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We provide a quantitative determination of the crystallization onset for twoelectrons in a parabolic two-dimensional confinement. This system is shown tobe well described by a roto-vibrational model, Wigner crystallization occurringwhen the rotational motion gets decoupled from the vibrational one. The Wignermolecule thus formed is characterized by its moment of inertia and by thecorresponding sequence of rotational excited states. The role of a verticalmagnetic field is also considered. Additional support to the analysis is givenby the Hartree-Fock phase diagram for the ground state and by the random-phaseapproximation for the moment of inertia and vibron excitations.Comment: 10 pages, 8 figures, replaced by the published versio

Roto-vibrational spectrum and Wigner crystallization in two-electron parabolic quantum dots