Ω-doubling and a limit for the enhancement of the electron EDM effect in diatomic molecules

The recent experimental results for the upper limit for the electron EDM in heavy diatomic molecules with open electron shells YbF, ThO as well as proposals for the similar measurements in other heavy heteronuclear diatomic molecules are analyzed. It is argued that the enhancement factor for the electron EDM in a molecule, presented as an “effective” electric field Eeff is limited by the value Eeff,max≈100⋅109 V/cm for the molecular states with any value of Ω in diatomic molecules.