Effective Range Expansion for the Interaction Defined on the Lattice

The relation between the interaction parameters for fermions on the spatial lattice and the two-body $T$ matrix is discussed. The presented method allows determination of the interaction parameters through the relatively simple computational scheme which include the effect of finite lattice spacing. In particular the relation between the interaction parameters and the effective range expansion parameters is derived in the limit of large lattices.Comment: Proceedings from XVI Nuclear Physics Workshop in Kazimierz Dolny, Poland. Accepted to publish in the International Journal of Modern Physics E, vol. 1

Neutron Stars and Quantum Billiards

Homogeneous neutron matter at subnuclear densities becomes unstable towards the formation of inhomogeneities. Depending on the average value of the neutron density one can observe the appearance of either bubbles, rods, tubes or plates embeded in a neutron gas. We estimate the quantum corrections to the ground state energy (which could be termed either shell correction or Casimir energy) of such phases of neutron matter. The calculations are performed by evaluating the contribution of the shortest periodic orbits in the Gutzwiller trace formula for the density of states. The magnitude of the quantum corrections to the ground state energy of neutron matter are of the same order as the energy differences between various phases.Comment: 11 pages, contribution to the Nobel Symposium on Quantum Chaos Y2K, Backaskog Castle, Sweden, June 13-17, 200