Mass dependence of the ground state of charged particles in a silicon crystal

We report a quantum-mechanical study of the ground state of a positively charged particle in an otherwise perfect Si crystal. Particles with intermediate masses between the positron and the deuteron are considered. We find that there are two substantially different limit behaviours, depending on the mass value, ranging from the extreme localization in the high-electronic-density region of the deuteron wave function to the almost uniform extension of the positron one, which on the contrary attributes the maximum of probability to the interstitial region. Moreover, we underline the behaviour of the intermediate mass particles, μ⁺ and π⁺, which exhibit a significant degree of delocalization of their wave functions.