  The density distribution of the one-dimensional Hubbard model in a harmonic
trapping potential is investigated in order to study the effect of the
confining trap. Strong superimposed oscillations are always present on top of a
uniform density cloud, which show universal scaling behavior as a function of
increasing interactions. An analytical formula is proposed on the basis of
bosonization, which describes the density oscillations for all interaction
strengths. The wavelength of the dominant oscillation changes with interaction,
which indicates the crossover to a spin-incoherent regime. Using the Bethe
ansatz the shape of the uniform fermion cloud is analyzed in detail, which can
be described by a universal scaling form.
