Available data on the polarization of the secondary proton (as a function of its momentum $K$) in the inelastic ({it p, p$$}) reactions with the $^{9}$Be, $^{12}$C, and $^{40}$Ca nuclei and differential cross section data (the momentum distributions) for the reactions at the initial proton energy 1 GeV and scattering angles $Theta$=21$^circ$ and $Theta$=24.5$^circ$ were analysed in a range of the high momenta $K$ close to the momentum corresponding to the proton elastic scattering off the investigated nucleus. A structure in the polarization and momentum distribution data at the high momenum $K$, related probably to quasi-elastic scattering off a $^{8}$Be-like nucleon cluster inside the nuclei, was observed.
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