Abstract
Scattering of low-energy electrons on atoms in a field of two different model potentials is investigated using effective range theory. A general formulation of the problem is such that it yields the scattering differential, momentum-transfer and total cross sections as functions of a few parameters that are derived from first principles and can easily be calculated for any electron-atom system. Long-range electron-atom interaction is represented by the polarization potential and the short-range potential is approximated by two significantly different functions. Possible solutions of collision Schrödinger equations in terms of special functions and related polynomials are discussed, and the scattering lengths for almost all electron-atom collision systems are calculated from numerical solutions of the corresponding wave equations.
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