Benchmarking projected Hartree-Fock as an approximation

We benchmark angular-momentum projected 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, which 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.

From bound states to the continuum

This white paper reports on the discussions of the 2018 Facility for Rare Isotope Beams Theory Alliance (FRIB-TA) topical program From bound states to the continuum: Connecting bound state calculations with scattering and reaction theory. One of the biggest and most important frontiers in nuclear theory today is to construct better and stronger bridges between bound state calculations and calculations in the continuum, especially scattering and reaction theory, as well as teasing out the influence of the continuum on states near threshold. This is particularly challenging as many-body structure calculations typically use a bound state basis, while reaction calculations more commonly utilize few-body continuum approaches. The many-body bound state and few-body continuum methods use different language and emphasize different properties. To build better foundations for these bridges, we present an overview of several bound state and continuum methods and, where possible, point to current and possible future connections.