Density Functional Theory Approach to Shell Model Hamiltonians

Density Functional Theory (DFT) is a well established method of obtaining ground state (g.s.) energies and one-body densities for systems of interacting fermions, such as electron and nucleons. DFT is mostly used in nuclear physics via short-range, Skyrme-type, interactions in coordinate space. We investigate a different density functional approach in finite model spaces, specific to shell model calculations. We attempt to extract the density functional form and the associated parameters in a fixed model space, by comparing the DFT results with the exact shell model calculations for small number of particles/holes. We than use the density functional to calculate cases with more particles that are more challenging for the shell model. Examples in the sd and fp model spaces will be presented.