Analytic velocity-dependent potential for bound and scattering states of electrons and atoms

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Abstract
In this work we represent the static potential of an electron interacting with an atom by a sum of two Debye-Hückel or Yukawa functions. We approximate the nonlocal exchange term by an attractive, velocity-dependent potential using the effective-mass approximation with a regularized Yukawa form factor. This is transformed to an approximate local but energy-dependent potential. We also include an imaginary term with a regularized Yukawa form factor in the static potential. We apply this framework to a description of the bound and scattering states of electrons interacting with atomic oxygen and electrons interacting with neon. The results suggest that a small degree of velocity or energy dependence yields improvements with respect to the use of strictly static electron-atom potentials. In applications to atomic physics the formalism which is economical in parameters should serve as a simple parametrization of experimental data and as a means of extrapolation and interpolation of experimental observations.