  A rotating bosonic many-body system in a harmonic trap is studied with the
3D-Cranked Hartree-Fock-Bogoliubov method at zero temperature, which has been
applied to nuclear many-body systems at high spin. This method is a variational
method extended from the Hartree-Fock theory, which can treat the pairing
correlations in a self-consistent manner. An advantage of this method is that a
finite-range interaction between constituent particles can be used in the
calculation, unlike the original Gross-Pitaevskii approach. To demonstrate the
validity of our method, we present a calculation for a toy model, that is, a
rotating system of ten bosonic particles interacting through the repulsive
quadrupole-quadrupole interaction in a harmonic trap. It is found that the
yrast states, the lowest-energy states for the given total angular momentum,
does not correspond to the Bose-Einstein condensate, except a few special
cases. One of such cases is a vortex state, which appears when the total
angular momentum $L$ is twice the particle number $N$ (i.e., $L=2N$).
