Short range asymptotic behavior of the wave-functions of interacting spin-half fermionic atoms with spin-orbit coupling: a model study

TL;DR

This paper analytically studies the short-range behavior of two interacting spin-half fermionic atoms with Rashba spin-orbit coupling, revealing perturbative effects of spin-orbit coupling on their wave-functions.

Contribution

It derives the analytic form of short-range wave-functions for interacting fermions with spin-orbit coupling, highlighting perturbative effects away from resonances.

Findings

Spin-orbit coupling affects short-range wave-function behavior perturbatively.

Analytic expressions for wave-functions are obtained in the zero momentum and angular momentum subspace.

Results are expected to be generally applicable beyond the specific model.

Abstract

We consider spin-half fermionic atoms with isotropic Rashba spin-orbit coupling in three directions. The interatomic potential is modeled by a square well potential. We derive the analytic form of the asymptotic wave-functions at short range of two fermions in the subspace of zero net momentum and zero total angular momentum. We show that the spin-orbit coupling has perturbative effects on the short range asymptotic behavior of the wave-functions away from resonances. We argue that our conclusion should hold generally.