  We study the optical loading of a trapped Bose-Einstein condensate by
spontaneous emission of atoms in excited electronic state in the
Boson-Accumulation Regime. We generalize the previous simplified analysis of
ref. [Phys. Rev. A 53, 2466 (1996)], to a 3D case in which more than one trap
level of the excited state trap is considered. By solving the corresponding
quantum many-body master equation, we demonstrate that also for this general
situation the photon reabsorption can help to increase the condensate fraction.
Such effect could be employed to realize a continuous atom laser, and to
overcome condensate losses.
