Three-neutron bound and continuum states

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 in the nonexistence 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.