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
and its isotopologues (D2+,
, 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.
The convergent close-coupling method has been used to solve the electron-hydrogen molecule scattering problem in the fixed-nuclei approximation. Excellent agreement with experiment is found for the grand total, elastic, electronic-excitation, and total ionization cross sections from the very low to the very high energies. This shows that for the electronic degrees of freedom the method provides a complete treatment of electron scattering on molecules as it does for atoms.
The single centre adiabatic-nuclei convergent close-coupling method has been used to investigate positron collisions with molecular hydrogen (H2) in the ground and first vibrationally excited state. Cross sections are presented over the energy range from 1 to 1000 eV for elastic scattering, vibrational excitation, total ionisation and the grand total cross section. The present adiabaticnuclei positron-H2 scattering length was calculated as A = −2.70 a0 for the ground state and A = −3.16 a0 for the first vibrationally excited state. The present elastic differential cross sections are also used to "correct" the low-energy grand total cross section measurements of the Trento group [Zecca et al. Phys. Rev. A 80, 032702 (2009)] for the forward angle scattering effect. In general the comparison with experiment is good. By performing convergence studies we estimate that our Rm = 1.448 a0 fixed-nuclei results are converged to within ±5% for the major scattering integrated cross sections.
We apply the adiabatic nuclei convergent close-coupling method to electron-impact dissociative excitation of H2 in the low energy regime. Differential and integrated cross sections are presented for excitation of the b 3 Σ + u state, the primary pathway to dissociation of H2 at low energies. Agreement with experiment is satisfactory. Results are also presented for the isotopologues D2, T2, HD, HT, and DT, which show a pronounced isotopologue effect near threshold in both the differential and integrated cross sections.
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