Theory of Quantum Crystals. III. Differential Equation for the Correlation Function

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Abstract
A differential equation for the short-range correlation function in quantum crystals is studied. The equation is derived within the context of a variational calculation using cluster-expansion techniques. The equation is solved by assuming an appropriate long-range behavior and fitting this to the numerical solution. The main results are that the energy is lowered by about 2 cal/mole and the exchange integral is increased by a factor of approximately 4 relative to previous results. Other quantities (pressure, compressibility, sound velocities, etc.) are essentially unchanged.