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Velocity of second sound and superfluid density near the superfluid transition in3He-4He mixtures

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Abstract

Using superleak condenser transducers, the velocity of second soundU 2 has been measured near the superfluid transition temperature Tλ in3He-4He mixtures with molar concentrationsX of3He of 0.0, 0.038, 0.122, 0.297, and 0.440. We have obtained the superfluid density ρs/ρ fromU 2 on the basis of linearized two-fluid hydrodynamics. The results for ρs/ρ are consistent with those obtained from the oscillating disk method, as expected from two-fluid hydrodynamics. The value of ρs/ρ at eachX could be expressed by a single power law, ρs/ρ=kεζ, where ɛ=1-T/Rλ, with the experimental uncertainty. It is found that the exponent ξ is independent of concentration forX≤0.44 within the experimental uncertainty. This concentration independence of ξ is in agreement with the universality concept. From the conclusion that the values of ξ are universal forX≤0.44, the concentration dependence of the superfluid component ρs is expressed by an empirical equation ρs(X, ɛ)=ψ2ρs(0, ɛ). It is found that ψ corresponds to the volume fraction of4He in the superfluid3He-4He mixture. The value of ψ is in agreement with that obtained from the measurement of the molar volume by others.

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Author notes

  1. F. Uehara

    Present address: Department of Science for Living, Tokai University, Kitakaname, Hiratsuka, Kanagawa, Japan

Authors and Affiliations

  1. Department of Applied Physics, Tokyo University of Education, Otsuka, Bunkyo-ku, Tokyo, Japan

    F. Uehara

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  1. F. Uehara
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This paper is based on a thesis submitted to Tokyo University of Education in partial fulfillment of the requirements for the Ph.D. degree.

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Uehara, F. Velocity of second sound and superfluid density near the superfluid transition in3He-4He mixtures. J Low Temp Phys 24, 769–790 (1976). https://doi.org/10.1007/BF00657179

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  • DOI: https://doi.org/10.1007/BF00657179

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