Self-consistent screening of a pseudo-atom in a nearly-free electron metal

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Abstract
For nearly free electron metals, we present a new self-consistent method of calculating, within the Screened Uniform Charge Model, the screening of a pseudo-atom. Each iterative cycle is as follows : from an approximate screening potential, wave-functions are calculated as if one pseudo-atom were perturbing an electron gas; from these wave-functions the change δρ in charge density can be calculated and from δρ a new screening potential is derived. A parameter in this cycle is adjusted so that the Friedel sum rule is satisfied. Calculations, which neglected exchange corrections, are presented in detail for sodium at two temperatures, 373°K and 480°K. The change with temperature in the s-wave ‘reduced phase shift’ is about 9%. The resistivity, thermopower, and temperature dependence of the resistivity of liquid sodium are calculated, and the results are in remarkable agreement with the experimental results. The advantages of our method over other screening methods are discussed. One of us (Md. M. Islam) wishes to thank the ‘Colombo Plan Authority’ for financial assistance throughout this work.