Nuclear excitation by two-photon electron transition

A new mechanism of nuclear excitation via two-photon electron transitions (NETP) is proposed and studied theoretically. As a generic example, detailed calculations are performed for the $E1E1$ $1s2s{}^1{S}_0\to 1s^2{}^1{S}_0$ two-photon decay of He-like ${}^{225}$Ac${}^{87+}$ ion with the resonant excitation of the $3\mathrm{/}2+$ nuclear state with the energy 40.09(5) keV. The probability for such a two-photon decay via the nuclear excitation is found to be $P_{\rm NETP} = 3.5 \times 10^{-9}$ and, thus, is comparable with other mechanisms, such as nuclear excitation by electron transition and by electron capture. The possibility for the experimental observation of the proposed mechanism is thoroughly discussed.