Pair creation by collision of intense laser pulse with high-frequency photon beam

We consider pair creation by collision of a couple of counterpropagating electromagnetic pulses with arbitrary frequency ratio, mostly in the context of setup with collision of optical and coherent hard X- (or gamma-) ray pulses. This problem is non-perturbative and in general does not admit exact analytical solutions. We discuss several known approaches according to the ratio of the parameters. Certain regions of the parameter space are not covered by the existing approximations or models. We present a new simplified exactly solvable model with one of the pulses being a delta-pulse. This model partially fills the yet unexplored gap in the space of parameters. The shape of the momentum distribution of the created particles in such a model is discussed. Even though the model may not have immediate implications for the forthcoming experiments, it can still provide some hints for better understanding of the fully non-perturbative regime and vacuum instability in QED interactions of extremely strong and short laser pulses.