  The stationary states of few bosons in a one-dimensional harmonic trap are
investigated throughout the crossover from weak to strongly attractive
interactions. For sufficient attraction, three different classes of states
emerge: (i) N-body bound states, (ii) bound states of smaller fragments, and
(iii) gas-like states that fermionize, that is, map to ideal fermions in the
limit of infinite attraction. The two-body correlations and momentum spectra
characteristic of the three classes are discussed, and the results are
illustrated using the soluble two-particle model.
