On the possibility of generating a 4-neutron resonance with a {\boldmath $T=3/2$} isospin 3-neutron force

TL;DR

This paper investigates the theoretical feasibility of creating a narrow four-neutron resonance by introducing a specific three-neutron force, analyzing its consistency with known nuclear states, and solving the four-neutron Schrödinger equation using complex scaling.

Contribution

The study introduces a phenomenological T=3/2 three-neutron force and analyzes its strength needed to generate a 4-neutron resonance, using ab initio calculations with complex scaling.

Findings

A remarkably attractive T=3/2 three-neutron force is required to produce a narrow 4-neutron resonance.

The proposed three-neutron force is consistent with low-lying T=1 states of light nuclei.

Complex scaling method effectively solves the 4-neutron Schrödinger equation for resonance analysis.

Abstract

We consider the theoretical possibility to generate a narrow resonance in the four neutron system as suggested by a recent experimental result. To that end, a phenomenological $T=3/2$ three neutron force is introduced, in addition to a realistic $NN$ interaction. We inquire what should be the strength of the $3n$ force in order to generate such a resonance. The reliability of the three-neutron force in the $T=3/2$ channel is exmined, by analyzing its consistency with the low-lying $T=1$ states of $^4$H, $^4$He and $^4$Li and the $^3{\rm H} + n$ scattering. The {\it ab initio} solution of the $4n$ Schr\"{o}dinger equation is obtained using the complex scaling method with boundary conditions appropiate to the four-body resonances. We find that in order to generate narrow $4n$ resonant states a remarkably attractive $3N$ force in the $T=3/2$ channel is required.