A microscopic framework for dynamical supersymmetry in nuclei

Abstract

We discuss and explore new aspects of the generalized Dyson mapping of nuclear collective superalgebras composed of an arbitrary fermion-pair algebra and a set of single-fermion creation/annihilation operators. It is shown that a direct consequence of the particular mapping procedure is the conservation of the total number of ideal particles in the resulting boson-fermion system. This provides a microscopic framework for the phenomenological supersymmetric models based on the U(6/2Omega) dynamical superalgebras. Attention is paid to the mapping of single-fermion creation and annihilation operators whose detailed form cannot be determined on the phenomenological level. We derive the general expansion of the single-fermion images that result from the similarity transformation employed to ensure non-redundant bosonisation in the ideal space. The method is then illustrated in an application to the SO(4) collective algebra, a natural extension of the SU(2) seniority model.