Polarization potential for dipole excitations

The long-range elastic scattering from a many-electron target is due to virtual dipole excitations. For large enough partial-wave quantum number L it is a weighted sum of contributions from single-orbital dipole excitations for which the second Born approximation is valid. It is shown analytically that the corresponding potential is strictly nonlocal but is phase equivalent for large enough L to the adiabatic potential -α/2$r^4$. A detailed numerical investigation is carried out for intermediate L values both of the T-matrix elements and the phase-equivalent local potential. An excellent simple approximation is found. Numerical examples involve the lowest dipole excitations of hydrogen and sodium atoms in electron scattering.