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Exchange and Correlation Terms The corrections due to the exchange interaction of the electrons were introduced into the TF model by Dirac, and later by Jensen. The resulting theory is called the Thomas-Fermi-Dirac (TFD) model. Recently, this model has been treated together with the electron-electron correlation effects (Gupta and Rajagopal, 1980) which also have some influence at high electron densities. The exchange interactions stem from Pauli's exclusion principle, which states that the wavefunctions of electrons in the same quantum state should be antisymmetric.
Both results are too complicated to be reproduced here, and the interested reader is referred to the original papers for more information. An approximate expression, which has the correct low and high temperature asymptotic behavior, was suggested by Perrot (1979) for Fxc, where is a dimensionless variable, a = (3\/2)4/3 /4 and 6 = 27/16 are numerical constants. 60) for T —> 0, whereas for T —> oc it predicts, in accordance with other calculations, a -7-"xc [n(r)] ~ T2 behavior. 38 ATOMIC PHYSICS IN HOT PLASMAS The high temperature asymptotic behavior of the free energy functional of thi correlation energy is given in the paper of Gupta and Rajagopal (1980): Density Gradient Corrections The quantum mechanical description of the electron as a wave necessitates another correction to the original TF theory.
1993) within the framework of the Thomas-Fermi-Dirac model with the Weizsacker correction. They, too, have used elliptical coordinates, and their definition of the shape of the quasi molecule is similar to that of Malnoult et al. Their results include the equipotentials and contours of the electron density as functions of the temperature for H-H, N-N and C-H quasi molecules. 6 Ion Correlation Models The ion correlation models (ICM) may be regarded as intermediate models between the Debye-Huckel theory and the ion sphere models, thereby closing the gap between weakly and strongly coupled plasmas.