Electron-atom spin asymmetry and two-electron photodetachment: Addenda to the Coulomb-dipole threshold law

In the light of a couple of new and important experiments in threshold ionization, several aspects of the Coulomb-dipole threshold law, $\mathcal{Q}\propto E{\left(\ln E\right)}^{-2\mathrm{}}M\left(E\right)\mathrm{}$ are reexamined. The principal results are as follows. (a) The logarithmic factor has a natural cutoff ${\left\{\ln \right[E \frac{\left(\mathrm{Ry}\right)}{5}\left]\right\}}^{-2\mathrm{}}$ when, as indicated, $E$ is expressed in Rydberg units. (b) The modulation factor for electron-impact ionization has the form $M\cong 1+\left(\frac{D}{\alpha }\right)sin(\alpha \ln E+\phi )$ in which the effect of a superposition of partial waves gives a factor $D$ which is expected to be less than one. This alters the relation between frequency and amplitude that is predicted to arise in the spin-asymmetry ratio as a function of $E$. Finally, (c) the range of validity of the threshold law ($E<\mathrm{}{E}_r$) is estimated in terms of a formula between $E_r$ and the dipole parameter $\alpha$ of $M\left(E\right)\mathrm{}$. Some implications of this, particularly for the recent two-electron photodetachment experiment of Donahue and co-workers [Phys. Rev. Lett 48 1538 (1982); 52 164(E) (1984)] are drawn.