Anisotropic pseudo-potential for polarized dilute quantum gases

TL;DR

This paper derives an anisotropic pseudopotential for polarized dilute quantum gases, useful for modeling interactions in systems with external fields, and expresses it in terms of scattering matrices and derivatives of delta functions.

Contribution

It introduces a rigorous derivation of an anisotropic pseudopotential incorporating dipolar and quadrupolar interactions, expanding the tools for modeling polarized quantum gases.

Findings

Pseudopotential expressed via reactance matrix and delta-function derivatives.

Includes both isotropic and anisotropic interaction components.

Provides two-body matrix element in plane wave basis.

Abstract

Anisotropic pseudopotential relevant to collisions of two particles polarized by external field is rigorously derived and its properties are investigated. Such low-energy pseudopotential may be useful in describing collective properties of dilute quantum gases, such as molecules polarized by electric field or metastable $^3P_2$ atoms polarized by magnetic field. The pseudopotential is expressed in terms of reactance (K--) matrix and derivatives of Dirac delta-function. In most applications it may be represented as a sum of traditional spherically-symmetric contact term and anisotropic part. The former contribution may be parameterized by a generalized scattering length. The anisotropic part of pseudopotential may be characterized by off-diagonal scattering length for dipolar interactions and off-diagonal scattering volume for quadrupolar interactions. Two-body matrix element of the pseudopotential in a basis of plane waves is also derived.