Theory for self-trapped holes in rare-gas solids. I. Formalism and result for solid argon

A simple method for calculating the state and the binding energy of self-trapped holes, which is based on the Hartree-Fock atomic wave function and the semiempirical interatomic potential, is presented. For the microscopic configuration of self-trapped states, not only the simplest two-center trapped state ($S_2$), similar to the $V_k$ center in the alkali halides, but also the simplest one-center trapped state ($S_1$) and other several microscopic configurations are taken into account. In the present paper, the case for solid argon is studied and the following results are obtained. Judging from the calculated binding energy, both $S_2$ and $S_1$ are energetically more favorable than the free-hole state. No strong evidence that $S_2$ is more stable than $S_1$, as in the alkali halides, is obtained. $S_2$ is similar to an ${\mathrm{Ar}}_2$ ${\mathrm{}}^{+}$ molecular ion with a considerably decreased pair distance, while in $S_1$ the hole is shared by nearly three Ar atoms situated in the bonding direction with a markedly decreased pair distance. The nonlinear effect of the hole-lattice interaction is essential for the existence of both trapped states. The effect of the electronic polarization by the excess charge of the hole is also studied.