Effective Field Theory and the Gamow Shell Model: The 6He Halo Nucleus

TL;DR

This paper integrates Halo/Cluster Effective Field Theory with the Gamow Shell Model to accurately describe the halo nucleus 6He, demonstrating the necessity of a three-body force for proper renormalization and binding energy prediction.

Contribution

It introduces a combined EFT and GSM framework for halo nuclei and shows the importance of a three-body force for correct system behavior.

Findings

Without three-body forces, the system collapses as cutoffs increase.

A single three-body force parameter suffices for proper renormalization.

The model reproduces the experimental binding energy of 6He.

Abstract

We combine Halo/Cluster Effective Field Theory (H/CEFT) and the Gamow Shell Model (GSM) to describe the $0^+$ ground state of $\rm{^6He}$ as a three-body halo system. We use two-body interactions for the neutron-alpha particle and two-neutron pairs obtained from H/CEFT at leading order, with parameters determined from scattering in the p$_{3/2}$ and s$_0$ channels, respectively. The three-body dynamics of the system is solved using the GSM formalism, where the continuum states are incorporated in the shell model valence space. We find that in the absence of three-body forces the system collapses, since the binding energy of the ground state diverges as cutoffs are increased. We show that addition at leading order of a three-body force with a single parameter is sufficient for proper renormalization and to fix the binding energy to its experimental value.