Non-divergent pseudo-potential treatment of spin-polarized fermions under 1D and 3D harmonic confinement
Atomic Physics
2009-11-10 v1
Abstract
Atom-atom scattering of bosonic one-dimensional (1D) atoms has been modeled successfully using a zero-range delta-function potential, while that of bosonic 3D atoms has been modeled successfully using Fermi-Huang's regularized s-wave pseudo-potential. Here, we derive the eigenenergies of two spin-polarized 1D fermions under external harmonic confinement interacting through a zero-range potential, which only acts on odd-parity wave functions, analytically. We also present a divergent-free zero-range potential treatment of two spin-polarized 3D fermions under harmonic confinement. Our pseudo-potential treatments are verified through numerical calculations for short-range model potentials.
Keywords
Cite
@article{arxiv.physics/0406022,
title = {Non-divergent pseudo-potential treatment of spin-polarized fermions under 1D and 3D harmonic confinement},
author = {K. Kanjilal and D. Blume},
journal= {arXiv preprint arXiv:physics/0406022},
year = {2009}
}
Comments
9 pages, 4 figures (subm. to PRA on 03/15/2004)