Particle permutation symmetry of multishell states. I. Two shells

Abstract

A method is developed for constructing N-particle states of definite symmetry from n1-particle and n2-particle states of definite symmetry where N=n1+n2. A canonical resolution of the attendant multiplicity question is given. The results, which are a first step toward the construction of appropriate coefficients of fractional parentage, do not rely upon any particular form for the N-particle Hamiltonian. Rather, the results are based entirely upon properties of the symmetric groups Sn1, Sn2, and SN. The group theoretic problem which is the construction of irreducible representations of SN from those of Sn1 ×Sn2 is solved using induced representation theory together with projection operator techniques.