Calculation of the dielectric function for a semiconductor model

The hamiltonian of Weaire and Thorpe (1971) is used to evaluate the dielectric function in the random-phase approximation for a periodic lattice. An analytic expression for this function is obtained and evaluated numerically. By choosing parameters appropriate to diamond it is found that the model reproduces the correct shape of the epsilon (q,0) curve and compares reasonably with the results of other calculations.