Two particles interacting via a contact interaction on $S^2$

TL;DR

This paper extends finite-volume Lüscher formulas to particles on a spherical surface, accurately determining their spectrum and applying it to predict properties of two-nucleon halo nuclei.

Contribution

It introduces a method to analyze two-particle spectra on a curved surface, extending existing formulas to non-trivial geometries.

Findings

Derived precise spectrum for two particles on $S^2$

Identified effects of non-inertial frames on solutions

Predicted spectra of two-nucleon halo nuclei and matched experimental data

Abstract

We consider two particles interacting via a contact interaction that are constrained to a sphere, or $S^2$. We determine their spectrum to arbitrary precision and for arbitrary angular momentum. We show how the non-inertial frame leads to non-trivial solutions for different angular momenta. Our results represent an extension of the finite-volume L\"uscher formulas but now to a non-trivial geometry. We apply our results to predict the spectrum of select two-nucleon halo nuclei and compare with experimental results.