Parity nonconservation that originates from the weak interaction of atomic
electrons with the nuclei in heliumlike gadolinium and europium is consider
ed. An experiment with a polarized ion beam is discussed. The mixed hyperfi
ne- and weak-quenching effect in Gd62+ and Eu61+ isotopes is shown to lead
to an asymmetry of the photon emission relative to the ion beam polarizatio
n. With complete beam polarization, the magnitude of the asymmetry in photo
n counting rates reaches about 0.39 x 10(-3) in gadolinium and is about 0.1
1 x 10(-3) in europium.