Relativistic calculation of fusion product spectra for thermonuclear plasmas

The first three moments of the energy distributions of products from fusion reactions in thermonuclear plasmas with Maxwellian ion velocity distributi ons are determined analytically. Relativistic kinematics is used allowing t he desired accuracy to be reached, which is 2 to 3 orders of magnitude bett er than previous analytical results. In particular, neutron spectra of the reactions D(d,n)He-3 and D(t,n)alpha for plasma ion temperatures 0 < T-i< 1 00 keV are studied for which the results are also given in tabulated form w ith interpolation formulas for the purpose of practical use. The neutron en ergy distributions are also calculated with numerical methods, in order to assess the analytical results. High accuracy calculations are motivated by the crucial role that neutron measurements are envisaged to play in the nex t step fusion experiments on burning plasmas, which are also discussed.