Possible critical regions for the ground state of a Bose gas in a spherical trap

With the help of perturbation theory, we study the ground state of a Bose gas in a spherical trap, using the solution in the Thomas–Fermi approximation as the zero approximation. We have found within a certain approximation that, in some very narrow intervals of values of the magnetic field of a trap, the solution deviates strongly from that in the Thomas–Fermi approximation. If the magnetic field is equal to one of such critical values, the size (or even the shape) of the condensate cloud should significantly differ from the Thomas–Fermi one.