Hartree-Fock-Bogoliubov solution of the pairing Hamiltonian in finite nuclei

TL;DR

This paper reviews the Hartree-Fock-Bogoliubov (HFB) theory for describing nucleonic superfluidity in finite nuclei, covering theoretical foundations, mathematical structure, and key aspects like pairing functional and continuum treatment.

Contribution

It provides a comprehensive overview of the HFB formalism applied to finite nuclei, including derivations, theoretical insights, and discussion of advanced topics like regularization and odd systems.

Findings

Derivation of HFB equations within nuclear density functional theory

Analysis of pairing functional and continuum structure

Discussion of regularization and odd particle number treatment

Abstract

We present an overview of the Hartree-Fock-Bogoliubov (HFB) theory of nucleonic superfluidity for finite nuclei. After introducing basic concepts related to pairing correlations, we show how the correlated pairs are incorporated into the HFB wave function. Thereafter, we present derivation and structure of the HFB equations within the superfluid nuclear density functional formalism and discuss several aspects of the theory, including the unitarity of the Bogoliubov transformation in truncated single-particle and quasiparticle spaces, form of the pairing functional, structure of the HFB continuum, regularization and renormalization of pairing fields, and treatment of pairing in systems with odd particle numbers.