User:Kdmeaney/sandbox

In nuclear fission, the released neutrons and gamma rays vary as a function of energy. The energy spectrum of the neutrons, also referred to as neutron temperature, is of specific importance for the fission chain reaction due to the variation of nuclear cross section and the need for neutron moderation. If the neutron spectrum is not moderated a nuclear reactor is a fast-neutron reactor.

Prompt neutron energy spectrum
A model put forward by V. Weisskopf in 1937 for low energy fission is approximating the neutron release as spallation released from the fission fragments. The spectrum of the released neutron from the fission fragment in the center of mass moving fragment frame is in the form :

$$\phi(\eta) \sim \frac{\eta}{T^2} e^{-\frac{\eta}{T}}$$

Where $$\eta$$ is the kinetic energy of neutrons and $$T$$ is the temperature of the fission daughter nucleus. The cascade of neutrons can be well approximated as a Maxwellian spectrum with an effective temperature, $$T_{eff}$$.

$$\phi(\eta) \sim \eta^{1/2} e^{-\frac{\eta}{T_{eff}}}$$

For a good fit to experiment the temperatures of the two fragments have to be known, as setting the temperatures of the light and heavy fragment equal to each other do not yield good results. Transforming the spectrum from the center of mass frame to the lab system yields the Watt spectrum.

The Watt spectrum