Single-Particle Theory for Systems at High Densities. I. Characteristic Reduction Parameters for the Mie—Lennard-Jones Pair Interaction Potential from Zero-Point Crystal Data

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Abstract
The energy and length reduction parameters for a 12:6 pair‐potential are characterized from the consideration of zero‐point crystal data. The crystal is considered to be represented by a single‐particle anharmonic Einstein model. This anharmonic potential is considered to be spherically symmetric and is developed according to the cell theory of Lennard‐Jones and Devonshire. No further approximations to the form of this potential are required in the evaluation of the energy eigenvalues from the wave equation. Both the Wentzel—Kramers—Brillouin approximation and a more exact finite difference method of evaluating the energy eigenvalues are discussed. The systems examined are argon, neon, deuterium, hydrogen, and helium.