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We have calculated the total cross section for k^+-4^He, 16^O, 40^Ca, intesat incident momenta of the kaon P_lab<1GeV . We derived the K^+-nucleon opticalpotential according to the exchange of 3- mesons (segma,roh,omega) and also for4- (segma,roh,omega, segma_0) exchanged between the reactants. We showed bothof the radial behavior of the real and the imaginary parts of the derivedpotential. Comparisons between the available experimental data, othertheoretical work and the calculated total cross sections for the three studiednuclei which have shown a reasonable agreement. The extended four mesonsexchanged optical potential gave better close results to the experimental data.Further, ratios of the total cross sections of the studied nuclei with respectto the total cross section with the deuteron nucleus for the two appliedoptical potentials were given. In addition, the ratio of the theoretical resultof the total cross section for the interaction of the K^+ meson with thedeuteron was compared with the corresponding experimental one to evaluate ourtheoretical results in a more clear manner.

Microscopic Description of K^+ Scattering on 4^He, 16^O and 40^Ca Nuclei using Meson Exchange Theory