Ground state of a Bose-Einstein condensate which scatters coherently laserradiation

We present a self-consistent: method of taking into account back action of a laser radiation to a Bose-Einstein condensate of neutral atoms. The light is coherently scattered inside the degenerate atomic sample, thus its inte nsity and, consequently, the atomic ground level AC Stark shift are spatial ly varying. This leads to a small deformation of the atomic cloud and, if t he external radiation is abruptly switched off, to generation of collective excitations.