The SPF–Dunham expansion for the potential well: A regression model for systematic analysis of differential elastic beam scattering cross sections

Abstract

The Simons–Parr–Finlan (SPF) modified Dunham expansion of the interatomic potential is utilized for a systematic least squares (nonlinear regression) analysis of thermal energy differential cross section data to yield a reliable determination of the interaction potential well V (r). The procedure provides potentials which produce excellent fits to both computer-generated differential cross sections and experimental angular distributions (from the literature). As an additional check, all eigenvalues calculated from the deduced potential wells are found to agree (within ?0.5 cm−1) with the known values, further indicating that the SPF potential well is nearly indistinguishable from that of the true V (r). In contrast to many ’’inversion’’ procedures in the literature, the present iterative method represents a straightforward, practical way to deduce V (r) from angular distribution data. In addition, the SPF expansion provides quite accurate analytical representations of the interatomic potentials for strongly bound diatomics (e.g., H2, CO, and I2) valid over a wide range of r, reproducing the exact eigenvalues to an accuracy within ?0.1% (of the well depth).