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

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