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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 H2 and electron scattering from the vibrationally excited molecular hydrogen ion H 2 + and its isotopologues (D2+, 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 energy-range and discussed in detail. In general, the CCC results are in good agreement with experiments.