Perturbative and non-perturbative methods for electron-impact ionization

Don Madison was a pioneer in applying perturbative distorted-wave methods to a wide range of electron ionizing collisions with atoms and molecules. For low and moderate electron energies, the most important term in the description of such collisions is the electron-electron interaction term in the many-body Hamiltonian, which often can be restricted to the interaction of the incoming electron with the scattered (ionized) electron. Perturbation theory is often applied, and retaining only the first term in this expansion allows for a computationally convenient description of the scattering event. This approach was widely adopted for many years and used to treat many scattering scenarios.



Other, non-perturbative, treatments were also developed that in principle include the electron-electron interaction to all orders. However, these require much larger computational resources and so have only become in widespread use in the last 20 or so years. Some of the more popular approaches include R-matrix methods, convergent close-coupling approaches, and time-dependent close-coupling techniques. Each of these methods solves the Schrodinger equation (each in a different numerical scheme) for the active electrons (normally only two) in the scattering event. While each technique has its own advantages and disadvantages, they have been shown to produce excellent agreement with each other and with experiment for a variety of cross sections for electron ionization of small targets, such as hydrogen (atomic and molecular), helium, and lithium.



This talk will survey the approaches often used in electron-impact ionization calculations and discuss where the various perturbative and non-perturbative methods are most useful. We will also discuss briefly the generation and use of ionization cross sections in plasma modeling and other applications.