Defining the $p$-wave scattering volume in the presence of dipolar interactions

TL;DR

This paper generalizes the concept of $p$-wave scattering volume to include dipolar interactions, providing a new framework for understanding ultracold collisions with anisotropic long-range forces.

Contribution

It introduces a novel definition of the $p$-wave scattering volume that accounts for dipolar interactions using an asymptotic model and a single parameter for short-range effects.

Findings

The generalized scattering volume captures the effects of dipolar interactions.

The approach incorporates anisotropic dipole-dipole potential explicitly.

Short-range interactions are characterized by a single parameter linked to $s$-wave scattering.

Abstract

The definition of the scattering volume for $p$-wave collisions needs to be generalized in the presence of dipolar interactions for which the potential decreases with the interparticle separation as $1/R^3$. Here, we propose a generalized definition of the scattering volume characterizing the short-range interactions in odd-parity waves, obtained from an analysis of the $p$-wave component of the two-body threshold wave function. Our approach uses an asymptotic model and introduces explicitly the anisotropic dipole-dipole interaction, which governs the ultracold collision dynamics at long-range. The short-range interactions, which are essential to describe threshold resonances, are taken into account by a single parameter which is determined by the field-free $s$-wave scattering length.