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arXiv · 2106.08841

Variational approximations to exact solutions in shell-model valence spaces: systematic calculations in the $sd$-shell

Adrián Sánchez-Fernández·Benjamin Bally·Tomás R. Rodríguez
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Abstract

We study the ability of variational approaches based on self-consistent mean-field and beyond-mean-field methods to reproduce exact energies and electromagnetic properties of the nuclei defined within the $sd$-shell valence space using the non-trivial USD Hamiltonian. In particular, Hartree-Fock-Bogoliubov (HFB), variation after particle-number projection (VAPNP) and projected generator coordinate methods (PGCM) are compared to exact solutions {obtained by} the full diagonalization of the Hamiltonian. We analyze the role played by the proton-neutron ($pn$) mixing as well as the quadrupole and pairing degrees of freedom (including both isoscalar and isovector channels) in the description of the spectra of even-even, even-odd and odd-odd nuclei in the whole $sd$-shell.

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Adrián Sánchez-Fernández, Benjamin Bally, Tomás R. Rodríguez. 2021-06-16. Variational approximations to exact solutions in shell-model valence spaces: systematic calculations in the $sd$-shell. https://doi.org/10.1103/physrevc.104.054306

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