Benchmarking angular-momentum 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 40Mg. 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.