  We report on the first ESR study of atomic hydrogen and tritium stabilized in
a solid T$_{2}$ and T$_{2}$:H$_{2}$ matrices down to 70$\,$mK. The
concentrations of T atoms in pure T$_{2}$ approached $2\times10^{20}$cm$^{-3}$
and record-high concentrations of H atoms $\sim1\times10^{20}$cm$^{-3}$ were
reached in T$_{2}$:H$_{2}$ solid mixtures where a fraction of T atoms became
converted into H due to the isotopic exchange reaction T+H$_2\rightarrow$TH+H.
The maximum concentrations of unpaired T and H atoms was limited by their
recombination which becomes enforced by efficient atomic diffusion due to a
presence of a large number of vacancies and phonons generated in the matrices
by $\beta$-particles. Recombination also appeared in an explosive manner both
being stimulated and spontaneously in thick films where sample cooling was
insufficient. We suggest that the main mechanism for H and T migration is
physical diffusion related to tunneling or hopping to vacant sites in contrast
to isotopic chemical reactions which govern diffusion of H and D atoms created
in H$_{2}$ and D$_{2}$ matrices by other methods.
