  We consider a dark matter halo (DMH) of a spherical galaxy as a Bose-Einstein
condensate of the ultra-light axions interacting with the baryonic matter. In
the mean-field limit, we have derived the integro-differential equation of the
Hartree-Fock type for the spherically symmetrical wave function of the DMH
component. This equation includes two independent dimensionless parameters: (i)
\b{eta}- the ratio of baryon and axion total mases and (ii) {\xi}- the ratio of
characteristic baryon and axion spatial parameters. We extended our dissipation
algorithm for studying numerically the ground state of the axion halo in the
gravitational field produced by the baryonic component. We calculated the
characteristic size, Xc, of DMH as a function of \b{eta} and {\xi} and obtained
an analytical approximation for Xc.
