Numerical method for the calculation of continuum excitation amplitudes in time-dependent external field problems

We introduce a new numerical method for calculating continuum excitation probabilities of complex physical systems under the influence of external, time-dependent, and nonperturbative fields. The method utilizes a discretized form of the Hamiltonian on a space lattice and is particularly suited for large scale computations involving many-body systems. We perform a comparative study for a model problem by solving the same time-dependent Schroedinger equation in spherical and cylindrical coordinates. As a realistic example, we apply the method to the problem of prompt nucleon emission in low energy heavy-ion reactions