Journal of Statistical Physics

, Volume 38, Issue 1–2, pp 273–312 | Cite as

Effective interactions in dilute mixtures of3He in4He

  • Weichan Hsu
  • David Pines


Nonlocal pseudopotentials which describe the effective interaction between3He quasiparticles, and between these quasiparticles and the background4He liquid, are obtained as a function of concentration and pressure by generalizing the Aldrich-Pines pseudopotentials for pure3He and4He to dilute mixtures. The hierarchy of physical effects which determine these pseudopotentials is established. Interaction-induced short-range correlations are the dominant physical feature; next in order of importance is the greater zero point motion associated with the replacement of a4He atom by a3He atom, while spin-induced “Pauli principle” correlations play a significantly smaller, albeit still important role. We find a consistent trend in the change of the effective direct quasiparticle interactions with increasing concentration, and show how the Aldrich-Pines pseudopotentials for pure3He quasiparticles represent a natural extension of our results for dilute mixtures. Our calculated nonlocal pseudopotential for3He quasiparticles is qualitatively similar to that proposed by Bardeen, Baym, and Pines; it changes sign at somewhat lower momentum transfers than the BBP result, varies little with concentration, and provides a physical basis for understanding the BBP result. The effective interaction between quasiparticles of parallel spin, here determined for the first time, is essentially repulsive in the very dilute limit; as the concentration increases, it becomes increasingly attractive at low momentum transfers, and resembles closely that between antiparallel spin quasiparticles at 5% concentration. The concentration-dependent transport properties calculated from these pseudopotentials (which involve only one phenomenological parameter) are in good agreement with experiment at saturated vapor pressure (SVP), 10 atm, and 20 atm. Maxima in the thermal conductivity and spin diffusion are predicted to occur at concetrations somewhat less than 4%. Because the effective quasiparticle interactions are somewhat more repulsive than those previously proposed, we find the transition of the3He quasiparticles to the superfluid state takes place at significantly lower temperatures than many previous estimates; our predicted maximum superfluid transition temperature is 2×10−8 K (for a 0.6% mixture at 20 atm).

Key words

Dilute3He-4He solutions quantum liquids 


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Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • Weichan Hsu
    • 1
  • David Pines
    • 1
  1. 1.Department of PhysicsUniversity of Illinois at Urbana-ChampaignUrbana

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