Infrared multiphoton decomposition: A comparison of approximate models and exact solutions of the energy-grained master equation

Abstract

The approximate ’’thermal’’ model and ’’continuum’’ model have been compared to exact calculations, and neither gives satisfactory results. In particular, the thermal model is based on an inaccurate and unphysical approximation to the correct molecular density of states, as well as a restrictive expression for the absorption cross sections. As an alternative to the approximate models, the exact stochastic method gives exact results and can be implemented using small computers or programmable pocket calculators. The results obtained from this method are exact and precision depends only upon the number of ’’trajectories’’ calculated. It was discovered that the yield versus fluence results from exact numerical integration of the master equation approximately conform to a cumulative log–normal distribution function in decomposition time or fluence. Thus, to a good degree of approximation, computed yield versus fluence results can be expressed simply in terms of a mean and a dispersion parameter. This suggests that the use of probability graph paper and the log–normal distribution function may prove to be a useful means for the presentation and analysis of experimental and computed data. Moreover, deviation from the log–normal distribution may indicate that the simple master equation is not a sufficient description of the experimental results.