  We define and study hole-like excitations (the Lieb II mode) in a weakly
interacting Bose liquid subject to external confinement. These excitations are
obtained by semiclassical quantization of gray solitons propagating on top of a
Thomas-Fermi background. Radiation of phonons by an accelerated gray soliton
leads to a finite life-time for the trapped Lieb II mode. It is shown that, for
a large number of trapped atoms, most of the Lieb II levels can be
experimentally resolved.
