Excitation of the Th229 nucleus via a two-photon electronic transition

We investigate the process of nuclear excitation via a two-photon electron transition (NETP) for the case of the doubly charged thorium. The theory of the NETP process has been devised originally for heavy helium like ions. In this work we study this process in the nuclear clock isotope $^{229}$Th in the $2+$ charge state. For this purpose we employ a combination of configuration interaction and many-body perturbation theory to calculate the probability of NETP in resonance approximation. The experimental scenario we propose for the excitation of the low lying isomeric state in $^{229}$Th is a circular process starting with a two-step pumping stage followed by NETP. The ideal intermediate steps in this process depend on the supposed energy $\hbar\omega_N$ of the nuclear isomeric state. For each of these energies the best initial state for NETP is calculated. Special focus is put on the most recent experimental results for $\hbar\omega_N$.