Adiabatic-nuclei calculations of electron and positron scattering from molecular hydrogen and its ion*

We report the extension of the convergent close-coupling (CCC) method for electron-molecule scattering [1] to the adiabatic-nuclei (AN) formulation which allows us to study the effects of nuclei motion and electron-impact dissociation processes. For H$_2^+$ and its isotopologues [2] we have modeled collisions with hot (vibrationally excited) molecules and compared with available experimental data for dissociative ionization, proton production, and the dissociative products kinetic energy release distributions. For H$_2$ we have performed AN calculations of positron scattering with emphasis on establishing convergent low-energy total and vibrational $0 \rightarrow 1$ excitation cross sections. To study electron collisions with H$_2$ we have developed a spheroidal coordinate formulation of the CCC method that allows for an accurate description of the target wave functions to large inter-nuclei distances. Excitation cross sections for vibrationally resolved transitions between low-lying H$_2$ states have been calculated and used to determine vibrational excitation of the H$_2$ ground state via excitation of electronically excited singlet states and radiative cascade. [1] Zammit et al., J. Phys. B {\bf 50}, 123001 (2017). [2] Zammit et al., Phys. Rev. A {\bf 90} 022711 (2014)\\ \\In collaboration with: M. C. Zammit, J. S. Savage, L. H. Scarlett, J. Tapley, I. Bray