Simple formulae for interpretation of the dead time  (first moment) method of reactor noise

The Markov Chain approach for solving problems related to the presence of a non extending dead time in a particle counting circuit with time correlated pulses was developed in an earlier paper. The formalism was applied to, among others, the dead time α (first moment) method of reactor noise. For this problem, however the solution obtained was largely numerical in character and had a tendency to break down for systems close to criticality. In the present paper, simple analytical expressions are derived for the count rate and Lex, the quantities of interest in this method. Comparisons with Monte Carlo simulations show that these formulae are accurate in the range of system parameters of practical interest.