Behavior of heat capacity of an attractive Bose-Einstein condensate approaching collapse

We report the calculation of heat capacity of an attractive Bose-Einstein condensate, with the number N of bosons increasing and eventually approaching the critical number N_cr for collapse, using the correlated potential harmonics (CPH) method. Boson pairs interact via the realistic van der Waals potential. It is found that the transition temperature T_c initially increases slowly, then rapidly as N becomes closer to N_cr. The peak value of heat capacity for a fixed N increases slowly with N, for N far away from N_cr. But after reaching a maximum, it starts decreasing when N approaches N_cr. The effective potential calculated by the CPH method provides insight into this strange behavior.