The nature of dark matter in modern physics is an important problem. Therefore, in this paper we consider a quantum system consisting of two identical particles. These particles are candidates for the role of dark matter. We will call them graviatoms and they could be formed in the early Universe. In this paper we have found the energy spectrum of the gravitatom from particles of dark matter, the Bohr radius, the intensity of gravitational radiation, the frequency of radiation, and the lifetime of a state. This lifetime is great for superheavy particles. Estimates of these values for different values of the masses of particles of dark matter are given.