  We study emission of a single photon from a spherically symmetric cloud of N
atoms (one atom is excited, N-1 are in ground state) and present an exact
analytical expression for eigenvalues and eigenstates of this many body
problem. We found that some states decay much faster then the single-atom decay
rate, while other states are trapped and undergo very slow decay. When size of
the atomic cloud is small compared with the radiation wave length we found that
the radiation frequency undergoes a large shift.
