Effective potentials for electron-atom scattering below inelastic thresholds. I. Asymptotic forms

It is shown that the effective potential for electron-atom scattering, below inelastic thresholds, has the asymptotic form - alpha r-4-( alpha q-6 beta -24 gamma k12)r-6- delta r-7+O(r-8). The expressions for alpha , alpha 1 and beta are well known. The main new result is that the non-adiabatic correction to the dipole polarisation potential is a linear function of k12, namely (6 beta +24 gamma k12)r-6. An exact expression is obtained for gamma . For e-H scattering, gamma =319/48. The term - delta r-7 arises from the fact that the dipole-polarised states have permanent quadrupole moments. For e-H scattering, delta approximately=48.

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