Generation of harmonics via multiphoton resonant excitation of hydrogenlike ions in an x-ray free-electron-laser field

The coherent radiation spectrum of highly charged hydrogenlike ions in an intense x-ray free-electron-laser field is considered. The spectrum corresponding to harmonic generation in the resonant multiphoton excitation regime is investigated both analytically and numerically, arising from the Dirac Hamiltonian. The obtained analytical results are based on the generalized rotating wave approximation and are in good agreement with performed numerical calculations. Estimations show that one can achieve efficient generation of coherent hard x-ray radiation using multiphoton resonant excitation by appropriate x-ray pulses.