The Princess Sirindhorn Neutron Monitor (PSNM) is an 18NM64 (with 18 counter tubes in a continuous row)
at 2560~m altitude in Doi Inthanon, Thailand. In late 2015, the electronics in the PSNM were upgraded so as to return
an absolute time, referenced to the GPS time, for each neutron count recorded. The timing accuracy is approximately
$\pm3$ $\mu$s. This permits extending the well-known concept of multiplicity
(multiple correlated counts in one detector) to what we refer to as `cross multiplicity'
or correlation of counts in one detector with those in another.
At present, the data are recorded as cross-counter time-delay histograms with 5-$\mu$s bins.
A cross-counter relative leader fraction $L_{ij}$ can be defined as the fraction of pulses
measured in counter number $i$ that are uncorrelated in time with the next pulse in counter $j$.
For simplicity, we derive average cross-counter leader fractions $L_\Delta$ with $\Delta=|i-j|$
as a function of counter tube separation, from a tube separation $\Delta=0$ (i.e., using the same tube)
to $\Delta=17$. For low tube separation, $L_\Delta$ rapidly increases with increasing $\Delta$,
as expected from the spatial spreading of neutrons produced by the same atmospheric secondary particle
inside the neutron monitor. At high tube separation, $L_\Delta$ increases slowly with increasing $\Delta$
and remains different from unity, which we interpret as due to multiple atmospheric secondaries
arriving in rapid succession after originating from the same primary cosmic ray.