Analytical error bars and RSD for neutron multiplicity counting

This paper derives the standard deviation of the moments of neutron multiplicity distributions for both random and (shift register) triggered counting gates by propagating the multinomial distribution of errors in the counting distribution. Exact and approximate analytical formulas for the singles, doubles, and triples error bars are given along with the corresponding RSD (relative standard deviation). These analytical formulas provide a simple way to analyze and predict error bars without needing empirical data or simulations. The comparison of these analytical error bars to actual measurement errors can reveal systematic errors that are not being accounted for in the modeling of the data.