EN
We present an internally consistent theory of amplification near the minimum of autoionizing states with quantitative application to calcium. We have included a completely specified three-photon pumping and we find certain unusual aspects of the system. We find conditions under which the system remains in a steady state, although being coupled to the continuum. For incoherent pumping we obtain quantitative results for the gain. Our results and their extensions are also discussed in the context of present-day experimental possibilities.