Relativistically correct DD and DT neutron spectra

We use relativistic kinematics to derive an expression for the energy spectrum of neutrons produced by fusion reactions in deuterium and deuterium–tritium thermal plasmas. The derivation does not require approximations and the obtained expression gives the exact shape of the spectrum. It is shown that the high-energy tail of the neutron spectrum is highly sensitive to the plasma temperature. Simple expressions for the plasma temperature as a function of the neutron spectrum full width at half maximum (FWHM) are given.