Polarized antiprotons can be produced in a storage ring by spin-dependent interaction in a purely electron-polarized hydrogen gas target. The polarizing process is based on spin transfer from the polarized electrons of the target atoms to the orbiting antiprotons. After spin filtering for about two beam lifetimes at energies T ≈ 40−170 MeV using a dedicated large acceptance ring, the antiproton beam polarization would reach P = 0.2 − 0. . Unfortunately, both approaches do not allow efficient accumulation in a storage ring, which would greatly enhance the luminosity. Spin splitting using the Stern-Gerlach separation of the given magnetic substates in a stored antiproton beam was proposed in 1985 [3]. Although the theoretical understanding has much improved since then [4], spin splitting using a stored beam has yet to be observed experimentally.Interest in the polarization of antiprotons has recently been stimulated by a proposal to build a High Energy Storage Ring (HESR) for antiprotons at the new Facility for Antiproton and Ion Research (FAIR) at the Gesellschaft für Schwerionenforschung (GSI) in Darmstadt [5]. A Letter-of-Intent for spin-physics experiments has been submitted by the PAX collaboration [6] to employ a polarized antiproton beam incident on a polarized internal storage cell target [7]. A beam of polarized antiprotons would enable new experiments, such as the first direct measurement of the transversity distribution of the valence quarks in the proton, a test of the predicted opposite sign of the Sivers-function -related to the quark distribution inside a transversely polarized nucleon -in Drell-Yan as compared to semi-inclusive deep-inelastic scattering, and a first measurement of the moduli and the relative phase of the time-like electric and magnetic form factors G E,M of the proton [6].In 1992 an experiment at the Test Storage Ring (TSR) at MPI Heidelberg showed that an initially unpolarized stored 23 MeV proton beam can be polarized by spindependent interaction with a polarized hydrogen gas target [8,9,10]. In the presence of polarized protons of magnetic quantum number m = , which eventually caused the stored beam to acquire a polarization parallel to the proton spin of the hydrogen atoms during spin filtering. In an analysis by Meyer three different mechanisms were identified, that add up to the measured result [11]. One of these mechanisms is spin transfer from the polarized electrons of the hydrogen gas target to the circulating protons. Horowitz and Meyer derived the spin transfer cross section p + e → p + e (using c = = 1) [12],where α is the fine-structure constant, a is the anomalous magnetic moment of the proton, m e and m p are the rest mass of electron and proton, p is the momentum in the CM system, a 0 = 52900 fm is the Bohr radius and C 2 0 = 2πη/[exp(2πη) − 1] is the square of the Coulomb wave function at the origin. The Coulomb parameter η is given by η = −zα/v (for antiprotons, η is positive). z is the beam charge number and v the relative velocity of particle and projectile in ...