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 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 $A=23,25,29,31\text{and}33$ 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 $A=29,31\text{and}33$ Urca pairs in neutron star crusts. The stellar weak rates, along with the neutrino energy emitted and the gamma heat production, are tabulated for $A=29\text{–}39$ nuclei.

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• Electroweak interactions in nuclear physics
• Nuclear astrophysics
• 20 ≤ A ≤ 38
• Shell model