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

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.

arXiv comment22 pages, 3 figures Accepted version (with some typo corrections)

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• Variational approximations to exact solutions in shell-model valence spaces: systematic calculations in the $sd$-shell
• Application of efficient generator-coordinate subspace-selection algorithm to neutrinoless double-$\beta$ decay
• Symmetry-projected variational calculations with the numerical suite TAURUS II. Configuration mixing of symmetry-projected reference states
• Quantum-number projected generator coordinate method for ${}^{21}$Ne with a chiral two-nucleon-plus-three-nucleon interaction
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• NuLattice: Ab initio computations of atomic nuclei on lattices
• Mean-field approximation on steroids: exact description of the deuteron
• Ab initio study in the island of inversion within the two-major-shell valence space