Theory of Laser-Assisted Nuclear Excitation by Electron Capture

The interplay of x-ray ionization and atomic and nuclear degrees of freedom is investigated theoretically in the process of laser-assisted nuclear excitation by electron capture. In the resonant process of nuclear excitation by electron capture, an incident electron recombines into a vacancy in the atomic shell with simultaneous nuclear excitation. Here we investigate the specific scenario in which the free electron and the required atomic shell hole are generated by an x-ray free electron laser pulse. We develop a theoretical description based on the Feshbach projection operator formalism and consider numerically experimental scenarios at the SACLA x-ray free electron laser. Our numerical results for excitation of the 29.2 keV nuclear state in $^{229}\text{Th}$ and the 14.4 keV M\"ossbauer transition in $^{57}\text{Fe}$ show low excitation rates but strong enhancement with respect to direct two photon nuclear excitation.