Hyperfine quenching rates of $nsnp\,^3P_0-ns^2\,^1S_0$ transition in $^{25}$Mg, $^{87}$Sr and $^{113}$Cd

Determining the $nsnp\,^3P_0$ state decay rate is important for the development of atmic clock based on $nsnp\,^3P_0-ns^2\,^1S_0$ transition. In the fermionic isotope there exist a decay channel for the $nsnp\,^3P_0-ns^2\,^1S_0$ transition through the nuclear hyperfine interaction which can contributes to the total $nsnp\,^3P_0$ lifetime. We computed the hyperfine quenching rates of the $nsnp\,^3P_0-ns^2\,^1S_0$ transition in $^{25}$Mg, $^{87}$Sr and $^{113}$Cd. The calculations are carried out using the ab-initio CI-all order package. Our final results of the hyperfine quenching rates are 0.43 mHz for $^{25}$Mg, 9.7 mHz for $^{87}$Sr and 77 mHz for $^{113}$Cd.