Study of three-neutron bound and continuum states

TL;DR

This paper investigates the existence of three-neutron resonance states using numerical Faddeev calculations and finds no evidence for such resonances, highlighting limitations of trapping methods.

Contribution

It provides a detailed analysis of three-neutron states with realistic potentials and critically examines different extrapolation methods for resonance identification.

Findings

No evidence of 3n resonance states with realistic NN potentials.

Extrapolation with attractive potentials suggests no resonance, while trapping methods may falsely indicate resonances.

Trapping method has a fundamental defect leading to potential false positives.

Abstract

The three-neutron ($3n$) system is studied by numerical calculations with the Faddeev three-body formalism for a realistic nucleon-nucleon (NN) potential. A response function for the transition from ${}^3\mathrm{H}$ to $3n$ continuum states by an isospin excitation operator is calculated, from which no evidence of $3n$ resonance state is found. Different methods to extrapolate the $3n$ energy from bound state energies with an extra attractive effect to the NN potential are examined. While extrapolations with attractive effects by enhanced NN potentials or three-body potentials result the non-existence of $3n$ resonance states, one by external trapping potentials leads to a positive $3n$ energy, which may be considered as a resonance state. It is found that this contradiction is due to a general defect of the trapping method.