Quasi-particle continuum and resonances in the Hartree-Fock-Bogoliubov theory

TL;DR

This paper investigates the structure of the unbound quasi-particle spectrum in weakly bound nuclei using various methods, highlighting the effectiveness of the stabilization method and Thomas-Fermi approximation for resonance analysis.

Contribution

The study introduces and compares methods for analyzing the unbound quasi-particle spectrum in HFB theory without imposing scattering boundary conditions, emphasizing the Thomas-Fermi approximation's effectiveness.

Findings

The stabilization method effectively estimates resonance widths except for very narrow resonances.

The Thomas-Fermi approximation is highly effective for large-box coordinate-space HFB calculations.

Various methods can analyze the unbound spectrum without imposing scattering boundary conditions.

Abstract

The quasi-particle energy spectrum of the Hartree-Fock-Bogoliubov (HFB) equations contains discrete bound states, resonances, and non-resonant continuum states. We study the structure of the unbound quasi-particle spectrum of weakly bound nuclei within several methods that do not rely on imposing scattering or outgoing boundary conditions. Various approximations are examined to estimate resonance widths. It is shown that the stabilization method works well for all HFB resonances except for very narrow ones. The Thomas-Fermi approximation to the non-resonant continuum has been shown to be very effective, especially for coordinate-space HFB calculations in large boxes that involve huge amounts of discretized quasi-particle continuum states.