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We report on a study of the exchange tunneling reactionD+HD$\rightarrow$D$_{2}$+H in a pure solid HD matrix and in a D$_{2}$ matrixwith 0.23$\%$ HD admixture at temperatures between 130$\,$mK and 1.5$\,$K. Wefound that the exchange reaction rates,$k_{exHD}\sim3\times10^{-27}$cm$^{3}$s$^{-1}$ in the pure HD matrix, and$k_{exD_{2}}=9(4)\times10^{-28}$cm$^{-3}$ in the D$_{2}$ matrix are nearlyindependent of temperature within this range. This confirms quantum tunnellingnature of these reactions, and their ability to proceed at temperatures down toabsolute zero. Based on these observations we concluded that exchange tunnelingreaction H+H$_{2}\rightarrow$H$_{2}$+H should also proceed in a H$_{2}$ matrixat the lowest temperatures. On contrary, the recombination of H atoms in solidH$_{2}$ and D atoms in solid D$_{2}$ is substantially suppressed at the lowesttemperatures as a result of increasing of violation for resonance tunneling ofatoms when they approach each other.

Tunneling chemical exchange reaction $\textrm{D}+\textrm{HD}\rightarrow\textrm{D}_{2}+\textrm{H}$ in solid HD and D$_2$ at temperatures below 1$\,$K