Electron, Positron and Photon Collisions with Atoms and Molecules
Electron collisions at intermediate energies
The intermediate energy regime is usually thought of as covering incident electron energies from athe ionization threshold to about three to four times this value. Hence the incident electron will have sufficient energy to ionize one of the electrons of the target atom or ion. Any accurate theoretical treatment must therefore have some means of including the effects of the infinite number of continuum states of the ionized target plus ejected electron, as well as the infinite number of bound states of the target atom/ion lying just below the ionization threshold.
The IERM and RMPS approaches are extensions of the low-energy R-matrix method in which the close-coupling expansion is augmented by the inclusion of a set of well-constructed pseudo-states to represent, in some average way, the high-lying Rydberg states and continuum states of the target that cannot be included explicitly. These approaches have been successfully applied to study electron scattering and electron-impact ionization, while the IERM method has recently been modified to study photo-double-ionization (Scott, Kinnen and McIntyre, 2012, Phys Rev A 86 032707) .
In order to complete envelope high-lying Rydberg states and target continuum states within the R-matrix internal region, it is necessary in these intermediate energy studies to significantly increase the ‘R-matrix’ boundary between the internal and external regions. This can typically increase to over 200au, compared with around 20au for low energy scattering problems. To accommodate this, it is possible to break up the internal region into smaller sectors, solve the Schrödinger equations in each of these, and then propagate a global R-matrix across the small sectors within the internal region, until the ‘R-matrix’ boundary is reached. This is the methodology behind the recently developed 2-D R-matrix propagator.