Non-divergent pseudo-potential treatment of spin-polarized fermions under 1D and 3D harmonic confinement

Details Non-divergent pseudo-potential treatment of spin-polarized fermions under 1D and 3D harmonic confinement Non-divergent pseudo-potential treatment of spin-polarized fermions under 1D and 3D harmonic confinement

2004-06-04

arxiv.org/abs/physics/0406022v1

Physics

Atomic Physics

9 pages, 4 figures (subm. to PRA on 03/15/2004)

Scientific paper

10.1103/PhysRevA.70.042709

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.

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