Refinement of thermonuclear reaction rates

•Refined approximations of the cross sections and the rates of D+D, D+T and D+He3 reactions are obtained.•The achieved accuracy is ∼0.3% for cross sections and ∼4% for reaction rates. It is up to ∼5 times more accurate than reported in literature.•A new mathematical technique for processing of experimental data measured with large errors is proposed.•A procedure of the confidence belt estimation is constructed. We propose a new mathematical technique for processing of experimental data measured with large errors. The method is applied to all available experiments on 4 major thermonuclear reactions taken into account in simulations of deuterium and deuterium–tritium fusion targets. We present new approximations for the dependence of the cross sections on energy and for the dependence of the reaction rates on temperature. Along with these approximations, we propose a procedure allowing to estimate their confidence belts. Such estimations were not known before. New approximations provide error ∼0.3% for the cross sections and ∼4% for the reaction rates. The present data are up to ∼5 times more accurate than reported in literature.