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. In this paper, 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$^+$). Finally, 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.