Thomas-Fermi wave vector

By comparing their model to experimental results obtained in Si, Ge, GaAs, and ZnSe, the authors have found that the empirical parameter C is roughly constant in the series C 1-56. They deduce, from (4.2.9), the coulomb hole expression as a function of the local density p(r), the Fermi fep and Thomas-Fermi wave vectors. 

Fig. 6.3 The wave-vector dependence of the Lindhard response function. X(<7/2Af), which has been normalized by the constant Thomas-Fermi response function, xtf The dashed curve shows an approximation (eqn (6.89)) to the Lindhard response function that does not include the weak logarithmic singularity in the slope at q 2kF = 1 (From Pettifor and Ward (1984).)...

There is a parallel between the wave packet-based semi-classical treatment of nuclear motion developed here and the Thomas-Fermi theory of an electronic system in a slowly varying vector potential. In the semi-classical electronic theory as well as here, one naturally arrives at a locally linear approximation to the scalar-potential-derived forces and a locally uniform approximation to the magnetic force derived from the vector potential. See, R. A. Harris and J. A. Cina, J. Chem. Phys. 79, 1381 (1983) C. J. Grayce and R. A. Harris, Molec. Phys. 71, 1 (1990). 

---