Nucleon-Nucleon Scattering in a Harmonic Potential

TL;DR

This paper demonstrates a method to extract free-space nucleon-nucleon scattering phase shifts from finite-volume energy eigenvalues obtained in a harmonic potential, potentially enabling ab-initio calculations for complex nuclear systems.

Contribution

It introduces a numerical approach to reconstruct scattering phase shifts from bound-state energy levels in a harmonic trap, linking finite-volume spectra to continuum scattering data.

Findings

Extracted phase shifts agree with exact solutions within uncertainties

Method can be applied to complex nuclear systems like n-d, n-t, or n-alpha

Potential for determining scattering amplitudes from bound-state calculations

Abstract

The discrete energy-eigenvalues of two nucleons interacting with a finite-range nuclear force and confined to a harmonic potential are used to numerically reconstruct the free-space scattering phase shifts. The extracted phase shifts are compared to those obtained from the exact continuum scattering solution and agree within the uncertainties of the calculations. Our results suggest that it might be possible to determine the amplitudes for the scattering of complex systems, such as n-d, n-t or n-alpha, from the energy-eigenvalues confined to finite volumes using ab-initio bound-state techniques.