The properties of dilute muonium impurities substitutionally trapped in solid Xe at low temperatures are calculated. It is shown that a variational Hartree approximation in which the first 16 shells around the impurity are relaxed to equilibrium provides a good description of the system. The results indicate that muonium forms a localized defect in the limit of zero temperature and, by comparison with experimental and theoretical studies of H impurities in solid H2, muonium should remain trapped for a period approaching its lifetime at temperatures below approximately 3 K. The distortion of the lattice parameters, ground state wave function, rms fluctuations of the muonium and Xe atoms about their equilibrium lattice positions, the energy required to substitutionally trap a muonium atom, and the local mode frequency of the impurity, are also calculated.
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