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Chinese Physics C

Structure of the Correlated Pairs

Lu Da

Published Jan 1, 2003• 0 citations
OpenAlex

Abstract

A similar method to the H-F method for particles is developed to determine the structure of the pairs. A scheme for dealing with the problem caused by the seniority mixing is also proposed. In this scheme the independent D pairs are constructed by the seniority particles introduced in this paper, and the definition of the S pair is modified in order that it can commute with the D pairs.

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A similar method to the H-F method for particles is developed to determine the structure of the pairs. A scheme for dealing with the problem caused by the seniority mixing is also proposed. In this scheme the independent D pairs are constructed by the seniority particles introduced in this paper, and the definition of the S pair is modified in order that it can commute with the D pairs.
The present paper attempts to give independent descriptions of the collective degrees of freedom of nuclei such as the monopole and quadrupole ones in order to avoid the seniority mixing problem. This is done by the operatorized Bogoliubov transformation (OBT) which separates the degree of freedom from the rest described by the seniority particle operator which is not coupling to the pairs, and in terms of which the independent pair is composed. The OBT is derived in such a way that it can be generalized easily to include a new kind of “seniority particle operator” neither coupling to the nor to the pairs. In terms of this new particle operator the independent pair or the independent odd particle in odd nuclei is constructed.
A charge independent pairing interaction in j-j coupling scheme and a charge-spin independent pairing interaction in L-S coupling scheme are exactly solved in a degenerate model by the aid of group theory. Groups used here are independent of the number of states concerned unlike the usual shell model technique. Our method is deeply connected with the generalized Bogoliubov transformation and it is conjectured that this transformation combined with projection into the definite number and the isospin (symmetry) state is very useful for the treatment of pair-interacting many body system. The classification of states through the group used here are equivalent to the seniority scheme generalized for unlike particles and degenerate levels. Our method simplifies mathematics somewhat and derives easily some new properties of seniority scheme for unlike particles.