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The interaction of two hydrogen impurities in jellium is calculated in the "overlapping-densities" approximation where the total displaced charge is the sum of two frozen single-ion screening densities. Using the fourth-order gradient expansion of the kinetic-energy functional, we obtain the results at various densities, corresponding to Al, Mg, and Na. The results provide an extension for the full treatment of the short-range proton-proton interaction to the asymptotic region where such exact calculation are as yet not available.
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Perrot et al. (1983) studied this question.
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