Multiphoton Absorption Above the Ionization Threshold

Abstract

The topic of this paper is above-threshold processes, where the number, N, of photons absorbed by an atom exceeds the minimum number, N₀, required to ionize the atom. In contrast to the case N=N₀. one encounters in the treatment of above-threshold o’ processes continuum-continuum matrix elements, whose evaluation presents a numerical problem far more challenging than the evaluation of bound-bound and bound-continuum matrix elements. This extra complexity is, however, somewhat artificial in the sense that nonnormalizable functions appear only as an artifact of the particular theoretical approach; the emergent electron is, after all, initially bound and can in principle be described by a normalizable wavepacket throughout the ionization process, even if the electron continues to absorb photons after it has sufficient energy to escape. The root of the difficulty lies in the (unphysical) requirement that the electron depart with a definite energy--for then it must be described by a nonnormalizable (continuum) wavefunction. Furthermore, the (physical) requirement that this wavefunction be regular at the origin implies that it has the character of a stationary wave, comprised of outgoing and ingoing parts. The ingoing part, as it stands, is unphysical; only when stationary waves of different energies, spread over a narrow bandwidth, are superposed does the wavefunction acquire the correct asymptotic character of an outgoing wave, which describes the electron leaving the atom.