The Detection Statistics of a Molecular-Beam Frequency Standard

The detection statistics of a molecular beam are analyzed, taking into account fluctuations in emission, transition and detection. It is discovered that the over-all process has a Poisson distribution. Because of the nature of this distribution, it is noted that the optimum method of estimating the average number of molecular transitions is by means of a long-time average of the detected current. The degree to which the detector current is a measure of the average number of molecular transitions in the device is established, with a certain minimum confidence, by use of the Tchebycheff Inequality.