Thomas-Fermi screening length

Within a jellium atom, the electron frequency is of order 1017/sec. compared with the plasmon frequency for jellium (1.1 x 1016/sec.) so an isolated jellium atom behaves as a dielectric. However, the valence electron screens any electric field caused by polarization. The screening length (Thomas-Fermi) is 0.47Ang., or 0.36 of the radius of the jellium atom. Thus the field of the positive ion is reduced by about 30% at R. 

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 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 [see Eq. (12)]. These models are thus considered to be less realistic than the model of this work.30... 

Thus, the ionic coulomb potential is damped exponentially within a Thomas-Fermi screening length = 1 /ktf. It follows from eqs (2.41) and (6.10) that... 

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. 

The Thomas-Fermi approximation is, unfortunately, a poor approximation for the sp-valent metals. 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. In practice, however, the variation in the ionic potential is measured by the core radius, Rc (cf Fig. 5.11), which is not large but of the same size as the screening length, XTF. Thus, we do not satisfy the criterion for the validity... 

Here, q is the inverse of a screening length related to the valence electron density which contributes to the screening and /u. is a Lagrange multiplier controlling the total number of particles. The boundary conditions to be used with Equation (23) are that V(r) must match Vc r) at Rs and that rV(r) -> -1 as r -> 0. Once we have solved the Thomas-Fermi equation, we have calculated the screened function, defined as the bare impurity potential divided to the screened one, namely Vb/V. 

Equation (2.289a) is the screening length computed within the Fermi-Thomas approximation for a free-electron gas. Using Eq.(2.289b) one finds that Vs r) has the form of a screened Coulomb potential ... 

In the case of a stationary charge this expression can be readily evaluated for the bulk and the surface, once an expression for the dielectric constant is known. We will determine the dielectric constant by means of Eq.(2.29lb) with the Fermi-Thomas expression for the screening length, Eq.(2.289b) (u = 0). One finds for the bulk potential ... 

Thermalization distance, 252, 254-260, 262 electron, 252-259 Thomas-Fermi screening length, 330, 344... 

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