Distortion of the ligand environment of Gd$^{3+}$ and Eu$^{2+}$ ions in garnets: Y$_{3}$Al$_{5}$O$_{12}$, Lu$_{3}$Al$_{5}$O$_{12}$, Y$_{3}$Ga$_{5}$O$_{12}$

Using the second-rank spin Hamiltonian experimental parameters of the rhombic Gd$^{3+}$ and Eu$^{2+}$ centers in three garnets, as well as the superposition approximation formalism, estimations of the relaxation of the impurity ions nearest environment have been made.