Benchmarking angular-momentum projected Hartree-Fock as an approximation

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 Mg-40. 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.

Automated summary

The study compares angular-momentum projected-after-variation Hartree-Fock calculations to full configuration-interaction results in a shell model basis, finding reasonably good agreement in the excitation spectra. Shape coexistence and mixing in shape coexistence improves the spectrum, particularly in the sd- and pf-shells. While the complex spectra of germanium isotopes present challenges, the projected Hartree-Fock method generally provides a better description of low-lying nuclear spectra than expected, with the use of gradient descent and unrestricted shapes being key to its success.