  We characterize the optical response of a three-level atom subjected to an
incoherent pump and continuously illuminated with a weak, quasi-resonant probe
field. To this end, we apply a wavefunction approach based on QED Hamiltonian
perturbation theory which allows for a reduction of the atomic dynamics to that
of an effective two-level atom, and for an implementation of the incoherent
effects that respects unitarity. Using a diagrammatic representation, we
identify and classify all the radiative processes. This allows us to compute
the scattered power, the spontaneous emission, and the stimulated emission, as
well as the total cross sections of extinction, absorption and scattering. We
find that, beside a general enhancement of the linewidth and an attenuation of
the spectral amplitudes, the pump reduces the nonradiative losses and provides
gains in the form of stimulated emission and incoherent radiation. For
sufficiently strong pump, gains and losses compensate, resulting in the
vanishing of extinction. In particular, for negligible nonradiative losses,
extinction vanishes for a pumping rate of $(1+\sqrt{5})/2$ times that of the
natural decay.
