  Spontaneous emission of a photon by an atom is described theoretically in
three dimensions with the initial wave function of a finite-mass atom taken in
the form of a finite-size wave packet. Recoil and wave-packet spreading are
taken into account. The total atom-photon wave function is found in the
momentum and coordinate representations as the solution of an initial-value
problem. The atom-photon entanglement arising in such a process is shown to be
closely related to the structure of atom and photon wave packets which can be
measured in the coincidence and single-particle schemes of measurements. Two
predicted effects, arising under the conditions of high entanglement, are
anomalous narrowing of the coincidence wave packets and, under different
conditions, anomalous broadening of the single-particle wave packets.
Fundamental symmetry relations between the photon and atom single-particle and
coincidence wave packet widths are established. The relationship with the
famous scenario of Einstein-Podolsky-Rosen is discussed.
