Prediction of I_g,6d_3/2 → I_g, 7p_1/2, I_g, 7s_1/2 → I_g, 7p_1/2 and I_g, 7p_1/2 → I_m, 7s_1/2 transition frequencies in ²²⁹Th³⁺ ion

The ²²⁹Th nucleus has attracted considerable attention due to the existence of its low-energy isomeric state; however, direct laser excitation in ionic systems poses significant challenges for current laser technologies. In the ²²⁹Th³⁺ ion, the electronic bridge (EB) process enables the conversion of direct laser excitation into an effective two-photon process (I_g, 6d_3/2 → I_g,7 p_1/2 → I_m,7s_1/2), thereby circumventing the requirement for laser radiation at 148 nm. In this work, we employ many-body perturbation theory (MBPT) to calculate the hyperfine structure constants and field shift factors for several low-lying excited states of the ²²⁹Th³⁺ ion. By combining these theoretical results with previously reported experimental data, we predict three transition frequencies associated with the EB process in the ²²⁹Th³⁺ ion and identify the most suitable transition pathway for EB-assisted nuclear excitation.