Photo-Double Ionization: Threshold Law and Low-Energy Behavior

The threshold law for photoejection of two electrons from atoms (PDI) is derived from a modification of the Coulomb-dipole (C-D) theory. The C-D theory applies to two-electron ejection from negative ions (photo-double detachment:PDD).The modification consists of correctly accounting for the fact that in PDI that the two escaping electrons see a Coulomb field, asymptotically no matter what their relative distances from the residual ion are. We find the analytic threshold law $\mathcal{Q}$$(E)$ i.e. the yield of residual ions to be $\mathcal{Q}$$_f(E) \propto E+C_WE^{\gamma_W}+CE^{5/4}\sin[\frac{1}{2}{\rm ln}E+\phi]/{\rm ln}(E)$. The first and third terms are beyond the Wannier law. The Wannier exponent for neutral targets is $\gamma_{W}$=1.056. The first and third terms are beyond the Wannier law. Our threshold law can only be rigorously justified for residual energies $\le 10^{-3}$eV. Nevertheless in the present experimental range (0.1 - 4 eV), our form, without the second (Wannier) term, can be well fit to the experimental results for He, Li, and Be, as compared to the Wannier law alone, which has a larger error for Li and Be, and for both of which the data also show indications of modulation. which are also well fit by our formula.