Opportunities for fundamental physics research with radioactive molecules.

Molecules containing short-lived, radioactive nuclei are uniquely positioned to enable a wide range of scientific discoveries in the areas of fundamental symmetries, astrophysics, nuclear structure, and chemistry. Recent advances in the ability to create, cool, and control complex molecules down to the quantum level, along with recent and upcoming advances in radioactive species production at several facilities around the world, create a compelling opportunity to coordinate and combine these efforts to bring precision measurement and control to molecules containing extreme nuclei. In this manuscript, we review the scientific case for studying radioactive molecules, discuss recent atomic, molecular, nuclear, astrophysical, and chemical advances which provide the foundation for their study, describe the facilities where these species are and will be produced, and provide an outlook for the future of this nascent field.

Local Bayesian Dirichlet mixing of imperfect models.

To improve the predictability of complex computational models in the experimentally-unknown domains, we propose a Bayesian statistical machine learning framework utilizing the Dirichlet distribution that combines results of several imperfect models. This framework can be viewed as an extension of Bayesian stacking. To illustrate the method, we study the ability of Bayesian model averaging and mixing techniques to mine nuclear masses. We show that the global and local mixtures of models reach excellent performance on both prediction accuracy and uncertainty quantification and are preferable to classical Bayesian model averaging. Additionally, our statistical analysis indicates that improving model predictions through mixing rather than mixing of corrected models leads to more robust extrapolations.

Surprising Charge-Radius Kink in the Sc Isotopes at N=20.

Charge radii of neutron deficient ^{40}Sc and ^{41}Sc nuclei were determined using collinear laser spectroscopy. With the new data, the chain of Sc charge radii extends below the neutron magic number N=20 and shows a pronounced kink, generally taken as a signature of a shell closure, but one notably absent in the neighboring Ca, K, and Ar isotopic chains. Theoretical models that explain the trend at N=20 for the Ca isotopes cannot reproduce this puzzling behavior.

Combined Theoretical Analysis of the Parity-Violating Asymmetry for

The recent experimental determination of the parity violating asymmetry A_{PV} in ^{48}Ca and ^{208}Pb at Jefferson Lab is important for our understanding on how neutrons and protons arrange themselves inside the atomic nucleus. To better understand the impact of these measurements, we present a rigorous theoretical investigation of A_{PV} in ^{48}Ca and ^{208}Pb and assess the associated uncertainties. We complement our study by inspecting the static electric dipole polarizability in these nuclei. The analysis is carried out within nuclear energy density functional theory with quantified input. We conclude that the simultaneous accurate description of A_{PV} in ^{48}Ca and ^{208}Pb cannot be achieved by our models that accommodate a pool of global nuclear properties, such as masses and charge radii, throughout the nuclear chart, and describe-within one standard deviation-the experimental dipole polarizabilities α_{D} in these nuclei.

Charge Radii of

Nuclear charge radii of ^{55,56}Ni were measured by collinear laser spectroscopy. The obtained information completes the behavior of the charge radii at the shell closure of the doubly magic nucleus ^{56}Ni. The trend of charge radii across the shell closures in calcium and nickel is surprisingly similar despite the fact that the ^{56}Ni core is supposed to be much softer than the ^{48}Ca core. The very low magnetic moment µ(^{55}Ni)=-1.108(20) µ_{N} indicates the impact of M1 excitations between spin-orbit partners across the N,Z=28 shell gaps. Our charge-radii results are compared to ab initio and nuclear density functional theory calculations, showing good agreement within theoretical uncertainties.

Evidence of Two-Source King Plot Nonlinearity in Spectroscopic Search for New Boson.

Optical precision spectroscopy of isotope shifts can be used to test for new forces beyond the standard model, and to determine basic properties of atomic nuclei. We measure isotope shifts on the highly forbidden ^{2}S_{1/2}→^{2}F_{7/2} octupole transition of trapped ^{168,170,172,174,176}Yb ions. When combined with previous measurements in Yb^{+} and very recent measurements in Yb, the data reveal a King plot nonlinearity of up to 240σ. The trends exhibited by experimental data are explained by nuclear density functional theory calculations with the Fayans functional. We also find, with 4.3σ confidence, that there is a second distinct source of nonlinearity, and discuss its possible origin.

Information Content of the Parity-Violating Asymmetry in

The parity-violating asymmetry A_{PV} in ^{208}Pb, recently measured by the PREX-2 Collaboration, is studied using modern relativistic (covariant) and nonrelativistic energy density functionals. We first assess the theoretical uncertainty on A_{PV} which is intrinsic to the adopted approach. To this end, we use quantified functionals that are able to accommodate our previous knowledge on nuclear observables such as binding energies, charge radii, and the dipole polarizability α_{D} of ^{208}Pb. We then add the quantified value of A_{PV} together with α_{D} to our calibration dataset to optimize new functionals. Based on these results, we predict a neutron skin thickness in ^{208}Pb r_{skin}=0.19±0.02 fm and the symmetry-energy slope L=54±8 MeV. These values are consistent with other estimates based on astrophysical data and are significantly lower than those recently reported using a particular set of relativistic energy density functionals. We also make a prediction for the A_{PV} value in ^{48}Ca that will be soon available from the CREX measurement.

Neutron Drip Line in the Ca Region from Bayesian Model Averaging.

The region of heavy calcium isotopes forms the frontier of experimental and theoretical nuclear structure research where the basic concepts of nuclear physics are put to stringent test. The recent discovery of the extremely neutron-rich nuclei around ^{60}Ca O. B. Tarasov et al. [Phys. Rev. Lett. 121, 022501 (2018)10.1103/PhysRevLett.121.022501] and the experimental determination of masses for ^{55-57}Ca S. Michimasa et al. [Phys. Rev. Lett. 121, 022506 (2018)10.1103/PhysRevLett.121.022506] provide unique information about the binding energy surface in this region. To assess the impact of these experimental discoveries on the nuclear landscape's extent, we use global mass models and statistical machine learning to make predictions, with quantified levels of certainty, for bound nuclides between Si and Ti. Using a Bayesian model averaging analysis based on Gaussian-process-based extrapolations we introduce the posterior probability p_{ex} for each nucleus to be bound to neutron emission. We find that extrapolations for drip-line locations, at which the nuclear binding ends, are consistent across the global mass models used, in spite of significant variations between their raw predictions. In particular, considering the current experimental information and current global mass models, we predict that ^{68}Ca has an average posterior probability p_{ex}≈76% to be bound to two-neutron emission while the nucleus ^{61}Ca is likely to decay by emitting a neutron (p_{ex}≈46%).

Electron and Nucleon Localization Functions of Oganesson: Approaching the Thomas-Fermi Limit.

Fermion localization functions are used to discuss electronic and nucleonic shell structure effects in the superheavy element oganesson, the heaviest element discovered to date. Spin-orbit splitting in the 7p electronic shell becomes so large (∼10 eV) that Og is expected to show uniform-gas-like behavior in the valence region with a rather large dipole polarizability compared to the lighter rare gas elements. The nucleon localization in Og is also predicted to undergo a transition to the Thomas-Fermi gas behavior in the valence region. This effect, particularly strong for neutrons, is due to the high density of single-particle orbitals.

Pairing Nambu-Goldstone Modes within Nuclear Density Functional Theory.

We show that the Nambu-Goldstone formalism of the broken gauge symmetry in the presence of the T=1 pairing condensate offers a quantitative description of the binding-energy differences of open-shell superfluid nuclei. We conclude that the pairing-rotational moments of inertia are excellent pairing indicators, which are free from ambiguities attributed to odd-mass systems. We offer a new, unified interpretation of the binding-energy differences traditionally viewed in the shell model picture as signatures of the valence nucleon properties. We present the first systematic analysis of the off-diagonal pairing-rotational moments of inertia and demonstrate the mixing of the neutron and proton pairing-rotational modes in the ground states of even-even nuclei. Finally, we discuss the importance of mass measurements of neutron-rich nuclei for constraining the pairing energy density functional.

The limits of the nuclear landscape.

In 2011, 100 new nuclides were discovered. They joined the approximately 3,000 stable and radioactive nuclides that either occur naturally on Earth or are synthesized in the laboratory. Every atomic nucleus, characterized by a specific number of protons and neutrons, occupies a spot on the chart of nuclides, which is bounded by 'drip lines' indicating the values of neutron and proton number at which nuclear binding ends. The placement of the neutron drip line for the heavier elements is based on theoretical predictions using extreme extrapolations, and so is uncertain. However, it is not known how uncertain it is or how many protons and neutrons can be bound in a nucleus. Here we estimate these limits of the nuclear 'landscape' and provide statistical and systematic uncertainties for our predictions. We use nuclear density functional theory, several Skyrme interactions and high-performance computing, and find that the number of bound nuclides with between 2 and 120 protons is around 7,000. We find that extrapolations for drip-line positions and selected nuclear properties, including neutron separation energies relevant to astrophysical processes, are very consistent between the models used.