Simple approximations and symmetry measures for model interactions
The operation of a central limit theorem in large model spaces yields a shape close to Gaussian for the smoothed eigenstate density distribution. This establishes the centroid and the width of the energy spectrum as quantities of fundamental importance and gives credence to a geometry associated with averages of the product of pairs of operators acting within a model space. The space is partitioned according to different group symmetries and simple approximations to the interaction Hamiltonian which reproduce the subspace centroids correctly and have a large fraction of the total width, are constructed, first in terms of the group invariants and then extended to include projections along other well-known operators to generate even a larger fraction of the full width. In the process a measure for the goodness of the group symmetries is developed. Numerical results for six ds shell interactions and for scalar-isospin, configuration-isospin, space symmetry, supermultiplet and SU(3) group structures are presented. © 1978.