Trapped planar three-boson system with spin 1 and with hard-core interactions

A two-dimensional spin 1 three-boson system trapped by a parabolic confinement and interacting with hard-core repulsion has been investigated. The spectrum has been analyzed in detail, in particular, the existence of breathing bands has been confirmed. Two density functions associated with the oscillations of breathing and deformation, respectively, have been defined to study the structure of low-lying states. The inherent nodal structure of wave functions is found to play a decisive role. The effect of rotation on the ground-state property has also been studied. Not only the angular momentum, the permutation symmetry will also transit in accord with the increase of the speed of rotation.