Shapes of leading tunnelling trajectories for single-electron molecular ionization

Based on the geometrical approach to tunnelling by Hislop and Sigal (1989 Mem. AMS 78 No 399), we introduce the concept of a leading tunnelling trajectory. It is then proven that leading tunnelling trajectories for single-active-electron models of molecular tunnelling ionization (i.e. theories where a molecular potential is modelled by a single-electron multi-centre potential) are linear in the case of short-range interactions and 'almost' linear in the case of long-range interactions. The results are presented on both the formal and physically intuitive levels. Physical implications of the obtained results are discussed.