Gamma ray heating and neutrino cooling rates due to weak interaction processes on s d $sd$ -shell nuclei in stellar cores

Abstract

Gamma ray heating and neutrino cooling rates, due to weak interaction processes, on \(sd\)-shell nuclei in stellar core are calculated using the proton neutron quasiparticle random phase approximation theory. The recent extensive experimental mass compilation of Wang et al. (Chin. Phys. C 36:1603, 2012), other improved model input parameters including nuclear quadrupole deformation (Raman et al. in At. Data Nucl. Data Tables 78(1):1–128, 2001; Moller et al. in At. Data Nucl. Data Tables 109:1–204, 2016) and physical constants are taken into account in the current calculation. The purpose of this work is two fold, one is to improve the earlier calculation of weak rates performed by Nabi and Klapdor-Kleingrothaus (At. Data Nucl. Data Tables 71:149, 1999a) using the same theory. We further compare our results with previous calculations. The selected \(sd\)-shell nuclei, considered in this work, are of special interest for the evolution of O–Ne–Mg core in 8–10 \(\mbox{M}_{\odot }\) stars due to competitive gamma ray heating rates and cooling by URCA processes. The outcome of these competitions is to determine, whether the stars end up as a white dwarf (Nabi in Phys. Rev. C 78(4):045801, 2008b), an electron-capture supernova (Jones et al. in Astrophys. J. 772(2):150, 2013) or Fe core-collapse supernova (Suzuki et al. in Astrophys. J. 817(2):163, 2016). The selected \(sd\)-shell nuclei for calculation of associated weak-interaction rates include \(^{20,23}\mathrm{O}\), \(^{20,23}\mathrm{F}\), \(^{20,23,24}\mathrm{Ne}\), \({}^{20,23\mbox{--}25}\mathrm{Na}\), and \({}^{23\mbox{--}25}\mathrm{Mg}\). The cooling and heating rates are calculated for density range (\(10 \leq \rho\ (\mbox{g}\,\mbox{cm}^{-3}) \leq 10^{11}\)) and temperature range (\(0.01\times 10^{9}\leq T(K)\leq 30\times 10^{9}\)). The calculated gamma heating rates are orders of magnitude bigger than the shell model rates (except for \(^{25}\mathrm{Mg}\) at low densities). At high temperatures the gamma heating rates are in reasonable agreement. The calculated cooling rates are up to an order of magnitude bigger for odd-A nuclei.