![]() It is based on the assumption that the potential varies much more slowly than the screening length of the electrons themselves, so that the local approximation for the kinetic energy, eqn (6.6), is valid. The Thomas-Fermi approximation is, unfortunately, a poor approximation for the sp- valent metals. Screening in metals is very effident even the low- density metal sodium with rs - 4 au has a Thomas-Fermi screening length as small as 1.3 au. It follows from eqs (2.41) and (6.10) that. Thus, the ionic coulomb potential is damped exponentially within a Thomas-Fermi screening length = 1 /ktf. These models are thus considered to be less realistic than the model of this work.30. Thus, the simple Thomas-Fermi result88 of C(dip) = 47r/ATF (Atf = Thomas-Fermi screening length) is greater than C(experiment)-1, and the same is true for the improved Thomas-Fermi results of Newns40 and the model of free electrons at an infinitely repulsive wall. It is also interesting that if some of the simple models for the bare metal surface are used to calculate the metal s contribution to the capacitance, a fit to experimental results would require unreasonable values for the solution contribution. Thus the field of the positive ion is reduced by about 30% at R. The screening length ( Thomas-Fermi) is 0.47Ang., or 0.36 of the radius of the jellium atom. However, the valence electron screens any electric field caused by polarization. compared with the plasmon frequency for jellium (1.1 x 1016/sec.) so an isolated jellium atom behaves as a dielectric. Within a jellium atom, the electron frequency is of order 1017/sec. ![]()
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