  We present an in-depth many-body investigation of the so-called mesoscopic
molecular ions that can build-up when an ion is immersed into an atomic
Bose-Einstein condensate in one dimension. To this end, we employ the
Multi-Layer Multi-Configuration Time-Dependent Hartree method for Mixtures of
ultracold bosonic species for solving the underlying many-body Schr\"odinger
equation. This enables us to unravel the actual structure of such massive
charged molecules from a microscopic perspective. Laying out their phase
diagram with respect to atom number and interatomic interaction strength, we
determine the maximal number of atoms bound to the ion and reveal spatial
densities and molecular properties. Interestingly, we observe a strong
interaction-induced localization, especially for the ion, that we explain by
the generation of a large effective mass, similarly to ions in liquid Helium.
Finally, we predict the dynamical response of the ion to small perturbations.
Our results provide clear evidence for the importance of quantum correlations,
as we demonstrate by benchmarking them with wave function ansatz classes
employed in the literature.
