Abstract
An expression for the Green's function (GF) of face centered cubic (FCC) lattice is evaluated analytically and numerically for a single impurity problem. The density of states (DOS), phase shift and scattering cross section are expressed in terms of complete elliptic integrals of the first kind.
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References
Bateman Manuscript Project (1963). Higher Transcendental Functions, Vol. I. A. Erdelyi et al., ed., McGraw-Hill, New York.
Berlin, T. H. and Kac, M. (1952). The spherical model of a ferromagent, Physical Review 86, 821.
Brout, R. (1960). Statistical mechanical theory of ferromagnetism. High density behavior. Physical Review. 118, 1009.
Domb, C. and Joyce, G. S. (1972). Cluster expansion for a polymer chain. Journal of Physics C: Solid State Physics 5, 956.
Doniach, S. and Sondheimer, E. H. (1974). Green's Functions for Solid State Physicists, Benjamin, Reading, Massachusetts.
Economou, E. N. (1983). Green Function in Quantum Physics, 2nd Edition, Springer-Verlag, Berlin.
Gradshteyn, I. S. and Ryzhik, I. M. (1965). Tables of Integrals, Series, and Products, Academic, New York.
Hijjawi, R. S. and Khalifeh, J. M. (2002). Remarks on the lattice Green's function, the general Glasser case. Journal of Theoretical Physics 41, 1769.
Inoue, M. (1974). Lattice Green's function for the face centered cubic lattice. Journal of Mathematical Physics 15, 704.
Joyce, G. S. (1971). Lattice Green's function for the anisotropic face centered cubic lattice. Journal of Physics C: Solid State Physics 4, L53.
Katsura, S., Morita, T., Inawashiro, S., Horiguci, T., and Abe, Y. (1971). Lattice Green's function (Introduction). Journal of Mathematical Physics 12, 892.
Li, Q., Soukoulis, C., Economou, E. N., and Grest, G. S. (1989). An isotropic tight-binding model for localization. Physical Review B 40, 2825.
Mano, K. (1974). Remarks on the Green's function for face-centered cubic lattices. Journal of Mathematical Physics 15, 2175.
Mano, K. (1975). Remarks on the Green's function for cubic lattices. Journal of Mathematical Physics 16, 1726.
Mattis, D. C. (1965). The Theory of Magnetism, Harper and Row, New York.
Montroll, E. W. (1956). Proceedings of 3rd Berkeley Symposium on Mathematical Statistics and Probability, J. Neyman, ed., vol. 3, University of California Press, Berkeley, California, pp. 209–246.
Montroll, E. W. and Wiess, G. W. (1965). Journal of Mathematical Physics 6, 167.
Morita, T. and Horiguci, T. (1971a). Calculation on the lattice Green's function for the BCC, FCC, and rectangular lattices. Journal of Mathematical Physics 12, 986.
Morita, T., and Horiguci, T. (1971b). Lattice Green's function for cubic lattices in terms of complete elliptic integral. Journal of Mathematical Physics 12, 981.
Sakaji, A., Hijjawi, R. S., Shawagfeh, N., and Khalifeh, J. M. (submitted). Applications on the Lattice Green's Functions for One and Two Dimensional Lattices.
Sakaji, A., Hijjawi, R. S., Shawagfeh, N., and Khalifeh, J. M. (2002a). Remarks on the lattice Green's function, the Glasser case. Journal of Mathematical Physics 43, 1.
Sakaji, A., Hijjawi, R. S., Shawagfeh, N., and Khalifeh, J. M. (2002b). Remarks on the lattice Green's function for the body centered cubic lattice. Journal of Theoretical Physics 41, 973.
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Hijjawi, R.S., Asad, J.H., Sakaj, A. et al. Lattice Green's Function for the Face Centered Cubic Lattice. Int J Theor Phys 44, 1259–1270 (2005). https://doi.org/10.1007/s10773-005-4684-z
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DOI: https://doi.org/10.1007/s10773-005-4684-z