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The standard distorted wave Bo approximation (DWBA) method has been extended to second-order Bo amplitude in order to describe the multiple interactions between the projectile and the atomic target.Second-order DWBA calculations have been preformed to investigate the triple differential cross sections (TDCS) of coplanar doubly symmetric (e,2e) collisions for the alkali target potassium at excess energies of 6 eV-60 eV.Compared with the previous first-order DWBA calculations,the present theoretical model improves the degree of agreement with experiments,especially for the backward scattering angle region of TDCS.This indicates that the present second-order Bo term is capable of giving a reasonable correction to the DWBA model in studying coplanar symmetric (e,2e) problems in low and intermediate energy ranges.