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Superheavy nuclei represent the heaviest atoms and nuclides known at the limit of mass and charge. The observed superheavy nuclei are all proton-rich; they decay primarily by emitting $\alpha$ particles and fission, with a possible small electron capture (EC) branch. Due to the huge atomic numbers and associated relativistic effects, EC-decays of superheavy systems are expected to differ from what is known in lighter nuclei. In this paper, using the quantified relativistic nuclear density functional theory and the quasiparticle random-phase approximation with the interaction optimized to experimental $\beta^-$-decay half-lives and Gamow-Teller resonance energies, we study the EC/$\beta^\pm$-decays in $Z = 101-118$ nuclei. Both allowed ($1^+$) and first-forbidden ($0^-, 1^-$ and $2^-$) transitions are considered. We show that the first-forbidden $1^-$ transitions dominate the decay rates in almost all studied nuclei. For proton-rich nuclei, EC dominates over $\beta^+$ decay. We identify 44 nuclei with EC/$\beta^+$ branching ratio larger than 5\%, indicating a possible competition with $\alpha$-decay and spontaneous fission channels., Comment: 7 pages, 4 figures, submitted for publication

Collinear laser spectroscopy measurements were performed on $^{68-74}$Ge isotopes ($Z = 32$) at ISOLDE-CERN, by probing the $4s^2 4p^2 \, ^3\!P_1 \rightarrow 4s^2 4p 5s \, ^3\!P_1^o$ atomic transition (269~nm) of germanium. Nuclear charge radii are determined via the measured isotope shifts, revealing a larger local variation than the neighboring isotopic chains. Nuclear density functional theory with the Fayans functionals Fy($\Delta r$,HFB) and Fy(IVP), and the SV-min Skyrme describes the experimental data for the differential charge radii $\delta\langle r^{2} \rangle$ and charge radii $R_{\rm c}$ within the theoretical uncertainties. The observed large variation in the charge radii of germanium isotopes is better accounted for by theoretical models incorporating ground state quadrupole correlations. This suggests that the polarization effects due to pairing and deformation contribute to the observed large odd-even staggering in the charge radii of the Ge isotopic chain., Comment: 6 pages,5 figures

Our understanding of nuclear properties in the vicinity of $^{100}$Sn, suggested to be the heaviest doubly magic nucleus with equal numbers of protons (Z=50) and neutrons (N=50), has been a long-standing challenge for experimental and theoretical nuclear physics. Contradictory experimental evidence exists on the role of nuclear collectivity in this region of the nuclear chart. Using precision laser spectroscopy, we measured the ground-state electromagnetic moments of indium (Z=49) isotopes approaching the N=50 neutron number down to 101In, and nuclear charge radii of 101-131In spanning almost the complete range between the two major neutron closed-shells at N=50 and N=82. Our results for both nuclear charge radii and quadrupole moments reveal striking parabolic trends as a function of the neutron number, with a clear reduction toward these two neutron closed-shells, thus supporting a doubly magic character of $^{100}$Sn. Two complementary nuclear many-body frameworks, density functional theory and ab initio methods, elucidate our findings. A detailed comparison with our experimental results exposes deficiencies of nuclear models, establishing a benchmark for future theoretical developments., Comment: 12 pages, 6 figures, 4 tables; text-identical to Nature Physics article (2024)

Examination of high-resolution, experimental fusion excitation functions for $^{16,17,18}$O + $^{12}$C reveals a remarkable irregular behavior that is rooted in the structure of both the colliding nuclei and the quasi-molecular composite system. The impact of the $\ell$-dependent fusion barriers is assessed using a time-dependent Hartree-Fock model. Barrier penetrabilities, taken directly from a density-constrained calculation, provide a significantly improved description of the experimental data as compared to the standard Hill-Wheeler approach. The remaining deviations between the parameter-free theoretical mean-field predictions and experimental fusion cross sections are exposed and discussed., Comment: Main manuscript, 6 pages, 4 figures; Supplemental material 2 videos and 1 figure

The boundaries of the Chart of Nuclides contain exotic isotopes that possess extreme proton-toneutron asymmetries. Here we report on strong evidence of 9N, one of the most exotic proton-rich isotopes where more than one half of its constitute nucleons are unbound. With seven protons and two neutrons, this extremely proton-rich system would represent the first-known example of a ground-state five-proton emitter. The invariant-mass spectrum of its decay products can be fit with two peaks whose energies are consistent with the theoretical predictions of an open-quantum-system approach, however we cannot rule out the possibility that only a single resonance-like peak is present in the spectrum., Comment: 4 figures, 7pages

The recent precise experimental determination of the monopole transition form factor from the ground state of $^4$He to its $0^+_2$ resonance via electron scattering has reinvigorated discussions about the nature of this first excited state of the $\alpha$ particle. The $0^+_2$ state has been traditionally interpreted in the literature as the isoscalar monopole resonance (breathing mode) or, alternatively, as a particle-hole shell-model excitation. To better understand the nature of this state, which lies only $\sim$ 410 keV above the proton emission threshold, we employ the coupled-channel representation of the no-core Gamow shell model. By considering the $[^3$H$ + p]$, $[^3$He$ + n]$, and $[^2$H+$^2$H] reaction channels, we explain the excitation energy and monopole form-factor of the $0^+_2$ state. We argue that the continuum coupling strongly impacts the nature of this state, which carries characteristics of the proton decay threshold., Comment: 6 pages, 4 figures, accepted in Phys. Rev. Lett

In the Ge-Sr mass region, isotopes with neutron number $N \leq 40$ are known to feature rapid shape changes with both nucleon number and angular momentum. To gain new insights into their structure, inelastic proton scattering experiments in inverse kinematics were performed on the rare isotopes $^{74,76}$Kr. This work focuses on observables related to the $J^{\pi} = 4^+_1$ states of the Kr isotopes and, in particular, on the hexadecapole degree of freedom. By performing coupled-channels calculations, hexadecapole deformation parameters $\beta_4$ were determined for the $J^{\pi} = 4^+_1$ states of $^{74,76}$Kr from inelastic proton scattering cross sections. Two possible coupled-channels solutions were found. A comparison to predictions from nuclear energy density functional theory, employing both non-relativistic and relativistic functionals, clearly favors the large, positive $\beta_4$ solutions. These $\beta_4$ values are unambiguously linked to the well deformed prolate configuration. Given the $\beta_2 - \beta_4$ trend, established in this work, it appears that $\beta_4$ values could provide a sensitive measure of the nuclear shell structure., Comment: 7 pages, 4 figures, accepted for publication in Physics Letters B

This whitepaper presents the research priorities decided on by attendees of the 2022 Town Meeting for Fundamental Symmetries, Neutrons and Neutrinos, which took place December 13-15, 2022 in Chapel Hill, NC, as part of the Nuclear Science Advisory Committee (NSAC) 2023 Long Range Planning process. A total of 275 scientists registered for the meeting. The whitepaper makes a number of explicit recommendations and justifies them in detail.

The electric dipole strength distribution in $^{40}$Ca between 5 and 25 MeV has been determined at RCNP, Osaka, from proton inelastic scattering experiments at very forward angles. Combined with total photoabsorption data at higher excitation energy, this enables an extraction of the electric dipole polarizability $\alpha_\mathrm{D}$($^{40}$Ca) = 1.92(17) fm$^3$. Together with the measured $\alpha_{\rm D}$ in $^{48}$Ca, it provides a stringent test of modern theoretical approaches, including coupled cluster calculations with chiral effective field theory interactions and state-of-the art energy density functionals. The emerging picture is that for this medium-mass region dipole polarizabilities are well described theoretically, with important constraints for the neutron skin in $^{48}$Ca and related equation of state quantities., Comment: 6 pages, 3 figures

We review the progress in atomic structure theory with a focus on superheavy elements and the aim to predict their ground state configuration and element's placement in the periodic table. To understand the electronic structure and correlations in the regime of large atomic numbers, it is important to correctly solve the Dirac equation in strong Coulomb fields, and also to take into account quantum electrodynamic effects. We specifically focus on the fundamental difficulties encountered when dealing with the many-particle Dirac equation. We further discuss the possibility for future many-electron atomic structure calculations going beyond the critical nuclear charge \(Z_{\rm crit}\approx 170\), where levels such as the \(1s\) shell dive into the negative energy continuum (\(E_{n\kappa}<-m_ec^2\)). The nature of the resulting Gamow states within a rigged Hilbert space formalism is highlighted.

The most important law of radioactivity is that of the exponential decay. In the realm of quantum mechanics, however, this decay law is neither rigorous nor fundamental. The deviations from the exponential decay have been observed experimentally at the early stage of a decay process, but there is little evidence for non-exponential behavior at long times. Yet such long-term non-exponentiality is expected theoretically to probe the non-resonant background components of the initial wave function which preserve the structural interference and the memory of how the state was created. In this paper, we propose new observables that can be used for experimental investigations of the post-exponential decay regime, including the decay of threshold resonances, particle correlations in three-body decays, and interference between near-lying resonances. While the specific examples presented in this work pertain to atomic nuclei, the properties of non-exponential decay are generic, i.e., they apply to other many-body open quantum systems, such as hadrons, atoms, molecules, and nanostructures., Comment: 10 pages, 7 figures

The nucleus 11C plays an important role in the boron-proton fusion reactor environment as a catalyzer of the 10B(p,{\alpha})7Be reaction which, by producing a long-lived isotope of 7Be, poisons the aneutronic fusion process 11B(p,2{\alpha})4He. The low-energy cross section of 10B(p,{\alpha})7Be depends on the near-threshold states 7/2+1 , 5/2+2 , 5/2+3 in 11C whose properties are primarily known from the indirect measurements. We investigate the continuum-coupling induced collectivization of these resonances in the shell model embedded in the continuum. We predict a significant enhancement of the 10B(p,{\alpha})7Be cross section at energies accessible to the laser-driven hot plasma facilities., Comment: 4 pages, 2 figures

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 $\mu(^{55}\mathrm{Ni})=-1.108(20)\,\mu_N$ indicates the impact of M1 excitations between spin-orbit partners across the $N,Z=28$ shell gaps. Our charge-radii results are compared to \textit{ab initio} and nuclear density functional theory calculations, showing good agreement within theoretical uncertainties.

We present the results of a National Science Foundation (NSF) Project Scoping Workshop, the purpose of which was to assess the current status of calculations for the nuclear matrix elements governing neutrinoless double-beta decay and determine if more work on them is required. After reviewing important recent progress in the application of effective field theory, lattice quantum chromodynamics, and ab initio nuclear-structure theory to double-beta decay, we discuss the state of the art in nuclear-physics uncertainty quantification and then construct a road map for work in all these areas to fully complement the increasingly sensitive experiments in operation and under development. The road map contains specific projects in theoretical and computational physics as well as an uncertainty-quantification plan that employs Bayesian Model Mixing and an analysis of correlations between double-beta-decay rates and other observables. The goal of this program is a set of accurate and precise matrix elements, in all nuclei of interest to experimentalists, delivered together with carefully assessed uncertainties. Such calculations will allow crisp conclusions from the observation or non-observation of neutrinoless double-beta decay, no matter what new physics is at play., Comment: This Project Scoping Workshop report is focused on the US context for the theory of neutrinloess double beta decay. Its authors plan to produce a journal article that addresses similar issues, but is more inclusive as regards non-US efforts on this problem. We would be happy to receive further input that will help us refine our text before it is submitted to the journal

Beta-delayed proton emission from the neutron halo ground state of $^{11}$Be raised much attention due to the unusually high decay rate. It was argued that this may be due to the existence of a resonance just above the proton decay threshold. In this Letter, we use the lenses of real-energy continuum shell model to describe several observables including the Gamow-Teller rates for the $\beta^-$-delayed $\alpha$ and proton decays, and argue that, within our model, the large $\beta^-{\rm p}$ branching ratio cannot be reconciled with other data., Comment: 5 pages, 3 figures

Collinear laser spectroscopy is performed on the nickel isotopes $^{58-68,70}$Ni, using a time-resolved photon counting system. From the measured isotope shifts, nuclear charge radii $R_c$ are extracted and compared to theoretical results. Three ab initio approaches all employ, among others, the chiral interaction NNLO$_{\rm sat}$, which allows an assessment of their accuracy. We find agreement with experiment in differential radii $\delta \left\langle r_\mathrm{c}^2 \right\rangle$ for all employed ab initio methods and interactions, while the absolute radii are consistent with data only for NNLO$_{\rm sat}$. Within nuclear density functional theory, the Skyrme functional SV-min matches experiment more closely than the Fayans functional Fy($\Delta r$,HFB).

Protons and neutrons in the atomic nucleus move in shells analogous to the electronic shell structures of atoms. Nuclear shell structure varies across the nuclear landscape due to changes of the nuclear mean field with the number of neutrons $N$ and protons $Z$. These variations can be probed with mass differences. The $N=Z=40$ self-conjugate nucleus $^{80}$Zr is of particular interest as its proton and neutron shell structures are expected to be very similar, and its ground state is highly deformed. In this work, we provide evidence for the existence of a deformed double shell closure in $^{80}$Zr through high precision Penning trap mass measurements of $^{80-83}$Zr. Our new mass values show that $^{80}$Zr is significantly lighter, and thus more bound than previously determined. This can be attributed to the deformed shell closure at $N=Z=40$ and the large Wigner energy. Our statistical Bayesian model mixing analysis employing several global nuclear mass models demonstrates difficulties with reproducing the observed mass anomaly using current theory., Comment: 11 pages; 5 figures; submitted version, revised version accepted in Nature Physics pending minor revisions

There has been an upsurge of interest in two-nucleon decays thanks to the studies of nucleon-nucleon correlations. In our previous work, based on a novel time-dependent three-body approach, we demonstrated that the energy and angular correlations of the emitted nucleons can shed light on the structure of nucleonic pairs formed inside the nucleus. In this work, we apply the new framework to study the decay dynamics and properties of some extreme proton-rich and neutron-rich oxygen isotopes, including two-proton ($2p$) decays of $^{11,12}$O and two-neutron ($2n$) decay of $^{26}$O. Here we show that the low-$\ell$ components of $^{11,12}$O wave functions, which are affected by continuum and configuration-interaction effects, strongly impact decay dynamics and asymptotic correlations. In the calculated wave functions of $^{11,12}$O, diproton and cigarlike structures merge together during the tunneling process and the resulting energy- and angular correlations are very consistent with the experimental data. The asymptotic correlations of the $2n$ decay of $^{26}$O dramatically change as the two-neutron decay energy approaches the zero-energy threshold. The small reported value of $Q_{2n}$ suggests that the $2n$ decay of this nucleus can be understood in terms of the universal phase-space limit., Comment: 7 pages, 4 figures. arXiv admin note: text overlap with arXiv:2104.03195

Single-nucleon knockout reaction studies of the proton-dripline nuclei $^9$C and $^{13}$O suggest an appreciable suppression of spectroscopic factors. In this work, we calculate the one-neutron and one-proton spectroscopic factors for the mirror pair $^9$C-$^9$Li and $^{13}$O using two variants of the continuum shell model: the complex-energy Gamow Shell Model and the real-energy Shell Model Embedded in the Continuum. Our results indicate that the continuum effects strongly suppress the spectroscopic factors of well-bound orbits in the dripline systems, but have less impact on the spectroscopic factors of weakly-bound states., Comment: 7 pages, 3 figures, 1 table

Three-body decay is a rare decay mode observed in a handful of unbound rare isotopes. The angular and energy correlations between emitted nucleons are of particular interest, as they provide invaluable information on the interplay between structure and reaction aspects of the nuclear open quantum system. To study the mechanism of two-nucleon emission, we developed a time-dependent approach that allows us to probe emitted nucleons at long times and large distances. We successfully benchmarked the new method against the Green's function approach and applied it to low-energy two-proton and two-neutron decays. In particular, we studied the interplay between initial-state nucleon-nucleon correlations and final-state interaction. We demonstrated that the time evolution of the two-nucleon wave function is strongly impacted by the diproton/dineutron dynamics and that the correlations between emitted nucleons provide invaluable information on the dinucleon structure in the initial-state., Comment: 4 figures

We describe the Bayesian Analysis of Nuclear Dynamics (BAND) framework, a cyberinfrastructure that we are developing which will unify the treatment of nuclear models, experimental data, and associated uncertainties. We overview the statistical principles and nuclear-physics contexts underlying the BAND toolset, with an emphasis on Bayesian methodology's ability to leverage insight from multiple models. In order to facilitate understanding of these tools we provide a simple and accessible example of the BAND framework's application. Four case studies are presented to highlight how elements of the framework will enable progress on complex, far-ranging problems in nuclear physics. By collecting notation and terminology, providing illustrative examples, and giving an overview of the associated techniques, this paper aims to open paths through which the nuclear physics and statistics communities can contribute to and build upon the BAND framework., Comment: 47 pages, 10 figures. Revised version includes minor corrections and changes in presentation. Matches journal version

Nuclear charge radii are sensitive probes of different aspects of the nucleon-nucleon interaction and the bulk properties of nuclear matter; thus, they provide a stringent test and challenge for nuclear theory. The calcium region has been of particular interest, as experimental evidence has suggested a new magic number at $N = 32$ [1-3], while the unexpectedly large increases in the charge radii [4,5] open new questions about the evolution of nuclear size in neutron-rich systems. By combining the collinear resonance ionization spectroscopy method with $\beta$-decay detection, we were able to extend the charge radii measurement of potassium ($Z =19$) isotopes up to the exotic $^{52}$K ($t_{1/2}$ = 110 ms), produced in minute quantities. Our work provides the first charge radii measurement beyond $N = 32$ in the region, revealing no signature of the magic character at this neutron number. The results are interpreted with two state-of-the-art nuclear theories. For the first time, a long sequence of isotopes could be calculated with coupled-cluster calculations based on newly developed nuclear interactions. The strong increase in the charge radii beyond $N = 28$ is not well captured by these calculations, but is well reproduced by Fayans nuclear density functional theory, which, however, overestimates the odd-even staggering effect. These findings highlight our limited understanding on the nuclear size of neutron-rich systems, and expose pressing problems that are present in some of the best current models of nuclear theory., Comment: submitted version; revision accepted in Nature Physics

Background: Weakly bound and unbound nuclei close to particle drip lines are laboratories of new nuclear structure physics at the extremes of neutron/proton excess. The comprehensive description of these systems requires an open quantum system framework that is capable of treating resonant and nonresonant many-body states on equal footing. Purpose: In this work, we construct the minimal complex-energy configuration interaction approach to describe binding energies and spectra of selected 5 $\leq$ A $\leq$ 11 nuclei. Method: We employ the complex-energy Gamow shell model (GSM) assuming a rigid $^4$He core. The effective Hamiltonian, consisting of a core-nucleon Woods-Saxon potential and a simplified version of the Furutani-Horiuchi-Tamagaki interaction with the mass-dependent scaling, is optimized in the sp space. To diagonalize the Hamiltonian matrix, we employ the Davidson method and the Density Matrix Renormalization Group technique. Results: Our optimized GSM Hamiltonian offers a good reproduction of binding energies and spectra with the root-mean-square (rms) deviation from experiment of 160 keV. Since the model performs well when used to predict known excitations that have not been included in the fit, it can serve as a reliable tool to describe poorly known states. A case in point is our prediction for the pair of unbound mirror nuclei $^{10}$Li-$^{10}$N in which a huge Thomas-Ehrman shift dramatically alters the pattern of low-energy excitations. Conclusion: The new model will enable comprehensive studies of structure and reactions aspects of light drip-line nuclei., Comment: 11 pages, 3 figures

The mesoscopic nature of the atomic nucleus gives rise to a wide array of macroscopic and microscopic phenomena. The size of the nucleus is a window into this duality: while the charge radii globally scale as $A^{1/3}$, their evolution across isotopic chains reveals unanticipated structural phenomena [1-3]. The most ubiquitous of these is perhaps the Odd-Even Staggering (OES) [4]: isotopes with an odd number of neutrons are usually smaller in size than the trend of their even-neutron neighbours suggests. This OES effect varies with the number of protons and neutrons and poses a significant challenge for nuclear theory [5-7]. Here, we examine this problem with new measurements of the charge radii of short-lived copper isotopes up to the very exotic $^{78}$Cu $(Z=29, N=49)$, produced at only 20 ions/s, using the highly-sensitive Collinear Resonance Ionisation Spectroscopy (CRIS) method at ISOLDE-CERN. Due to the presence of a single proton outside of the closed Z=28 shell, these measurements provide crucial insights into the single-particle proton structure and how this affects the charge radii. We observe an unexpected reduction in the OES for isotopes approaching the $N=50$ shell gap. To describe the data, we applied models based on nuclear Density Functional Theory [2,8] (DFT) and ab-initio Valence-Space In-Medium Similarity Renormalization Group (VS-IMSRG) theory [9,10]. Through these comparisons, we demonstrate a relation between the global behavior of charge radii and the saturation density of nuclear matter, and show that the local charge radii variations, which reflect the many-body polarization effects due to the odd neutron, naturally emerge from the VS-IMSRG calculations.

Measurements of atomic transitions in different isotopes offer key information on the nuclear charge radius. The anticipated high-precision experimental techniques, augmented by atomic calculations, will soon enable extraction of the higher-order radial moments of the charge density distribution. To assess the value of such measurements for nuclear structure research, we study the information content of the fourth radial moment $\rf$ by means of nuclear density functional theory and a multiple correlation analysis. We show that $\rf$ can be directly related to the surface thickness of nuclear density, a fundamental property of the atomic nucleus that is difficult to obtain for radioactive systems. Precise knowledge of these radial moments is essential to establish reliable constraints on the existence of new forces from precision isotope shift measurements ., Comment: 5 pages, 4 figures

The presence of cluster-like narrow resonances in the vicinity of reaction/decay thresholds is a ubiquitous phenomenon with profound consequences. We argue that the continuum coupling, present in the open quantum system description of the atomic nucleus, can profoundly impact the nature of near-threshold states. In this Letter, we discuss the structure of the recently observed near-threshold resonance in $^{11}$B, whose very existence explains the puzzling beta-delayed proton emission of the neutron-rich $^{11}$Be., Comment: 4 pages, 3 figures

${\rm \bf Background:}$ The recent observation of the unbound nucleus $^{11}$O offers the unique possibility to study how the structure and dynamics of two-proton ($2p$) decay is affected by the removal of one neutron from $^{12}$O, and provides important information on the Thomas-Ehrman effect in the mirror pairs $^{11}_{~8}$O$_3$-$^{11}_{~3}$Li$_8$ and $^{12}_{~8}$O$_4$-$^{12}_{~4}$Be$_8$, which involve the $2p$ emitters $^{11}$O and $^{12}$O. ${\rm \bf Purpose:}$ We investigate how continuum effects impact the structure and decay properties of $^{11}$O and $^{12}$O, and their mirror partners. ${\rm \bf Methods:}$ We solve the three-body core-nucleon-nucleon problem using the Gamow coupled-channel (GCC) method. The GCC Hamiltonian employs a realistic finite-range valence nucleon-nucleon interaction and the deformed cores of $^{9,10}$C, $^{9}$Li, and $^{10}$Be. ${\rm \bf Results:}$ We calculate the energy spectra and decay widths of $^{11}$O and $^{12}$O as well as those of their mirror nuclei. In particular, we investigate the dynamics of the $2p$ decay in the ground state of $^{12}$O by analyzing the evolution of the $2p$ configuration of the emitted protons as well as their angular correlations in the coordinate space. We also show how the analytic structure of the resonant states of $^{10}$Li and $^{10}$N impacts the low-lying states of $^{11}$Li and $^{11}$O. ${\rm \bf Conclusions:}$ We demonstrate that, in both nuclei $^{11}$O and $^{12}$O, there is a competition between direct and "democratic" $2p$ ground-state emission. The broad structure observed in $^{11}$O is consistent with four broad resonances, with the predicted $3/2^-_1$ ground state strongly influenced by the broad threshold resonant state in $^{10}$N, which is an isobaric analog of the antibound (or virtual) state in $^{10}$Li., Comment: 9 pages, 8 figures

The structure of the extremely proton-rich nucleus $^{11}_{~8}$O$_3$, the mirror of the two-neutron halo nucleus $^{11}_{~3}$Li$_8$, has been studied experimentally for the first time. Following two-neutron knockout reactions with a $^{13}$O beam, the $^{11}$O decay products were detected after two-proton emission and used to construct an invariant-mass spectrum. A broad peak of width $\sim$3\,MeV was observed. Within the Gamow coupled-channel approach, it was concluded that this peak is a multiplet with contributions from the four-lowest $^{11}$O resonant states: $J^{\pi}$=3/2$^-_1$, 3/2$^-_2$, 5/2$^+_1$, and 5/2$^+_2$. The widths and configurations of these states show strong, non-monotonic dependencies on the depth of the $p$-$^9$C potential. This unusual behavior is due to the presence of a broad threshold resonant state in $^{10}$N, which is an analog of the virtual state in $^{10}$Li in the presence of the Coulomb potential. After optimizing the model to the data, only a moderate isospin asymmetry between ground states of $^{11}$O and $^{11}$Li was found., Comment: 6 pages, three figures

In multipole-bound anions, the excess electron is attached by a short-range multipole potential of a neutral molecule. Such anions are prototypical marginally-bound open quantum systems. In particular, around the critical multipole moment required to attach the valence electron, multipole-bound anions exhibit critical behavior associated with a transition from bound states dominated by low-$\ell$ partial waves to the electron continuum. In this work, multipole-bound anions are described using a nonadiabatic electron-plus-rotor model. The electron-molecule pseudo-potential is represented by a short-range multipole field with a Gaussian form-factor. The resulting coupled-channel Schr\"odinger equation is solved by means of the Berggren expansion method, in which the electron's wave function is decomposed into bound states, narrow resonances, and the non-resonant scattering continuum. We show that the Gaussian model predicts the critical transition at the detachment threshold. Resonant states, including bound states, decaying resonances, subthreshold resonances, and antibound states are studied, and exceptional points where two resonant states coalesce are predicted. We discuss the transition of rotational band structures around the threshold and study the effects of channel coupling on the decay width of resonant poles., Comment: 10 pages, 13 figures

In July 2018 an FRIB Theory Alliance program was held on the implications of GW170817 and its associated kilonova for r-process nucleosynthesis. Topics of discussion included the astrophysical and nuclear physics uncertainties in the interpretation of the GW170817 kilonova, what we can learn about the astrophysical site or sites of the r process from this event, and the advances in nuclear experiment and theory most crucial to pursue in light of the new data. Here we compile a selection of scientific contributions to the workshop, broadly representative of progress in r-process studies since the GW170817 event., Comment: Proceedings for the FRIB Theory Alliance workshop "FRIB and the GW170817 kilonova", held 16-27 July 2018 at the Facility for Rare Isotope Beams, Michigan State University, East Lansing, MI USA; 44 pages, 14 figures

We demonstrate that the intricate energy spectrum of neutron-rich helium isotopes can be straightforwardly described by taking advantage of the low-energy properties of neutron-neutron interaction and the scale separation that is present in diluted dripline systems. By using arguments based on the halo effective field theory, we carry out a parameter reduction of the complex-energy configuration interaction framework in the $spd$ space, including resonant and scattering states. By adjusting only one parameter, the strength of the spin-singlet central neutron-neutron interaction, we reproduce experimental energies and widths of $^{5-8}$He within tens of keV precision. We predict a parity inversion of narrow resonances in $^{9}$He and show that the ground state of $^{10}$He is an $s$-wave-dominated threshold configuration that could decay through two-neutron emission.

This is an exciting time for the study of r-process nucleosynthesis. Recently, a neutron star merger GW170817 was observed in extraordinary detail with gravitational waves and electromagnetic radiation from radio to gamma rays. The very red color of the associated kilonova suggests that neutron star mergers are an important r-process site. Astrophysical simulations of neutron star mergers and core collapse supernovae are making rapid progress. Detection of both, electron neutrinos and antineutrinos from the next galactic supernova will constrain the composition of neutrino-driven winds and provide unique nucleosynthesis information. Finally FRIB and other rare-isotope beam facilities will soon have dramatic new capabilities to synthesize many neutron-rich nuclei that are involved in the r-process. The new capabilities can significantly improve our understanding of the r-process and likely resolve one of the main outstanding problems in classical nuclear astrophysics. However, to make best use of the new experimental capabilities and to fully interpret the results, a great deal of infrastructure is needed in many related areas of astrophysics, astronomy, and nuclear theory. We will place these experiments in context by discussing astrophysical simulations and observations of r-process sites, observations of stellar abundances, galactic chemical evolution, and nuclear theory for the structure and reactions of very neutron-rich nuclei. This review paper was initiated at a three-week International Collaborations in Nuclear Theory program in June 2016 where we explored promising r-process experiments and discussed their likely impact, and their astrophysical, astronomical, and nuclear theory context., Comment: 132 pages, 18 figures, submitted to Journal of Physics G

Fragment mass distributions from fission of excited compound nucleus $^{178}$Pt have been deduced from the measured fragment velocities. The $^{178}$Pt nucleus was created at the JAEA tandem facility in a complete fusion reaction $^{36}$Ar + $^{142}$Nd, at beam energies of 155, 170 and 180 MeV. The data are indicative of a mixture of the mass-asymmetric and mass-symmetric fission modes associated with higher and lower total kinetic energies of the fragments, respectively. The measured fragment yields are dominated by asymmetric mass splits, with the symmetric mode contributing at the level of $\approx1/3$. This constitutes the first observation of a multimodal fission in the sub-lead region. Most probable experimental fragment-mass split of the asymmetric mode, $A_{L}/A_{H}\approx 79/99$, is well reproduced by nuclear density functional theory using the UNEDF1-HFB and D1S potentials. The symmetric mode is associated by theory with very elongated fission fragments, which is consistent with the observed total kinetic energy/fragment mass correlation., Comment: 6 pages, 4 figures

Two-proton (2$p$) radioactivity is a rare decay mode found in a few proton-unbound nuclei. The $2p$-decay lifetime and properties of emitted protons carry invaluable information on nuclear structure in the presence of low-lying proton continuum. The recently measured $2p$ decay of $^{67}$Kr [Phys. Rev. Lett. 117, 162501 (2016)] turned out to be unexpectedly fast. Since $^{67}$Kr is expected to be a deformed system, we investigate the impact of deformation effects on the $2p$ radioactivity. We apply the recently developed Gamow coupled-channel framework, which allows for a precise description of three-body systems in the presence of rotational and vibrational couplings. This is the first application of a three-body approach to a two-nucleon decay from a deformed nucleus. We show that deformation couplings significantly increase the $2p$ decay width of $^{67}$Kr; this finding explains the puzzling experimental data. The calculated angular proton-proton correlations reflect a competition between $1p$ and $2p$ decay modes in this nucleus., Comment: 3 figures

The structure of weakly bound and unbound nuclei close to particle drip lines is one of the major science drivers of nuclear physics. A comprehensive understanding of these systems goes beyond the traditional configuration interactions approach formulated in the Hilbert space of localized states (nuclear shell model) and requires an open quantum system description. The complex-energy Gamow Shell Model (GSM) provides such a framework as it is capable of describing resonant and non-resonant many-body states on equal footing. To make reliable predictions, quality input is needed that allows for the full uncertainty quantification of theoretical results. In this study, we carry out the optimization of an effective GSM (one-body and two-body) interaction in the $psdf$ shell model space. The resulting interaction is expected to describe nuclei with $5 \leqslant A \leqslant 12$ at the $p-sd$-shell interface. The optimized one-body potential reproduces nucleon-$^4$He scattering phase shifts up to an excitation energy of 20 MeV. The two-body interaction built on top of the optimized one-body field is adjusted to the bound and unbound ground-state binding energies and selected excited states of the Helium, Lithium, and Beryllium isotopes up to $A=9$. A very good agreement with experiment was obtained for binding energies. First applications of the optimized interaction include predictions for two-nucleon correlation densities and excitation spectra of light nuclei with quantified uncertainties. The new interaction will enable comprehensive and fully quantified studies of structure and reactions aspects of nuclei from the $psd$ region of the nuclear chart., Comment: 11 pages, 6 figures, 9 tables

Theoretical calculations suggest the presence of low-lying excited states in $^{25}$O. Previous experimental searches by means of proton knockout on $^{26}$F produced no evidence for such excitations. We search for excited states in $^{25}$O using the ${ {}^{24}\text{O} (d,p) {}^{25}\text{O} }$ reaction. The theoretical analysis of excited states in unbound $^{25,27}$O is based on the configuration interaction approach that accounts for couplings to the scattering continuum. We use invariant-mass spectroscopy to measure neutron-unbound states in $^{25}$O. For the theoretical approach, we use the complex-energy Gamow Shell Model and Density Matrix Renormalization Group method with a finite-range two-body interaction optimized to the bound states and resonances of $^{23-26}$O, assuming a core of $^{22}$O. We predict energies, decay widths, and asymptotic normalization coefficients. Our calculations in a large $spdf$ space predict several low-lying excited states in $^{25}$O of positive and negative parity, and we obtain an experimental limit on the relative cross section of a possible ${ {J}^{\pi} = {1/2}^{+} }$ state with respect to the ground-state of $^{25}$O at $\sigma_{1/2+}/\sigma_{g.s.} = 0.25_{-0.25}^{+1.0}$. We also discuss how the observation of negative parity states in $^{25}$O could guide the search for the low-lying negative parity states in $^{27}$O. Previous experiments based on the proton knockout of $^{26}$F suffered from the low cross sections for the population of excited states in $^{25}$O because of low spectroscopic factors. In this respect, neutron transfer reactions carry more promise.

${\bf Background:}$ Weakly bound and unbound nuclear states appearing around particle thresholds are prototypical open quantum systems. Theories of such states must take into account configuration mixing effects in the presence of strong coupling to the particle continuum space. ${\bf Purpose:}$ To describe structure and decays of three-body systems, we developed a Gamow coupled-channel (GCC) approach in Jacobi coordinates by employing the complex-momentum formalism. We benchmarked the new framework against the complex-energy Gamow Shell Model (GSM). ${\bf Methods:}$ The GCC formalism is expressed in Jacobi coordinates, so that the center-of-mass motion is automatically eliminated. To solve the coupled-channel equations, we use hyperspherical harmonics to describe the angular wave functions while the radial wave functions are expanded in the Berggren ensemble, which includes bound, scattering and Gamow states. ${\bf Results:}$ We show that the GCC method is both accurate and robust. Its results for energies, decay widths, and nucleon-nucleon angular correlations are in good agreement with the GSM results. ${\bf Conclusions:}$ We have demonstrated that a three-body GSM formalism explicitly constructed in cluster-orbital shell model coordinates provides similar results to a GCC framework expressed in Jacobi coordinates, provided that a large configuration space is employed. Our calculations for $A=6$ systems and $^{26}$O show that nucleon-nucleon angular correlations are sensitive to the valence-neutron interaction. The new GCC technique has many attractive features when applied to bound and unbound states of three-body systems: it is precise, efficient, and can be extended by introducing a microscopic model of the core., Comment: 10 pages, 8 figures

In this work, we study the odd-even effect in binding energies and charge radii, and systematic behavior of differential radii, to identify the underlying components of the effective nuclear interaction. We apply nuclear density functional theory using a family of Fayans and Skyrme energy density functionals fitted to similar datasets but using different optimization protocols. We inspect various correlations between differential charge radii, odd-even staggering in energies and radii, and nuclear matter properties. Detailed analysis is carried out for medium-mass and heavy semi-magic nuclei with a particular focus on the Ca chain. By making the surface and pairing terms dependent on density gradients, the Fayans functional offers the superb simultaneous description of odd-even staggering effects in energies and charge radii. Conversely, when the data on differential radii are added to the pool of fit-observables, the coupling constants determining the strengths of the gradient terms of Fayans functional are increased by orders of magnitude. The Skyrme functional optimized in this work with the generalized Fayans pairing term offers results of similar quality. We quantify these findings by performing correlation analysis based on the statistical linear regression technique. The nuclear matter parameters characterizing Fayans and Skyrme functionals optimized to similar datasets are fairly close., Comment: 13 pages, 10 figures, 5 tables

The binding-energy pattern along the neutron-rich oxygen chain, governed by an interplay between shell effects and many-body correlations impacted by strong couplings to one- and two-neutron continuum, make these isotopes a unique testing ground for nuclear models. In this work, we investigate ground states and low-lying excited states of $^{23-28}$O using the complex-energy Gamow Shell Model and Density Matrix Renormalization Group method with a finite-range two-body interaction optimized to the bound states and resonances of $^{23-26}$O, assuming a core of $^{22}$O. Our results suggest that the ground-state of $^{28}$O has a threshold character, i.e., is very weakly bound or slightly unbound. We also predict narrow excited resonances in $^{25}$O and $^{27}$O. The inclusion of the large continuum space significantly impacts predicted binding energies of $^{26-28}$O. This implies that the careful treatment of neutron continuum is necessary prior to assessing the spectroscopic quality of effective interactions in this region.

Background: Deformed neutron-rich magnesium isotopes constitute a fascinating territory where the interplay between collective rotation and single-particle motion is strongly affected by the neutron continuum. The unbound $fp$-shell nucleus $ ^{39}\text{Mg} $ is an ideal candidate to study this interplay. Purpose: In this work, we predict the properties of low-lying resonant states of $ ^{39}\text{Mg} $, using a suite of realistic theoretical approaches rooted in the open quantum system framework. Method: To describe the spectrum and decay modes of $ ^{39}\text{Mg} $ we use the conventional Shell Model, Gamow Shell Model, Resonating Group Method, Density Matrix Renormalization Group method, and the non-adiabatic Particle-Plus-Rotor model formulated in the Berggren basis. Results: The unbound ground state of $ ^{39}\text{Mg} $ is predicted to be either a $ J^{\pi} = {7/2}^- $ state or a $ {3/2}^- $ state. A narrow $ J^{\pi} = {7/2}^- $ ground-state candidate exhibits a resonant structure reminiscent of that of its one-neutron halo neighbor $ ^{37}\text{Mg} $, which is dominated by the $ f_{7/2} $ partial wave at short distances and a $ p_{3/2} $ component at large distances. A $ J^{\pi}={3/2}^- $ ground-state candidate is favored by the large deformation of the system. It can be associated with the $ {1/2}^- [321] $ Nilsson orbital dominated by the $\ell=1$ wave; hence its predicted width is large. The excited $J^{\pi} = {1/2}^-$ and $5/2^-$ states are expected to be broad resonances, while the $ J^{\pi} = {9/2}^- $ and $ {11/2}^- $ members of the ground-state rotational band are predicted to have very small neutron decay widths. Conclusion: We demonstrate that the subtle interplay between deformation, shell structure, and continuum coupling can result in a variety of excitations in an unbound nucleus just outside the neutron drip line., Comment: 9 pages, 6 figures

An electron localization measure was originally introduced to characterize chemical bond structures in molecules. Recently, a nucleon localization based on Hartree-Fock densities has been introduced to investigate $\alpha$-cluster structures in light nuclei. Compared to the local nucleonic densities, the nucleon localization function has been shown to be an excellent indicator of shell effects and cluster correlations. Using the spatial nucleon localization measure, we investigate the emergence of fragments in fissioning heavy nuclei. To illustrate basic concepts of nucleon localization, we employ the self-consistent energy density functional method with a quantified energy density functional optimized for fission studies. We study the particle densities and spatial nucleon localization distributions along the fission pathways of $^{264}$Fm, $^{232}$Th and $^{240}$Pu. We demonstrate that the fission fragments are formed fairly early in the evolution, well before scission. We illustrate the usefulness of the localization measure by showing how the hyperdeformed state of $^{232}$Th can be understood in terms of a quasimolecular state made of $^{132}$Sn and $^{100}$Zr fragments. Compared to nucleonic distributions, the nucleon localization function more effectively quantifies nucleonic clustering: its characteristic oscillating pattern, traced back to shell effects, is a clear fingerprint of cluster/fragment configurations. This is of particular interest for studies of fragment formation and fragment identification in fissioning nuclei., Comment: 7 pages, 8 figures

In quadrupole-bound anions, an extra electron is attached at a sufficiently large quadrupole moment of a neutral molecule, which is lacking a permanent dipole moment. The nature of the bound states and low-lying resonances of such anions is of interest for understanding the threshold behavior of open quantum systems in general. In this work, we investigate the properties of quadrupolar anions as extreme halo systems, the formation of rotational bands, and the transition from a subcritical to supercritical electric quadrupole moment. We solve the electron-plus-molecule problem using a non-adiabatic coupled-channel formalism by employing the Berggren ensemble, which explicitly contains bound states, narrow resonances, and the scattering continuum. We demonstrate that binding energies and radii of quadrupolar anions strictly follow the scaling laws for two-body halo systems. Contrary to the case of dipolar anions, ground-state band of quadrupolar anions smoothly extend into the continuum, and many rotational bands could be identified above the detachment threshold. We study the evolution of a bound state of an anion as to dives into the continuum at a critical quadrupole moment and we show that the associated critical exponent is consistent with the second-order phase transition. Everything considered, quadrupolar anions represent a perfect laboratory for the studies of marginally bound open quantum systems.