Benchmarking projected Hartree-Fock as an approximation

TL;DR

This paper evaluates the effectiveness of angular-momentum projected Hartree-Fock calculations as an approximation to full configuration-interaction results, showing reasonable agreement in excitation spectra and highlighting the importance of shape coexistence and advanced optimization techniques.

Contribution

It demonstrates that projected Hartree-Fock with shape mixing and gradient descent can effectively approximate complex nuclear spectra, improving upon traditional methods.

Findings

Good agreement in excitation spectra for many nuclides

Shape coexistence improves spectral accuracy in sd- and pf-shells

Broad reproduction of odd-even staggering in binding energies

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.