TY - JOUR
T1 - Inversion of gas-surface scattering data for potential determination using functional sensitivity analysis. I. A case study for the He-Xe/C(0001) potential
AU - Ho, Tak San
AU - Rabitz, Herschel Albert
PY - 1991/1/1
Y1 - 1991/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=1542470623&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=1542470623&partnerID=8YFLogxK
U2 - 10.1063/1.459902
DO - 10.1063/1.459902
M3 - Article
AN - SCOPUS:1542470623
SN - 0021-9606
VL - 94
SP - 2305
EP - 2314
JO - The Journal of chemical physics
JF - The Journal of chemical physics
IS - 3
ER -