Quantum Monte Carlo calculations of two neutrons in finite volume

TL;DR

This paper uses quantum Monte Carlo methods to study two neutrons in a finite volume, analyzing finite-volume effects and extracting scattering parameters relevant for nuclear physics.

Contribution

It introduces auxiliary-field diffusion Monte Carlo calculations for two neutrons with contact and chiral interactions, comparing results with exact methods and analyzing finite-volume effects.

Findings

Finite-volume effects are quantitatively characterized.

Scattering parameters are extracted using L"uscher's formula.

Results agree with exact diagonalization for small systems.

Abstract

Ab initio calculations provide direct access to the properties of pure neutron systems that are challenging to study experimentally. In addition to their importance for fundamental physics, their properties are required as input for effective field theories of the strong interaction. In this work, we perform auxiliary-field diffusion Monte Carlo calculations of the ground and first excited state of two neutrons in a finite box, considering a simple contact potential as well as chiral effective field theory interactions. We compare the results against exact diagonalizations and present a detailed analysis of the finite-volume effects, whose understanding is crucial for determining observables from the calculated energies. Using the L\"uscher formula, we extract the low-energy S-wave scattering parameters from ground- and excited-state energies for different box sizes.