Systematic Errors Specific to Mott Polarimetry

Gay and Dunning [5] identify two sources of systematic error unique to Mott polarimeters:

• The incoming electron beam may be misaligned (figure 3.3.)

  Figure 3.3: A Misaligned Incident Electron Beam. Based on a diagram by Gay & Dunning [5]

  

• The two detectors may have efficiencies $\eta_1$ and $\eta_2$, which are less than unity. More crucially for asymmetry measurements (equation 3.6,) it may be that $\eta_1\neq\eta_2$.

Gay & Dunning [5] show that each of these effects introduces a multiplicative relative systematic error in the electron arrival rate at one channeltron compared with that at the other, which invalidates the use of the raw asymmetry as a polarization indicator (equation 3.6.) A technique has been developed [5,34] which allows the elimination of a systematic error of this nature. In this scenario, the rates of electron arrival $R_{ij}$ on channeltrons $i = 1$ and $i = 2$ for beams of polarizations of equal magnitude $\vert P\vert$, in opposite directions $j=\uparrow{}$ and $j=\downarrow{}$. The polarization is then given^3.1by [5,34]

$$P = \frac{\sqrt{R_{1\uparrow}R_{2\downarrow}}-\sqrt{R_{1\dow... ...{2\downarrow}}+\sqrt{R_{1\downarrow}R_{2\uparrow}})}\textrm{.}$$ (3.7)