Energy distributions in multiple photon absorption experiments

Photofragmentation experiments on molecules and clusters often involve multiple photon absorption. The distributions of the absorbed number of photons are frequently approximated by Poisson distributions. For realistic laser beam profiles, this approximation fails seriously due to the spatial variation of the mean number of absorbed photons across the laser beam. We calculate the distribution of absorbed energy for various laser and molecular-beam parameters. For a Gaussian laser beam, the spatially averaged distributions have a power-law behavior for low energy with a cutoff at an energy which is proportional to fluence. The power varies between -1 for an almost parallel laser beam and -5/2 for a divergent beam (on the scale of the molecular beam). We show that the experimental abundance spectra of fullerenes and small carbon clusters can be used to reconstruct the distribution of internal energy in the excited C60 molecule prior to fragmentation and find good agreement with the calculated curves.