Atomic Electron Motion for M\"oller Polarimetry in a Double-Arm Mode

We analyse an effect of electron Fermi motion at atomic shells on the accuracy of electron beam polarization measurements with a M\"oller polarimeter operating in a double--arm mode. It is demonstrated that the effect can result in either {\it increase} or {\it decrease} of the measured polarization depending on the detector positions. The effect is simulated for the M\"oller polarimeter to be installed at CEBAF Hall A.