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

Abstract

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 $\frac{3a_0{\beta }_1{\left(e^{\prime }\right)}^2}{q^6}$, where $e^{\prime }$ 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 ${\beta }_1$ to a wide class of atoms. We have also obtained rigorous if sometimes crude upper and lower bounds on ${\beta }_1$ 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 ${\beta }_1$ have been obtained for He, Li, Ne, and Na. Statistical moment studies lead to estimates of ${\beta }_1$ for the rare-gas atoms.