Abragam &etal; (PhysicaB81, 245 (1976)) proposed a relaxation mechanism for far nuclei via dipole–dipole reservoir (DDR) of own nuclei of paramagnetic centers which do not “freeze” at ultra low temperatures. In order to verify the possibility of such a process, they proved that the matrix elements of flip-flops of own nuclei are the electron matrix elements due to the mixing of electron and nuclear spin states as a result of superfine interaction. This is equivalent to an increase in heat capacity (“increase in weight”) of the DDR of own nuclei. Such a “heavier” DDR subsequently plays the role of a thermodynamic subsystem through which far nuclei relax to the lattice, a narrow bottleneck being observed on the second relaxation region. Since this mechanism can play a dominating role in low-temperature nuclear relaxation as well as in other processes, it is important to obtain the Hamiltonian of a “heavier” DDR in explicit form, to calculate its heat capacity, and to estimate the effective relaxation rate of far nuclei via DDR, which has been accomplished in the present publication. ©1997 American Institute of Physics.