Overlap of electron shells in $\beta$ and double-$\beta$ decays

The $ \beta $-decay and electron-capture channels, which are not accompanied by the excitation of the electron shell, are suppressed due to the nonorthogonality of the electron wave functions of the parent and daughter atoms. The dominant suppression is due to the valence-shell electrons, which are involved in the formation of chemical bonds with other atoms. A change in the chemical composition of a substance leads to a significant change in the overlap amplitude. The core-shell electrons are less sensitive to the environment and their overlap amplitude is more stable. The suppression effect is evaluated for the electron capture with $^{163}$Ho and the $2\beta^-$ decays with $^{76}$Ge and $^{136}$Xe.