# Analytical coupled-channels treatment of two-body scattering in the presence of three-dimensional isotropic spin-orbit coupling

## TL;DR

This paper develops an analytical framework to understand how three-dimensional isotropic spin-orbit coupling affects two-body scattering, revealing significant modifications in phase accumulation even at large length scales.

## Contribution

It introduces a generalized local frame transformation method to analytically describe phase accumulation in two-body scattering with spin-orbit coupling, validated by numerical comparisons.

## Key findings

- Phase accumulation is significantly modified by spin-orbit coupling.
- Analytical phase shifts match numerical results across energies.
- The framework simplifies understanding of spin-orbit effects in cold atom scattering.

## Abstract

It is shown that the single-particle spin-orbit coupling terms, which---in the cold atom context---are associated with synthetic gauge fields, can significantly and non-trivially modify the phase accumulation at small interparticle distances even if the length scale $(k_{\text{so}})^{-1}$ associated with the spin-orbit coupling term is significantly larger than the van der Waals length $r_{\text{vdW}}$ that characterizes the two-body interaction potential. A theoretical framework, which utilizes a generalized local frame transformation and accounts for the phase accumulation analytically, is developed. Comparison with numerical coupled-channels calculations demonstrates that the phase accumulation can, to a very good approximation, be described over a wide range of energies by the free-space scattering phase shifts---evaluated at a scattering energy that depends on $k_{\text{so}}$---and the spin-orbit coupling strength $k_{\text{so}}$.