Verification of Feynman-α formula including the effect of delayed neutrons

Abstract

The Feynman-Y function formulas, including the effect of delayed neutrons with point kinetics approximation, have been widely investigated. The formula that considers the prompt-prompt correlation and neglects the prompt-delayed correlation was well-established in the past. Although the formulas that consider the prompt-delayed correlation have been proposed, their verification has not yet been presented because the correlation is too small to be quantitatively identified. Using the joint detection probability based on a heuristic approach, this study derives the Feynman-Y function formula that considers prompt-delayed correlation. The formula is verified by comparing it with a Monte Carlo simulation. The prompt-delayed correlation effect is discussed using numerical examples. The correlation effect is negligible in most subcritical multiplying systems. However, the effect becomes increasingly significant as the multiplying system approaches criticality.