Effect of atomic electrons on the $7.6$-eV nuclear transition in ${}^{229}\mathrm{Th}{}^{3+}$

We have considered an effect of atomic electrons on the nuclear ${}^{229m}\mathrm{Th}$-${}^{229g}\mathrm{Th}$ transition in ${}^{229}\mathrm{Th}{}^{3+}$ due to the electronic bridge process. 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 (${\Gamma }_{\mathrm{EB}}$) to the probability of the nuclear radiative transition (${\Gamma }_N$) for the electronic $5f_{5/2}\to 6d_{3/2},6d_{5/2},7s$ and the $7s\to 7p_{1/2},7p_{3/2}$ transitions and found ${\Gamma }_{\mathrm{EB}}/{\Gamma }_N~0.01-0.1$ for the former and ${\Gamma }_{\mathrm{EB}}/{\Gamma }_N~20$ for the latter.

Figure 1

The single and double solid lines relate to the electronic and the nuclear transitions, correspondingly. The dashed line is the photon line.

Figure 2

The single and double solid lines relate to the electronic and the nuclear transitions, correspondingly. The dashed line is the photon line. The wavy line is the Coulomb interaction between electrons.