  Due to electron-nucleus weak interaction, atomic bound states with different
parities turn out to be mixed. We discuss a prospect for measuring the mixing
parameter between the nearly degenerate metastable states 1s_{1/2} 2s_{1/2} : J
= 0 and 1s_{1/2} 2p_{1/2} : J = 0 in heliumlike Uranium. Our analysis is based
on the polarization properties of the photons emitted in the two-photon decays
of such states.
