Quantum Distributions of Muonium and Hydrogen in Crystalline Silicon

Quantum states of normal muonium and atomic hydrogen in crystalline silicon are investigated with the path integral molecular dynamics method using interatomic potentials based on the density functional theory. It is shown that, in spite of instability in the potential energy surface, muonium has a high density at the center of the silicon cage ( $T$ site) due to quantum effect in agreement with previous $\mu$SR experiments. A distinct and more classical distribution is suggested for hydrogen.