Electron scattering assisted by an intense electromagnetic field: Exact solution of a simplified model

Electron scattering by a layered (stepwise constant) potential is calculated in the presence of strong electromagnetic radiation. The numerical solution converges to high accuracy. We study threshold phenomena, resonant emission and absorption of many photons, multiphoton ionization, and the interaction of decaying ''bound'' states with each other and with the continuum. We demonstrate the close connection between electron scattering and multiphoton ionization. A theoretical treatment in terms of dressed states accounts well for most of our results