Hyperspherical Description of the Degenerate Fermi Gas: S-wave Interactions
Abstract
We present a unique theoretical description of the physics of the spherically trapped -atom degenerate Fermi gas (DFG) at zero temperature based on an ordinary Schr\"{o}dinger equation with a microscopic, two body interaction potential. With a careful choice of coordinates and a variational wavefunction, the many body Schr\"{o}dinger equation can be accurately described by a \emph{linear}, one dimensional effective Schr\"{o}dinger equation in a single collective coordinate, the rms radius of the gas. Comparisons of the energy, rms radius and peak density of ground state energy are made to those predicted by Hartree-Fock (HF). Also the lowest radial excitation frequency (the breathing mode frequency) agrees with a sum rule calculation, but deviates from a HF prediction.
Keywords
Cite
@article{arxiv.cond-mat/0607340,
title = {Hyperspherical Description of the Degenerate Fermi Gas: S-wave Interactions},
author = {Seth T. Rittenhouse and M. J. Cavagnero and Javier von Stecher and Chris H. Greene},
journal= {arXiv preprint arXiv:cond-mat/0607340},
year = {2009}
}