Fission Neutron Spectra and Nuclear Temperatures

It is shown that Weisskopf's nuclear evaporation theory, when allowance is made for the expected distribution of nuclear temperatures of fission fragments, predicts an essentially Maxwellian distribution of fission neutron energies in the laboratory system. This is found to be in excellent agreement with all available data. On the assumption that neutron emission is symmetrical about 90° in the center-of-mass system, the average energy $\overline{E}$ of the fission neutron energy spectrum should be $\overline{E}={\overline{E}}_f+2\mathrm{}\overline{T}$, in which ${\overline{E}}_f$ and $\overline{T}$ are the average values of the fission fragment energy per nucleon and the nuclear temperature. Experimentally, ${\overline{E}}_f\cong 0.78$ Mev for all cases reported, giving fission fragment nuclear temperatures of 0.6 to 0.7 Mev for measured fission neutron spectra. This gives $a=12\mathrm{}\pm 2$ ${\mathrm{Mev}}^{-1\mathrm{}}$ for the equation $E_e=a{T}^2=\mathrm{excitation}\mathrm{energy}$. The same concepts lead to the prediction $\overline{T}\cong \frac{2}{3}{\left[\frac{(\overline{\nu }+1)E_0}{2a}\right]}^{\frac{1}{2}}$, or $\overline{E}\cong 0.78 \mathrm{Mev}+0.621\mathrm{}{(\overline{\nu }+1)}^{\frac{1}{2}}$ for ${\mathrm{U}}^{235}$+$n$; $E_0$ is the excitation energy change per emitted neutron, about 6.7 Mev, and $\overline{\nu }$ is the average number of neutrons emitted per fission. This equation, which is approximately valid for all present experimental data, leads to the prediction that $\frac{d\overline{E}}{d{E}_x}\cong 0.025$ for ${\mathrm{U}}^{235}$ ($E_x$ is the excitation energy of the fissioning nuclide). The center-of-mass energy spectrum of fission neutrons has also been calculated, as well as effects of anisotropy of emission on the laboratory fission neutron spectrum.