We develop a quantum theory of atomic Rayleigh scattering. Scattering is considered as a relaxation of incident photons from a selected mode of free space to the reservoir of the other free space modes. Additional excitations of the reservoir states which appear are treated as scattered light. We show that an entangled state of the excited atom and the incident photon is formed during the scattering. Due to entanglement, a photon is never completely absorbed by the atom. We show that even if the selected mode frequency is incommensurable with any atomic transition frequency, the scattered light spectrum has a maximum at the frequency of the selected mode. The linewidth of scattered light is much smaller than that of the spontaneous emission of a single atom, therefore, the process can be considered as elastic. The developed theory does not use the phenomenological concept of virtual level.
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