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

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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).