Solving for the Particle-Number-Projected HFB Wavefunction

TL;DR

This paper extends a particle-number-conserving nuclear pairing theory to more general cases where multiple single-particle levels share quantum numbers, using equations of motion for density matrices, and tests it on simple models.

Contribution

It introduces a generalized approach for particle-number projection in HFB wavefunctions using equations of motion, broadening previous BCS-type models.

Findings

Successfully applied to two-level model with factorizable pairing

Extended to semi-realistic zero-range delta interaction model

Demonstrated effectiveness in more complex pairing scenarios

Abstract

Recently we proposed a particle-number-conserving theory for nuclear pairing [Jia, Phys. Rev. C 88, 044303 (2013)] through the generalized density matrix formalism. The relevant equations were solved for the case when each single-particle level has a distinct set of quantum numbers and could only pair with its time-reversed partner (BCS-type Hamiltonian). In this work we consider the more general situation when several single-particle levels could have the same set of quantum numbers and pairing among these levels is allowed (HFB-type Hamiltonian). The pair condensate wavefunction (the HFB wavefunction projected onto good particle number) is determined by the equations of motion for density matrix operators instead of the variation principle. The theory is tested in the simple two-level model with factorizable pairing interactions and the semi-realistic model with the zero-range delta interaction.