Weak interaction rates of $sd$-shell Urca pairs in stellar environment using a shell-model approach

Abstract

In this work, the weak interaction rates of $sd$-shell nuclei in the hot and dense stellar environment are calculated using the shell model. The {\it ab initio} effective interactions are employed for the calculation of Gamow-Teller strengths and weak rates in addition to the phenomenological interaction. The weak rates are evaluated in a fine grid of density and temperature. The electron capture and ${\beta }^{-}$-decay rates of Urca pairs of nuclei with $A=23,25,29,31$ and 33 are evaluated as a function of ${\log }_{10}\rho Y_e$ and the corresponding Urca density is obtained. The screening effects are also included for the evaluation of these stellar weak rates. In addition, the intrinsic cooling strength is evaluated for $A=29,31$ and 33 Urca pairs in neutron star crusts. The stellar weak rates, along with the neutrino energy emitted and the gamma heat production, are tabulated for $A=29-39$ nuclei.

16 pages, 18 figures

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