Color centers envisioned as confined quantum systems: the case of F, F' and F$_{2}^{+}$ centers

Abstract

Color centers in alkali halides, as well as point defects with dimensions of a few nanometers, have been considered to be confined systems and were studied with a variational formalism within a semi-continuum model. This new approach was applied to the well-known F, F' and F$_{2}^{+}$ centers, which are assumed to be cavities of a determined shape that can trap one or two electrons. Inside of the cavity, the electron is subject to a constant potential ($V_{0}$) related to the Madelung energy and outside of it, the potential is Coulomb type due to a continuum polarizable medium. Because the F, F' and F$_{2}^{+}$ confined systems were considered to be hydrogen-like, helium-like and H$_{2}^{+}$-like molecular ion systems, respectively, the \emph{ansatz} functions were constructed from wave functions corresponding to these kinds of systems. For these systems, the energy transition ($\Delta E$) from the ground state to the first excited state in KCl crystals was calculated and compared with experimental and calculated values obtained from the literature. The $\Delta E$ behavior is shown for different values of $V_{0}$. It is worth mentioning that the formalism presented in this work would be useful for both graduate and undergraduate students embarking on the study of some properties of confined quantum systems, or some simple nanostructures as well.