For target and recoil polarization in pion electroproduction
the following coordinate systems are used in the literature:
(all calculations will be done in the cm frame)

1) {x,y,z} in the reaction plane:
           z  : in the direction of the virtual photon (k)
           y  : = k x q  perpendicular to the photon (k) and the pion (q)
           x  : = y x z  in the reaction plane of pion and photon

2) {x',y',z'} in the reaction plane:
           z' : in the direction of the pion (q)
           y´ : = k x q  identical to y
           x' : = y' x z'  in the reaction plane of pion and photon

3) {t,n,l} in the reaction plane:
           l  : in the direction of the outgoing nucleon (-q)
           n  : = k x q  identical to y
           t  : = n x l  in the reaction plane of pion and photon

4) {1,2,3} in the scattering plane:
           3  : photon (k) identical to z
           2  : = ki x kf perpendicular to the scattering plane of the electron
           1  : = 2 x 3  


Note: Only system 4) is independent of the pion and nucleon in the final state.
      It is the only system which can be used in inclusive reactions.


For the Response Functions we use 1) for both target and recoil polarization

For the Transverse Polarization Observables 
       we use 1) for target and 2) for recoil polarization 
       in accordance to the standard definition in pion photoproduction

For the Target- or Recoil Polarization Programs 
       any one of systems 1) - 4) can be selected.

For integrated cross sections we will use system 4).