The degenerate Fermi gas with renormalized density-dependent interactions in the K harmonic approximation

We present a simple implementation of a density-dependent, zero-range interactions in a degenerate Fermi gas described in hyperspherical coordinates. The method produces a 1D effective potential which accurately describes the ground state energy as a function of the hyperradius, the rms radius of the two spin component gas throughout the unitarity regime. In the unitarity regime the breathing mode frequency is found to limit to the non-interacting value. A dynamical instability, similar to the Bosenova, is predicted to be possible in gases containing more than three spin components, for large, negative, two-body scattering lengths.