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The interaction of two Maxwellian distributions of particles will differ from the interaction of the two particles at their respective Maxwell averages if the strength of the interaction varies significantly with energy over the widths of the distributions. This effect is considered here in particular for fusion (both D-T and D-D) for the mean energy of the reacting particles as a function of temperature and for the spectrum of the neutrons produced.
Henry Brysk (Sun,) studied this question.