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

Abstract

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.