Thomas-Fermi oscillations

Bloch (1933a,b) first pointed out that in the Thomas-Fermi-Dirac statistical model the spectral distribution of atomic oscillator strength has the same shape for all atoms if the transition energy is scaled by Z. Therefore, in this model, I< Z Bloch estimated the constant of proportionality approximately as 10-15 eV. Another calculation using the Thomas-Fermi-Dirac model gives I tZ = a + bZ-2/3 with a = 9.2 and b = 4.5 as best adjusted values (Turner, 1964). This expression agrees rather well with experiments. Figure 2.3 shows the variation of IIZ vs. Z. 

Fig. 3 Exact and Thomas-Fermi ratio of the reduced Laplacian q of Eiq. (11) to the square of the reduced gradient s of Eq. (9), as a function of position z, for the Airy gas model with force F = 0.10. Also shown for comparison is the same ratio in the true Aiiy gas, where the Friedel oscillations [9] appear to be damped with increasing z- The visible difference between the tiue...

Thomas-Fermi screening length electron density/number of oscillators complex refractive index refractive index potential of zero charge reflectivity... 

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