A polarized, internal electron target gradually polarizes a proton bea
m in a storage ring. Here we derive the spin-transfer cross section fo
r e over arrow pointing right(p,p over arrow pointing right)e scatteri
ng. A recent measurement of the polarizing effect of a polarized atomi
c hydrogen target is explained when the effect of the atomic electrons
is included. We also consider the interaction of a stored beam with a
pure electron target which can be realized either by a comoving elect
ron beam or by trapping of electrons in a potential well. In the futur
e, this could provide a practical way to polarize antiprotons.