Angular correlations of final particles and gamma rays in determining the orientations of tensor characteristics of excited nuclear states

Measurements have been made on the spin tensors $\rho_{k\kappa}(\vartheta_{y})$ of even rank in the density matrix for the 2$^+$ state of $^{12}$С formed in $^{12}$С$^\ast$ with $E_{\alpha}=30$ MeV and $^{13}$C($^3$Не, $\alpha'$)$^{12}$С$^\ast$ with $E_{{^3}\text{He}}=22.5$ MeV. The resulting $\rho_{k\kappa}(\vartheta_{y})$ have been used to obtain the angular dependence of the orientation tensors for the quadrupole and hexadecapole moments of the 2$^+$ state of $^{12}$С.