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 k 1 2 )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 k 1 2 , namely (6 beta +24 gamma k 1 2 )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.