Nuclear structure in a hierarchy of ideal spaces

Abstract

A new method permitting nuclear structure calculations for a system with an arbitrary number of fermions in an arbitrary number of subshells is developed through a generalization of the ideal space concept used in the boson methods. The nuclear shell problem is transcribed into a hierarchy of ideal spaces; the one-to-one correspondence between the states in each ideal space permits the generation of complete bases of antisymmetric states. The Hamiltonian matrix elements for the system are given. A generalization of the fractional parentage coefficients for such systems is obtained. The symmetries of those coefficients lead to a very important reduction in the complexity of the matrix elements.