Chapter 6 Quantum Mechanical Methods for Loss-Excitation and Loss-Ionization in Fast Ion–Atom Collisions

Abstract

Inelastic collisions between bare nuclei and hydrogen-like atomic systems are characterized by three main channels: electron capture, excitation, and ionization. Capture dominates at lower energies, whereas excitation and ionization prevail at higher impact energies. At intermediate energies and in the region of resonant scattering near the Massey peak, all three channels become competitive. For dressed or clothed nuclei possessing electrons, such as hydrogen-like ions, several additional channels open up, including electron loss (projectile ionization or stripping). The most important aspect of electron loss is the competition between one- and two-electron processes. Here, in a typical one-electron process, the projectile emits an electron, whereas the target final and initial states are the same. A prototype of double-electron transitions in loss processes is projectile ionization accompanied with an alteration of the target state. In such a two-electron process, the target could be excited or ionized. The relative importance of these loss channels with single- and double-electron transitions involving collisions of dressed projectiles with atomic systems is also strongly dependent on the value of the impact energy. Moreover, impact energies determine which theoretical method is likely to be more appropriate to use for predictions of cross sections. At low energies, an expansion of total scattering wave functions in terms of molecular orbitals is adequate. This is because the projectile spends considerable time in the vicinity of the target, and as a result, a compound system comprised of the projectile and the target can be formed in a metastable molecular state which is prone to decay. At high energies, a perturbation series expansion is more appropriate in terms of powers of interaction potentials. In the intermediate energy region, atomic orbitals are often used with success while expanding the total scattering wave functions. The present work is focused on quantum mechanical perturbation theories applied to electron loss collisions involving two hydrogen-like atoms. Both the one- and two-electron transitions (target unaffected by collision, as well as loss-ionization) are thoroughly examined in various intervals of impact energies varying from the threshold via the Massey peak to the Bethe asymptotic region. Systematics are established for the fast, simple, and accurate computations of cross sections for loss-excitation and loss-ionization accounting for the entire spectra of all four particles, including two free electrons and two free protons. The expounded algorithmic strategy of quantum mechanical methodologies is of great importance for wide applications to particle transport physics, especially in fusion research and hadron radiotherapy. This should advantageously replace the current overwhelming tendency in these fields for using phenomenological modeling with artificial functions extracted from fitting the existing experimental/theoretical data bases for cross sections.