Implementation of the three-neutron quantization condition

TL;DR

This paper implements a numerical approach to the three-neutron quantization condition, demonstrating how symmetries simplify calculations and exploring the potential of three-neutron spectroscopy to inform neutron interactions.

Contribution

The paper provides a practical implementation of the three-neutron quantization condition, including matrix construction, symmetry projection, and initial results with two-neutron interactions.

Findings

Finite-volume spectra computed in different frames.

Symmetry considerations reduce computational complexity.

Initial results show potential for constraining neutron interactions.

Abstract

We present an implementation of the three-neutron quantization condition (QC) derived in previous work. We construct the matrices appearing in the QC and determine solutions numerically. The symmetries of the QC allow the projection onto irreducible representations of the appropriate little group (depending on frame momentum), restricting the size of the matrices and reducing computational complexity. In this initial study, we include only two-neutron interactions, which are modeled based on experimental data for $I=1$ scattering amplitudes. We show examples of the finite-volume spectrum in two frames and for a range of energies, illustrating the potential and also the challenges of using three-neutron spectroscopy to constrain the underlying interactions.