Exotic modes of excitation and weak interaction rates at finite temperature

The interplay of isospin asymmetry and finite temperature in nuclei plays an important role on properties of nuclear excitations and weak interaction rates in stellar environment. Recently a fully self-consistent microscopic framework, based on Hartree-Fock plus random phase approximation using Skyrme functionals, has been introduced for description of excitations and weak-interaction cross sections at finite temperature. Another self-consistent framework involving nuclei at finite temperature has also been developed within relativistic mean field theory using effective Lagrangians with density dependent meson-nucleon vertex functions. Nuclear excitations are studied using finite temperature random phase approximation for the range of temperatures T = 0-2 MeV, as well as in nuclei far from stability. In the focus of research are the structure properties of exotic modes of excitation (e.g. pygmy dipole resonances) and charge-exchange modes (e.g. Gamow-Teller resonances and forbidden transitions). It is shown that finite temperature effects include novel low-energy multipole excitations and modifications of the Gamow-Teller transition spectra. Using a representative set of Skyrme functionals, as well as covariant energy density functional with DD-ME2 parameterization, both theory frameworks have been applied in calculations of electron-capture cross sections relevant in the stage of supernova precollapse.