Vibrational and rotational transitions in low-energy electron-diatomic-molecule collisions. I. Close-coupling theory in the moving body-fixed frame

We present a vibrational-rotational close-coupling formulation of electron-diatomic-molecule scattering in a body-fixed frame, with the target molecular axis chosen to be the $z$ axis. The resulting coupled differential equation is solved in the moving body-fixed frame throughout the entire region of space. The coupled differential equation and asymptotic boundary conditions are given in terms of definite parity, which are necessary for reducing the number of coupled channels. Procedures for evaluating cross sections employing this body-fixed formulation are outlined, thus rendering the present formulation directly applicable to numerical calculations. We discuss the advantages of the body-fixed formulation over a space-fixed formulation for introducing approximation schemes, for studying resonance scattering of vibrational transition, and for electron-heavy-molecule collisions. Aside from the formal e$\stackrel{\mathrm{´}}{\mathrm{q}}$uivalence between the two formulations, conditions are also discussed for obtaining identical results from them when a (finite) truncated basic set is used.