# Excitation of the $^{229}$Th nucleus via a two-photon electronic transition

## TL;DR

This paper explores a novel method to excite the $^{229}$Th nucleus using a two-photon electronic transition, combining advanced theoretical calculations to propose a feasible experimental approach for nuclear excitation.

## Contribution

It extends the theory of nuclear excitation via two-photon electron transitions to the $^{229}$Th ion, providing detailed calculations and an experimental scenario for nuclear state excitation.

## Key findings

- Calculated NETP probabilities for $^{229}$Th in resonance conditions.
- Identified optimal initial states for different nuclear energy levels.
- Proposed a multi-step experimental excitation scheme.

## Abstract

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 $\hbar\omega_N$.