# spin conservation in exchange polarization process

Exchange polarization is the process by which spin is transferred between an electron beam and a system of polarized atoms (with a single valence spin). The process occurs as a result of the Pauli Exclusion principle. See Burke and Schey Phys. Rev. 126 163 (1962).

The type of scattering processes that can occur at |up up> $\rightarrow$ |up up>, |up down> $\rightarrow$ |up down>, |up down> $\rightarrow$ |down up> etc. where up and down refer to the spin of the electron in the beam or the atom. In any case, you can see that the spin is preserved in each instance.

However, when one goes through the mathematics using the density matrix formalism for general initial polarizations of the electron beam and atoms, the resulting polarization $P'_e + P'_a \neq P_e + P_a$ which to me is impossible given that each scattering channel conserves spin. This can be see in the paper cited above (n + p in their notation) and also in the Mott & Massey monograph (Vol. 2 p. 542) and the book Polarized Electrons by Kessler. None of the authors mention any problem with spin conservation and I am confounded at the moment.