The polarisation potential for electron-atom scattering is investigated analytically in momentum space. Contributions from discrete and continuum excitations are treated in detail. The equivalent local polarisation potential V (P) is derived, and calculated for the case of hydrogen at several energies. Contributions to the polarisability, defined as -8 pi times the derivative of V(P) at P=0, and terms of range as long as r -4 are zero unless the corresponding potential contains a singular integral, which is investigated in detail. A contrast is drawn with the adiabatic potential, which is local but different from the equivalent potential.
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McCarthy et al. (1981) studied this question.
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