New)
Fig. 1. Dipole resonance in 9 0 Z r - "zero approximation". dipole a b s o r p t i o n s p e c t r u m in the n u c l e u s 9 0 Zr . A l l p a r a m e t e r s a r e the s a m e a s in r e f . 3. A s it
509
Volume 22, n u m b e r 4
PHYSICS
LETTERS
1 S e p t e m b e r 1966
Of c o u r s e , a s in p r e v i o u s c a l c u l a t i o n s of t h e giant resonance where only particle-hole excitat i o n s w e r e t a k e n i n t o a c c o u n t , t h e p r o b l e m of t h e e n e r g y s p e c t r u m of t h e p h o t o p r o d u c t s r e m a i n s u n solved. We shall discuss it in subsequent papers. W i t h t h e i n c r e a s e of t h e m a s s n u m b e r A t h e s p l i t t i n g of t h e T = ½ (N-Z) a n d T = ½ (N-Z) + 1 states increases, according to rough estimates of t h e s y m m e t r y e n e r g y , a s ( N - Z ) / A . T h u s , i n t h e h e a v i e s t n u c l e i t h e (~,p) c r o s s s e c t i o n m a x i m u m s h o u l d b e m o r e t h a n 10 M e V a p a r t f r o m t h e (~,n) c r o s s s e c t i o n m a x i m u m . R e s u l t s of t h e microscopic calculation for 208pb will be reported in a short time.
Fig. 2. Dipole r e s o n a n c e in 9 0 Z r - with corfiguration mixing. The e x p e r i m e n t a l data on the c r o s s section of (~,p) and (%n) r e a c t i o n s a r e taken f r o m ref.2. i s s e e n f r o m fig. 2, t h e c o n t e n t of t h e e f f e c t i s well reproduced. One should note an appreciable a b s o r p t i o n in t h e e n e r g y i n t e r v a l b e t w e e n t h e proton and neutron thresholds (8.3-11.9 MeV).
HARTREE-FOCK M. BOUTEN,
TYPE
References 1. S. F a l l i e r o s , G. Boulard and R.M. Ventor, P h y s i c s L e t t e r s 19 (1965) 398. 2. B . C . Ishkhanov, I.K. Kapitonov and L. Mailing, L e t t e r to J E T P (in p r e s s ) . 3. V.V. Balashov and E. L. Yadrovsky, Phys. Lett. 22 (1966) 507. 4. N.N. Balamatov, B . C . IshkhanQv and V. G. Shevchenko, Vestnik MGU, N2 (1964).
CALCULATION
ON
12C
L. S C H O T S M A N S a n d P . V A N L E U V E N
Studiecentrum voor Kernenergie, Mol, Belgium Received 20 July 1966
A variational calculation using a projected Slater d e t e r m i n a n t shows that the admixture of 0d and Of o s c i l l a t o r s t a t e s is v e r y i m p o r t a n t for the ground state of 12C. T h e s e a d m i x t u r e s i n c r e a s e the binding e n ergy by 10 MeV.
In t h i s n o t e we p r e s e n t t h e r e s u l t s of a c a l c u l a t i o n of s i n g l e p a r t i c l e o r b i t a l s a n d b i n d i n g e n e r gy of 12C. A s a p r e l i m i n a r y c a l c u l a t i o n , we c o n s i d e r e d a s i n g l e S l a t e r d e t e r m i n a n t of 12 p a r t i c l e s a s a t r i a l function and minimised the internal energy
Table 1 H a r t r e e - F o c k single p a r t i c ~ e n e r g i e s ~ and o r b i t a l s for ~ C . £ (MeV)
nlmlm 0s0½
-25.226 H i n t = ~i Ti - TC" M. + i < ~ j Vij" -
-
T h e t w o - b o d y i n t e r a c t i o n Vii i s p u r e l y c e n t r a l a n d has a weakly repulsive core followed by an attract i v e t a i l , r e s e m b l i n g t h e l o n g - r a n g e p a r t of a p o -
510
3.402
0p0½
0pl½
0pl~
1 s0½ -0.032
0.999
0
0
0
0
0
1
0
0
3.402
0
0
0
1
0
14.584
0
1
0
0
0
28.162
0.032
0
0
0
0.999
t e d by two o r d e r s . H o w e v e r , it h a s to be taken into c o n s i d e r a t i o n that the n e u t r o n r e d u c e d - w i d t h v a l u e s , c h a r a c t e r i z i n g the d e g r e e of i s o s p i n p u r i t y v i o l a t i o n , a r e e x t r e m e l y s e n s i t i v e to a lot of v a r i o u s p a r a m e t e r s of the c a l c u l a t i o n . It i s s u f f i c i e n t to note that the b a c k g r o u n d of the s t a t e s with T = T o i s v e r y n o n u n i f o r m a c c o r d i n g to the c a l c u l a t i o n , t h e r e a r e a g r e a t n u m b e r of r e s o n a n c e s with T = T o in the r e g i o n 12.0 - 17.0 MeV: 12.49; 13.67; 14.08; 14.35; 14.47; 15.95 MeV etc.
A d e t a i l e d ru n of the c a l c u l a t i o n p a r a m e t e r s will be c a r r i e d out e l s e w h e r e . T h e a n a l y s i s of the analogue r e s o n a n c e s of 90Zr with o t h e r spin v a l u e s (0-, 1-, 3-) and a d i s c u s s i o n of the c o r r e s p o n d i n g s t a t e s of 9 0 y will be r e p o r t e d t h e r e a s well.
ON
(y,p)
1 September 1966
P H Y SI C S L E T T E R S
AND
In any c a s e , the r e s u l t s obtained by now on the nucleon widths m ay be c o n s i d e r e d a s a convincing a r g u m e n t f o r a high validity of i s o s p i n in the r e gion of n u c l e i width A ~ 100.
References 1. V.V.Balashov, P. Doleshal, G. Ya. Korotkih and V. N. Fetisov, Yadernaja Physika 2 (1965) 643. 2. J. Sehr~ler, Nuovo Cim. 60 (1959) 512. 3. V.A.Kravtsov, Massy atomov (Atomizdat 1965). 4. J.D. Fox et al,, Phys. Lett. 12 (1964) 198. 5. V.V. Batashov, K.A. Tumanov and Yu. M. Shirokov, Yaderniye reaktsiyi pri malih i srednih energiyah. (Moscow, 1958) p.548. 6. L.A. Sliv and Yu. T. Kharitonov, Ydernaya Physika 1 (1965) 1129. 7. G.S.Mani, G.C.Dutt, Phys. Letters 16 (1965) 50.
(y,n) REACTIONS MECHANISM IN AND HEAVY NUCLEI REGION
THE
MEDIUM
V. V. BALASHOV and E. L. YADROVSKY Research Institute of Nuclear Physics of Moscow State University, Moscow, USSR Received 20 July 1966
Coupling in additional configurations necessary to obtain levels of good isospin pushes the (y,p) cross section to higher energies than the (y,n) one. m6 M~,'b
R e c e n t l y , F a l l i e r o s e t al. [1] s u g g e s t e d that the known u p w a r d s shift of the c r o s s s e c t i o n m a x i m u m of the r e a c t i o n (y,p) with r e s p e c t to the (7,n) c r o s s s e c t i o n m a x i m u m i s c o n n e c te d with the i s o t o p i c s p l i t t i n g of the dipole giant r e s o n a n ce. The c a l c u l a t i o n of M a i l i n g et al. [2] f o r Ni have shown that in the l ig h t n u c l e i r e g i o n t h i s a s s u m p t i o n i s valid. How f a r t h i s e f f e c t p e r s i s t s when we go o v e r to the m e d i u m - w e i g h t and h e a v y n u c l e i depends on i s o t o p i c spin a c c u r a c y in t h i s n u c l e i r e g i o n and on the way of f o r m a t i o n of a c o l l e c t i v e state in e a c h of the two t r a n s i t i o n gr oups : T = ½ (N-Z); T = ½ (N-Z) + 1. In a p r e v i o u s work of the a u t h o r s [3] an a n a l y s i s of n u cl eo n widths of i s o b a r i c - analogue s t a t e s was c a r r i e d out, which d e m o n s t r a t e d high p u r i t y of i s o t o p i c spin in n u c l e i with N - Z >> 1. In the p r e s e n t p a p e r , in the f r a m e work of the m e t h o d d e s c r i b e d in r e f . 3 we c o n s i d e r e d the
r-] - - T~5
- - TJ,6
1604
,,otl $0-
~10-
0
8
~2
f6
2O
2~
E¢ (New)
Fig. 1. Dipole resonance in 9 0 Z r - "zero approximation". dipole a b s o r p t i o n s p e c t r u m in the n u c l e u s 9 0 Zr . A l l p a r a m e t e r s a r e the s a m e a s in r e f . 3. A s it
509
Volume 22, n u m b e r 4
PHYSICS
LETTERS
1 S e p t e m b e r 1966
Of c o u r s e , a s in p r e v i o u s c a l c u l a t i o n s of t h e giant resonance where only particle-hole excitat i o n s w e r e t a k e n i n t o a c c o u n t , t h e p r o b l e m of t h e e n e r g y s p e c t r u m of t h e p h o t o p r o d u c t s r e m a i n s u n solved. We shall discuss it in subsequent papers. W i t h t h e i n c r e a s e of t h e m a s s n u m b e r A t h e s p l i t t i n g of t h e T = ½ (N-Z) a n d T = ½ (N-Z) + 1 states increases, according to rough estimates of t h e s y m m e t r y e n e r g y , a s ( N - Z ) / A . T h u s , i n t h e h e a v i e s t n u c l e i t h e (~,p) c r o s s s e c t i o n m a x i m u m s h o u l d b e m o r e t h a n 10 M e V a p a r t f r o m t h e (~,n) c r o s s s e c t i o n m a x i m u m . R e s u l t s of t h e microscopic calculation for 208pb will be reported in a short time.
Fig. 2. Dipole r e s o n a n c e in 9 0 Z r - with corfiguration mixing. The e x p e r i m e n t a l data on the c r o s s section of (~,p) and (%n) r e a c t i o n s a r e taken f r o m ref.2. i s s e e n f r o m fig. 2, t h e c o n t e n t of t h e e f f e c t i s well reproduced. One should note an appreciable a b s o r p t i o n in t h e e n e r g y i n t e r v a l b e t w e e n t h e proton and neutron thresholds (8.3-11.9 MeV).
HARTREE-FOCK M. BOUTEN,
TYPE
References 1. S. F a l l i e r o s , G. Boulard and R.M. Ventor, P h y s i c s L e t t e r s 19 (1965) 398. 2. B . C . Ishkhanov, I.K. Kapitonov and L. Mailing, L e t t e r to J E T P (in p r e s s ) . 3. V.V. Balashov and E. L. Yadrovsky, Phys. Lett. 22 (1966) 507. 4. N.N. Balamatov, B . C . IshkhanQv and V. G. Shevchenko, Vestnik MGU, N2 (1964).
CALCULATION
ON
12C
L. S C H O T S M A N S a n d P . V A N L E U V E N
Studiecentrum voor Kernenergie, Mol, Belgium Received 20 July 1966
A variational calculation using a projected Slater d e t e r m i n a n t shows that the admixture of 0d and Of o s c i l l a t o r s t a t e s is v e r y i m p o r t a n t for the ground state of 12C. T h e s e a d m i x t u r e s i n c r e a s e the binding e n ergy by 10 MeV.
In t h i s n o t e we p r e s e n t t h e r e s u l t s of a c a l c u l a t i o n of s i n g l e p a r t i c l e o r b i t a l s a n d b i n d i n g e n e r gy of 12C. A s a p r e l i m i n a r y c a l c u l a t i o n , we c o n s i d e r e d a s i n g l e S l a t e r d e t e r m i n a n t of 12 p a r t i c l e s a s a t r i a l function and minimised the internal energy
Table 1 H a r t r e e - F o c k single p a r t i c ~ e n e r g i e s ~ and o r b i t a l s for ~ C . £ (MeV)
nlmlm 0s0½
-25.226 H i n t = ~i Ti - TC" M. + i < ~ j Vij" -
-
T h e t w o - b o d y i n t e r a c t i o n Vii i s p u r e l y c e n t r a l a n d has a weakly repulsive core followed by an attract i v e t a i l , r e s e m b l i n g t h e l o n g - r a n g e p a r t of a p o -
510
3.402
0p0½
0pl½
0pl~
1 s0½ -0.032
0.999
0
0
0
0
0
1
0
0
3.402
0
0
0
1
0
14.584
0
1
0
0
0
28.162
0.032
0
0
0
0.999