We propose a new method to calculate stellar weak-interaction rates. It is based on the thermofield dynamics formalism and allows calculation of the weak-interaction response of nuclei at finite temperatures. The thermal evolution of the GT + distributions is presented for the sample nuclei 54,56 Fe and 76,78,80 Ge. For Ge we also calculate the strength distribution of first-forbidden transitions. We show that thermal effects shift the GT + centroid to lower excitation energies and make possible negative-and low-energy transitions. In our model we demonstrate that the unblocking effect for GT + transitions in neutron-rich nuclei is sensitive to increasing temperature. The results are used to calculate electron capture rates and are compared to those obtained from the shell model.
We study inelastic neutrino scattering off hot nuclei for temperatures relevant under supernova conditions. The method we use is based on the quasiparticle random phase approximation extended to finite temperatures within the thermo field dynamics (TQRPA). The method allows a transparent treatment of upward and downward transitions in hot nuclei, avoiding the application of Brink's hypothesis. For the sample nuclei 56 Fe and 82 Ge we perform a detailed analysis of thermal effects on the strength distributions of allowed Gamow-Teller (GT) transitions which dominate the scattering process at low neutrino energies. For 56 Fe and 82 Ge the finite temperature cross-sections are calculated by taking into account the contribution of allowed and forbidden transitions. The observed enhancement of the cross-section at low neutrino energies is explained by considering thermal effects on the GT strength. For 56 Fe we compare the calculated cross-sections to those obtained earlier from a hybrid approach that combines large-scale shell-model and RPA calculations.
We have calculated electron capture rates for neutron-rich N = 50 nuclei ( 78 Ni, 82 Ge, 86 Kr, 88 Sr) within the Thermal QRPA approach at temperatures T = 0, corresponding to capture on the ground-state, and at T = 10 GK (0.86 MeV), which is a typical temperature at which the N = 50 nuclei are abundant during a supernova collapse. In agreement with recent experiments, we find no Gamow-Teller (GT+) strength at low excitation energies, E < 7 MeV, caused by Pauli blocking induced by the N = 50 shell gap. At the astrophysically relevant temperatures this Pauli blocking of the GT+ strength is overcome by thermal excitations across the Z = 40 proton and N = 50 neutron shell gaps, leading to a sizable GT contribution to the electron capture. At the high densities, at which the N = 50 nuclei are important for stellar electron capture, forbidden transitions contribute noticeably to the capture rate. Our results indicate that the neutron-rich N = 50 nuclei do not serve as an obstacle of electron capture during the supernova collapse. PACS numbers: 26.50.+x, 23.40.-s 21.60.Jz, 24.10.Pa,
A self-consistent version of the Thermal Random Phase Approximation (TSCRPA) is developed within the Matsubara Green's Function (GF) formalism. The TSCRPA is applied to the many level pairing model. The normal phase of the system is considered. The TSCRPA results are compared with the exact ones calculated for the Grand Canonical Ensemble. Advantages of the TSCRPA over the Thermal Mean Field Approximation (TMFA) and the standard Thermal Random Phase Approximation (TRPA) are demonstrated. Results for correlation functions, excitation energies, single particle level densities, etc., as a function of temperature are presented.
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