  We consider the criterion for Bose condensation for particles in a harmonic
trap. For a fixed angular momentum, the lowest energy state for a cloud of
bosons with attractive interactions is the ground state of the cloud with all
the angular momentum in the center-of-mass motion, and the one-particle reduced
density matrix generally does not have a single large eigenvalue, but a number
of them, suggesting that the state is an example of a fragmented condensate
(Wilkin, Gunn, and Smith, Phys. Rev. Lett. 80, 2265 (1998)). We show that a
convenient way to describe correlations in the system is by defining an
internal one-particle reduced density matrix, in which the center-of-mass
motion is eliminated, and that this has a single eigenvalue equal to the number
of particles for the problem considered here. Our considerations indicate that
care is necessary in formulating a criterion for Bose-Einstein condensation.
