# Scattering phase shifts and mixing angles for an arbitrary number of coupled channels on the lattice

## TL;DR

This paper introduces a lattice method to determine scattering phase shifts and mixing angles for multiple coupled channels, extending previous techniques limited to two channels, applicable to particles with any spin.

## Contribution

The paper presents a novel lattice approach for extracting scattering parameters in systems with arbitrary coupled channels, surpassing previous two-channel limitations.

## Key findings

- Method accurately reproduces continuum phase shifts and mixing angles.
- Applicable to particles with any spin, demonstrated with spin-1 bosons.
- Shows agreement with Schrödinger equation solutions for test potentials.

## Abstract

We present a lattice method for determining scattering phase shifts and mixing angles for the case of an arbitrary number of coupled channels. Previous nuclear lattice effective field theory simulations were restricted to mixing of up to two partial waves for scattering of two spin-$1/2$ particles, which is insufficient for analyzing nucleon-nucleus or nucleus-nucleus scattering processes. In the proposed method, the phase shifts and mixing angles are extracted from the radial wave functions obtained by projecting the three-dimensional lattice Hamiltonian onto the partial wave basis. We use a spherical wall potential as a boundary condition along with a channel-mixing auxiliary potential to construct the full-rank $S$ matrix. Our method can be applied to particles with any spin, but we focus here on scattering of two spin-$1$ bosons involving up to four coupled channels. For a considered test potential, the phase shifts and mixing angles extracted on the lattice are shown to agree with the ones calculated by solving the Schr\"odinger equation in the continuum.