Prompt Neutron Multiplicity Distributions Inferred from $gamma$-ray and Fission Fragment Energy Measurements

We propose a novel method to extract the prompt neutron multiplicity distribution, $P( u)$, in fission reactions based on correlations between prompt neutrons, $gamma$ rays, and fragment kinetic energy arising from energy conservation. In this approach, only event-by-event measurements of the total $gamma$-ray energy released as a function of the total kinetic energy (TKE) of the fission fragments are performed, and no neutron detection is required. Using the $texttt{CGMF}$ fission event generator, we illustrate the method and explore the accuracy of extracting the neutron multiplicity distribution when taking into account the energy resolution and calibration of the energy measurements. We find that a TKE resolution of under 2 MeV produces reasonably accurate results, independent of typical $gamma$-ray energy measurement resolution.