Dipole threshold laws for single and double detachment from negative ions

The threshold behavior of the cross section when electron detachment leaves behind a neutral atom (or molecule) with an electric dipole moment is derived through the formalism of quantum-defect theory. The cross section is a constant with a superimposed modulation with energy which has negligible amplitude for realistic situations such as the photodetachment of ${\mathrm{H}}^{\mathrm{-}}$ accompanied by excitation. The threshold behavior for double detachment is also derived on the basis of a Coulomb-dipole description of the two electrons. It is shown that no oscillations will be observed in the cross section for this process.