Four-level model of ion－ion laser-induced collisional energy transfer and numerical calculations for Ca⁺－Sr⁺ system

The four-level model of laser-induced collisional energy transfer (LICET) for ion--ion collision system is established based on the time-dependent Schr?dinger equation for the electron dynamics, through which the equations of motion of the probability amplitudes and cross section of the collision system are obtained. Numerical calculations are performed for the Ca^+--Sr^+ system, with the results showing that the peak of the LICET spectrum appears at a resonant frequency of the transfer laser. The magnitude of the obtained collision cross section is in the order of 10^-16 cm^2, and is comparable to that obtained in atomic systems, which indicates the validity of the established four-level model.