In a cicularly polarized radiation field (dipole approximation), for electrons scattered by Coulomb potential, the Schr?dinger equation is handled by using a unitary transformation and a dressed potential. When the dressed potential is expanded into a proper form, the equations for the radial wave function are separated by Floquet partial expansion and they are integrable in weak coupling approximation. Therefore, the approximate wave function, S-matrix and the cross section can be expressed analytically. The comparison to the numerical iterated solution is discussed.
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