The production of unstable vector mesons V = ρ, ω, φ, K*0(892), J/ψ etc. on different nuclei provides the possibility to determine the total cross section of vector meson interaction with nucleon. This interaction is defined by a set of amplitudes that correspond to the transverse (helicity λ=±1) or longitudinal (λ=0) polarization of the vector meson. The total cross section for the interaction of transversely polarized vector mesons with nucleon σT = (VTN) can be extracted from the coherent photoproduction of vector mesons on nuclei γ+A→V+A , while the vector mesons production in the charge exchange reactions as π±(K±) +A →V0 (K*0)+A’ provides the unique opportunity to obtain the not yet measured total cross section for longitudinally polarized vector meson interacting with nucleon σL= σ(VLN). Spin dichroism (dependence of interaction on particle polarization) has been known for many years in the case when the constituents of the particle are in the D-wave state. A good example of such dependence is the deuteron interaction with matter. The importance of the knowledge of σL and possibility to extract its value from experiments on nuclear target is shortly discussed.