The electronic structure of hydrogen and muonium in simple metals is investigated. The spherical solid model potential is used for the discrete lattice and the Blatt correction for lattice dilation. The proton and muon are kept at the octahedral sites in the fcc and hcp lattices and self-consistent non-linear screening calculations are carried out. The scattering phase shifts, electronic charge density, effective impurity potential, self-energy, charge transfer, residual resistivity and Knight shift are calculated. The spherical solid potential changes the scattering character of impurity. The phase shifts are found slowly converging. The scattering is more prominent in Al than in Mg and Cu. The virtual bound states of proton and muon are favoured in all the three metals. The calculated value of residual resistivity for CuH is in good agreement with the experimental value. The results for Knight shift forμ⁺ in Cu and Mg are in reasonable agreement with the experimental values while those forμ⁺ in Al are lower than the experimental value. The analytical expressions for effective impurity potential and electronic charge density are suggested.

In this work, the dielectric property of a nanocomposite (NC) consisting of silver nanoparticle and E7 liquid crystal (LC) has been investigated theoretically at different temperatures. The study shows that the surface plasmon resonance (SPR) and filling fraction of the silver nanoparticle significantly change the dielectric property of the NC. To study the optical property of the defective periodic structure, the NC was considered as a defect layer in a semifinite one-dimensional periodic structure (1DPS) of $\rm{TiO_{2}}$ and $\rm{SiO_{2}}$ layers, i.e. $\rm{(TiO_{2}|SiO_{2})^{5}|NC|(TiO_{2}|SiO_{2})^{5}}$. The optical properties of the 1DPS with the NC as the defect layer have been studied by the simple transfer matrix method (TMM). Moreover, the transmission and absorption characteristics of the 1DPS in the presence of silver nanoparticle in the NC have been studied with different orientations of the LC molecule.