On the experimental verification of a hypothesis about the "megaatom" state in a Bose — Einstein condensate

A scenario of the experiment on the observation of the specific narrowing of nuclear radiative gamma lines in a Bose — Einstein condensate (BEC) due to the quantum coherence of atoms is proposed which could be used to confirm the appearance of the so-called megaatom state in the BEC. The expected narrowing of the gamma lines can occur due to the motion suppression of individual atoms and partial elimination of the inhomogeneous (Doppler) broadening. Quantitative estimates are performed, in particular, for the case of Mössbauer spectroscopy.