  We present a general method for the derivation of various statistical
quantities describing the detection of a beam of atoms emerging from a
micromaser. The user of non-normalized conditioned density operators and a
linear master equation for the dynamics between detection events is discussed
as are the counting statistics, sequence statistics, and waiting time
statistics. In particular, we derive expressions for the mean number of
successive detections of atoms in one of any two orthogonal states of the
two-level atom. We also derive expressions for the mean waiting times between
detections. We show that the mean waiting times between de- tections of atoms
in like states are equivalent to the mean waiting times calculated from the
uncorrelated steady state detection rates, though like atoms are indeed
correlated. The mean waiting times between detections of atoms in unlike states
exhibit correlations. We evaluate the expressions for various detector
efficiencies using numerical integration, reporting re- sults for the standard
micromaser arrangement in which the cavity is pumped by excited atoms and the
excitation levels of the emerging atoms are measured. In addition, the atomic
inversion and the Fano-Mandel function for the detection of de-excited atoms is
calculated for compari- son to the recent experimental results of Weidinger et
al. [1], which reports the first observation of trapping states.
