Above Threshold Ionization photoelectron spectra look the way that they do because of single-electron effects!

Below you will find pairs of graphs, the top of which is experimental data obtained by The Van Woerkom Group and the bottom of which is calculation performed by Harm Muller at FOM. They are photoelectron spectra of Argon atoms in the presence of ultra-short, high-intensity laser light. We use 800 nm, 120 fs laser pulses at a 1 kHz repetition rate, focused into an argon-backfilled vacuum chamber, with pressures low enough to assure that there are no space-charge effects. We employ a restricted volume technique of time-of-flight spectroscopy to determine the kinetic energy (KE) of the electrons. Our electronics allow us a resolution of better than 40 ps and our KE resolution is approximately 20 meV, even for energies greater than 30 eV. The restricted volume (allowing only photoelectrons ejected from a 500 µm radius surrounding the focus) technique allows for facile spatial deconvolution of the data. A l/2 wave plate/polarizing cube pair are used to manipulate the intensity of the light; we obtained photoelectron spectra from 35 different intensities, ranging from 3 - 10.5 * 10$13W/cm2$, and a wide range of kinetic energies, which run from 0.4 eV to out past 45 eV. The calculation is a numerical integration of the Schršdinger equation for a model argon atom in the SAE approximation. The atom is represented by a three-dimensional potential well with a repulsive core, fitted to reproduce the bound-state spectrum of argon. The time-dependant Schršdinger equation is integrated in the velocity gauge, on a radial-position, angular momentum grid. The propagation uses a half-implicit split-operator scheme accurate to second order in the time step. Fourth-order implicit finite-difference expressions are used to approximate the radial derivatives. The pulse is modeled as a 45-cycle flat top pulse with a 1/2-cycle turn-on and turn-off. To account for the spin-orbit splitting of the core, the J=3/2 and J=1/2 ionization states are each modeled as separate species, and then added in a two-to-one (respectively) ratio.

The graphs below each have photoelectron spectra from various intensities (represented by different colors). The intensity is given in units of 10$13W/cm2$.

Note that for all intensities and all kinetic energies, that there is an amazing similarity between the data and calculation! Keep in mind that the calculation only takes into account single-electron, single-ionization effects.