The radiative recombination of an electron with H- and Li-like [Formula Presented] in its ground state is studied. An experiment is proposed in which both the electron and the ion are polarized in the same direction, along or opposite to the initial electron momentum. Since, owing to the Pauli principle, the electron can be captured into the ground state of He- and Be-like uranium, respectively, only via a spin-flip transition, one may uniquely identify spin-flip transitions for arbitrary photon emission angles. The cross section of the process is calculated for a wide range of initial electron energies. 5555 2002 The American Physical Society.