Nonstructural theory of the exciton states in solid rare gases

Abstract

We develop a simple nonstructural theory of the exciton states in solid rare gases. The potential energy in the Schrödinger equation of the free rare-gas atom is parametrized in the simplest form which reproduces the exact experimental excited atomic levels. The same equation is modified to describe the exciton states in the solid phase simply by introducing the effective mass $\mu$ and by screening the Coulomb potential outside the atom with the dielectric constant ${\epsilon }_0$ of the solid. In this way the exciton levels in the effective-mass approximation become continuously the excited atomic levels, as the effective Rydberg approaches the Rydberg constant. This solves the dilemma between the Wannier and the Frenkel models for all spectroscopic terms, i.e., for the high as well as for the low exciton levels. It also solves the problem for the whole series of solid rare gases, in which quite different values of $\mu$ and ${\epsilon }_0$ occur. Complete agreement is achieved in the comparison of the theoretical results with the experimental data. Accurate values are also obtained for $\mu$ and for the energy gaps $E_g^s$; they differ substantially from those generally accepted within the framework of the Wannier model. The exchange and spin-orbit interactions are shown to be identical in the solid phases and in the free atoms.