Refined approximations of cross sections and reactivities significant for controlled thermonuclear fusion

For simulations of controlled fusion problems, $4$ major reactions are conventionally accounted for. In the present work, we compare cross sections of many thermonuclear reactions between lightest elements. We show that along with the traditional reactions, considerable contribution can be given by the reaction $\mathrm{T+T}\to2n+{}^4_2\mathrm{He}$. At low temperatures, two reactions $\mathrm{D}+p\to\gamma+{}^3_2\mathrm{He}$ and $\mathrm{T}+p\to\gamma+{}^4_2\mathrm{He}$ also have considerable contribution, the rest reactions are likely to be neglected. For the outlined reactions, we perform a more thorough processing of experimental data and construct high-precision approximations. For the new reactions, the accuracy of the $\mathrm{S}$-factor is $2{-}6\%$ and that of the reactivities is $3{-}5\%$.