Benchmarking projected Hartree-Fock as an approximation

Abstract

We benchmark angular-momentum projected{-after-variation} Hartree-Fock calculations as an approximation to full configuration-interaction results in a shell model basis. For such a simple approximation we find reasonably good agreement between excitation spectra, including for many odd-$A$ and odd-odd nuclides. We frequently find shape coexistence, in the form of multiple Hartree-Fock minima; {mixing in shape coexistence, the first step beyond single-reference projected Hartree-Fock}, demonstrably improves the spectrum in the $sd$- and $pf$-shells. The complex spectra of germanium isotopes present a challenge: for even $A$ the spectra are only moderately good and those of odd $A$ bear little resemblance to the configuration-interaction results. Despite this failure we are able to broadly reproduce the odd-even staggering of ground state binding energies, save for germanium isotopes with $N>40$. To illustrate potential applications, we compute the spectrum of the recently measured dripline nuclide ${}^{40}$Mg. All in all, projected Hartree-Fock often provides a better description of low-lying nuclear spectra than one might expect. Key to this is the use of gradient descent and unrestricted shapes.

arXiv comment21 pages, 11 figures, 2 tables

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• A Pfaffian formulation for matrix elements of three-body operators in multiple quasi-particle configurations
• The pervasiveness of shape coexistence in nuclear pair condensates
• A Problem in the Statistical Description of Beta-Delayed Neutron Emission
• Systematic analysis of double Gamow-Teller sum rules
• Symmetry breaking and restoration on a fermionic quantum ring
• Benchmarking projected generator coordinate method for nuclear Gamow-Teller transitions