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Collective nuclear excitations, like giant resonances, are sensitive to nuclear deformation, as evidenced by alterations in their excitation energies and transition strength distributions. A common theoretical framework to study these collective modes, the random-phase approximation (RPA), has to deal with large dimensions spanned by all possible particle-hole configurations satisfying certain symmetries. This work aims to establish a new theoretical framework to study the impact of deformation on spin-isospin excitations, that can provide fast and reliable solutions of the RPA equations. The nuclear ground state is determined with the axially-deformed relativistic Hartree-Bogoliubov (RHB) model based on relativistic point-coupling energy density functionals (EDFs). To study the excitations in the charge-exchange channel, an axially-deformed proton-neutron relativistic quasiparticle RPA (pnRQRPA) is developed in the linear response approach. After benchmarking the axially-deformed pnRQRPA in the spherical limit, a study of spin-isospin excitations including Fermi, Gamow-Teller (GT), and Spin-Dipole (SD) is performed for selected $pf$-shell nuclei. For GT transitions, it is demonstrated that deformation leads to considerable fragmentation of the strength function. A mechanism inducing the fragmentation is studied by decomposing the total strength to different projections of total angular momentum $K$ and constraining the nuclear shape to either spherical, prolate or oblate. A similar fragmentation is also observed for SD transitions, although somewhat moderated by the complex structure of these transitions, while the Fermi strength is almost shape-independent. The axially-deformed pnRQRPA introduced in this work opens perspectives for future studies of deformation effects on astrophysically relevant weak interaction processes, in particular beta decay and electron capture., Comment: 22 pages, 11 figures, submitted to Physical Review C

In numerous astrophysical scenarios, such as core-collapse supernovae and neutron star mergers, as in well as heavy-ion collision experiments, transitions between thermally populated nuclear excited states have been shown to play an important role. Due to its simplicity and excellent extrapolation ability, the finite-temperature quasiparticle random phase approximation (FT-QRPA) presents itself as an efficient method to study the properties of hot nuclei. The statistical ensembles in the FT-QRPA make the theory much richer than its zero-temperature counterpart, but also obscure the meaning of various physical quantities. In this work, we clarify several aspects of the FT-QRPA, including notations seen in the literature, and demonstrate how to extract physical quantities from the theory. To exemplify the correct treatment of finite-temperature transitions, we place special emphasis on the charge-exchange transitions described within the proton-neutron FT-QRPA (FT-PNQRPA). With the FT-PNQRPA built on the nuclear energy-density functional theory, we obtain solutions using a relativistic matrix approach and also the non-relativistic finite amplitude method. We show that the Ikeda sum rule is fulfilled with the proper treatment of de-excitations from thermally populated excited states. Additionally, we demonstrate the impact of these transitions on stellar electron capture (EC) rates in ${}^{58,78}$Ni. While their inclusion does not influence the EC rates in ${}^{58}$Ni, the rates in ${}^{78}$Ni are dominated by de-excitations for temperatures $T > 0.5$ MeV. In systems with a large negative $Q$-value, the inclusion of de-excitations within the FT-QRPA is necessary for a complete description of reaction rates at finite temperature., Comment: 19 pages, 4 figures, submitted for publication

Background: Magnetic quadrupole (M2) excitation represents a fundamental feature in atomic nucleus associated to nuclear magnetism induced by spin and orbital transition operator. So far it has only been investigated within the non-relativistic theoretical approaches, and available experimental data are rather limited. Purpose: We aim to investigate the properties of M2 transitions in closed and open-shell nuclei using the framework of relativistic nuclear energy density functional. The calculated M2 transition strengths could be used to constrain the quenching of the spin gyromagnetic factors. Methods: The M2 excitations are described using the relativistic quasiparticle random phase approximation (RQRPA) with the residual interaction extended with the isovector-pseudovector term. Results: The M2 transition strength distributions are described and analyzed for closed and open shell nuclei. The results are compared with available experimental data and the strength missing from the experiment is discussed. The evolution of M2 transition properties has been investigated within the $^{36-64} \rm Ca$ isotope chain. Conclusion: The main M2 transitions have rather rich underlying structure and their collectivity increases with the mass number due to larger number of contributing particle-hole configurations. Pairing correlations in open shell nuclei have strong effect, causing the M2 strength reduction and shifting of the centroid energies to higher values. The analysis of M2 transition strengths indicate that considerable amount of experimental strength may be missing, mainly due to limitations to rather restricted energy ranges. The calculated M2 strengths for Ca isotopes, together with the future experimental data will allow constraining the quenching of the $g$ factors in nuclear medium., Comment: 14 pages, 9 figures

The temperature dependence of stellar electron-capture (EC) rates is investigated, with a focus on nuclei around $N=50$, just above $Z=28$, which play an important role during the collapse phase of core-collapse supernovae (CCSN). Two new microscopic calculations of stellar EC rates are obtained from a relativistic and a non-relativistic finite-temperature quasiparticle random-phase approximation approaches, for a conventional grid of temperatures and densities. In both approaches, EC rates due to Gamow-Teller transitions are included. In the relativistic calculation contributions from first-forbidden transitions are also included, and add strongly to the EC rates. The new EC rates are compared with large-scale shell model calculations for the specific case of $^{86}$Kr, providing insight into the finite-temperature effects on the EC rates. At relevant thermodynamic conditions for core-collapse, the discrepancies between the different calculations of this work are within about one order of magnitude. Numerical simulations of CCSN are performed with the spherically-symmetric GR1D simulation code to quantify the impact of such differences on the dynamics of the collapse. These simulations also include EC rates based on two parametrized approximations. A comparison of the neutrino luminosities and enclosed mass at core bounce shows that differences between simulations with different sets of EC rates are relatively small ($\approx 5\%$), suggesting that the EC rates used as inputs for these simulations have become well constrained.

The finite-temperature linear response theory based on the finite-temperature relativistic Hartree-Bogoliubov (FT-RHB) model is developed in the charge-exchange channel to study the temperature evolution of spin-isospin excitations. Calculations are performed self-consistently with relativistic point-coupling interactions DD-PC1 and DD-PCX. In the charge-exchange channel, the pairing interaction can be split into isovector ($T = 1$) and isoscalar ($T = 0$) parts. For the isovector component, the same separable form of the Gogny D1S pairing interaction is used both for the ground-state calculation as well as for the residual interaction, while the strength of the isoscalar pairing in the residual interaction is determined by comparison with experimental data on Gamow-Teller resonance (GTR) and Isobaric analog resonance (IAR) centroid energy differences in even-even tin isotopes. The temperature effects are introduced by treating Bogoliubov quasiparticles within a grand-canonical ensemble. Thus, unlike the conventional formulation of the quasiparticle random-phase approximation (QRPA) based on the Bardeen-Cooper-Schrieffer (BCS) basis, our model is formulated within the Hartree-Fock-Bogoliubov (HFB) quasiparticle basis. Implementing a relativistic point-coupling interaction and a separable pairing force allows for the reduction of complicated two-body residual interaction matrix elements, which considerably decreases the dimension of the problem in the coordinate space. The main advantage of this method is to avoid the diagonalization of a large QRPA matrix, especially at finite temperature where the size of configuration space is significantly increased. The implementation of the linear response code is used to study the temperature evolution of IAR, GTR, and spin-dipole resonance (SDR) in even-even tin isotopes in the temperature range $T = 0 - 1.5$ MeV., Comment: 20 pages, 9 figures, submitted for publication

Nuclear matrix elements (NMEs) for two-neutrino double-beta decay ($2\nu\beta\beta$) are studied in the framework of relativistic nuclear energy density functional (REDF). The properties of nuclei involved in the decay are obtained using the relativistic Hartree-Bardeen-Cooper-Schrieffer theory and relevant nuclear transitions are described using the relativistic proton-neutron quasiparticle random phase approximation based on relativistic energy density functional (REDF-QRPA). Three effective interactions have been employed, including density-dependent meson-exchange (DD-ME2) and point coupling interactions (DD-PC1 and DD-PCX), and pairing correlations are described consistently both in $T=1$ and $T=0$ channels using a separable pairing interaction. The optimal values of $T=0$ pairing strength parameter $V_{0pp}$ are constrained by the experimental data on $\beta$-decay half lives. The $2\nu\beta\beta$ matrix elements and half-lives are calculated for several nuclides experimentally known to undergo this kind of decay: $^{48}$Ca, $^{76}$Ge, $^{82}$Se, $^{96}$Zr, $^{100}$Mo, $^{116}$Cd, $^{124}$Xe, $^{128}$Te, $^{130}$Te, $^{136}$Xe and $^{150}$Nd. The model dependence of the NMEs and their sensitivity on $V_{0pp}$ is investigated, and the NMEs obtained using optimal values of $V_{0pp}$ are discussed in comparison to previous studies. The results of the present work represent an important benchmark for the future applications of the relativistic framework in studies of neutrinoless double-beta decay., Comment: 18 pages, 12 figures, accepted for publication in Physical Review C

Spin-isospin transitions in nuclei away from the valley of stability are essential for the description of astrophysically relevant weak interaction processes. While they remain mainly beyond the reach of experiment, theoretical modeling provides important insight into their properties. In order to describe the spin-isospin response,vcthe proton-neutron relativistic quasiparticle random phase approximation (PN-RQRPA) is formulated using the relativistic density-dependent point coupling interaction, and separable pairing interaction in both the $T=1$ and $T=0$ pairing channels. By implementing recently established DD-PCX interaction with improved isovector properties relevant for the description of nuclei with neutron-to-proton number asymmetry, the isobaric analog resonances (IAR) and Gamow-Teller resonances (GTR) have been investigated. In contrast to other models that usually underestimate the IAR excitation energies in Sn isotope chain, the present model accurately reproduces the experimental data, while the GTR properties depend on the isoscalar pairing interaction strength. This framework provides not only an improved description of the spin-isospin response in nuclei, but it also allows future large scale calculations of charge-exchange excitations and weak interaction processes in stellar environment., Comment: 40 pages, 6 figures, revised version

The evolution of electromagnetic transitions along isotope chains is of particular importance for the nuclear structure and dynamics, as well as for the r-process nucleosynthesis. Recent measurement of inelastic proton scattering on even-even $^{112-124}$Sn isotopes provides a novel insight into the isotopic dependence of E1 and M1 strength distributions. We investigate M1 transitions in even-even $^{100-140}$Sn isotopes from a theoretical perspective, based on relativistic nuclear energy density functional. The M1 transition strength distribution is characterized by an interplay between single and double-peak structures, that can be understood from the evolution of single-particle states, their occupations governed by the pairing correlations, and two-quasiparticle transitions involved. It is shown that discrepancy between model calculations and experiment on B(M1) transition strength is considerably reduced than previously known, and the quenching of the g-factors for the free nucleons needed to reproduce the experimental data on M1 transition strength amounts $g_{eff}/g_{free}$=0.80-0.93. Since some of the B(M1) strength above the neutron threshold may be missing in the inelastic proton scattering measurement, further experimental studies are required to confirm if only small modifications of the bare g-factors are actually needed when applied in finite nuclei., Comment: 8 pages, 7 figures, revised version

$\beta$-decay properties of nuclei are investigated within the relativistic nuclear energy density functional framework by varying the temperature and density, conditions relevant to the final stages of stellar evolution. Both thermal and nuclear pairing effects are taken into account in the description of nuclear properties and in the finite temperature proton-neutron relativistic quasiparticle random-phase approximation (FT-PNRQRPA) to calculate the relevant allowed and first-forbidden transitions in the $\beta$-decay. The temperature and density effects are studied on the $\beta$-decay half-lives between temperatures $T = 0-1.5$ MeV, and at densities $\rho Y_e = 10^7$ g/cm${}^3$ and $10^9$ g/cm${}^3$. The relevant Gamow-Teller transitions are also investigated for Ti, Fe, Cd, and Sn isotopic chains at finite temperatures. We find that the $\beta$-decay half-lives increase with increasing density $\rho Y_e$, whereas half-lives generally decrease with increasing temperature. It is shown that the temperature effects decrease the half-lives considerably in nuclei with longer half-lives at zero temperature, while only slight changes for nuclei with short half-lives are obtained. We also show the importance of including the de-excitation transitions in the calculation of the $\beta$-decay half-lives at finite temperatures. Comparing the FT-PNQRPA results with the shell-model calculations for $pf-$shell nuclei, a reasonable agreement is obtained for the temperature dependence of $\beta$-decay rates. Finally, large-scale calculations of $\beta$-decay half-lives are performed at temperatures $T_9(\text{K}) = 5$ and $T_9(\text{K}) = 10$ and densities $\rho Y_e = 10^7$ g/cm${}^3$ and $10^9$ g/cm${}^3$ for even-even nuclei in the range $8 \leq Z \leq 82$, relevant for astrophysical nucleosynthesis mechanisms., Comment: 15 pages, 7 figures, submitted for publication

The electron capture process plays an important role in the evolution of the core collapse of a massive star that precedes the supernova explosion. In this study, the electron capture on nuclei in stellar environment is described in the relativistic energy density functional framework, including both the finite temperature and nuclear pairing effects. Relevant nuclear transitions $J^\pi = 0^\pm, 1^\pm, 2^\pm$ are calculated using the finite temperature proton-neutron quasiparticle random phase approximation with the density-dependent meson-exchange effective interaction DD-ME2. The pairing and temperature effects are investigated in the Gamow-Teller transition strength as well as the electron capture cross sections and rates for ${}^{44}$Ti and ${}^{56}$Fe in stellar environment. It is found that the pairing correlations establish an additional unblocking mechanism similar to the finite temperature effects, that can allow otherwise blocked single-particle transitions. Inclusion of pairing correlations at finite temperature can significantly alter the electron capture cross sections, even up to a factor of two for ${}^{44}$Ti, while for the same nucleus electron capture rates can increase by more than one order of magnitude. We conclude that for the complete description of electron capture on nuclei both pairing and temperature effects must be taken into account., Comment: 16 pages, 11 figures, submitted to Physical Review C

The dipole polarizability of stable even-mass tin isotopes 112,114,116,118,120,124 was extracted from inelastic proton scattering experiments at 295 MeV under very forward angles performed at RCNP. Predictions from energy density functionals cannot account for the present data and the polarizability of 208Pb simultaneously. The evolution of the polarizabilities in neighboring isotopes indicates a kink at 120Sn while all model results show a nearly linear increase with mass number after inclusion of pairing corrections., Comment: 10 pages, 6 figures, submitted to Phys. Lett. B

Magnetic dipole (M1) excitations build not only a fundamental mode of nucleonic transitions, but they are also relevant for nuclear astrophysics applications. We have established a theory framework for description of M1 transitions based on the relativistic nuclear energy density functional. For this purpose the relativistic quasiparticle random phase approximation (RQRPA) is established using density dependent point coupling interaction DD-PC1, supplemented with the isovector-pseudovector interaction channel in order to study unnatural parity transitions. The introduced framework has been validated using the M1 sum rule for core-plus-two-nucleon systems, and employed in studies of the spin, orbital, isoscalar and isovector M1 transition strengths, that relate to the electromagnetic probe, in magic nuclei $^{48}$Ca and $^{208}$Pb, and open shell nuclei $^{42}$Ca and $^{50}$Ti. In these systems, the isovector spin-flip M1 transition is dominant, mainly between one or two spin-orbit partner states. It is shown that pairing correlations have a significant impact on the centroid energy and major peak position of the M1 mode. The M1 excitations could provide an additional constraint to improve nuclear energy density functionals in the future studies., Comment: 13 pages, 7 figures, accepted for publication in Physical Review C

The relativistic and nonrelativistic finite temperature proton-neutron quasiparticle random phase approximation (FT-PNQRPA) methods are developed to study the interplay of the pairing and temperature effects on the Gamow-Teller excitations in open-shell nuclei, as well as to explore the model dependence of the results by using two rather different frameworks for effective nuclear interactions. The Skyrme-type functional SkM* is employed in the nonrelativistic framework, while the density-dependent meson-exchange interaction DD-ME2 is implemented in the relativistic approach. Both the isoscalar and isovector pairing interactions are taken into account within the FT-PNQRPA. Model calculations show that below the critical temperatures the Gamow-Teller excitations display a sensitivity to both the finite temperature and pairing effects, and this demonstrates the necessity for implementing both in the theoretical framework. The established FT-PNQRPA opens perspectives for the future complete and consistent description of astrophysically relevant weak interaction processes in nuclei at finite temperature such as $\beta$-decays, electron capture, and neutrino-nucleus reactions., Comment: 15 pages, 6 figures, published in Physical Review C

With the goal of determining the $\theta_{13}$ neutrino oscillation mixing angle, the measurements of reactor antineutrino fluxes at the Double Chooz, RENO and Daya Bay experimental facilities have uncovered a systematic discrepancy between the number of observed events and theoretical expectations. In the \emph{ab initio} approach, the total reactor antineutrino spectrum is a weighted sum of spectra resulting from all $\beta$ branches of all fission products in the reactor core. At all three facilities a systematic deviation of the number of observed events from the number of predicted events was noticed, i.e., approximately 6\% of the predicted neutrinos were not observed. This discrepancy was named the reactor neutrino anomaly. In theoretical studies it is assumed that all the decays are allowed in shape, but a quarter of all transitions are actually forbidden and may have a complex energy dependence that will affect the total reactor antineutrino spectrum. In order to estimate the effect of forbidden transitions, we perform a fully self-consistent calculation of spectra from all contributing transitions and compare the results with a purely allowed approximation., Comment: 10 pages, 4 figures

We introduce a new relativistic energy density functional constrained by the ground state properties of atomic nuclei along with the isoscalar giant monopole resonance energy and dipole polarizability in $^{208}$Pb. A unified framework of the relativistic Hartree-Bogoliubov model and random phase approximation based on the relativistic density-dependent point coupling interaction is established in order to determine the DD-PCX parameterization by $\chi^2$ minimization. This procedure is supplemented with the co-variance analysis in order to estimate statistical uncertainties in the model parameters and observables. The effective interaction DD-PCX accurately describes the nuclear ground state properties including the neutron-skin thickness, as well as the isoscalar giant monopole resonance excitation energies and dipole polarizabilities. The implementation of the experimental data on nuclear excitations allows constraining the symmetry energy close to the saturation density, and the incompressibility of nuclear matter by using genuine observables on finite nuclei in the $\chi^2$ minimization protocol, rather than using pseudo-observables on the nuclear matter, or by relying on the ground state properties only, as it has been customary in the previous studies., Comment: 6 pages, 3 figures, submitted to Physical Review C

This contribution reviews the present status on the available constraints to the nuclear equation of state (EoS) around saturation density from nuclear structure calculations on ground and collective excited state properties of atomic nuclei. It concentrates on predictions based on self-consistent mean-field calculations, which can be considered as an approximate realization of an exact energy density functional (EDF). EDFs are derived from effective interactions commonly fitted to nuclear masses, charge radii and, in many cases, also to pseudo-data such as nuclear matter properties. Although in a model dependent way, EDFs constitute nowadays a unique tool to reliably and consistently access bulk ground state and collective excited state properties of atomic nuclei along the nuclear chart as well as the EoS. For comparison, some emphasis is also given to the results obtained with the so called {\it ab initio} approaches that aim at describing the nuclear EoS based on interactions fitted to few-body data only. Bridging the existent gap between these two frameworks will be essential since it may allow to improve our understanding on the diverse phenomenology observed in nuclei. Examples on observations from astrophysical objects and processes sensitive to the nuclear EoS are also briefly discussed. As the main conclusion, the isospin dependence of the nuclear EoS around saturation density and, to a lesser extent, the nuclear matter incompressibility remain to be accurately determined. Experimental and theoretical efforts in finding and measuring observables specially sensitive to the EoS properties are of paramount importance, not only for low-energy nuclear physics but also for nuclear astrophysics applications., Comment: Progress in Particle and Nuclear Physics (accepted)

The model dependence in the correlations of the neutron-skin thickness in heavy nuclei with various symmetry energy parameters is analyzed by using several families of systematically varied microscopic mean field models. Such correlations show a varying degree of model dependence once the results for all the different families are combined. Some mean field models associated with similar values of the symmetry energy slope parameter at saturation density $L$, and pertaining to different families, yield a greater-than-expected spread in the neutron-skin thickness of the $^{208}$Pb nucleus. The effective value of the symmetry energy slope parameter $L_{\rm eff}$, determined by using the nucleon density profiles of the finite nucleus and the density derivative $S^\prime(\rho)$ of the symmetry energy starting from about saturation density up to low densities typical of the surface of nuclei, seems to account for the spread in the neutron-skin thickness for the models with similar $L$. The differences in the values of $L_{\rm eff}$ are mainly due to the small differences in the nucleon density distributions of heavy nuclei in the surface region and the behavior of the symmetry energy at subsaturation densities., Comment: 10 pages including 6 figures

The information on the symmetry energy and its density dependence is deduced by comparing the available data on the electric dipole polarizability $\alpha_D$ of ${}^{68}$Ni, ${}^{120}$Sn, and ${}^{208}$Pb with the predictions of the Random Phase Approximation, using a representative set of nuclear energy density functionals. The calculated values of $\alpha_D$ are used to validate different correlations involving $\alpha_D$, the symmetry energy at the saturation density $J$, the corresponding slope parameter $L$ and the neutron skin thickness $\Delta r_{\!np}$, as suggested by the Droplet Model. A subset of models that reproduce simultaneously the measured polarizabilities in ${}^{68}$Ni, ${}^{120}$Sn, and ${}^{208}$Pb are employed to predict the values of the symmetry energy parameters at saturation density and $\Delta r_{\!np}$. The resulting intervals are: $J\!=\!30 \text{-}35$ MeV, $L\!=\!20 \text{-} 66$ MeV; and the values for $\Delta r_{\!np}$ in ${}^{68}$Ni, ${}^{120}$Sn, and ${}^{208}$Pb are in the ranges: 0.15\text{-}0.19 fm, 0.12\text{-}0.16 fm, and 0.13\text{-}0.19 fm, respectively. The strong correlation between the electric dipole polarizabilities of two nuclei is instrumental to predict the values of electric dipole polarizabilities in other nuclei., Comment: 12 pages, 2 tables and 6 figures

We introduce a hybrid method to determine the neutrino mass hierarchy by simultaneous measurements of responses of at least two detectors to antineutrino and neutrino fluxes from accretion and cooling phases of core-collapse supernovae. The (anti)neutrino-nucleus cross sections for $^{56}$Fe and $^{208}$Pb are calculated in the framework of the relativistic nuclear energy density functional and weak interaction Hamiltonian, while the cross sections for inelastic scattering on free protons $\mathrm{p}(\bar{\nu}_\mathrm{e},\mathrm{e}^{+})\mathrm{n}$ are obtained using heavy-baryon chiral perturbation theory. The modelling of (anti)neutrino fluxes emitted from a protoneutron star in a core-collapse supernova include collective and Mikheyev-Smirnov-Wolfenstein effects inside the exploding star. The particle emission rates from the elementary decay modes of the daughter nuclei are calculated for normal and inverted neutrino mass hierarchy. It is shown that simultaneous use of (anti)neutrino detectors with different target material allows to determine the neutrino mass hierarchy from the ratios of $\nu_\mathrm{e}$- and $\bar{\nu}_\mathrm{e}$-induced particle emissions. This hybrid method favors neutrinos from the supernova cooling phase and the implementation of detectors with heavier target nuclei ($^{208}$Pb) for the neutrino sector, while for antineutrinos the use of free protons in mineral oil or water is the appropriate choice., Comment: 22 pages, 7 figures, 3 tables

Relativistic energy density functionals have become a standard framework for nuclear structure studies of ground-state properties and collective excitations over the entire nuclide chart. We review recent developments in modeling nuclear weak-interaction processes: charge-exchange excitations and the role of isoscalar proton-neutron pairing, charged-current neutrino-nucleus reactions relevant for supernova evolution and neutrino detectors, and calculation of beta-decay rates for r-process nucleosynthesis., Comment: 22 pages, 12 figures, submitted for publication

In this contribution, we review some works related with the extraction of the symmetry energy parameters from isovector nuclear excitations, like the giant resonances. Then, we move to the general issue of how to assess whether correlations between a parameter of the nuclear equation of state and a nuclear observable are robust or not. To this aim, we introduce the covariance analysis and we discuss some counter-intuitive, yet enlightening, results from it., Comment: To be published in the proceedings of the 2014 Zakopane Conference on Nuclear Physics (Acta Physica Polonica B)

We present the covariance analysis of two successful nuclear energy density functionals, (i) a non-relativistic Skyrme functional built from a zero-range effective interaction, and (ii) a relativistic nuclear energy density functional based on density dependent meson-nucleon couplings. The covariance analysis is a useful tool for understanding the limitations of a model, the correlations between observables and the statistical errors. We show, for our selected test nucleus 208Pb, that when the constraint on a property A included in the fit is relaxed, correlations with other observables B become larger; on the other hand, when a strong constraint is imposed on A, the correlations with other properties become very small. We also provide a brief review, partly connected with the covariance analysis, of some instabilities displayed by several energy density functionals currently used in nuclear physics., Comment: Accepted in JPhysG; Focus issue "Enhancing the interaction between nuclear experiment and theory through information and statistics" (ISNET)

We study relationships between properties of collective excitations in finite nuclei and the phase transition density $n_t$ and pressure $P_t$ at the inner edge separating the liquid core and the solid crust of a neutron star. A theoretical framework that includes the thermodynamic method, relativistic nuclear energy density functionals and the quasiparticle random-phase approximation is employed in a self-consistent calculation of $(n_t,P_t)$ and collective excitations in nuclei. The covariance analysis shows that properties of charge-exchange dipole transitions, isovector giant dipole and quadrupole resonances and pygmy dipole transitions are correlated with the core-crust transition density and pressure. A set of relativistic nuclear energy density functionals, characterized by systematic variation of the density dependence of the symmetry energy of nuclear matter, is used to constrain possible values for $(n_t,P_t)$. By comparing the calculated excitation energies of giant resonances, energy weighted pygmy dipole strength, and dipole polarizability with available data, we obtain the weighted average values: $n_t = 0.0955 \pm 0.0007$ fm$^{-3}$ and $P_t = 0.59 \pm 0.05$ MeV fm$^{-3}$., Comment: 4 pages, 3 figures, paper submitted for publication

The DIRHB package consists of three Fortran computer codes for the calculation of the ground-state properties of even-even atomic nuclei using the framework of relativistic self-consistent mean-field models. Each code corresponds to a particular choice of spatial symmetry: the DIRHBS, DIRHBZ and DIRHBT codes are used to calculate nuclei with spherical symmetry, axially symmetric quadrupole deformation, and triaxial quadrupole shapes, respectively. Reflection symmetry is assumed in all three cases. The latest relativistic nuclear energy density functionals are implemented in the codes, thus enabling efficient and accurate calculations over the entire nuclide chart., Comment: Accepted for publication in Computer Physics Communications

The $^{208}$Pb($p$,$n\gamma\bar p$) $^{207}$Pb reaction at a beam energy of 30 MeV has been used to excite the anti-analog of the giant dipole resonance (AGDR) and to measure its $\gamma$-decay to the isobaric analog state in coincidence with proton decay of IAS. The energy of the transition has also been calculated with the self-consistent relativistic random-phase approximation (RRPA), and found to be linearly correlated to the predicted value of the neutron-skin thickness ($\Delta R_{pn}$). By comparing the theoretical results with the measured transition energy, the value of 0.190 $\pm$ 0.028 fm has been determined for $\Delta R_{pn}$ of $^{208}$Pb, in agreement with previous experimental results. The AGDR excitation energy has also been used to calculate the symmetry energy at saturation ($J=32.7 \pm 0.6$ MeV) and the slope of the symmetry energy ($L=49.7 \pm 4.4$ MeV), resulting in more stringent constraints than most of the previous studies., Comment: 6 pages, 5 figures. arXiv admin note: text overlap with arXiv:1205.2325

The Coulomb Dissociation (CD) cross sections of the stable isotopes 92,94,100Mo and of the unstable isotope 93Mo were measured at the LAND/R3B setup at GSI Helmholtzzentrum f\"ur Schwerionenforschung in Darmstadt, Germany. Experimental data on these isotopes may help to explain the problem of the underproduction of 92,94Mo and 96,98Ru in the models of p-process nucleosynthesis. The CD cross sections obtained for the stable Mo isotopes are in good agreement with experiments performed with real photons, thus validating the method of Coulomb Dissociation. The result for the reaction 93Mo(g,n) is especially important since the corresponding cross section has not been measured before. A preliminary integral Coulomb Dissociation cross section of the 94Mo(g,n) reaction is presented. Further analysis will complete the experimental database for the (g,n) production chain of the p-isotopes of molybdenum., Comment: Talk given at the Conference Nuclear Physice in Astrophysics VI (NPA6), Lisbon, Portugal, May 19-24 2013. To appear in the NPA6 Proceedings in Journal of Physics: Conference Series (JPCS). 6 pages, 6 figures

The energy of the charge-exchange Anti-analog Giant Dipole Resonance (AGDR) has been calculated for the 208Pb isotope using the state-of-the-art fully self-consistent relativistic proton-neutron quasiparticle random-phase approximation based on the Relativistic Hartree-Bogoliubov model. It is shown that the AGDR centroid energy is very sensitively related to the corresponding neutron-skin thickness. The neutron-skin thickness of 208Pb has been determined very precisely by comparing the theoretical results with the available experimental data on E(AGDR). The result DR(pn)= 0.161(42) agrees nicely with the previous experimental results., Comment: arXiv admin note: substantial text overlap with arXiv:1302.6007, arXiv:1205.2325

Parity-violating electron scattering provides a model-independent determination of the nuclear weak-charge form factor that has widespread implications across such diverse areas as fundamental symmetries, nuclear structure, heavy-ion collisions, and neutron-star structure. We assess the impact of precise measurements of the weak-charge form factor of ${}^{48}$Ca and ${}^{208}$Pb on a variety of nuclear observables, such as the neutron skin and the electric-dipole polarizability. We use the nuclear Density Functional Theory with several accurately calibrated non-relativistic and relativistic energy density functionals. To assess the degree of correlation between nuclear observables and to explore systematic and statistical uncertainties on theoretical predictions, we employ the chi-square statistical covariance technique. We find a strong correlation between the weak-charge form factor and the neutron radius, that allows for an accurate determination of the neutron skin of neutron-rich nuclei. We determine the optimal range of the momentum transfer $q$ that maximizes the information content of the measured weak-charge form factor and quantify the uncertainties associated with the strange quark contribution. Moreover, we confirm the role of the electric-dipole polarizability as a strong isovector indicator. Accurate measurements of the weak-charge form factor of ${}^{48}$Ca and ${}^{208}$Pb will have a profound impact on many aspects of nuclear theory and hadronic measurements of neutron skins of exotic nuclei at radioactive-beam facilities., Comment: 10 pages, 4 figures

We study the electric dipole polarizability $\alpha_D$ in ${}^{208}$Pb based on the predictions of a large and representative set of relativistic and non-relativistic nuclear mean field models. We adopt the droplet model as a guide to better understand the correlations between $\alpha_D$ and other isovector observables. Insights from the droplet model suggest that the product of $\alpha_D$ and the nuclear symmetry energy at saturation density $J$ is much better correlated with the neutron skin thickness $\Delta r_{np}$ of ${}^{208}$Pb than the polarizability alone. Correlations of $\alpha_D J$ with $\Delta r_{np}$ and with the symmetry energy slope parameter $L$ suggest that $\alpha_D J$ is a strong isovector indicator. Hence, we explore the possibility of constraining the isovector sector of thenuclear energy density functional by comparing our theoretical predictions against measurements of both $\alpha_D$ and the parity-violating asymmetry in ${}^{208}$Pb. We find that the recent experimental determination of $\alpha_D$ in ${}^{208}$Pb in combination with the range for the symmetry energy at saturation density $J=[31\pm (2)_{\rm est.}]$\,MeV suggests $\Delta r_{np}({}^{208}{\rm Pb}) = 0.165 \pm (0.009)_{\rm exp.} \pm (0.013)_{\rm theo.} \pm (0.021)_{\rm est.} {\rm fm}$ and $L= 43 \pm(6)_{\rm exp.} \pm (8)_{\rm theo.}\pm(12)_{\rm est.}$ MeV.

Experimental and theoretical efforts are being devoted to the study of observables that can shed light on the properties of the nuclear symmetry energy. We present our new results on the excitation energy [X. Roca-Maza et al., Phys. Rev. C 87, 034301 (2013)] and polarizability of the Isovector Giant Quadrupole Resonance (IVGQR), which has been the object of new experimental investigation [S. S. Henshaw et al., Phys. Rev. Lett. 107, 222501 (2011)]. We also present our theoretical analysis on the parity violating asymmetry at the kinematics of the Lead Radius Experiment [S. Abrahamyan et al. (PREx Collaboration), Phys. Rev. Lett. 108, 112502 (2012)] and highlight its relation with the density dependence of the symmetry energy [X. Roca-Maza et al., Phys. Rev. Lett. 106, 252501 (2011)]., Comment: Proceedings - International Nuclear Physics Conference (INPC), Firenze 2 - 7 June 2013

We formulate the finite-temperature relativistic Hartree-Bogoliubov theory for spherical nuclei based on a point-coupling functional, with the Gogny or separable pairing force. Using the functional PC-PK1, the framework is applied to the study of pairing transitions in Ca, Ni, Sn, and Pb isotopic chains. The separable pairing force reproduces the gaps calculated with the Gogny force not only at zero temperature, but also at finite temperatures. By performing a systematic calculation of the even-even Ca, Ni, Sn, and Pb isotopes, it is found that the critical temperature for a pairing transition generally follows the rule $T_c =0.6 \Delta_n(0)$, where $\Delta_n(0)$ is the neutron pairing gap at zero temperature. This rule is further verified by adjusting the pairing gap at zero temperature with a strength parameter., Comment: 19 pages, 7 figures

The incompressibility of finite fermionic systems is investigated using analytical approaches and microscopic models. The incompressibility of a system is directly linked to the zero-point kinetic energy of constituent fermions, and this is a universal feature of fermionic systems. In the case of atomic nuclei, this implies a constant value of the incompressibility in medium-heavy and heavy nuclei. The evolution of nuclear incompressibility along Sn and Pb isotopic chains is analyzed using global microscopic models, based on both non-relativistic and relativistic energy functionals. The result is an almost constant incompressibility in stable nuclei and systems not far from stability, and a steep decrease in nuclei with pronounced neutron excess, caused by the emergence of a soft monopole mode in neutron-rich nuclei., Comment: 7 pages, 5 figures

We examine a method to determine the neutron-skin thickness of nuclei using data on the charge-exchange anti-analog giant dipole resonance (AGDR). Calculations performed using the relativistic proton-neutron quasiparticle random-phase approximation (RQRPA) reproduce the isotopic trend of the excitation energies of the AGDR, as well as that of the spin-flip giant dipole resonances (IVSGDR), in comparison to available data for the even-even isotopes 112-124Sn. It is shown that the excitation energies of the AGDR, obtained using a set of density-dependent effective interactions which span a range of the symmetry energy at saturation density, supplemented with the experimental values, provide a stringent constraint on the value of the neutron-skin thickness. For 124Sn, in particular, we determine the value DRpn=0.21(5) fm. The result of the present study shows that a measurement of the excitation energy of the AGDR in (p,n) reactions using rare-isotope beams in inverse kinematics, provides a valuable method for the determination of the neutron-skin thickness in exotic nuclei.

Recent improvements in the experimental determination of properties of the Isovector Giant Quadrupole Resonance (IVGQR), as demonstrated in the A=208 mass region, may be instrumental for characterizing the isovector channel of the effective nuclear interaction. We analyze properties of the IVGQR in 208Pb, using both macroscopic and microscopic approaches. The microscopic method is based on families of non-relativistic and covariant Energy Density Functionals (EDF), characterized by a systematic variation of isoscalar and isovector properties of the corresponding nuclear matter equations of state. The macroscopic approach yields an explicit dependence of the nuclear symmetry energy at some subsaturation density, for instance S(\rho=0.1 fm^{-3}), or the neutron skin thickness \Delta r_{np} of a heavy nucleus, on the excitation energies of isoscalar and isovector GQRs. Using available data it is found that S(\rho=0.1 fm{}^{-3})=23.3 +/- 0.6 MeV. Results obtained with the microscopic framework confirm the correlation of the \Delta r_{np} to the isoscalar and isovector GQR energies, as predicted by the macroscopic model. By exploiting this correlation together with the experimental values for the isoscalar and isovector GQR energies, we estimate \Delta r_{np} = 0.14 +/- 0.03 fm for 208Pb, and the slope parameter of the symmetry energy: L = 37 +/- 18 MeV.

The static dipole polarizability, $\alpha_{\rm D}$, in ${}^{208}$Pb has been recently measured with high-resolution via proton inelastic scattering at the Research Center for Nuclear Physics (RCNP). This observable is thought to be intimately connected with the neutron skin thickness, $r_{\rm skin}$, of the same nucleus and, more fundamentally, it is believed to be associated with the density dependence of the nuclear symmetry energy. The impact of $r_{\rm skin}$ on $\alpha_{\rm D}$ in ${}^{208}$Pb is investigated and discussed on the basis of a large and representative set of relativistic and non-relativistic nuclear energy density functionals (EDF)., Comment: Proceedings of NSD12, Opatija, Croatia, 9-13 July 2012

Background: In the environment of high neutrino-fluxes provided in core-collapse supernovae or neutron star mergers, neutrino-induced reactions with nuclei contribute to the nucleosynthesis processes. A number of terrestrial neutrino detectors are based on inelastic neutrino-nucleus scattering and modeling of the respective cross sections allow predictions of the expected detector reaction rates. Purpose: To provide a self-consistent microscopic description of neutrino-nucleus cross sections involving a large pool of Z = 8 - 82 nuclei for the implementation in models of nucleosynthesis and neutrino detector simulations. Methods: Self-consistent theory framework based on relativistic nuclear energy density functional is employed to determine the nuclear structure of the initial state and relevant transitions to excited states induced by neutrinos. The weak neutrino-nucleus interaction is employed in the current-current form and a complete set of transition operators is taken into account. Results: We perform large-scale calculations of charged-current neutrino-nucleus cross sections, including those averaged over supernova neutrino fluxes, for the set of even-even target nuclei from oxygen toward lead (Z = 8 - 82), spanning N = 8 - 182 (OPb pool). The model calculations include allowed and forbidden transitions up to J = 5 multipoles. Conclusions: The present analysis shows that the self-consistent calculations result in considerable differences in comparison to previously reported cross sections, and for a large number of target nuclei the cross sections are enhanced. Revision in modeling r-process nucleosynthesis based on a self-consistent description of neutrino-induced reactions would allow an updated insight into the origin of elements in the Universe and it would provide the estimate of uncertainties in the calculated element abundance patterns., Comment: 25 pages, 12 figures, submitted to Physical Review C

The gamma-decay of the anti-analog of the giant dipole resonance (AGDR) has been measured to the isobaric analog state excited in the p(124Sn,n) reaction at a beam energy of 600 MeV/nucleon. The energy of the transition was also calculated with state-of-the-art self-consistent random-phase approximation (RPA) and turned out to be very sensitive to the neutron-skin thickness (\DeltaR_(pn)). By comparing the theoretical results with the measured one, the \DeltaR_(pn) value for 124Sn was deduced to be 0.175 \pm 0.048 fm, which agrees well with the previous results. The energy of the AGDR measured previously for ^(208)Pb was also used to determine the \DeltaR_(pn) for ^(208)Pb. In this way a very precise \DeltaR_(pn) = 0.181 \pm 0.031 neutron-skin thickness has been obtained for 208Pb. The present method offers new possibilities for measuring the neutron-skin thicknesses of very exotic isotopes., Comment: 5 pages, 3 figures

Background: Inelastic neutrino-nucleus scattering through the weak neutral-current plays important role in stellar environment where transport of neutrinos determine the rate of cooling. Since there are no direct experimental data on neutral-current neutrino-nucleus cross sections available, only the modeling of these reactions provides the relevant input for supernova simulations. Purpose: To establish fully self-consistent framework for neutral-current neutrino-nucleus reactions based on relativistic nuclear energy density functional. Methods: Neutrino-nucleus cross sections are calculated using weak Hamiltonian and nuclear properties of initial and excited states are obtained with relativistic Hartree-Bogoliubov model and relativistic quasiparticle random phase approximation that is extended to include pion contributions for unnatural parity transitions. Results: Inelastic neutral-current neutrino-nucleus cross sections for 12C, 16O, 56Fe, 56Ni, and even isotopes {92-100}Mo as well as respective cross sections averaged over distribution of supernova neutrinos. Conclusions: The present study provides insight into neutrino-nucleus scattering cross sections in the neutral channel, their theoretical uncertainty in view of recently developed microscopic models, and paves the way for systematic self-consistent large-scale calculations involving open-shell target nuclei., Comment: 25 pages, 9 figures, 2 tables, submitted to Physical Review C

The relativistic proton-neutron quasiparticle random phase approximation (pn-RQRPA) is applied in the calculation of the L=0 strength in charge-exchange reactions on $^{48}$Ca, $^{90}$Zr, $^{208}$Pb and nuclei in the Sn isotopic chain. The microscopic theoretical framework is based on the relativistic Hartree-Bogoliubov (RHB) model for the nuclear ground state. The calculation is fully self-consistent, i.e. the same interaction is used both in the RHB equations that determine the quasiparticle basis, and in the matrix equations of the pn-RQRPA. The inclusion of the higher-order terms that include the effect of finite momentum transfer, primarily the isovector spin monopole (IVSM) term, in the transition operator shifts a portion of the strength to the high-energy region above the Gamow-Teller (GT) resonance. The total strength is slightly enhanced in nuclei with small neutron-to-proton ratio but remains unchanged with increasing neutron excess. Based on the strength obtained using the full L=0 transition operator in the pn-RQRPA calculation, we have estimated the impact of the IVSM on the strength measured in the charge-exchagne reactions on $^{90}$Zr and found that the data are consistent with the Ikeda sum rule., Comment: 23 pages, 7 figures, 3 tables, submitted to Physical Review C

We extend the formalism of weak interaction processes, obtaining new expressions for the transition rates, which greatly facilitate numerical calculations, both for neutrino-nucleus reactions and muon capture. We have done a thorough study of exclusive (ground state) properties of $^{12}$B and $^{12}$N within the projected quasiparticle random phase approximation (PQRPA). Good agreement with experimental data is achieved in this way. The inclusive neutrino/antineutrino ($\nu/\tilde{\nu}$) reactions $^{12}$C($\nu,e^-)^{12}$N and $^{12}$C($\tilde{\nu},e^+)^{12}$B are calculated within both the PQRPA, and the relativistic QRPA (RQRPA). It is found that the magnitudes of the resulting cross-sections: i) are close to the sum-rule limit at low energy, but significantly smaller than this limit at high energies both for $\nu$ and $\tilde{\nu}$, ii) they steadily increase when the size of the configuration space is augmented, and particulary for $\nu/\tilde{\nu}$ energies $> 200$ MeV, and iii) converge for sufficiently large configuration space and final state spin., Comment: Proceedings of the International Nuclear Physics Conference 2010, Vancouver, BC - Canada 4-9 Jul 2010

The self-consistent random phase approximation (RPA), based on the framework of relativistic energy density functionals, is employed in the study of isovector and isoscalar dipole response in $^{68}$Ni, $^{132}$Sn, and $^{208}$Pb. The evolution of pygmy dipole states (PDS) in the region of low excitation energies is analyzed as a function of the density-dependence of the symmetry energy for a set of relativistic effective interactions. The occurrence of PDS is predicted in the response to both the isovector and isoscalar dipole operators, and its strength is enhanced with the increase of the symmetry energy at saturation and the slope of the symmetry energy. In both channels the PDS exhausts a relatively small fraction of the energy-weighted sum rule but a much larger percentage of the inverse energy-weighted sum rule. For the isovector dipole operator the reduced transition probability $B(E1)$ of the PDS is generally small because of pronounced cancellation of neutron and proton partial contributions. The isoscalar reduced transition amplitude is predominantly determined by neutron particle-hole configurations, most of which add coherently, and this results in a collective response of the PDS to the isoscalar dipole operator., Comment: submitted to Phys. Rev. C

The recent high-resolution measurement of the electric dipole (E1) polarizability (alphad) in 208Pb [Phys. Rev. Lett. 107, 062502 (2011)] provides a unique constraint on the neutron-skin thickness of this nucleus. The neutron-skin thickness (rskin) of 208Pb is a quantity of critical importance for our understanding of a variety of nuclear and astrophysical phenomena. To assess the model dependence of the correlation between alphad and rskin, we carry out systematic calculations for 208Pb, 132Sn, and 48Ca based on the nuclear density functional theory (DFT) using both non-relativistic and relativistic energy density functionals (EDFs). Our analysis indicates that whereas individual models exhibit a linear dependence between alphad and rskin, this correlation is not universal when one combines predictions from a host of different models. By averaging over these model predictions, we provide estimates with associated systematic errors for rskin and alphad for the nuclei under consideration. We conclude that precise measurements of rskin in both 48Ca and 208Pb---combined with the recent measurement of alphad---should significantly constrain the isovector sector of the nuclear energy density functional., Comment: Manuscript contains 5 pages, 2 figures, and 1 table. Submitted to Physical Review Letters

Low-energy strength is predicted for the isoscalar monopole response of neutron-rich Ni isotopes, in calculations performed using the microscopic Skyrme HF+RPA and relativistic RHB+RQRPA models. Both models, although based on different energy density functionals, predict the occurrence of pronounced monopole states in the energy region between 10 MeV and 15 MeV, well separated from the isoscalar GMR. The analysis of transition densities and corresponding particle-hole configurations shows that these states represent almost pure neutron single hole-particle excitations. Even though their location is not modified with respect to the corresponding unperturbed states, their (Q)RPA strength is considerably enhanced by the residual interaction. The theoretical analysis predicts the gradual enhancement of low-energy monopole strength with neutron excess., Comment: 4 pages, 6 figures, submitted to Physical Review C

Charged-current neutrino-nucleus cross sections for 54,56Fe and 58,60Ni are calculated and compared using frameworks based on relativistic and Skyrme energy density functionals, and the shell model. The current theoretical uncertainties in modeling neutrino-nucleus cross sections are assessed in relation to the predicted Gamow-Teller transition strength and available data, multipole decomposition of the cross sections, and cross sections averaged over the Michel flux and Fermi-Dirac distribution. Employing different microscopic approaches and models, the DAR neutrino-56Fe cross section and its theoretical uncertainty are estimated: _th=(258+-57) 10^{-42} cm^2, in very good agreement with the experimental value: _exp=(256+-108+-43) 10^{-42} cm^2., Comment: 13 pages, 6 figures, accepted for publication in Phys. Rev. C

We extend the formalism of weak interaction processes, obtaining new expressions for the transition rates, which greatly facilitate numerical calculations, both for neutrino-nucleus reactions and muon capture. Explicit violation of CVC hypothesis by the Coulomb field, as well as development of a sum rule approach for the inclusive cross sections have been worked out. We have done a thorough study of exclusive (ground state) properties of $^{12}$B and $^{12}$N within the projected quasiparticle random phase approximation (PQRPA). Good agreement with experimental data achieved in this way put in evidence the limitations of standard RPA and the QRPA models, which come from the inability of the RPA in opening the $p_{3/2}$ shell, and from the non-conservation of the number of particles in the QRPA. The inclusive neutrino/antineutrino ($\nu/\tilde{\nu}$) reactions $^{12}$C($\nu,e^-)^{12}$N and $^{12}$C($\tilde{\nu},e^+)^{12}$B are calculated within both the PQRPA, and the relativistic QRPA (RQRPA). It is found that the magnitudes of the resulting cross-sections: i) are close to the sum-rule limit at low energy, but significantly smaller than this limit at high energies both for $\nu$ and $\tilde{\nu}$, ii) they steadily increase when the size of the configuration space is augmented, and particulary for $\nu/\tilde{\nu}$ energies $> 200$ MeV, and iii) converge for sufficiently large configuration space and final state spin. The quasi-elastic $^{12}$C($\nu,\mu^-)^{12}$N cross section recently measured in the MiniBooNE experiment is briefly discussed. We study the decomposition of the inclusive cross-section based on the degree of forbiddenness of different multipoles. A few words are dedicated to the $\nu/\tilde{\nu}$-$^{12}$C charge-exchange reactions related with astrophysical applications., Comment: 21 pages, 13 figures, 1 table, submitted to Physical Review C

This article provides an insight into several open problems in the quest for novel modes of excitation in nuclei with isospin asymmetry, deformation and finite temperature characteristic in stellar environment. Major unsolved problems include the nature of pygmy dipole resonances, the quest for various multipole and spin-isospin excitations both in neutron-rich and proton drip-line nuclei mainly driven by loosely bound nucleons, excitations in unstable deformed nuclei and evolution of their properties with the shape phase transition. Exotic modes of excitation in nuclei at finite temperatures characteristic for supernova evolution present open problems with possible impact in modeling astrophysically relevant weak interaction rates. All these issues challenge self-consistent many body theory frameworks at the frontiers of on-going research, including nuclear energy density functionals, both phenomenological and constrained by the strong interaction physics of QCD, models based on low-momentum two-nucleon interaction V_{low-k} and correlated realistic nucleon-nucleon interaction V_{UCOM}, supplemented by three-body force, as well as two-nucleon and three-nucleon interactions derived from the chiral effective field theory. Joined theoretical and experimental efforts, including research with radioactive isotope beams, are needed to provide insight into dynamical properties of nuclei away from the valley of stability, involving the interplay of isospin asymmetry, deformation and finite temperature., Comment: 14 pages, submitted to the Journal of Physics G special issue on Open Problems in Nuclear Structure (OPeNST)

A fully self-consistent microscopic framework for evaluation of nuclear weak-interaction rates at finite temperature is introduced, based on Skyrme functionals. The single-nucleon basis and the corresponding thermal occupation factors of the initial nuclear state are determined in the finite-temperature Skyrme Hartree-Fock model, and charge-exchange transitions to excited states are computed using the finite-temperature RPA. Effective interactions are implemented self-consistently: both the finite-temperature single-nucleon Hartree-Fock equations and the matrix equations of RPA are based on the same Skyrme energy density functional. Using a representative set of Skyrme functionals, the model is applied in the calculation of stellar electron-capture cross sections for selected nuclei in the iron mass group and for neutron-rich Ge isotopes., Comment: 31 pages, 13 figures, submitted to Physical Review C

The multipole response of nuclei at temperatures T=0-2 MeV is studied using a self-consistent finite-temperature RPA (random phase approximation) based on relativistic energy density functionals. Illustrative calculations are performed for the isoscalar monopole and isovector dipole modes and, in particular, the evolution of low-energy excitations with temperature is analyzed, including the modification of pygmy structures. Both for the monopole and dipole modes, in the temperature range T=1-2 MeV additional transition strength appears at low energies because of thermal unblocking of single-particle orbitals close to the Fermi level. A concentration of dipole strength around 10 MeV excitation energy is predicted in $^{60,62}$Ni, where no low-energy excitations occur at zero temperature. The principal effect of finite temperature on low-energy strength that is already present at zero temperature, e.g. in $^{68}$Ni and $^{132}$Sn, is the spreading of this structure to even lower energy and the appearance of states that correspond to thermally unblocked transitions., Comment: 12 pages, 3 figures, 1 table, submitted to Phys. Lett. B