Effect of atomic electrons on 7.6 eV nuclear transition in $^{229}$Th$^{3+}$*

We have considered an effect of atomic electrons due to the electronic bridge process on the nuclear $^{229m}$Th -- $^{229g}$Th transition in $^{229}$Th$^{3+}$. Based on a recent experimental result we assumed the energy difference between the isomeric and the ground nuclear states to be equal to 7.6 eV. We have calculated the ratios of the electronic bridge process probability ($\Gamma_{\rm EB}$) to the probability of the nuclear radiative transition ($\Gamma_N$) for the electronic $5f_{5/2} \rightarrow 6d_{3/2},6d_{5/2},7s$ and the $7s \rightarrow 7p_{1/2},7p_{3/2}$ transitions and found $\Gamma_{\rm EB}/\Gamma_N \sim 0.01\div0.1$ for the former and $\Gamma_{\rm EB}/\Gamma_N \sim 20$ for the latter.