Multiphoton ionization of the delta-function atom

We study the one-dimensional and three-dimensional delta-function atom in an electric field with sinusoidal time dependence. Using the exact continuum states of the one-dimensional model we calculate the spectra of the photoelectrons. The spectra show a series of very high and sharp multiphoton peaks. The ponderomotive shift of these peaks is analysed. The three-dimensional problem is reduced to an integro-differential equation in time which can be converted into a Volterra integral equation. The latter is well suited for functional analytic discussion and numerical solution.