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Reaction cross section data of $^{4}$He scattering are available for some nuclides including $^{208}$Pb. PREX II collaboration reported a thick neutron skin for $^{208}$Pb. [Purpose] Our purpose is to deduce neutron skin thicknesses of $^{208}$Pb and some other nuclides from reaction cross sections calculated in terms of the double folding model with the $g$-matrix. 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