Proton polarization is determined by scattering the protons in an analyzer. The spin-orbit nuclear force causes an azimuthal asymmetry in the scattering of polarized protons. There is a left/right asymmetry for spin up/down protons, and there is an up/down asymmetry for spin left/right protons.
The magnitude of the asymmetry for a particular polarimeter, and the probability of scattering, is in general calibrated with experimental data using protons of known polarization. It is not calculated from theory. In general, intermediate energy proton polarimeters have used carbon analyzers. While hydrogen has a higher analyzing power, carbon is more effective for optimizing the polarimeter design by giving a compact, dense, inexpensive, stable, and nondangerous analyzer. Some applications do merit a technically more demanding liquid hydrogen analyzer.
A standard mode of operation in polarimeters used in Los Alamos mostly during the 1980s was to adjust the carbon analyzer thickness to cause one degree multiple scattering of the protons. Thickness then ranged from several cm for 200 MeV protons up to about 30 cm for 800 MeV protons. More recent systematic studies by the Saclay POMME calibration show that larger thicknesses improve the polarimeter figure of merit. The increased scattering percentage more than compensates for a slightly reduced analyzing power and increased multiple scattering - which leads to less certainty in the scattering angle and vertex.
The FPP built for Jefferson Lab Hall A uses 5 independently and remotely controllable blocks of carbon to adjust the analyzer thickness. The block thicknesses are: 9", 6", 3", 1.5", and 0.75", in order from front to back. The thicker blocks are composed of multiple 3" thick segments. Each block is vertically split in the middle, with a 45 degree cut, and has two sections that open to the sides. In the thicker blocks, each 3" segment has its own 45 degree cut.The efficiency and average analyzing power of the block depend on the proton energy. In general, the region of interest is scattering angles between 5 and 20 degrees. For smaller angles, multiple Coulomb scattering, with no analyzing power, overwhelms the nuclear scattering and there is no usable polarization information. There are very few proton scattering events at larger angles. The region moves inward slightly as energy increases. The average analyzing power peaks at about 0.5 for about 230 MeV protons, and decreases smoothly to about 0.1 for few GeV protons. The probability of scattering for our thicknesses ranges from about 0.01 to 0.1 as energy is increased.
The carbon blocks are operated remotely through EPICS. The system has been developed primarily by Christophe Baubert, who has made on line information available.
Revised May 6, 1996 Norma Lucero