Non-Born-Oppenheimer, nBO, one-particle nuclear and electron densities for a Hooke-Coulomb model of a three-body system are presented. These densities are obtained using exact closed-form analytic solutions to this problem as well as variational solutions. Moreover, the densities are calculated using different reference points, such as the global center of mass [. cm], the geometric centers between both identical [. gc12] and non-identical particles [. cm13], and the location of the non-identical particle [. p3]. It is shown that the topology of these nBO densities depends upon the choice of the reference points. This result is in turn used to argue that in a nBO regime the topological properties of the one-particle density cannot be univocally correlated with molecular structure, in the way it is done for the Born-Oppenheimer approximation.
