  Non-local energy transfer between bound electronic states close to the
ionisation threshold is employed for efficient state preparation in dilute atom
systems from technological foundations to quantum computing. The generalisation
to electronic transitions into and out of the continuum is lacking quantum
simulations necessary to motivate such potential experiments. Here, we present
the first development of a electron-dynamical model simulating fully
three-dimensional atomic systems for this purpose. We investigate the viability
of this model for the prototypical case of recombination of ultracold
barium(II) by environment-assisted electron capture thanks to a rubidium atom
in its vicinity. Both atomic sites are modelled as effective one-electron
systems using the Multi Configuration Time Dependent Hartree (MCTDH) algorithm
and can transfer energy by dipole-dipole interaction. We find that the
simulations are robust enough to realise assisted capture over a dilute
interatomic distance which we are able to quantify by comparing to simulations
without interatomic energy exchange. For our current parameters not yet
optimised for reaction likelihood, an environment-ionising assisted capture has
a probability of $1.9\times10^{-5}~\%$ over the first $15~\mathrm{fs}$ of the
simulation. The environment-exciting assisted-capture path to
$[\text{Ba}^{+*}\text{Rb}^{*}]$ appears as a stable long-lived intermediate
state with a probability of $8.2\times10^{-4}~\%$ for at least $20~\mathrm{fs}$
after the capture has been completed. This model shows potential to predict
optimised parameters as well as to accommodate the conditions present in
experimental systems as closely as possible. We put the presented setup forward
as a suitable first step to experimentally realise environment-assisted
electron capture with current existing technologies.
