Self-consistent cluster calculation of binding energy and potential for positive muons in copper and copper-impurity systems

The binding energy, potential profile, and electronic structure for positive muons in copper are calculated with the use of a molecular-cluster model in the framework of the self-consistent local-density theory. Spin polarization was considered in calculations on finite clusters including ${\mathrm{Cu}}_{14}$ and an interstitial positive muon. Different positions of the muon along the body diagonal [111], and slightly displaced from the diagonal, covering the path between octahedral O to tetrahedral T sites were considered. Both the binding energy Δ$E_{\mathrm{tot}(\mathrm{r}\to )}$ and the muon potential $V^{\mu }$(r→) exhibit a double minimum, with the O site more stable. The effects of Cu vacancies and Ni impurities on the muon in copper are considered also. Binding-energy curves show the attraction of the Cu vacancy and Ni impurity for the muon. Valence-charge-density distribution profiles for different positions of a muon along the [111] direction in μ-${\mathrm{Cu}}_{14}$, μ-${\mathrm{Cu}}_{13}$, and μ-Ni-${\mathrm{Cu}}_{13}$ clusters are calculated.