# Watt Spectrum The Watt Spectrum (or Watt Distribution) is the distribution of the number of neutrons with energy in the fission spectrum. It can be approximated with the following *Watt function*. $ P(E) = 0.4865\,\text{sinh}(\sqrt{2E})e^{-E} \, \, [\text{MeV}^{-1}] $ If you look at the spectrum on the log scale, you'll see that there are very few (almost no) fission neutrons that are in the "slow" regime (< 1 MeV). You can also approximate this distribution as $P(E) = \sqrt{E}e^{-E/T}$ where $T = 1.3$ MeV per Knoll Radiation You can use the Watt spectrum to find the neutron flux spectrum. This is done by taking the [[Convolution]] of the neutron flux distribution and the excitation function, and the flux distribution follows directly from the Watt Spectrum function. $ \Phi(E) \propto P(E)\cdot v $ $ \Psi = \int \Phi(E) \sigma(E) \, dE $ $ \implies \Psi = \int P(E)\cdot v \cdot \sigma(E) \, dE $