Triple differential cross sections (TDCSs) for (e, 2e) processes on the valence electrons of
H-, Li-, Na- and K-like positive ions are calculated for asymmetric coplanar geometries and
intermediate incident energies. Although the proper boundary conditions are
not respected, both the long-range Coulomb interaction in the initial and final
channels, and the short-range effects, are taken into account in the Coulomb Born
approximation through the use of two effective charges. The latter are obtained within the
framework of the frozen-core Hartree–Fock approximation which is also used for
describing the bound state wavefunctions. An approximate scaling law for the TDCSs
is predicted for the ionization of sequences of isoelectronic ions, provided the
incident and ejected energies are properly scaled. The calculations illustrate that the
scaling is generally well verified, in particular for increasing ionicity within a
sequence. Moreover, as one moves from the H- to K-like sequences, more TDCS
structure is observed. Two main peaks are always situated close to the direction
of the momentum transfer and opposite direction, although with strong shifts.
Contrary to what is observed for the ionization of outer-shells electrons in neutral
atoms, the dominant peak of all cross sections is in the opposite direction to the
momentum transfer, a signature of strong elastic scattering from the nucleus.