The Statistical Mechanics of the Interdependent Electrons in the Screening Constant Model of the Many-Electron-Atom.

by J. M. Green

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Description of an operator treatment of the nonlinear (or many body) problem in statistical mechanics which arises when one uses the screening-constant model to approximate the energy of an atomic configuration. Exact symbolic expressions are obtained for the electron occupation numbers and for the thermodynamically induced electron-electron correlations. Asymptotic forms are derived which may be used for the direct computation of these quantities. The forms exhibit explicitly the connection between the electron-electron interaction energy and the electron correlation, and extend the classical occupation-number theory to second order in Z/kT. Finally, the significant asymptotic equations are numerically tested by comparing them with the results from an equation of state computation that is performed by evaluating in detail every term of the partition function of a simple four-level atomic system. Description of an operator treatment of the nonlinear (or many body) problem in statistical mechanics which arises when one uses the screening-constant model to approximate the energy of an atomic configuration. Exact symbolic expressions are obtained for the electron occupation numbers and for the thermodynamically induced electron-electron correlations. Asymptotic forms are derived which may be used for the direct computation of these quantities. The forms exhibit explicitly the connection between the electron-electron interaction energy and the electron correlation, and extend the classical occupation-number theory to second order in Z/kT. Finally, the significant asymptotic equations are numerically tested by comparing them with the results from an equation of state computation that is performed by evaluating in detail every term of the partition function of a simple four-level atomic system. 55 pp

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