A new seniority scheme for non-degenerate single particle orbits

Ulrich Mutz

M. Ichimura

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.

Brian P. Anderson

Akito Arima, Hideo Kawarada

The seniority scheme introduced by Racah is generalized in the case of degenerate levels. Many formulae for the pure configuration j n are modified in order to calculate matrix elements in this generalized seniority scheme. It is especially the most interesting result that the diagonal matrix element of two-body operators between the states with the same seniority v can be expressed in terms of the matrix elements in the v -particle system. This result, of course, holds in the case of the pure configuration.

Débora Peres Menezes, Dennis Bonatsos A, Abraham Klein

Puru Jena, T. Pradhan