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We report a first-principles theoretical study of hyperfine interactions,zero-point effects and defect energetics of muonium and hydrogen impurities insilicon and germanium. The spin-polarized density functional method is used,with the crystalline orbitals expanded in all-electron Gaussian basis sets. Thebehaviour of hydrogen and muonium impurities at both the tetrahedral andbond-centred sites is investigated within a supercell approximation. Todescribe the zero-point motion of the impurities, a double adiabaticapproximation is employed in which the electron, muon/proton and host latticedegrees of freedom are decoupled. Within this approximation the relaxation ofthe atoms of the host lattice may differ for the muon and proton, although inpractice the difference is found to be slight. With the inclusion of zero-pointmotion the tetrahedral site is energetically preferred over the bond-centredsite in both silicon and germanium. The hyperfine and superhyperfineparameters, calculated as averages over the motion of the muon, agreereasonably well with the available data from muon spin resonance experiments.Comment: 20 pages, including 9 figures. To appear in Phys. Rev.

Muonium as a hydrogen analogue in silicon and germanium: Quantum effects and hyperfine parameters