Convergent Close-Coupling Calculations for Electron-Atom and Electron-Molecule Scattering

The Convergent Close-Coupling (CCC) method developed in our group has been applied extensively to study electron-atom/ion collisions and recently has been extended to electron collisions with diatomic molecules. This approach relies on the ability to represent the infinite number of target bound states and its continuum via a finite number of states obtained by a diagonalization of the target in a square-integrable (Sturmian) one-electron basis. We normally use a Laguerre basis though other choices are possible, for example a boxed-based basis or a B-spline basis. The choice of the basis is governed by the physical problem under consideration. As the size of a Sturmian basis increases the calculated negative energy states (relative to the corresponding ionization stage of the target) converge to the target true bound states and the positive energy states provide an increasingly dense representation of the target continuum. We then perform a multichannel expansion of the total (projectile plus target electrons) wave function and formulate a set of close-coupling equations. These equations are transformed into momentum space where they take the form of the Lippmann-Schwinger equations for the T-matrix. A solution of the T-matrix equations is obtained at each total energy E by converting them into a set of linear equations that are solved by standard techniques. We perform a partial-wave expansion of the projectile wave function and take into account the symmetry of the scattering system (e.g, total spin, parity, etc.) in order to reduce the size of the coupled equations and make calculations feasible. As soon as the T-matrix is obtained we can evaluate scattering amplitudes and cross sections for the transitions of interest. For the case of molecular targets the formulation is done within the fixed-nuclei approximation. We adopt a single-centre approach in CCC calculations. This allows us to utilize a great deal of computational development thoroughly tested for collisions with atoms. An account of nuclear motion is done as post-processing of the fixed nuclei results that require performing fixed-nuclei calculations at a (large) number of inter-nuclei distances R.