The Determination of the Electron Helicity
          in the Hall C Beamline via Moller Scattering

                            T.Reichelt
                          November 2000

The injector electronics provides the scattering events with
a label h+ (h- being internally generated as the logically 
inverse) depending of the sense of polarization of the laser 
light produced in the optical set-up.This label does in general
not reflect the true electron helicity.The relationship between
the true helicity and the label has been deduced by Moller 
scattering for the run period of November 2000. 

1. QED states for 90-degrees-Moller scattering in the CMS that 
    the cross-section with spin directions of the target 
    and the beam electron being opposite to each other is  
    larger than the cross-section where the spins are parallel 
    to each other.This is a consequence of the Pauli principle.

2. The Moller polarimeter is operated in such a way that
    it measures coincidence count rates in a small intervall
    of the CMS scattering angle around 90 degrees.The  
    count rate for spin directions opposite is therefore larger  
    than for spin directions parallel. 

3. A measurement with a Hall probe in the field of the Moller
    solenoid had the result ,that the magnetic field vector is    
    parallel to the beam direction.The field direction is here 
    the conventional one,i.e. as follows from the Lorentz force.
    Consequently the foil magnetisation is directed in the   
    same sense.Since for electrons the spin vector is oppo= 
    site to their magnetic moment,the polarization vector of 
    the target electrons and therefore their spin direction 
    is opposite to the beam direction.

    It has to be noted here,that the power supply is not 
    equipped with an inverter of the polarity. ( A push button
    on the front panel is ineffective ).Unless the leads to the
    solenoid are inverted,the polarity and therefore the field
    direction are always as stated above.A change in the
    injector electronics can,however,easily change the
    the h-label and the true helicity. 

4. The Moller analyzer calculates the asymmetry a :

                 a = ( h+ events - h- events )/ sum
   
    h+ and h- are here the labels as given by the electronics.

   Moller measurements gave the following results :

               lamda/2 plate  "in"   :   a > 0
               lamda/2 plate "out"  :   a < 0

   With the results of 1.,2. and 3. this can be summarized in :

   lamda/2 plate "in"  :   h+ means beam polarization > 0
   i.e. the beam consists mostly of electrons with  
   positive helicity.Consequently for events labeled h-
   the beam consists mostly of electrons with negative
   helicity.For lamda/2 plate "out" the opposite is true.




   This relation between the label,the position of the lamda/2  
   plate and the true helicity has been deduced for the runs
   taken in November 2000.It remains valid also for other
   run periods,provided the Moller measurements give a 
   positive polarization when the lamda/2 plate is " in".