The final important cut to be made on the data is a cut on the velocity ratio, or . is the ratio of the velocity of the particle deduced from the time of flight between the analyzer and the catcher and the velocity expected based on the time-of-flight to the first plane . is simply defined as
where d is the distance between the analyzer and the catcher planes, and and are the respective times of hits in the analyzer and catcher planes. is calculated from nn relativistic kinematics using the neutron energy, , which has been determined from the time-of-flight of the neutron to the analyzer plane:
where is 939.57 MeV, and is the polar scattering angle. The velocity ratio is then simply
For a event the velocity ratio should be unity. Figure shows a typical velocity ratio histogram.
Figure: Velocity ratio histogram. The dashed line represents where the observed interplane velocity equals the expected velocity.
As would be expected, and is obvious from figure , the resolution on the interplane velocity is not very good. However, this cut can still help remove a number of bad events. Any events with the wrong plane hit sequence, such as stray neutrons or cosmic rays travelling the wrong direction through the detector, will be cut out. events will be cut out because the Q value of these reactions will slow the outgoing neutrons compared to those free scattered off the protons in the scintillator. Also, events are cut because the velocity is much greater than expected for a neutron. The last significant form of event that the velocity ratio cut helps to clean up is wrap-around neutrons. These very slow neutrons generated by a previous beam pulse could arrive at the analyzer plane at the same time as the faster neutrons from the pulse being measured, which would dilute the results. However, the subsequent requirement of substantiated interplane velocity will get rid of those slow neutrons and significantly reduce the background.
It is obvious from the continuum seen in figure that it is impossible to completely separate the np elastic scattering events from other, less useful events. Attempts to model the analyzing power as a sum of the contributions of all possible reactions have proven quite difficult, and this is why is measured empirically. The of any polarimeter of this type will fall short of the expectations of free np elastic scattering (see figure ), but that will not invalidate the measurement of the polarimeter's analyzing power nor compromise its ability to measure neutron polarization.