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.

Nuclear density functional theory is the only microscopical theory that can be applied throughout the entire nuclear landscape. Its key ingredient is the energy density functional. In this work, we propose a new parameterization UNEDF2 of the Skyrme energy density functional. The functional optimization is carried out using the POUNDerS optimization algorithm within the framework of the Skyrme Hartree-Fock-Bogoliubov theory. Compared to the previous parameterization UNEDF1, restrictions on the tensor term of the energy density have been lifted, yielding a very general form of the energy density functional up to second order in derivatives of the one-body density matrix. In order to impose constraints on all the parameters of the functional, selected data on single-particle splittings in spherical doubly-magic nuclei have been included into the experimental dataset. The agreement with both bulk and spectroscopic nuclear properties achieved by the resulting UNEDF2 parameterization is comparable with UNEDF1. While there is a small improvement on single-particle spectra and binding energies of closed shell nuclei, the reproduction of fission barriers and fission isomer excitation energies has degraded. As compared to previous UNEDF parameterizations, the parameter confidence interval for UNEDF2 is narrower. In particular, our results overlap well with those obtained in previous systematic studies of the spin-orbit and tensor terms. UNEDF2 can be viewed as an all-around Skyrme EDF that performs reasonably well for both global nuclear properties and shell structure. However, after adding new data aiming to better constrain the nuclear functional, its quality has improved only marginally. These results suggest that the standard Skyrme energy density has reached its limits and significant changes to the form of the functional are needed.Comment: 18 pages, 13 figures, 12 tables; resubmitted for publication to Phys. Rev. C after second review by refere

Axially deformed solution of the Skyrme-Hartree-Fock-Bogolyubov equations using the transformed harmonic oscillator basis (II) hfbtho v2.00d: a new version of the program. AbstractWe describe the new version 2.00d of the code hfbtho that solves the nuclear Skyrme Hartree-Fock (HF) or Skyrme Hartree-Fock-Bogolyubov (HFB) problem by using the cylindrical transformed deformed harmonic oscillator basis. In the new version, we have implemented the following features: (i) the modified Broyden method for non-linear problems, (ii) optional breaking of reflection symmetry, (iii) calculation of axial multipole moments, (iv) finite temperature formalism for the HFB method, (v) linear constraint method based on the approximation of the Random Phase Approximation (RPA) matrix for multi-constraint calculations, (vi) blocking of quasi-particles in the Equal Filling Approximation (EFA), (vii) framework for generalized energy density with arbitrary density-dependences, and (viii) shared memory parallelism via OpenMP pragmas. Keywords: Hartree-Fock; Hartree-Fock-Bogolyubov; Nuclear many-body problem; Skyrme interaction; Self-consistent mean field; Density functional theory; Generalized energy density functional; Nuclear matter; Quadrupole deformation; Octupole deformation; Constrained calculations; Potential energy surface; Pairing; Particle number projection; Nuclear radii; Quasiparticle spectra; Harmonic oscillator; Coulomb field; Transformed harmonic oscillator; Finite temperature; Shared memory parallelism. Nature of physical problemThe solution of self-consistent mean-field equations for weakly-bound paired nuclei requires a correct description of the asymptotic properties of nuclear quasiparticle wave functions. In the present implementation, this is achieved by using the single-particle wave functions of the transformed harmonic oscillator, which allows for an accurate description of deformation effects and pairing correlations in nuclei arbitrarily close to the particle drip lines. Method of solutionThe program uses the axial Transformed Harmonic Oscillator (THO) single-particle basis to expand quasiparticle wave functions. It iteratively diagonalizes the Hartree-Fock-Bogolyubov Hamiltonian based on generalized Skyrme-like energy densities and zero-range pairing interactions until a self-consistent solution is found. A previous version of the program was presented in: M.V. Stoitsov, J. Dobaczewski, W. Nazarewicz, P. Ring, Comput. Phys. Commun. 167 (2005) 43-63. Summary of revisions1. The modified Broyden method has been implemented, 2. Optional breaking of reflection symmetry has been implemented, 3. The calculation of all axial multipole moments up to λ = 8 has been implemented, 2 4. The finite temperature formalism for the HFB method has been implemented, 5. The linear constraint method based on the approximation of the Random Phase Approximation (RPA) matrix for multi-constraint calculations has been implemented, 6. The blocking of quasi-particles in the Equal Filling Approximation (EFA) has been implemented, 7. The f...

During the last decade, six new superheavy elements were added into the seventh period of the periodic table, with the approval of their names and symbols. This milestone was followed by proclaiming 2019 the International Year of the Periodic Table of Chemical Elements by the United Nations General Assembly. According to theory, due to their large atomic numbers, the new arrivals are expected to be qualitatively and quantitatively different from lighter species. The questions pertaining to superheavy atoms and nuclei are in the forefront of research in nuclear and atomic physics, and chemistry. This Colloquium offers a broad perspective on the field and outlines future challenges. References

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 [1] and the experimental determination of masses for 55−57 Ca [2] 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 Gaussianprocess-based extrapolations we introduce the posterior probability pex 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 pex ≈ 76% to be bound to two-neutron emission while the nucleus 61 Ca is likely to decay by emitting a neutron (pex ≈ 46%).

The modelling of nuclear reactions and radioactive decays in astrophysical or earth-based conditions requires detailed knowledge of the masses of essentially all nuclei. Microscopic mass models based on nuclear energy density functionals (EDFs) can be descriptive and used to provide this information. The concept of intrinsic symmetry breaking is central to the predictive power of EDF approaches, yet is generally not exploited to the utmost by mass models because of the computational demands of adjusting up to about two dozen parameters to thousands of nuclear masses. We report on a first step to bridge the gap between what is presently feasible for studies of individual nuclei and large-scale models: we present a new Skyrme-EDF-based model that was adjusted using a three-dimensional coordinate-space representation, for the first time allowing for both axial and triaxial deformations during the adjustment process. To compensate for the substantial increase in computational cost brought by the latter, we have employed a committee of multilayer neural networks to model the objective function in parameter space and guide us towards the overall best fit. The resulting mass model BSkG1 is computed with the EDF model independently of the neural network. It yields a root mean square (rms) deviation on the 2457 known masses of 741 keV and an rms deviation on the 884 measured charge radii of 0.024 fm.

Background: Neutron-skin thickness is an excellent indicator of isovector properties of atomic nuclei. As such, it correlates strongly with observables in finite nuclei that depend on neutron-to-proton imbalance and the nuclear symmetry energy that characterizes the equation of state of neutron-rich matter. A rich worldwide experimental program involving studies with rare isotopes, parity-violating electron scattering, and astronomical observations is devoted to pinning down the isovector sector of nuclear models. Purpose: We assess the theoretical systematic and statistical uncertainties of neutron-skin thickness and relate them to the equation of state of nuclear matter, and in particular to nuclear symmetry energy parameters. Methods: We use the nuclear superfluid density functional theory with several Skyrme energy density functionals and density dependent pairing. To evaluate statistical errors and their budget, we employ the statistical covariance technique. Results: We find that the errors on neutron skin increase with neutron excess. Statistical errors due to uncertain coupling constants of the density functional are found to be larger than systematic errors, the latter not exceeding 0.06 fm in most neutron-rich nuclei across the nuclear landscape. The single major source of uncertainty is the poorly determined slope L of the symmetry energy that parametrizes its density dependence. Conclusions: To provide essential constraints on the symmetry energy of the nuclear energy density functional, next-generation measurements of neutron skins are required to deliver precision better than 0.06 fm.

Nuclear masses play a fundamental role in understanding how the heaviest elements in the Universe are created in the r-process. We predict r-process nucleosynthesis yields using neutron capture and photodissociation rates that are based on nuclear density functional theory. Using six Skyrme energy density functionals based on different optimization protocols, we determine for the first time systematic uncertainty bands -related to mass modelling -for r-process abundances in realistic astrophysical scenarios. We find that features of the underlying microphysics make an imprint on abundances especially in the vicinity of neutron shell closures: abundance peaks and troughs are reflected in trends of neutron separation energy. Further advances in nuclear theory and experiments, when linked to observations, will help in the understanding of astrophysical conditions in extreme r-process sites. Introduction -Understanding the origin of elements in nature is one of the outstanding questions in science. Here, the synthesis of the heavy elements represents a difficult interdisciplinary challenge. Half of the heavy elements up to bismuth and all of the thorium and uranium in the Universe are produced by the rapid capture of neutrons in the r-process [1]. This process requires high neutron densities and involves extreme neutron-rich nuclei not yet produced in the laboratory.In recent years, much progress has been made toward this problem in both astrophysics and nuclear physics. In astrophysics, multidimensional hydrodynamic simulations including improved microphysics indicate that (i) neutrino-driven winds following core-collapse supernovae are not neutron-rich enough to produce heavy elements as suggested in [2] (see Ref.[3] for a review); (ii) a rare kind of core-collapse supernova triggered by magnetic fields leads to neutron-rich jets where the r-process can occur [4][5][6]; and (iii) neutron star mergers (as suggested in [7] and preliminarily studied in [8]) -are excellent candidates for the synthesis of heavy elements [9][10][11] even if their contribution to the early galaxy is still under discussion. Some studies show that neutron star mergers provide an important contribution to the solar system rprocess, but this is not enough to explain the abundances in the oldest observed stars, see e.g., [12][13][14]. In contrast, other models can explain the r-process abundances at all metallicities solely based on the neutron star merger scenario [15].Experimentally, there has been impressive progress in approaching r-process nuclei, see [16][17][18][19][20][21] and references quoted therein. New-generation radioactive ion beam facilities [22][23][24] will be able to reach a range of nuclei