Theoretical investigation of 2+2 resonance enhanced multi-photon ionization probability

The analytic formula of the ionization probability in the process of 2+2 resonance enhanced multi-photon ionization (REMPI) is derived from the dynamic rate equation about the interaction of photon and material. Based on the formula, the influence of laser intensity, laser pulse duration and collision relaxation rate on the ionization probability is investigated theoretically. It is shown that the ionization probability increases with the laser intensity and laser pulse duration. The ionization probability will get to one until two steps saturation with the increase of laser intensity. After that, the ionization probability will oscillates narrowly around the saturation value if the laser intensity increases further. The results also show that the ionization probability will decrease in linear manner nearly with the increase of collision relaxation rate. But the variation is small. So the influence of the collision relaxation rate (or even sample pressure) on the ionization probability can be ignored. In the practical use of REMPI, higher sample pressure will reduce the intensity of the detection signal is due to the collision complex of the positive and negative ions. This will reduce the collection efficiency of the ions, and influence the magnitude of the ion signal further.