Thomas-Fermi scattering

The positive particles with effective mass w+ interact with the conducting electrons through a screened Coulomb potential with Thomas-Fermi scattering. The result for the diffusivity of these particles takes the form... 

The Xa multiple scattering method generates approximate singledeterminant wavefunctions, in which the non-local exchange interaction of the Hartree-Fock method has been replaced by a local term, as in the Thomas-Fermi-Dirac model. The orbitals are solutions of the one-electron differential equation (in atomic units)... 

Lindhard et al. used a Thomas-Fermi potential and calculated the differential scattering cross section for multiple collisions as... 

Fig. 2. Comparison of the Coulomb potential and the screened Thomas-Fermi-Moliere (TFM) potential for the scattering of He ions off Ni. The typical impact parameter range of Rutherford back scattering (RBS) and low energy ion scattering (ISS or LEIS) are indicated by arrows [8]. Reprinted with permission from E. Taglauer and John Wiley Sons Ltd., 1997.

Slater proposes an effective quantum number n = 3.7, the atomic factor can only be presented in the form of a sum with an infinite number of components. The series may be terminated if the effective quantum number for the N shell is taken as 3.5, 4.0, or 4.5. We calculated values of the atomic factor for the neutral Br atom with different values of n. The most satisfactory agreement with the theoretical form factors, calculated according to the Thomas—Fermi—Dirac model, was obtained at n — 4.5 screening coefficients proposed in [11] were used in the calculations. The equation of the atomic scattering function for the N shell in the case of a spherically symmetrical electron density distribution and n — 4.5 has the following form ... 

Refinements of the Thomas-Fermi theory have been considered, for example, by March and Murray [201]. By treating scattering of electron waves from a test charge using first-order wave theory, they obtained the following modified Poisson equation... 

When applying the theory to scattering experiments on molecular gases, it must again be remembered that the actual scattering observed is the sum of the coherent and the incoherent scattering. The latter is composed additively of the incoherent scattering of the various atoms in the molecule, which may, e.g., be calculated by the method of Thomas and Fermi as described at the end of section 7. 

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