We consider tunnel ionization of an atom or molecule in a strong field within an analytical treatment of the $R$-matrix method, in which an imaginary boundary is set up inside the classically forbidden region that acts as a source of ionized electrons. These electrons are then propagated in the semiclassical approximation, and relying on a numerical solution of the inner region, which is accessible using quantum chemical techniques, we describe the subsequent evolution of the ionized electron and the ionic core.

Importantly, we show that correlation interactions between the ionized electrons and those left behind in the core can play a role during ionization, and that interactions can occur while the electron is still inside the classically forbidden region that enable tunnelling from channels normally subject to far greater exponential suppression since they are subject to higher and wider tunnelling barriers.

This interaction can be described analytically using saddle-point methods that find the dominant contributions to the temporal, spatial and momentum integrals that make up the expressions for the ionization yield. However, these methods yield results for the angular distributions of the ionized electron that do not necessarily match experiment and which yield physically unsatisfactory solutions.

In this report we develop a formalism to evaluate these integrals exactly, which yields more precise calculations of the angular distributions while at the same time providing the language, in terms of exchange of angular momentum, with which to understand their origins and their differences from previous cases, thus giving an insight into the fundamental physics of the correlation interaction process.