  We investigate low-density, quantum-degenerate gases in the presence of a
localised attractive potential in the centre of a one-dimensional harmonic
trap.The attractive potential is modelled using a parameterised delta-function,
allowing us to determine all single particle eigenfunctions analytically. From
these we calculate the ground state many-body properties for a system of
spin-polarised fermions and, using the Bose-Fermi mapping theorem, extend the
results to strongly interacting bosonic systems. We discuss the single particle
densities, the pair correlation functions, the reduced single particle density
matrices and the momentum distributions as a function of particle number and
strength of the attractive point potential. As an important experimental
observable, we place special emphasis on spatial coherence properties of such
samples.
