The H ... H, H ... D, and D ... D spin-pair radicals have been thoroughly investigated in neon, argon, krypton, and xenon matrices near 4 K by electron spin resonance (ESR). A theoretical model has been developed that treats these spin-pairs as weakly interacting atoms. The model includes the effects of (3)Sigma/(1)Sigma mixing in the analysis of the observed ESR spectral results and yields a consistent set of magnetic parameters for these three isotopomers in all four rare gas hosts. The consideration of H atoms interacting with other H atoms over a distribution of internuclear distances in the rare gas lattice is included in the theoretical and experimental analyses. Application of the model to earlier ESR results for H ... CH3 reveals a value for its Heisenberg exchange interaction (J) which is found to be considerably larger than that for the H ... H spin-pair. The effects of methane and neon on the J value are calculated for these spin-pairs. The H ... H case is unusual in that the nuclear hyperfine interaction (A) is considerably larger than D (the anisotropic dipole-dipole magnetic interaction between electrons) which is much larger than J. The H ... H spin-pairs exhibit internuclear distances greater than 7 Angstrom and have the following magnetic parameters (MHz) based upon this model of "weakly interacting atoms;" g(iso) = 2.0016, A(iso) = 1426, D = - 200, and J = 6. Since a distribution of distances is involved, other spin-pairs would be separated by even greater distances in the matrix and thus have smaller absolute values of D and J.