Howard Fenker, JLab
December 8, 2000 for GEN Collaboration Meeting
Thanks to Dr. Pauli of the Exclusion Principle, the scattering cross section between two electrons is dependent on their relative spin orientations.
A Moller Polarimeter exploits this difference in order to measure the polarization of an electron beam. The (polarized) beam is made to strike an iron foil in which the atomic electrons are polarized by an external magnetic field. In Hall-C the field is about 3 Tesla, aligned parallel to the beam direction. The foil is perpendicular to the field. The resulting target polarization is well known (about 8%). Thus, an asymmetry in the scattering rate as the sign of the beam polarization is reversed (other conditions remaining the same) can be used as a measure of the magnitude of the beam polarization.
The Hall-C Moller Polarimeter uses carefully placed lead glass blocks to detect Moller electrons which were scattered at 90 degrees in the center of mass. A pair of quadrupoles and a set of movable collimators are tuned to insure that this is the case. (In the lab the scattering angle is of order 10 milliradians and is energy dependent.) This exploits the high sensitivity of the cross section to relative spin alignment which occurs at 90 degrees (the analyzing power, or Azz). As shown in the figure below, the overall cross section is low in this region, but, importantly, it varies quite slowly.
Where Azz is the analyzing power for center of mass scattering angle theta, PT and PB are the target and beam polarizations, respectively, and sigma_zero is the cross section for unpolarized scattering. E_e_cms is the electron energy within the center of mass system, and alpha is the fine-structure constant.
The cross section is small for 90° scattering, but the analyzing power is large and, importantly, the product varies slowly in that region. The analyzing power is negative, meaning that if both polarizations have the same sign the cross section is reduced. Anti-parallel spins yield a larger cross section. It is this difference that is measured by the Møller polarimeter.
The arrangement of
The Moller detector system consists of a target ladder (holding four foil targets), the superconducting solenoid for brute-force polarization of the target, the cryogenics system associated with the solenoid, three power supplies for the solenoid and the two quadurpoles, the two quadrupoles, the collimator box with motion controls, two lead glass shower counters for Moller electron coincidence detection, 28 hodoscope channels and associated electronics for tuning the quads, timing logic, data acquisition modules, controls software, and analysis software. While the Hall-C staff will initially configure and commission the polarimeter for each experiment, experimenters are responsible for verifying that the system is functioning adequately for their needs. Moller runs are performed by the experimenters.
A rather thorough writeup of the procedure for tuning and using the polarimeter is documented in the Hall C Operating Manual referenced from the Hall -C Operating Procedures and Manuals page. The web-based version is, in fact, the official reference copy of this document. For detailed information, you should refer to that document, which has the advantage that it is periodically updated and corrected. There is also a one page Step by Step guide to taking Moller runs.