Heavy atomic nuclei have an excess of neutrons over protons, which leads to the formation of a neutron skin whose thickness is sensitive to details of the nuclear force. This links atomic nuclei to properties of neutron stars, thereby relating objects that differ in size by orders of magnitude. The nucleus²⁰⁸Pb is of particular interest because it exhibits a simple structure and is experimentally accessible. However, computing such a heavy nucleus has been out of reach for ab initio theory. By combining advances in quantum many-body methods, statistical tools and emulator technology, we make quantitative predictions for the properties of²⁰⁸Pb starting from nuclear forces that are consistent with symmetries of low-energy quantum chromodynamics. We explore 10⁹different nuclear force parameterizations via history matching, confront them with data in select light nuclei and arrive at an importance-weighted ensemble of interactions. We accurately reproduce bulk properties of²⁰⁸Pb and determine the neutron skin thickness, which is smaller and more precise than a recent extraction from parity-violating electron scattering but in agreement with other experimental probes. This work demonstrates how realistic two- and three-nucleon forces act in a heavy nucleus and allows us to make quantitative predictions across the nuclear landscape.

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.

The nuclear charge radius of ${}^{32}\mathrm{Si}$ was determined using collinear laser spectroscopy. The experimental result was confronted with ab initio nuclear lattice effective field theory, valence-space in-medium similarity renormalization group, and mean field calculations, highlighting important achievements and challenges of modern many-body methods. The charge radius of ${}^{32}\mathrm{Si}$ completes the radii of the mirror pair ${}^{32}\mathrm{Ar}\text{−}{}^{32}\mathrm{Si}$, whose difference was correlated to the slope $L$ of the symmetry energy in the nuclear equation of state. Our result suggests $L\le 60\mathrm{MeV}$, which agrees with complementary observables.

We present converged ab initio calculations of structure factors for elastic spin-dependent WIMP scattering off all nuclei used in dark matter direct-detection searches: ${}^{19}\mathrm{F}$, ${}^{23}\mathrm{Na}$, ${}^{27}\mathrm{Al}$, ${}^{29}\mathrm{Si}$, ${}^{73}\mathrm{Ge}$, ${}^{127}\mathrm{I}$, and ${}^{129,131}\mathrm{Xe}$. From a set of established two- and three-nucleon interactions derived within chiral effective field theory, we construct consistent WIMP-nucleon currents at the one-body level, including effects from axial-vector two-body currents. We then apply the in-medium similarity renormalization group to construct effective valence-space Hamiltonians and consistently transformed operators of nuclear responses. Combining the recent advances of natural orbitals with three-nucleon forces expressed in large spaces, we obtain basis-space converged structure factors even in heavy nuclei. Generally results are consistent with previous calculations but large uncertainties in ${}^{127}\mathrm{I}$ highlight the need for further study.