  We propose a novel approach for solving the scattering of light onto a
two-level atom coupled to a one-dimensional waveguide. We first express the
physical quantity of interest in terms of Feynman diagrams and treat the atom
as a non-saturable linear beamsplitter. By using the atomic response to our
advantage, a relevant substitution is then made that captures the nonlinearity
of the atom, and the final result is obtained in terms of simple integrals over
the initial incoming wavepackets. The procedure is not limited to
post-scattering quantities and allows for instance to derive the atomic
excitation during the scattering event.
