By solving the Eliashberg equations for the gap function, the superconducting transition temperature of a proposed low-temperature liquid state of metallic hydrogen is found to be comparable to that obtained, with similar approximations, for the solid. This indicates that metallic hydrogen may be a superconducting liquid in the density range 1.6>~rₛ>~1.3, where the melting point is expected to be fairly low.
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Jaffe et al. (1981) studied this question.
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