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Register a new userModeling nuclear weak-interaction processes with relativistic energy density functionals
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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.
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We present the simplest nuclear energy density functional (NEDF) to date, determined by only 4 significant phenomenological parameters, yet capable of fitting measured nuclear masses with better accuracy than the Bethe-Weizsacker mass formula, while also describing density structures (charge radii, neutron skins etc.) and time-dependent phenomena (induced fission, giant resonances, low energy nuclear collisions, etc.). The 4 significant parameters are necessary to describe bulk nuclear properties (binding energies and charge radii); an additional 2 to 3 parameters have little influence on the bulk nuclear properties, but allow independent control of the density dependence of the symmetry energy and isovector excitations, in particular the Thomas-Reiche-Kuhn sum rule. This Hohenberg-Kohn-style of density functional theory successfully realizes Weizsackers ideas and provides a computationally tractable model for a variety of static nuclear properties and dynamics, from finite nuclei to neutron stars, where it will also provide a new insight into the physics of the r-process, nucleosynthesis, and neutron star crust structure. This new NEDF clearly separates the bulk geometric properties - volume, surface, symmetry, and Coulomb energies which amount to 8MeV per nucleon or up to 2000MeV per nucleus for heavy nuclei - from finer details related to shell effects, pairing, isospin breaking, etc. which contribute at most a few MeV for the entire nucleus. Thus it provides a systematic framework for organizing various contributions to the NEDF. Measured and calculated physical observables - symmetry and saturation properties, the neutron matter equation of state, and the frequency of giant dipole resonances - lead directly to new terms not considered in current NEDF parameterizations.
We study a particular class of relativistic nuclear energy density functionals in which only nucleon degrees of freedom are explicitly used in the construction of effective interaction terms. Short-distance (high-momentum) correlations, as well as intermediate and long-range dynamics, are encoded in the medium (nucleon density) dependence of the strength functionals of an effective interaction Lagrangian. Guided by the density dependence of microscopic nucleon self-energies in nuclear matter, a phenomenological ansatz for the density-dependent coupling functionals is accurately determined in self-consistent mean-field calculations of binding energies of a large set of axially deformed nuclei. The relationship between the nuclear matter volume, surface and symmetry energies, and the corresponding predictions for nuclear masses is analyzed in detail. The resulting best-fit parametrization of the nuclear energy density functional is further tested in calculations of properties of spherical and deformed medium-heavy and heavy nuclei, including binding energies, charge radii, deformation parameters, neutron skin thickness, and excitation energies of giant multipole resonances.
Recent experimental data and progress in nuclear structure modeling have lead to improved descriptions of astrophysically important weak-interaction processes. The review discusses these advances and their applications to hydrostatic solar and stellar burning, to the slow and rapid neutron-capture processes, to neutrino nucleosynthesis, and to explosive hydrogen burning. Special emphasis is given to the weak-interaction processes associated with core-collapse supernovae. Despite some significant progress, important improvements are still warranted. Such improvements are expected to come from future radioactive ion-beam facilities.
The relativistic density functional with minimal density dependent nucleon-meson couplings for nuclei and nuclear matter is extended to include tensor couplings of the nucleons to the vector mesons. The dependence of the minimal couplings on either vector or scalar densities is explored. New parametrisations are obtained by a fit to nuclear observables with uncertainties that are determined self-consistently. The corresponding nuclear matter parameters at saturation are determined including their uncertainties. An improvement in the description of nuclear observables, in particular for binding energies and diffraction radii, is found when tensor couplings are considered, accompanied by an increase of the Dirac effective mass. The equations of state for symmetric nuclear matter and pure neutron matter are studied for all models. The density dependence of the nuclear symmetry energy, the Dirac effective masses and scalar densities is explored. Problems at high densities for parametrisations using a scalar density dependence of the couplings are identified due to the rearrangement contributions in the scalar self-energies that lead to vanishing Dirac effective masses.
Reactions with radioactive nuclear beams at relativistic energies have opened new doors to clarify the mechanisms of stellar evolution and cataclysmic events involving stars and during the big bang epoch. Numerous nuclear reactions of astrophysical interest cannot be assessed directly in laboratory experiments. Ironically, some of the information needed to describe such reactions, at extremely low energies (e.g., keVs), can only be studied on Earth by using relativistic collisions between heavy ions at GeV energies. In this contribution, we make a short review of experiments with relativistic radioactive beams and of the theoretical methods needed to understand the physics of stars, adding to the knowledge inferred from astronomical observations. We continue by introducing a more detailed description of how the use of relativistic radioactive beams can help to solve astrophysical puzzles and several successful experimental methods. State-of-the-art theories are discussed at some length with the purpose of helping us understand the experimental results reported. The review is not complete and we have focused most of it to traditional methods aiming at the determination of the equation of state of symmetric and asymmetric nuclear matter and the role of the symmetry energy. Whenever possible, under the limitations of our present understanding of experimental data and theory, we try to pinpoint the information still missing to further understand how stars evolve, explode, and how their internal structure might be.
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