Measurement of quadrupole moments of unstable nuclei during channeling and the possibility of revealing the effect of vector polarization of tensor-polarized beams of nuclei

General relations are deduced which describe the spin dynamics of beams of nuclei with the initial tensor and vector polarizations upon planar channeling in bent crystals. Our analysis demonstrates the possibility of revealing the effect of vector polarization, as predicted by Baryshevsky and Sokolsky, which occurs upon the planar channeling of a beam of nuclei with initial tensor polarization. The planar channeling of a beam of nuclei with the initial tensor and vector polarizations may be used to determine the quadrupole moments of unstable nuclei with a small lifetime of up to the order of 10^?7 s. The quadrupole moments of nuclei with a lifetime on the order of 10^?7 s cannot be measured by known techniques, including optical methods.