DERIVATION OF CORRECTIONS TO THE DEBYE-HUECKEL FREE ENERGY BY THE METHOD OF GAUSSIAN RANDOM FUNCTIONS
This study was undertaken in order to verify the Yukhnovskii result for the free energy of a partially ionized gas, preferably by the use of a different mathematical method, to simplify the calculations, so that one might better understand the nature of the physical probiem, and to develop the theory of Gaussian random functions as a tool for practical calculations in statistical mechanics. The starting point for the calculation is the canonical partition function for a gas of several species of particles (electrons, ions, and neutral atoms) that are assumed to interact by pair potentials only, there being both long and short range interactions. The integrand of the partition function is kept finite by including a short range repulsion between particles of opposite charge. It is shown that the partition fanction for this system can be represented as the average of a functional of Gaussian random functions. An exact transformation of the random functions is then made, the partition function being given as a product of two factors upon completion of the transformation. One factor yields the Debye-Hueckel term. The second factor permits an expansion in the Mayer functions, since the transformation replaces the long range Coulomb potential by the short range Debye shielded potential, and yields correction terms in the form of a modified virial series. The main result is in complete agreement with the result of Yuknnovskii. The advantage of the method of random functions is that the result is obtained by a straightforward calculation using one method only. (auth)
- Research Organization:
- Originating Research Org. not identified
- NSA Number:
- NSA-17-031233
- OSTI ID:
- 4671722
- Resource Relation:
- Other Information: Thesis. Orig. Receipt Date: 31-DEC-63
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
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