Inversion of gas-surface scattering data for potential determination using functional sensitivity analysis. I. A case study for the He-Xe/C(0001) potential

A general iterative inversion procedure based on functional sensitivity analysis is presented for determining the gas-surface interaction potential from low energy elastic scattering data. Formally, Tikhonov regularization, singular function analysis, and a recently developed exact transformation technique are implemented to render the inversion stable and efficient. Specifically, the simulation of helium scattering from a rigid periodic xenon monolayer on the graphite (0001) face is considered. It is found that the functional sensitivity densities of the diffraction intensities with respect to the He-Xe/C(001) potential contain profound information, thus are invaluable in guiding the inversion of scattering data to yield the potential. Although, unequivocal determination of the full three-dimensional potential from the inevitably incomplete experimental data may be difficult, we demonstrate that simulated input data consisting of a finite number of polar scan specular intensities can be used to accurately recover the underlying He-Xe/C(0001) potential. The recovered potential has been obtained without imposing any explicit functional form on the potential per se. The resulting procedure is quite promising for treating real laboratory data.