Hartree--Fock--Bogoliubov Approximation for Finite Systems

TL;DR

This paper analyzes the spectral properties of the Hartree-Fock-Bogoliubov equations in finite systems, focusing on the asymptotic behavior of quasiparticle wave functions, density distributions, and the effects of hole-particle coupling.

Contribution

It provides insights into the asymptotic behavior and normalization of quasiparticle wave functions, highlighting the continuum nature of deeply bound hole states due to coupling effects.

Findings

Deeply bound hole states acquire a width and behave as continuum states.

Proper normalization of quasiparticle wave functions is essential.

Coupling between hole and particle states affects spectral properties.

Abstract

Some general features of the spectrum of the Hartree-Fock-Bogoliubov equations are examined. Special attention is paid to the asymptotic behavior of the single quasiparticle wave functions (s.qp.w.fs.), matter density distribution and density of the pair condensate. It is shown that due to the coupling between hole and particle states,the deeply bound hole states acquire a width and have to be treated as continuum states. The proper normalization of the s.qp.w.fs. is discussed.