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In stellar environments nuclei appear at finite temperatures, becoming extremely hot in core-collapse supernovae and neutron star mergers. However, due to theoretical and computational complexity, most model calculations of nuclear properties are performed at zero temperature, while those existing at finite temperatures are limited only to selected regions of the nuclide chart. In this study we perform the global calculation of nuclear properties for even-even $8 \leq Z \leq 104$ nuclei at temperatures in range $0\le T \le 2$ MeV. Calculations are based on the finite temperature relativistic Hartree-Bogoliubov model supplemented by the Bonche-Levit-Vautherin vapor subtraction procedure. We find that near the neutron-drip line the continuum states have significant contribution already at moderate temperature $T\approx 1$ MeV, thus emphasising the necessity of the vapor subtraction procedure. Results include neutron emission lifetimes, quadrupole deformations, neutron skin thickness, proton and neutron pairing gaps, entropy and excitation energy. Up to the temperature $T\approx 1$ MeV nuclear landscape is influenced only moderately by the finite-temperature effects, mainly by reducing the pairing correlations. As the temperature increases further, the effects on nuclear structures become pronounced, reducing both the deformations and the shell effects., Comment: 18 pages, 14 figures, submitted to Physical Review C

A clear connection can be established between properties of nuclear matter and finite-nuclei observables, such as the correlation between the slope of the symmetry energy and dipole polarizability, or between compressibility and the isoscalar monopole giant resonance excitation energy. Establishing a connection between realistic atomic nuclei and an idealized infinite nuclear matter leads to a better understanding of underlying physical mechanisms that govern nuclear dynamics. In this work, we aim to study the dependence of the binding energies and related quantities (e.g. location of drip lines, the total number of bound even-even nuclei) on the symmetry energy $S_2(\rho)$. The properties of finite nuclei are calculated by employing the relativistic Hartree-Bogoliubov (RHB) model, assuming even-even axial and reflection symmetric nuclei. Calculations are performed by employing two families of relativistic energy density functionals (EDFs), based on different effective Lagrangians, constrained to a specific symmetry energy at saturation density $J$ within the interval of $30$--$36$ MeV. Nuclear binding energies and related quantities of bound nuclei are calculated between $8 \leq Z \leq 104$ from the two-proton to the two-neutron drip line. As the neutron drip line is approached, the interactions with stiffer $J$ tend to predict more bound nuclei, resulting in a systematic shift of the two-neutron drip line towards more neutron-rich nuclei. Consequentially, a correlation between the number of bound nuclei $N_{nucl}$ and $S_2(\rho)$ is established for a set of functionals constrained using the similar optimization procedures. The direction of the relationship between the number of bound nuclei and symmetry energy highly depends on the density under consideration., Comment: 9 pages, 5 figures

Starting from a quantum theory of dissipation for nuclear collective motion, the time-dependent generator coordinate method (TDGCM) is extended to allow for dissipation effects in the description of induced fission dynamics. The extension is based on a generalization of the GCM generating functions that includes excited states, and the resulting equation of motion in the collective coordinates and excitation energy. With the assumption of a narrow hamiltonian kernel, an expansion in a power series in collective momenta leads to a Schr\"odinger-like equation that explicitly includes a dissipation term, proportional to the momentum of the statistical wave function. An illustrative calculation is performed for induced fission of $^{228}$Th. The three-dimensional model space includes the axially-symmetric quadrupole and octupole shape variables, and the nuclear temperature. When compared to data for photo-induced fission of $^{228}$Th, the calculated fission yields demonstrate the important role of the additional term in the hamiltonian that explicitly takes into account the dissipation of energy of collective motion into intrinsic degrees of freedom., Comment: 9 pages, 7 figures

The role of dynamical pairing in induced fission dynamics is investigated using the time-dependent generator coordinate method in the Gaussian overlap approximation, based on the microscopic framework of nuclear energy density functionals. A calculation of fragment charge yields for induced fission of $^{228}$Th is performed in a three-dimensional space of collective coordinates that, in addition to the axial quadrupole and octupole intrinsic deformations of the nuclear density, also includes an isoscalar pairing degree of freedom. It is shown that the inclusion of dynamical pairing has a pronounced effect on the collective inertia, the collective flux through the scission hyper-surface, and the resulting fission yields, reducing the asymmetric peaks and enhancing the contribution of symmetric fission, in better agreement with the empirical trend., Comment: 8 pages, 6 figures. arXiv admin note: text overlap with arXiv:2004.10089

Starting from a general many-body fermionic Hamiltonian, we derive the equations of motion (EOM) for nucleonic propagators in a superfluid system. The resulting EOM is of the Dyson type formulated in the basis of Bogoliubov's quasiparticles. As the leading contributions to the dynamical kernel of this EOM in strongly-coupled regimes contain phonon degrees of freedom in various channels, an efficient method of calculating phonon's characteristics is required to successfully model these kernels. The traditional quasiparticle random phase approximation (QRPA) solvers are typically used for this purpose in nuclear structure calculations, however, they become very prohibitive in non-spherical geometries. In this work, by linking the notion of the quasiparticle-phonon vertex to the variation of the Bogoliubov's Hamiltonian, we show that the recently developed finite-amplitude method (FAM) can be efficiently employed to compute the vertices within the FAM-QRPA. To illustrate the validity of the method, calculations based on the relativistic density-dependent point-coupling Lagrangian are performed for the single-nucleon states in heavy and medium-mass nuclei with axial deformations. The cases of $^{38}$Si and $^{250}$Cf are presented and discussed., Comment: Article: 11 pages, 6 figures

A model is developed, based on the density functional perturbation theory and the inverse Kohn-Sham method, that can be used to improve relativistic nuclear energy density functionals towards an exact but unknown Kohn-Sham exchange-correlation functional. The improved functional is determined by empirical exact ground-state densities of finite systems. A test of the model and an illustrative calculation are performed, starting from two different approximate functionals, to reproduce the parameters and density dependence of a target functional, using exact ground-state densities of symmetric N=Z systems.

A microscopic method for calculating nuclear level densities (NLD) is developed, based on the framework of energy density functionals. Intrinsic level densities are computed from single-quasiparticle spectra obtained in a finite-temperature self-consistent mean-field (SCMF) calculation that takes into account nuclear deformation, and is specified by the choice of the energy density functional (EDF) and pairing interaction. The total level density is calculated by convoluting the intrinsic density with the corresponding collective level density, determined by the eigenstates of a five-dimensional quadrupole or quadrupole plus octupole collective Hamiltonian. The parameters of the Hamiltonian (inertia parameters, collective potential) are consistently determined by deformation-constrained SCMF calculations using the same EDF and pairing interaction. The model is applied in the calculation of NLD of $^{94,96,98}$Mo, $^{106,108}$Pd, $^{106,112}$Cd, $^{160,162,164}$Dy, $^{166}$Er, and $^{170,172}$Yb, in comparison with available data. It is shown that the collective enhancement of the intrinsic level density, consistently computed from the eigenstates of the corresponding collective Hamiltonian, leads to total NLDs that are in excellent agreement with data over the whole energy range of measured values., Comment: 9 pages, 7 figures

Collective mass tensors derived in the cranking approximation to the adiabatic time-dependent Hartree-Fock-Bogoliubov (ATDHFB) method are employed in a study of induced fission dynamics. Together with a collective potential determined in deformation-constrained self-consistent mean-field calculations based on nuclear energy density functionals, the mass tensors specify the collective Hamiltonian that governs the time evolution of the nuclear wave function from an initial state at equilibrium deformation, up to scission and the formation of fission fragments. In an illustrative calculation of low-energy induced fission of $^{228}$Th, $^{230}$Th, $^{234}$U, and $^{240}$Pu, we compare the non-perturbative and perturbative cranking ATDHFB mass tensors in the plane of axially-symmetric quadrupole and octupole deformations, as well as the resulting charge yields., Comment: 7 pages, 7 figures. arXiv admin note: text overlap with arXiv:1902.09535

Low-energy positive and negative parity collective states in the equilibrium minimum, and the dynamics of induced fission of actinide nuclei are investigated in a unified theoretical framework based on the generator coordinate method (GCM) with the Gaussian overlap approximation (GOA). The collective potential and inertia tensor, both at zero and finite temperature, are computed using the self-consistent multidimensionally constrained relativistic mean field (MDC-RMF) model, based on the energy density functional DD-PC1. Pairing correlations are treated in the BCS approximation with a separable pairing force of finite range. A collective quadrupole-octupole Hamiltonian characterized by zero-temperature axially-symmetric deformation energy surface and perturbative cranking inertia tensor, is used to model the low-lying excitation spectrum. The fission fragment charge distributions are obtained by propagating the initial collective states in time with the time-dependent GCM+GOA that uses the same quadrupole-octupole Hamiltonian, but with the collective potential and inertia tensor computed at finite temperature. The illustrative charge yields of $^{228}$Th, $^{234}$U, $^{240}$Pu, $^{244}$Cm, and $^{250}$Cf are in very good agreement with experiment, and the predicted mass asymmetry is consistent with the result of a recent microscopic study that has attributed the distribution (peak) of the heavier-fragment nuclei to shell-stabilized octupole deformations., Comment: 10 pages, 8 figures. arXiv admin note: text overlap with arXiv:1809.06144

Spectroscopic properties of low-lying states and cluster structures in $^{12}$C are analyzed in a "beyond mean-field framework" based on global energy density functionals (EDFs). To build symmetry-conserving collective states, axially-symmetric and reflection-asymmetric solutions of the relativistic Hartree-Bogoliubov equations are first projected onto good values of angular momentum, particle number, and parity. Configuration mixing is implemented using the generator coordinate method formalism. It is shown that such a global microscopic approach, based on a relativistic EDF, can account for the main spectroscopic features of $^{12}$C, including the ground-state and linear-chain bands as well as, to a certain approximation, the excitation energy of the Hoyle state. The calculated form factors reproduce reasonably well the available experimental values, and display an accuracy comparable to that of dedicated microscopic cluster models., Comment: 10 pages, 6 figures

The dynamics of induced fission of $^{226}$Th is investigated in a theoretical framework based on the finite-temperature time-dependent generator coordinate method (TDGCM) in the Gaussian overlap approximation (GOA). The thermodynamical collective potential and inertia tensor at temperatures in the interval $T=0 - 1.25$ MeV are calculated using the self-consistent multidimensionally constrained relativistic mean field (MDC-RMF) model, based on the energy density functional DD-PC1. Pairing correlations are treated in the BCS approximation with a separable pairing force of finite range. Constrained RMF+BCS calculations are carried out in the collective space of axially symmetric quadrupole and octupole deformations for the asymmetric fissioning nucleus $^{226}$Th. The collective Hamiltonian is determined by the temperature-dependent free energy surface and perturbative cranking inertia tensor, and the TDGCM+GOA is used to propagate the initial collective state in time. The resulting charge and mass fragment distributions are analyzed as functions of the internal excitation energy. The model can qualitatively reproduce the empirical triple-humped structure of the fission charge and mass distributions already at $T=0$, but the precise experimental position of the asymmetric peaks and the symmetric-fission yield can only be accurately reproduced when the potential and inertia tensor of the collective Hamiltonian are determined at finite temperature, in this particular case between $T=0.75$ MeV and $T=1$ MeV., Comment: 9 pages, 7 figures

A study of parameter sensitivity of nuclear energy density functionals, initiated in the first part of this work \cite{NV.16}, is extended by the inclusion of data on ground-state properties of finite nuclei in the application of the manifold boundary approximation method (MBAM). Density functionals used in self-consistent mean-field calculations, and nuclear structure models based on them, are generally "sloppy" and exhibit an exponential range of sensitivity to parameter variations. Concepts of information geometry are used to identify the presence of effective functionals of lower dimension in parameter space associated with parameter combinations that can be tightly constrained by data. The MBAM is used in an iterative procedure that systematically reduces the complexity and the dimension of parameter space of a sloppy functional, with properties of nuclear matter and data on finite nuclei determining not only the values of model parameters, but also the optimal functional form of the density dependence., Comment: Accepted for publication in Physical Review C. arXiv admin note: text overlap with arXiv:1606.08617

Concepts from information geometry are used to analyse parameter sensitivity for a nuclear energy density functional, representative of a class of semi-empirical functionals that start from a microscopically motivated ansatz for the density dependence of the energy of a system of protons and neutrons. It is shown that such functionals are sloppy, characterized by an exponential range of sensitivity to parameter variations. Responsive to only a few stiff parameter combinations, they exhibit an exponential decrease of sensitivity to variations of the remaining soft parameters. By interpreting the space of model predictions as a manifold embedded in the data space, with the parameters of the functional as coordinates on the manifold, it is also shown that the exponential distribution of model manifold widths corresponds to the distribution of parameter sensitivity. Using the Manifold Boundary Approximation Method, we illustrate how to systematically construct effective nuclear density functionals of successively lower dimension in parameter space until sloppiness is eventually eliminated and the resulting functional contains only stiff combinations of parameters., Comment: 11 figures

Studies of fission dynamics, based on nuclear energy density functionals, have shown that the coupling between shape and pairing degrees of freedom has a pronounced effect on the nonperturbative collective inertia and, therefore, on dynamic (least-action) spontaneous fission paths and half-lives. Collective potentials and nonperturbative cranking collective inertia tensors are calculated using the multidimensionally-constrained relativistic mean-field (MDC-RMF) model. Pairing correlations are treated in the BCS approximation using a separable pairing force of finite range. Pairing fluctuations are included as a collective variable using a constraint on particle-number dispersion. Fission paths are determined with the dynamic programming method by minimizing the action in multidimensional collective spaces. The dynamics of spontaneous fission of $^{264}$Fm and $^{250}$Fm are explored. Fission paths, action integrals and corresponding half-lives computed in the three-dimensional collective space of shape and pairing coordinates, using the relativistic functional DD-PC1 and a separable pairing force of finite range, are compared with results obtained without pairing fluctuations. Results for $^{264}$Fm are also discussed in relation with those recently obtained using the HFB model. The inclusion of pairing correlations in the space of collective coordinates favors axially symmetric shapes along the dynamic path of the fissioning system, amplifies pairing as the path traverses the fission barriers, significantly reduces the action integral and shortens the corresponding SF half-life., Comment: 10 pages, 8 figures. arXiv admin note: text overlap with arXiv:1511.05689

Recent microscopic studies, based on the theoretical framework of nuclear energy density functionals, have analyzed dynamic (least action) and static (minimum energy) fission paths, and it has been shown that in addition to the important role played by nonaxial and/or octupole collective degrees of freedom, fission paths crucially depend on the approximations adopted in calculating the collective inertia. The dynamics of spontaneous fission of $^{264}$Fm and $^{250}$Fm is explored. The fission paths, action integrals and the corresponding half-lives predicted by the functionals PC-PK1 and DD-PC1 are compared and, in the case of $^{264}$Fm, discussed in relation with recent results obtained using the HFB model based on the Skyrme functional SkM$^*$ and a density dependent mixed pairing interaction. Deformation energy surfaces, collective potentials, and perturbative and nonperturbative cranking collective inertia tensors are calculated using the multidimensionally-constrained relativistic Hartree-Bogoliubov (MDC-RHB) model, with the energy density functionals PC-PK1 and DD-PC1. Pairing correlations are treated in the Bogoliubov approximation using a separable pairing force of finite range. The least-action principle is employed to determine dynamic spontaneous fission paths., Comment: Submitted to Physical Review C

A quantitative analysis of the evolution of nuclear shapes and shape phase transitions, including regions of short-lived nuclei that are becoming accessible in experiments at radioactive-beam facilities, necessitate accurate modeling of the underlying nucleonic dynamics. Important theoretical advances have recently been made in studies of complex shapes and the corresponding excitation spectra and electromagnetic decay patterns, especially in the "beyond mean-field" framework based on nuclear density functionals. Interesting applications include studies of shape evolution and coexistence in N = 28 isotones, the structure of lowest $0^+$ excitations in deformed N $\approx$ 90 rare-earth nuclei, and quadrupole and octupole shape transitions in thorium isotopes., Comment: To be published in focus issue of Journal of physics G "Shape coexistence in nuclei"

The stability of model parameters for a class of relativistic energy density functionals, characterized by contact (point-coupling) effective inter-nucleon interactions and density-dependent coupling parameters, is analyzed using methods of statistical analysis. A set of pseudo-observables in infinite and semi-infinite nuclear matter is used to define a quality measure $\chi^2$ for subsequent analysis. We calculate uncertainties of model parameters and correlation coefficients between parameters, and determine the eigenvectors and eigenvalues of the matrix of second derivatives of $\chi^2$ at the minimum. This allows to examine the stability of the density functional in nuclear matter, and to deduce weakly and strongly constrained combinations of parameters. In addition, we also compute uncertainties of observables that are not included in the calculation of $\chi^2$: binding energy of asymmetric nuclear matter, surface thickness of semi-infinite nuclear matter, binding energies and charge radii of finite nuclei., Comment: Submitted to JPhysG Focus issue "Enhancing the interaction between nuclear experiment and theory through information and statistics" (ISNET)

The role of saturation for cluster formation in finite systems such as atomic nuclei is analyzed by considering three length-scale ratios, and performing deformation-constrained self-consistent mean-field calculations. The effect of clusterisation in deformed light systems is related to the saturation property of the inter-nucleon interaction. The formation of clusters at low nucleon density is illustrated by expanding the radius of $^{16}$O. A phase diagram shows that the formation of clusters can be interpreted as a hybrid state between the crystal and the liquid phases. In the hybrid cluster phase the confining potential attenuates the delocalization generated by the effective nuclear interaction.

A new implementation of the finite amplitude method (FAM) for the solution of the relativistic quasiparticle random-phase approximation (RQRPA) is presented, based on the relativistic Hartree-Bogoliubov (RHB) model for deformed nuclei. The numerical accuracy and stability of the FAM -- RQRPA is tested in a calculation of the monopole response of $^{22}$O. As an illustrative example, the model is applied to a study of the evolution of monopole strength in the chain of Sm isotopes, including the splitting of the giant monopole resonance in axially deformed systems., Comment: 11 pager, published in Physical Review C

The 1S0 pairing gap in isospin-symmetric nuclear matter and finite nuclei is investigated using the chiral nucleon-nucleon potential at the N3LO order in the two-body sector, and the N2LO order in the three-body sector. To include realistic nuclear forces in RHB (Relativistic Hartree Bolgoliubov) calculations we rely on a separable form of the pairing interaction adjusted to the bare nuclear force. The separable pairing force is applied to the analysis of pairing properties for several isotopic and isotonic chains of spherical nuclei., Comment: 13 pages, 3 figures, submitted to PRC

Relativistic energy density functionals (EDF) have become a standard tool for nuclear structure calculations, providing a complete and accurate, global description of nuclear ground states and collective excitations. Guided by the medium dependence of the microscopic nucleon self-energies in nuclear matter, semi-empirical functionals have been adjusted to the nuclear matter equation of state and to bulk properties of finite nuclei, and applied to studies of arbitrarily heavy nuclei, exotic nuclei far from stability, and even systems at the nucleon drip-lines. REDF-based structure models have also been developed that go beyond the static mean-field approximation, and include collective correlations related to the restoration of broken symmetries and to fluctuations of collective variables. These models are employed in analyses of structure phenomena related to shell evolution, including detailed predictions of excitation spectra and electromagnetic transition rates., Comment: To be published in Progress in Particle and Nuclear Physics