Stellar electron-capture rates on nuclei based on a microscopic Skyrme functional

Abstract

We compute electron-capture rates for 54,56 Fe and Ge isotopes using a self-consistent microscopic approach. The single-nucleon basis and the occupation factors in the target nucleus are calculated in the finite-temperature Skyrme Hartree-Fock model, and the J π = 0 ± , 1 ± , 2 ± charge-exchange transitions are determined in the finitetemperature random-phase approximation (RPA). The scheme is self-consistent; i.e., both the Hartree-Fock and the RPA equations are based on the same Skyrme functional. Several interactions are used in order to provide a theoretical uncertainty on the electron-capture rates for different astrophysical conditions. Comparing electron-capture rates obtained either with different Skyrme sets or with different available models indicates that differences up to one to two orders of magnitude can arise.

Contribution of excited states to stellar weak-interaction rates in odd-Anuclei

“…Q EC energies close to zero as in 45 Sc lead to intermediate rates, and positive values of Q EC cause much higher rates. This general behavior and sensitivity of the rates to both density and temperature has been observed in different calculations in this mass region from SM [8][9][10] to RPA [15,16,[18][19][20][21] calculations. A comparison of the rates obtained within this formalism and other SM and RPA calculations for even-even pf -shell nuclei can be found in Ref.…”

“…Various approaches have been developed in the past to describe the spin-isospin nuclear excitations in QRPA [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. In this section we show briefly the theoretical framework used in this work to describe the nuclear part of the weak-interaction rates.…”

“…Thus, in Refs. [18,19] a fully self-consistent microscopic framework was used for the calculation of weakinteraction rates at finite temperature based on spherical meanfield models with Skyrme functionals and a finite-temperature RPA. EC was calculated from various Skyrme interactions to estimate the resulting theoretical uncertainty.…”

“…Since then, improvements in the weak rates have been focused on the description of the nuclear-structure aspect of the problem. Different approaches are found in the literature and can be roughly divided into shell model (SM) [7][8][9][10] and proton-neutron quasiparticle random-phase approximation (QRPA) [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] categories. Hybrid models using RPA methods on top of a temperature-dependent description of the parent nucleus using a shell-model Monte Carlo approach have also been developed to calculate stellar EC rates [26].…”

Stellar electron capture rates on neutron-rich nuclei and their impact on stellar core collapse

“…A full diagonalization of the shell model Hamiltonian is not yet feasible for open shell neutron-rich nuclei with A > 65, which dominate electron capture for densities larger than 10 10 g/cm 3 [15]. Calculations exist employing alternative approaches, such as RPA [30,31] or QRPA [32]. In general, these are less accurate than shell-model calculations [33] since it is not clear whether all correlations are correctly included.…”