The production of unstable particles on different nuclei provides the possibility to determine the total cross section of the interaction of vector mesons $$V=\rho ,\omega ,\varphi , K^{*0}(892),J/\psi $$
V
=
ρ
,
ω
,
φ
,
K
∗
0
(
892
)
,
J
/
ψ
etc. with nucleons. This interaction is defined by a set of amplitudes that correspond to the transverse (helicity $$\lambda =\pm 1$$
λ
=
±
1
) or longitudinal ($$\lambda =0$$
λ
=
0
) polarization of the vector meson. The total cross section for the interaction of transversely polarized vector mesons with nucleon $$\sigma _T=\sigma (V_T N)$$
σ
T
=
σ
(
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 $$\pi ^\pm (K^\pm )+A\rightarrow V^0(K^{*0})+A'$$
π
±
(
K
±
)
+
A
→
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 $$\sigma _L=\sigma (V_L N)$$
σ
L
=
σ
(
V
L
N
)
. We shortly discuss the importance of the knowledge of $$\sigma _L$$
σ
L
and possibility to extract its value from experiments on nuclear target.