  The occupancies and entropic entanglement measures for the ground state of
two particles in a two-dimensional harmonic anisotropic trap are studied. We
implement a method to study the large interaction strength limit for different
short- and long-range interaction potentials that allows to obtain the exact
entanglement spectrum and several entropies. We show that for long-range
interactions, the von Neumann, min-entropy and the family of R\'enyi entropies
remain finite for the anisotropic traps and diverge logarithmically for the
isotropic traps. In the short-range interaction case the entanglement measures
diverge for any anisotropic parameter due to the divergence of uncertainty in
the momentum since for short-range interactions the relative position width
vanishes. We also show that when the reduced density matrix has finite support
the R\'enyi entropies present a non-analytical behaviour.
