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The stationary states of few bosons in a one-dimensional harmonic trap areinvestigated throughout the crossover from weak to strongly attractiveinteractions. For sufficient attraction, three different classes of statesemerge: (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 thelimit of infinite attraction. The two-body correlations and momentum spectracharacteristic of the three classes are discussed, and the results areillustrated using the soluble two-particle model.

Excitations of attractive 1-D bosons: Binding vs. fermionization