Symmetry-projected variational calculations with the numerical suite TAURUS I. Variation after particle-number projection

TL;DR

The paper introduces TAURUS_vap, a versatile numerical code for symmetry-unrestricted variational calculations with particle-number projection, applicable to various nuclear states and interactions, enhancing capabilities in nuclear structure modeling.

Contribution

The paper presents a new computational tool that performs variation after particle-number projection for diverse nuclear states without assuming specific orbitals or parity.

Findings

Successfully demonstrated calculations with empirical and chiral interactions.

Applicable to even-even, odd-even, and odd-odd nuclei.

Flexible in handling multiple constraints and symmetries.

Abstract

We present the numerical code TAURUS_vap that solves the variation after particle-number projection equations for symmetry-unrestricted real Bogoliubov quasiparticle states represented in a spherical harmonic oscillator basis. The model space considered is invariant under spatial and isospin rotations but no specific set of orbits is assumed such that the code can carry out both valence-space and no-core calculations. In addition, no number parity is assumed for the Bogoliubov quasiparticle states such that the code can be used to describe even-even, odd-even and odd-odd nuclei. The variational procedure can be performed under several simultaneous constraints on the expectation values of a variety of operators such as the multipole deformations, the pairing field or the components of the angular momentum. To demonstrate the potential and versatility of the code, we perform several example calculations using an empirical shell-model interaction as well as a chiral interaction. The ability to perform advanced variational Bogoliubov calculations offered by this code will, we hope, be beneficial to the shell model and ab initio communities.