Asymptotic form of molecular continuum wave function for system of non-overlapping atomic potentials

The asymptotic behavior of the molecular continuum wave function has been analyzed within a model of non-overlapping atomic potentials. It is been shown that the representation of the wave function far from a molecule as a plane wave and single spherical wave emitted by the molecular center cannot be corrected. Because of the multicenter character of the problem, the asymptotic form of the wave function must contain N spherical waves with centers at the nuclei of the N atoms that form the molecule. A method of partial waves for a spherically non-symmetrical target is considered for the simplest multicenter target formed by two non-overlapping potentials. The results are compared with those obtained within the single spherical wave approximation. It has been shown that the use of this approximation results in significant mistakes in differential and total cross sections of electron elastic scattering by a target.

💡 Research Summary

The paper investigates the asymptotic form of the molecular continuum wave function within a model consisting of non‑overlapping atomic potentials. Traditional scattering theory often represents the wave function at large distances from a molecule as the sum of an incident plane wave and a single outgoing spherical wave (SSW) emanating from the molecular centre. The authors demonstrate that this representation is fundamentally inadequate for a system composed of several well‑separated atomic scatterers. Because each atomic nucleus acts as an independent source of scattered radiation, the correct asymptotic expansion must contain a separate spherical wave for every nucleus. In mathematical terms, the wave function far from the target should be written as

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