A generalized expression for the statistical field has been obtained which includes the Thomas-Fermi and Thomas-Fermi-Dirac fields as special cases. The behavior of the energy, charge density, boundary density, and electron groups has been investigated for various fields. Fields with exchange are obtained with behave like the Thomas-Fermi field at the boundary. A singularity in the Thomas-Fermi-Dirac density matrix has been found which leads to an oscillation in the sign of the charge in high angular momentum states. This singularity is related to the necessity for terminating the Thomas-Fermi-Dirac distribution at a finite boundary. Comparison of the Fourier components and wave functions calculated from statistical density matrices for ${\mathrm{Cu}}^{+}$ with the corresponding Hartree-Fock values has revealed that it would not be useful to use the statistical density matrix as a starting point for a Hartree-Fock calculation.

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