We develop an approximate field theory for particles interacting with a generalized Yukawa potential. This theory improves and extends a previous splitting field theory, originally developed for counterions around a fixed charge distribution. The resulting theory bridges between the second virial approximation, which is accurate at low particle densities, and the mean-field approximation, accurate at high densities. We apply this theory to charged, screened ions in bulk solution, modeled to interact with a Yukawa potential; the theory is able to accurately reproduce the thermodynamic properties of the system over a broad range of conditions. The theory is also applied to "dressed counterions," interacting with a screened electrostatic potential, contained between charged plates. It is found to work well from the weak coupling to the strong coupling limits. The theory is able to reproduce the counterion profiles and force curves for closed and open systems obtained from Monte Carlo simulations.

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We have performed a systematical calculation for Cr and Dy co-doped ZnO by the first principles method using Quantum-Espresso. A lot of interesting results were found from the analysis of energy band structures and density of states. From spin-polarized calculations within the framework of density functional theory, we have noticed that the value of total magnetization of co-doped ZnO is substantially enhanced compared to that of pure ZnO, and total magnetic moments mainly come from the contribution of Cr 3d and Dy 4f states. Our findings indicate that Cr and Dy co-doped ZnO are capable magneto-electronic materials and they can be used for nanoscale spintronics device material.

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