a Quantum Two-Level System with Applications to Photoemission from Metals.

A quantum system is studied which serves as a model for photoemission from the filled bands in certain metals and for tunneling in metals. This system comprises a set of two levels populated by a single particle interacting with a many-body, fermionic system taken to be a free-electron gas. The relevance of the model to photoemission is discussed. The modification of the tunneling rate of the single particle between its two levels due to its interaction with the free-electron gas is discussed in terms of a physical picture with parallels to excitons in insulators. The spectral functions for the Green's function of the two-level system is computed numerically from which a tunneling rate is extracted, and the dependence of the tunneling rate on the parameters in the model is explored. Implications for the bandwidths of narrow, filled bands in simple metals as measured in angle-resolved photoemission and for experimental line widths is discussed.