Scattering cluster wave functions on the lattice using the adiabatic projection method

TL;DR

This paper introduces a method to directly compute scattering observables from asymptotic cluster wave functions on the lattice, improving accuracy over traditional energy level methods.

Contribution

It demonstrates that scattering phase shifts can be extracted directly from asymptotic cluster wave functions, reducing sensitivity to errors compared to previous approaches.

Findings

Scattering phase shifts obtained from asymptotic wave functions are more accurate.

The method works effectively in both one and three dimensions.

It reduces the impact of stochastic and systematic errors.

Abstract

The adiabatic projection method is a general framework for studying scattering and reactions on the lattice. It provides a low-energy effective theory for clusters which becomes exact in the limit of large Euclidean projection time. Previous studies have used the adiabatic projection method to extract scattering phase shifts from finite periodic-box energy levels using L\"uschers method. In this paper we demonstrate that scattering observables can be computed directly from asymptotic cluster wave functions. For a variety of examples in one and three spatial dimensions, we extract elastic phase shifts from asymptotic cluster standing waves corresponding to spherical wall boundary conditions. We find that this approach of extracting scattering wave functions from the adiabatic Hamiltonian to be less sensitive to small stochastic and systematic errors as compared with using periodic-box energy levels.