Abstract: Dalgarno-Lewis approach is an elegant perturbation method which provides exact correction terms to a given order and it avoies the difficulties of summing up infinite terms in the ordinary perturbation approaches.We expound Dalgarno-Lewis method and apply it to the problems of energy levels and wave functions of an atom in a semi-space with a coulomb potential and an external weak electric field.The energy levels up to third order and wave functions to first order are calculated.The results are concise and regular in forms,which show the advantages of the Dalgarno-Lewis perturbation method.

Key words: perturbation theory, Dalgarno-Lewis method, energy correction, wave function