Measuring contributions from single and multiple atmospheric secondary cosmic rays in the {\it Princess Sirindhorn Neutron Monitor} using cross-counter neutron time delay distributions
Neutron monitors (NMs) are ground-based devices designed to measure cosmic-ray count rates by monitoring atmospheric neutrons from cosmic-ray showers. We present results from new electronics that have recorded cross-counter time delay histograms for the {\it Princess Sirindhorn Neutron Monitor} (PSNM) at the summit of Doi Inthanon, Thailand. From these histograms, we have extracted the cross-counter leader fraction ($L$) and corrected it for atmospheric effects. For large counter separation, we measure nearly constant $L\approx0.997$, implying that 0.3\% of counts in one counter are temporally associated with later counts on a given distant counter. Monte Carlo simulations confirm that individual secondary particles cannot account for the associated counts at large counter separation, which instead requires a contribution from multiple secondary particles in the same cosmic ray shower that is apparently independent of distance over 3 to 7.5 m. We infer that $\approx$4.5\% of PSNM counts are associated with a later count in at least one of its 18 counters from a different secondary particle in the same shower. Monte Carlo simulations of atmospheric showers and NM yield functions can be validated using our measurements of neutron multiplicity across counters and the contributions of single and multiple secondary particles. These measurements also improve understanding of the single-counter $L$, which has been used for precise tracking of cosmic-ray spectral variations and extending the range of NM observations to higher energies.