In this paper we prove a new optimal bound on the logarithmic slope of theelastic slope when: elastic cross section and differential cross sections inforward and backward directions are known from experimental data. The resultson the experimental tests of this new optimal bound are presented in Sect. 3for the principal meson-nucleon elastic scatterings: pion-nucleon, kaon-nucleonat all available energies. Then we have shown that the saturation of thisoptimal bound is observed with high accuracy practically at all availableenergies in meson-nucleon scattering.
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