- Email: [email protected]
89. Remarks about pear-shaped nuclei
1166
ABSTRACTS
87. A l p h a d i s i n t e g r a t i o n a n d t h e s h e l l m o d e l . Physico Technical Institute, Leningrad, U.S.S.R.
L . A . SLIV.
1. A l p h a - d i s i n t e g r a t i o n of nuclei in the v i c i n i t y of P b possesses some specific peculiarities, the s t u d y of which is i m p o r t a n t . f o r an elucidation of t h e m e c h a n i s m of the p h e n o m e n o n itself. 2. If the lifetimes of t h e isotopes Bi, Po, A t a n d R n are c o m p u t e d according to t h e formula for the alpha-disintegration of spherical nuclei, and c o m p a r e d w i t h experim e n t a l data, the following relationships are o b s e r v e d : a. T h e lifetime of different isotopes of the s a m e e l e m e n t depends on the n u m b e r of n e u t r o n s and reaches a m a x i m u m w h e n N = 126. b. W h e n t h e n u m b e r of n e u t r o n s in the nucleus is g r e a t e r or less t h a n 126, t h e lifet i m e decreases to values k n o w n for g r e a t l y d r a w n o u t nuclei. A t the same time, from o t h e r d a t a it follows t h a t nuclei in t h e v i c i n i t y of P t possess no s t a t i o n a r y deformation, b u t undergo only surface oscillations. 3. I n this s t u d y the p r o b a b i l i t y of a l p h a - d i s i n t e g r a t i o n has been c o m p u t e d for a nucleus performing surface oscillations w i t h an a m p l i t u d e d e p e n d i n g on the n u m b e r of nucleons outside the filled shells, and w i t h a surface alpha-particle distribution f u n c t i o n which has m a x i m a at the d e f o r m a t i o n points. 4. S o m e considerations are p u t forward in f a v o u r of such a scheme, and it is shown t h a t the a b o v e m e n t i o n e d peculiarities of a l p h a - d i s i n t e g r a t i o n of n o n - d e f o r m e d nuclei can be explained rationally.
88. E x c i t a t i o n of r o t a t i o n a l s t a t e s i n a l p h a - d e c a y V. M. STRUTINSKY. Moscow I n s t i t u t e of Physics, Moscow, U.S.S.R.
of e v e n - e v e n
nuclei.
The p r o b a b i l i t y of e x c i t a t i o n of r o t a t i o n a l states in m-decay of e v e n - e v e n nuclei is ~alculated. The case of small nuclear d e f o r m a t i o n is considered. I t is s h o w n t h a t t h e power series expansion of the two first t e r m s of t h e quasi-classical series, So and S1, on sin20 (prolate nucleus) and cos20 (oblate nucleus) is a t t h e same t i m e t h e p o w e r series expansion on the nuclear d e f o r m a t i o n p a r a m e t e r ~ (0 is t h e angle b e t w e e n t h e nuclear s y m m e t r y axis and the m-particle direction). So and St are calculated w i t h an a c c u r a c y of ~2. The d e p e n d e n c e of the ~-particle w a v e f u n c t i o n upon t h e b o u n d a r y condition on t h e nuclear surface is discussed, and it is shown t h a t t h e p r o b a b i l i t y of e x c i t a t i o n of t h e lower r o t a t i o n a l s t a t e s does n o t p r a c t i c a l l y d e p e n d on t h e b o u n d a r y condition. The nuclear d e f o r m a t i o n is d e t e r m i n e d f r o m the i n t e n s i t y of the t r a n s i t i o n to t h e 2 + r o t a t i o n a l state.
89. R e m a r k s a b o u t p e a r - s h a p e d n u c l e i . V. M. STRUTINSKY. MOSCOW I n s t i t u t e of Physics, Moscow, U.S.S.R. 1. I t is shown t h a t the i n t e r a c t i o n of t w o nucleon states w i t h t h e a s y m m e t r i c a l d e f o r m a t i o n of the nuclear surface can lead to t h e s t a b i l i t y of a s y m m e t r i c a l n u c l e a r deformation. The role of this effect in a s y m m e t r y of nuclear fission is discussed. 2. The collective dipole m o m e n t of a pear-shaped nucleus is calculated. T h e dipole polarization of a nucleus is assumed to be a result of t h e inner electrical field of t h e a s y m m e t r i c a l l y d e f o r m e d nucleus. The interference of t h e t e r m s c o n n e c t e d w i t h
MODELS AND THEORIES
| 167
quadrupole (gz) and octupole (g3) deformations produces the dipole m o m e n t proportional to ~9. ~3. For the uranium group nuclei the collective dipole m o m e n t is of order of 0.05 to 0.1 R0. The importance of the measurement of the probability of dipole and octupole transitions is pointed out as such data should supply information about the collective or individual particle nature of 1-- states in even-even nuclei.
90. M o m e n t of i n e r t i a of a s y s t e m of i n t e r a c t i n g p a r t i c l e s . and G. F. FILLIPOV. A c a d e m y of Science of the U.S.S.R., Moscow, U.S.S.R.
A. S. DAVYDOV
The question of isolation of the collective degrees of freedom in a system consisting of N interacting particles is investigated. I t is shown t h a t with certain special states of internal motion the energy of the system m a y be expressed as the sum of the energy of internal motion and the energy of rotation determined by the moment of the system. The problem is first solved for the case of a system consisting of three spinless particles. Then a system of N spinless particles interacting through random central forces is considered.
91. O n t h e q u a s i - m a g n e t i c i n t e r a c t i o n b e t w e e n n u c l e o n s p i n and n u c l e a r r o t a t i o n . D. F. ZARETSKY and A. V. SHIJTKO. Academy of Science of the U.S.S.R., Moscow, U.S.S.R. The term in the Hamiltonian of a non-spherical nucleus due to quasi-magnetic interaction between the nucleon spin and the rotation of the nucleus as a whole is investigated. The interaction has the form: Hl~s = --. (2/mc 2) $
[VU(r) •
VOTH]
where 2 is a phenomenological non-dimensional constant, VOTH -- the velocity of the collective motion of the nucleon in the rotating coordinate system. This interaction is employed for an interpretation of the structure of the rotational spectra of certain non-spherical nuclei with spin of ½. I t is assumed that H u n d ' s coupling case " b " is achieved in these nuclei. I t is indicated t h a t spin-rotation interaction m ay play an important role in the coupling scheme suggested by A. B o h r , B. M o t t e l s o n and S. N i l s s o n .
92. A n a l y s i s of s i n g l e c h a n n e l r e a c t i o n s . E. CLEMENTEL, Instituto di Fisica, Universit~ di Pado~a and C. VILLI, Instituto di fisica, Universit~ di Trieste, Italia. A method valid in S-and P - w a v e approximation 1) for phaseshift analysis of single channel scattering experiments has been extended to include D-waves and Coulomb effects. The least squares fit of the experimental data according to the expansion k~o(/~) = EA n cosn 0 provides the angular distribution coefficients A n, which are the primary data needed in the analysis. Expressing the real and imaginary part of the forward cross-section in terms of these coefficients, and taking into account the dependence of the A n's on the phaseshifts it is possible to show t h a t four sets of five phaseshifts are compatible, at a given energy, with the experimental data. This multiplicity is due, besides to the well known P-state ambiguity, to a D-state ambiguity. This method is valid also for incoming charged particles, but in this case an iteration
ABSTRACTS
87. A l p h a d i s i n t e g r a t i o n a n d t h e s h e l l m o d e l . Physico Technical Institute, Leningrad, U.S.S.R.
L . A . SLIV.
1. A l p h a - d i s i n t e g r a t i o n of nuclei in the v i c i n i t y of P b possesses some specific peculiarities, the s t u d y of which is i m p o r t a n t . f o r an elucidation of t h e m e c h a n i s m of the p h e n o m e n o n itself. 2. If the lifetimes of t h e isotopes Bi, Po, A t a n d R n are c o m p u t e d according to t h e formula for the alpha-disintegration of spherical nuclei, and c o m p a r e d w i t h experim e n t a l data, the following relationships are o b s e r v e d : a. T h e lifetime of different isotopes of the s a m e e l e m e n t depends on the n u m b e r of n e u t r o n s and reaches a m a x i m u m w h e n N = 126. b. W h e n t h e n u m b e r of n e u t r o n s in the nucleus is g r e a t e r or less t h a n 126, t h e lifet i m e decreases to values k n o w n for g r e a t l y d r a w n o u t nuclei. A t the same time, from o t h e r d a t a it follows t h a t nuclei in t h e v i c i n i t y of P t possess no s t a t i o n a r y deformation, b u t undergo only surface oscillations. 3. I n this s t u d y the p r o b a b i l i t y of a l p h a - d i s i n t e g r a t i o n has been c o m p u t e d for a nucleus performing surface oscillations w i t h an a m p l i t u d e d e p e n d i n g on the n u m b e r of nucleons outside the filled shells, and w i t h a surface alpha-particle distribution f u n c t i o n which has m a x i m a at the d e f o r m a t i o n points. 4. S o m e considerations are p u t forward in f a v o u r of such a scheme, and it is shown t h a t the a b o v e m e n t i o n e d peculiarities of a l p h a - d i s i n t e g r a t i o n of n o n - d e f o r m e d nuclei can be explained rationally.
88. E x c i t a t i o n of r o t a t i o n a l s t a t e s i n a l p h a - d e c a y V. M. STRUTINSKY. Moscow I n s t i t u t e of Physics, Moscow, U.S.S.R.
of e v e n - e v e n
nuclei.
The p r o b a b i l i t y of e x c i t a t i o n of r o t a t i o n a l states in m-decay of e v e n - e v e n nuclei is ~alculated. The case of small nuclear d e f o r m a t i o n is considered. I t is s h o w n t h a t t h e power series expansion of the two first t e r m s of t h e quasi-classical series, So and S1, on sin20 (prolate nucleus) and cos20 (oblate nucleus) is a t t h e same t i m e t h e p o w e r series expansion on the nuclear d e f o r m a t i o n p a r a m e t e r ~ (0 is t h e angle b e t w e e n t h e nuclear s y m m e t r y axis and the m-particle direction). So and St are calculated w i t h an a c c u r a c y of ~2. The d e p e n d e n c e of the ~-particle w a v e f u n c t i o n upon t h e b o u n d a r y condition on t h e nuclear surface is discussed, and it is shown t h a t t h e p r o b a b i l i t y of e x c i t a t i o n of t h e lower r o t a t i o n a l s t a t e s does n o t p r a c t i c a l l y d e p e n d on t h e b o u n d a r y condition. The nuclear d e f o r m a t i o n is d e t e r m i n e d f r o m the i n t e n s i t y of the t r a n s i t i o n to t h e 2 + r o t a t i o n a l state.
89. R e m a r k s a b o u t p e a r - s h a p e d n u c l e i . V. M. STRUTINSKY. MOSCOW I n s t i t u t e of Physics, Moscow, U.S.S.R. 1. I t is shown t h a t the i n t e r a c t i o n of t w o nucleon states w i t h t h e a s y m m e t r i c a l d e f o r m a t i o n of the nuclear surface can lead to t h e s t a b i l i t y of a s y m m e t r i c a l n u c l e a r deformation. The role of this effect in a s y m m e t r y of nuclear fission is discussed. 2. The collective dipole m o m e n t of a pear-shaped nucleus is calculated. T h e dipole polarization of a nucleus is assumed to be a result of t h e inner electrical field of t h e a s y m m e t r i c a l l y d e f o r m e d nucleus. The interference of t h e t e r m s c o n n e c t e d w i t h
MODELS AND THEORIES
| 167
quadrupole (gz) and octupole (g3) deformations produces the dipole m o m e n t proportional to ~9. ~3. For the uranium group nuclei the collective dipole m o m e n t is of order of 0.05 to 0.1 R0. The importance of the measurement of the probability of dipole and octupole transitions is pointed out as such data should supply information about the collective or individual particle nature of 1-- states in even-even nuclei.
90. M o m e n t of i n e r t i a of a s y s t e m of i n t e r a c t i n g p a r t i c l e s . and G. F. FILLIPOV. A c a d e m y of Science of the U.S.S.R., Moscow, U.S.S.R.
A. S. DAVYDOV
The question of isolation of the collective degrees of freedom in a system consisting of N interacting particles is investigated. I t is shown t h a t with certain special states of internal motion the energy of the system m a y be expressed as the sum of the energy of internal motion and the energy of rotation determined by the moment of the system. The problem is first solved for the case of a system consisting of three spinless particles. Then a system of N spinless particles interacting through random central forces is considered.
91. O n t h e q u a s i - m a g n e t i c i n t e r a c t i o n b e t w e e n n u c l e o n s p i n and n u c l e a r r o t a t i o n . D. F. ZARETSKY and A. V. SHIJTKO. Academy of Science of the U.S.S.R., Moscow, U.S.S.R. The term in the Hamiltonian of a non-spherical nucleus due to quasi-magnetic interaction between the nucleon spin and the rotation of the nucleus as a whole is investigated. The interaction has the form: Hl~s = --. (2/mc 2) $
[VU(r) •
VOTH]
where 2 is a phenomenological non-dimensional constant, VOTH -- the velocity of the collective motion of the nucleon in the rotating coordinate system. This interaction is employed for an interpretation of the structure of the rotational spectra of certain non-spherical nuclei with spin of ½. I t is assumed that H u n d ' s coupling case " b " is achieved in these nuclei. I t is indicated t h a t spin-rotation interaction m ay play an important role in the coupling scheme suggested by A. B o h r , B. M o t t e l s o n and S. N i l s s o n .
92. A n a l y s i s of s i n g l e c h a n n e l r e a c t i o n s . E. CLEMENTEL, Instituto di Fisica, Universit~ di Pado~a and C. VILLI, Instituto di fisica, Universit~ di Trieste, Italia. A method valid in S-and P - w a v e approximation 1) for phaseshift analysis of single channel scattering experiments has been extended to include D-waves and Coulomb effects. The least squares fit of the experimental data according to the expansion k~o(/~) = EA n cosn 0 provides the angular distribution coefficients A n, which are the primary data needed in the analysis. Expressing the real and imaginary part of the forward cross-section in terms of these coefficients, and taking into account the dependence of the A n's on the phaseshifts it is possible to show t h a t four sets of five phaseshifts are compatible, at a given energy, with the experimental data. This multiplicity is due, besides to the well known P-state ambiguity, to a D-state ambiguity. This method is valid also for incoming charged particles, but in this case an iteration