Structure of the liquid alkali metals by an optimized iterative solution of the Percus-Yevick equations

Abstract

The structure of the liquid alkali metals is obtained by an optimized iterative solution of the Percus-Yevick theory and by using recent pseudopotential models and screening functions for these metals. This solution involves an optimized expression for the correction function to g(r), knowing one guess and one calculated result for g(r). This is obtained by setting a weighted residual corresponding to the Percus-Yevick equation equal to zero. The residual is evaluated to first-order in a change in this correction function. This is usually a good approximation after the first few iterations where a more restrictive expression for the correction function is proposed. Convergence of this optimum iteration procedure to an error of 0.1% in the norm of the correction function is accomplished within 100 iterations. Complete results are presented for the five liquid alkali metals near their melting point. The method gives a successful qualitative check of the effective Ashcroft-Singwi potentials used (initially obtained from a best fit to the force constants in the solid alkalis), particularly in K, Rb, and Cs.

Pair‐Correlation Functions for Liquid Noble Metals through Percus‐Yevick Theory

“…We chose to reproduce the Monte-Carlo results of Wood and Parker [17] for the L J potential with k,T = 2.74 and reduced density, n*(= noa) = = 516. These parameters were considered to offer a critical test because it is known [16] that it is most difficult to obtain a good solution to the PY equation a t a high density and a low temperature. Our tests produced gratifying results, the agreement being well within O.lyo, starting from poor guess values.…”

“…However, it is also known to yield apparently diverging results in the straight iterative solution of the integral equation [16]. Computationally, the region in which the PY operator is a contraction mapping operator is small as measured by a normed distance from the true solution.…”