The production of unstable particles on different nuclei provides the possibility to determine the total cross section of the interaction of vector mesons V=rho ,omega ,varphi , K^{*0}(892),J/psi etc. with nucleons. This interaction is defined by a set of amplitudes that correspond to the transverse (helicity lambda =pm 1) or longitudinal (lambda =0) polarization of the vector meson. The total cross section for the interaction of transversely polarized vector mesons with nucleon sigma _T=sigma (V_T N) has been extracted from the coherent photoproduction of vector mesons off nuclei, while the vector meson production in charge exchange reactions as pi ^pm (K^pm )+Arightarrow V^0(K^{*0})+A' provides the unique opportunity to obtain the not yet measured total cross section for longitudinally polarized vector meson interacting with nucleon sigma _L=sigma (V_L N). We shortly discuss the importance of the knowledge of sigma _L and possibility to extract its value from experiments on nuclear target.