  The spin polarization of electrons from multiphoton ionization of Xe by 395
nm circularly polarized laser pulses at $6\cdot10^{13}$ W/cm$^2$ has been
measured. At this photon energy of 3.14 eV the above threshold ionization peaks
connected to Xe$^+$ ions in the ground state ($J=3/2$, ionization potential
$I_p=12.1$ eV) and the first exicted state ($J=1/2$, $I_p=13.4$ eV) are clearly
separated in the electron energy distribution. These two combs of ATI peaks
show opposite spin polarizations. The magnitude of the spin polarization is a
factor of two higher for the $J=1/2$ than for the $J=3/2$ final ionic state. In
turn the data show that the ionization probability is strongly dependent on the
sign of the magnetic quantum number.
