Dominant Nonadiabatic Contribution to the Long-Range Electron-Atom Interaction

In the scattering of low-energy electrons or positrons by spherically symmetric atoms, a significant role is played by the long-range interactions. These originate partially in the adiabatic polarization of the atom, which contributes $\frac{1}{{q}^{4}}$, $\frac{1}{{q}^{6}}$, and higher terms, where $q$ is the electron-atom separation. There is also a non-adiabatic contribution, which behaves asymptotically as $\frac{3{a}_{0}{\ensuremath{\beta}}_{1}{({e}^{\ensuremath{'}})}^{2}}{{q}^{6}}$, where ${e}^{\ensuremath{'}}$ is the charge of the incident particle; this contribution was first studied by Mittleman and Watson in the case of hydrogen. We have obtained a useful if formally trivial extension of their results on ${\ensuremath{\beta}}_{1}$ to a wide class of atoms. We have also obtained rigorous if sometimes crude upper and lower bounds on ${\ensuremath{\beta}}_{1}$ which depend upon the availability of some information on the low-lying atomic energy levels and the associated oscillator strengths, and on the electric dipole polarizability. Bounds on ${\ensuremath{\beta}}_{1}$ have been obtained for He, Li, Ne, and Na. Statistical moment studies lead to estimates of ${\ensuremath{\beta}}_{1}$ for the rare-gas atoms.