Bose-Einstein Condensation in a Two-Dimensional System with Sixty Bosons

A 60-boson system confined on a sphere has been qualitatively studied based on symmetry considerations. The low-lying spectrum is dominated by the ground rotation band based on the fullerene structure. In this band all the L = 1 to L = 5 states are found to be prohibited by symmetry. Therefore, there is a large gap lying between the ground state and the first excited state. The magnitude of this gap, which is associated with the critical temperature of Bose-Einstein condensation, has been evaluated. It is found that, the smaller the radius of the sphere of confinement, the higher the critical temperature.