The capture of polarized electrons by H-like ions provides a method for polarizing the nuclei of He-like heavy ions with zero total electron angular momentum in storage rings for high-energy ions. A detailed analysis for 151 63 Eu ions with nuclear spin I = 5/2 predicts a nuclear polarization degree of about 47% already after one passage through a target containing 100% polarized electrons. Almost 50% of the polarized He-like ions are predicted to be in states with zero total electron angular momentum. Such ions were recently considered as the most promising candidates in experiments at storage rings for the search for violations of the fundamental symmetries and for a nuclear and an electron electric dipole moment.