Two and Three Nucleons in a Trap and the Continuum Limit

TL;DR

This paper models two- and three-nucleon systems in a harmonic trap using pionless effective field theory, deriving interactions, energy levels, and phase shifts, and compares results with experimental data.

Contribution

It introduces a method to analyze few-nucleon systems in a trap using EFT up to NLO, including the three-nucleon force and continuum limit extraction.

Findings

Accurate trapped energy levels for two and three nucleons.

Determination of the three-nucleon force for triton stability.

Good agreement of quartet scattering length with experimental data.

Abstract

We describe systems of two and three nucleons trapped in a harmonic-oscillator potential with interactions from the pionless effective field theory up to next-to-leading order (NLO). We construct the two-nucleon interaction using two-nucleon scattering information. We calculate the trapped levels in the three-nucleon system with isospin $T=1/2$ and determine the three-nucleon force needed for stability of the triton. We extract neutron-deuteron phase shifts, and show that the quartet scattering length is in good agreement with experimental data.