Electron- and positron-molecule scattering: development of the molecular convergent close-coupling method

Starting from first principles, this tutorial describes the development of the adiabatic-nuclei convergent close-coupling (CCC) method and its application to electron and (single-centre) positron scattering from diatomic molecules. We give full details of the single-centre expansion CCC method, namely the formulation of the molecular target structure; solving the momentum-space coupled-channel Lippmann-Schwinger equation; deriving adiabatic-nuclei cross sections and calculating V-matrix elements. Selected results are presented for electron and positron scattering from molecular hydrogen H-2 and electron scattering from the vibrationally excited molecular hydrogen ion H-2(+) and its isotopologues (D-2(+), T-2(+), HD+, HT+ and TD+). Convergence in both the close-coupling (target state) and projectile partial-wave expansions of fixed-nuclei electron-and positron-molecule scattering calculations is demonstrated over a broad energyrange and discussed in detail. In general, the CCC results are in good agreement with experiments.