Specific features of the electron paramagnetic resonance spectrum in the vicinity of the convergence of the transitions of gadolinium centers in Pb$_5$(Ge$_{1-x}$Si$_x$)$_3$O$_{11}$

An anomalous electron paramagnetic resonance spectrum of the transitions -1/2 $\leftrightarrow$ +1/2 of four Gd$^{3+}$–Si dimer clusters in the Pb$_5$(Ge$_{1-x}$Si$_x$)$_3$O$_{11}$ crystals doped with gadolinium has been found in the vicinity of the orientation of the magnetic field along the optic axis of the crystal. It has been assumed that this spectrum is caused by rapid transitions between the spin packets of the initial resonances due to the crossrelaxation. A computer simulation of the spectrum has been carried out. The results obtained adequately describe the experiment.