Green's function method for single-particle resonant states in relativistic mean field theory

TL;DR

This paper develops a Green's function approach within relativistic mean field theory to accurately compute single-particle bound and resonant states, demonstrating excellent agreement with other established methods.

Contribution

It introduces a Green's function method in coordinate space for relativistic mean field theory to unify the treatment of bound and resonant states.

Findings

Accurately extracts energies and widths of resonant states.

Achieves excellent agreement with other methods.

Provides a unified framework for bound and resonant states.

Abstract

Relativistic mean field theory is formulated with the Green's function method in coordinate space to investigate the single-particle bound states and resonant states on the same footing. Taking the density of states for free particle as a reference, the energies and widths of single-particle resonant states are extracted from the density of states without any ambiguity. As an example, the energies and widths for single-neutron resonant states in $^{120}$Sn are compared with those obtained by the scattering phase-shift method, the analytic continuation in the coupling constant approach, the real stabilization method and the complex scaling method. Excellent agreements are found for the energies and widths of single-neutron resonant states.