Time-Resolved Interatomic Coulomb Elec\-tron Capture by Ba\textsuperscript{+} through Rb proximity

A time-resolved numerical investigation of the Interatomic Coulomb Electron Capture (ICEC) is presented. In the ICEC process, a species $A$ captures a free electron by long-range energy transfer through Coulomb interaction to a bound electron in a neighbouring species $B$. From a theoretical perspective, ICEC was first predicted for atoms and molecules through asymptotic approximation [1], and then successfully modelled by time-dependent techniques in low-dimensional systems [2]. From the experimental side, on the other hand, techniques for trapping ultracold ions and atom clouds are advancing. This may enable time-resolved ICEC experiments in the near future. We thus numerically study the dynamics of such an exemplary experiment at ultracold temperatures, with a barium cation trapped in a cloud of rubidium atoms, in order to predict and pave the way for time-resolved ICEC experiments.\\ ~[1] Gokhberg / Cederbaum, Phys.~Rev.~A \textbf{82} (2010).\\ ~[2] Pont \textit{et al.}, J.~Phys.~Condens.~Matter \textbf{28} (2016).