New approach to multishell calculations in multiple angular momentum coupling schemes.

Abstract

The procedure developed recently to calculate single-shell wave functions and matrix elements for multiple angular momentum shell-model calculations is extended to the multishell case. This was based on a factorization procedure introduced by Jahn. As a consequence of the factorization, coefficients of fractional parentage between states of arbitrary symmetry must be constructed to build up single-shell N-particle states from single-shell N-1-particle states. Multishell N-particle states are built up recursively from multishell N-1-particle states by using outer-product isoscalar factors. Symmetrized multishell states in one angular momentum subspace are combined with states of conjugate symmetry in a second angular momentum subspace to construct fermion wave functions. This is done using inner-product isoscalar factors. The coefficients of fractional parentage, outer-product isoscalar factors, and inner-product isoscalar factors are computed recursively using a matrix diagonalization algorithm. Shell-model matrix elements are constructed from these factors by using a new sum over path overlaps method. This computational procedure involving factorization is substantially more efficient than computational procedures which do not exploit factorization.