A NEW APPROACH TO THE CALCULATION OF DEFORMED NUCLEI

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A NEW APPROACH TO THE CALCULATION OF DEFORMED NUCLEI

Yu. Grin

To cite this version:

Yu. Grin. A NEW APPROACH TO THE CALCULATION OF DEFORMED NUCLEI. Journal de

Physique Colloques, 1971, 32 (C6), pp.C6-201-C6-201. �10.1051/jphyscol:1971641�. �jpa-00214859�

JOURNAL

DE

Colloque C6, supplkment au no 11-12, Tome 32, Novembre-Dkcembre 1971, page C6-201

A NEW APPROACH TO THE CALCULATION OF DEFORMED NUCLEI

Yu. T. GRIN

Kurchatov Institut of Atomic Energy, Moscou, USS R

RCsumC. - L'utilisation de la methode de l'harmonique K pour le calcul des noyaux dCformes est presentee.

Abstract.

The application of the K-harmonic method for the calculation of deformed nuclei is given.

Investigation of the structure of light nuclei is of great interest for the nuclear theory. The characteristic feature of this structure is existence of many-particle excitations. Thus, the theory should use realistic N-N potentials describing N-N scattering phases up to about 300 MeV and a t the same time allowing to explain structure of bound (or quasibound) nuclear states, particularly, many-particle excitation structure.

Recently the method of hyperspherical functions (K-harmonics) has been developed for the description of the structure of light deformed nuclei [I]. In this method (the simplest variant of which can be regarded as the variation method) the wave function of the nucleus consisting of A nucleons is taken as

where q(Xi) is the wave function of the collective motion depending on the collective variables in the system connected with the main nucleus axes

@( ... ^F, ...) is the internal wave function depending on nucleon coordinates counted from the center of the nucleus mass. %(Xi) is the normalization factor.

The @( ... F, ...) function is assumed to be harmonic along three coordinate axes and is defined by the quantum numbers of K,, K,, K,-harmonics along the appropriate axes. It is chosen as a determinant constructed fiom the one-particle function U, which for conciseness of notation we shall denote by the index [n, n, n,].

A

where L,, is the spin-isospin function, K i = nis.

s = 1

The function with K = K,, will always correspond to the ground state. The order of population is as

follows : [OOO] ; [loo] ; [OlO] ; [OOl] ; [200] ; [020] ; [002] ; [I 101 ; [loll, etc. The sequence of popula- tion inside the shell i.e. with the given total K = K, + K, + K3 but different Kl, K,, K3 is deter- mined by the minimality of the state energy.

The equation for q(Xi) has the form

h2 d2

- -

2 m z1 ^[*+

+ ^{( A + 2 K i - 2)(A + 2 K i - 4)}

4 x;

where W(Xi) is the matrix element of the N-N inter- action. The nucleon-nucleon potential is central and is written as

where are the projection operators acting upon the spin and isospin particle variables. Thus, choosing a definite N-N potential one can solve equation 3, determine p(Xi) and then, knowing the total wave function, find the characteristics of the deformed nuclei.

The ground states of nuclei in the 0 p and 0 d-1 s shells were investigated in works [2] and [3]. Binding energies, radii, quadrupole moments and forms were calculated. The excited states of cluster type in C12, 016, ca40 were studied in works [4] and [5]. It was found that many excited states have nucleon distribu- tion substantially different from that in the ground state.

The comparison of the calculated data with the experiment shows that such a n approach describes the experiment well. The method appeared to be convenient for the description of deformed and cluster states.

It should be pointed out that no prescribed self- consistent field is used in this method.

References

[I] GRIN (Yu. T.), J. NucI. Phys. (USSR), 1970, 12, 927. [41 GRIN (Yu. T.), LEINSON (L. B.), J. Nuel. Phys. (USSR), [2] GRIN (Yu. T.), KOCHETOV (A. B.), J. Nuel. Phys. 1971, 14, 536.

(USSR), 1970, 12, 1154. [5] GRIN flu. T.), LEINSON (L. B.), Phys. Letters (to be [3] GRIN (Yu. T.), KOCHETOV (A. B.), ANAN'KIN (A. I.), published).

J . Nucl. Phys. (USSR), 1971, 14, 953.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971641