Time resolved study of recoil induced rotation by X ray pump X ray probe spectroscopy

Modern stationary X ray spectroscopy is unable to resolve rotational structure. In the present paper, we propose to use time resolved two color X ray pump probe spectroscopy with picosecond resolution for real time monitoring of the rotational dynamics induced by the recoil effect. The proposed technique consists of two steps. The first short pump X ray pulse ionizes the valence electron, which transfers angular momentum to the molecule. The second time delayed short probe X ray pulse resonantly excites a 1s electron to the created valence hole. Due to the recoil induced angular momentum the molecule rotates and changes the orientation of transition dipole moment of core excitation with respect to the transition dipole moment of the valence ionization, which results in a temporal modulation of the probe X ray absorption as a function of the delay time between the pulses. We developed an accurate theory of the X ray pump probe spectroscopy of the recoil induced rotation and study how the energy of the photoelectron and thermal dephasing affect the structure of the time dependent X ray absorption using the CO molecule as a case study. We also discuss the feasibility of experimental observation of our theoretical findings, opening new perspectives in studies of molecular rotational dynamic