  The Rayleigh scattering of x-rays by many-electron highly charged ions is
studied theoretically. The many-electron perturbation theory, based on a
rigorous quantum electrodynamics approach, is developed and implemented for the
case of the elastic scattering of (high-energetic) photons by helium-like ion.
Using this elaborate approach, we here investigate the many-electron effects
beyond the independent-particle approximation (IPA) as conventionally employed
for describing the Rayleigh scattering. The total and angle-differential cross
sections are evaluated for the x-ray scattering by helium-like Ni$^{26+}$,
Xe$^{52+}$, and Au$^{77+}$ ions in their ground state. The obtained results
show that, for high-energetic photons, the effects beyond the IPA do not exceed
2% for the scattering by a closed $K$-shell.
