Shapes of leading tunnelling trajectories for single-electron molecular ionization

TL;DR

This paper introduces the concept of a leading tunnelling trajectory in molecular ionization and proves its linearity in models with short-range interactions, with near-linearity in long-range cases, providing insights into tunnelling behavior.

Contribution

It extends the geometrical approach to tunnelling by defining and analyzing the shape of leading tunnelling trajectories in molecular ionization models.

Findings

Leading tunnelling trajectories are linear for short-range interactions.

Trajectories are 'almost' linear for long-range interactions.

Results are discussed at formal and physical levels.

Abstract

Based on the geometrical approach to tunnelling by P.D. Hislop and I.M. Sigal [Memoir. AMS 78, No. 399 (1989)], 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.