International Journal of Theoretical Physics, Vol. 41, No. 9, September 2002 ( C  2002) Lattice Green’s Function in the General Glasser Case R. S. Hijjawi 1 and J. M. Khalifeh 1,2 Received January 22, 2002 We have investigated the lattice Green’s function for the general Glasser cubic lattice. Expressions for its density of states, phase shift, and scattering cross section in terms of complete elliptic integrals of the first kind are derived. KEY WORDS: general Glasser lattice; Green’s function. 1. INTRODUCTION The lattice Green’s function (Economon, 1983) is defined as G( E ) =  (2π ) d  1BZ F (  k ) E − E (  k )  dk (1.1) where E (  k ) represents a dispersion relation, F (  k ) is an appropriate function,  denotes the volume of the crystal in the real space, d is the dimension, and 1BZ indicates that the integration is carried over the first Brillouin zone. In this paper we report on the lattice Green’s function and the paper is or- ganized as follows. Section 2 is devoted to the general definition of the diagonal lattice Green’s function and its form, inside and outside the band, for the cubic lattice in terms of the first kind elliptic integrals. This section also contains the formulae for the density of states (DOS), the phase shift, and the cross section for a point defect case. In Section 3 we present the results and discussion for the special Glasser case. Finally, the details of the Green’s function derivation inside the band are given in Appendix A. 1 Department of Physics, University of Jordan, Amman, Jordan. 2 To whom correspondence should be addressed at Department of Physics, University of Jordan, Amman 11942, Jordan; e-mail: jkalifa@sci.ju.edu.jo. 1769 0020-7748/02/0900-1769/0 C  2002 Plenum Publishing Corporation