  An inversion method is formulated for extracting entanglement-related
information on two-particle interactions in a one-dimensional system from
measurable one-particle position- and momentum-distribution functions. The
method is based on a shell-like expansion of these norm-1 measured quantities
in terms of product states taken from a parametric orthonormal complete set.
The mathematical constraints deduced from these point-wise expansions are
restricted by the underlying physics of our harmonically confined and
interacting Heisenberg model. Based on these exact results, we introduce an
approximate optimization scheme for different inter-particle interactions and
discuss it from the point of view of entropic correlation measures.
