Limiting supersaturation of 3 He - 4 He solutions at temperatures near the absolute zero

The kinetics of homogeneous nucleation in supersaturated superfluid 3 He - 4 He solutions has been considered in the transition region from the thermo activated nucleation to the quantum subbarrier tunneling of nuclei. The stability boundary of the metastable superfluid phase with respect to infinitesimal perturbations of the composition - diffusion spinodal - has been approximated. Consideration is given to the feasibility of a variety of the homogeneous nucleation theory approximations in the vicinity of absolute zero. Limiting supersaturations of 3 He - 4 He solutions have been calculated. The kinetics of thermo-activated and quantum nucleation has been discussed in the neighbourhood of the diffusion spinodal and the temperatures of going from one nucleation regime to another have been evaluated