Energy functional for the three-level Lipkin model

We compute the energy functional of a three-level Lipkin model via a Legrendre transform and compare exact numerical results with analytical solutions obtained from the random phase approximation (RPA). Except for the region of the phase transition, the RPA solutions perform very well. We also study the case of three non-degenerate levels and again find that the RPA solution agrees well with the exact numerical result. For this case, the analytical results give us insight into the form of the energy functional in the presence of symmetry-breaking one-body potentials.Comment: 6 pages, 5 figure

Final Report "Structure of Rare Isotopes"

The Junior Investigator grant 'Structure of Rare Isotopes' (DE-FG02-07ER41529) supported research in low-energy nuclear theory from September 1, 2007 to August 31, 2010. It was the main goal of the proposed research to develop and optimize an occupation-number-based energy functional for the computation of nuclear masses, and this aim has been reached. Furthermore, progress was made in linking two and three-body forces from low-momentum interactions to pairing properties in nuclear density functionals, and in the description of deformed nuclei within an effective theory

A classical two-body Hamiltonian model and its mean field approximation

We extend a recent billiard model of the nuclear N-body Hamiltonian to consider a finite two-body interaction. This permits a treatment of the Hamiltonian by a mean field theory, and also allows the possibility to model reactions between nuclei. The density and the mean field potential can be accurately described by a scaling function which shows the qualitative features of the liquid drop picture of the nucleus.Comment: 9 pages, 2 PS-figures, uses psfig.st