Abstract
The homomorphic-cluster coherent-potential approximation is applied to obtain the average Green's function for spatially disordered systems in two and three dimensions, which is described by a tight-binding one-electron Hamiltonian with transfer energy between two $1s$ hydrogenic orbitals. The effective medium to be determined self-consistently is assumed to be an appropriate lattice, and a modified Hertz distribution is used for the random distribution of nearest-neighbor distance. With the use of the $L(E)$ criterion for localization, Anderson's transition is predicted to occur at a critical density ${\ensuremath{\rho}}^{\frac{1}{2}}{a}_{B}=0.403$ in two dimensions and ${\ensuremath{\rho}}^{\frac{1}{3}}{a}_{B}=0.252$ in three dimensions, where $\ensuremath{\rho}$ is the number density of atoms and ${a}_{B}$ is the effective Bohr radius.
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