Transport in very dilute solutions of 3He in superfluid 4He

Physical Review B - Condensed Matter and Materials Physics

Volumn 88, Issue 1, 2013, Pages

  Baym, Gordon ^a,b   Beck, D H ^a   Pethick, C J ^a,b,c  

^a United States of America   (United States)

^b UNIVERSITY OF COPENHAGEN   (Denmark)

^c STOCKHOLM UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84880793053     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.88.014512     Document Type: Article

References (30)

1. R. Golub and S. K. Lamoreaux, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(94)90084-1 237, 1 (1994).
2. This experiment utilizes the absorption of ultracold polarized neutrons on polarized 3 He atoms via the reaction n + 3 He → p + t + 764 keV.
3. R. L. Rosenbaum, J. Landau, and Y. Eckstein, J. Low Temp. Phys. JLTPAC 0022-2291 10.1007/BF00655864 16, 131 (1974).
4. S. K. Lamoreaux, G. Archibald, P. D. Barnes, W. T. Buttler, D. J. Clark, M. D. Cooper, M. Espy, G. L. Greene, R. Golub, M. E. Hayden, C. Lei, L. J. Marek, J.-C. Peng, and S. Penttila, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2002-00408-4 58, 718 (2002).
5. M. Hayden, S. K. Lamoreaux, and R. Golub, AIP Conf. Proc. APCPCS 0094-243X 10.1063/1.2354645 850, 147 (2006).
6. G. Baym, D. H. Beck, and C. J. Pethick (to be published).
7. G. Baym and C. Ebner, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.164.235 164, 235 (1967).
8. H. J. Maris, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.49.341 49, 341 (1977).
9. G. Baym, R. G. Barrera, and C. J. Pethick, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.22.20 22, 20 (1969).
10. R. M. Bowley, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2002-00409-9 58, 725 (2002).
11. The phonon contributions to the dissipative second viscosity terms in the superfluid acceleration equation vanish, see Ref..
12. I. M. Khalatnikov, Introduction to the Theory of Superfluidity (W. A. Benjamin, New York, 1965), pp. 65, 133.
13. I. M. Khalatnikov, Ref. 12, Chap. 25; I. M. Khalatnikov and V. N. Zharkov, Zh. E. T. F. 32, 1108 (1957)
14. I. M. Khalatnikov and V. N. Zharkov [Sov. Phys. JETP 5, 905 (1957)].
15. J. Wilks, The Properties of Liquid and Solid Helium (Clarendon, Oxford, 1967), Sec. 9.5.
16. L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Pergamon, New York, 1987), Sec. 59.
17. G. Baym and C. Ebner, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.170.346 170, 346 (1968).
18. Note that in the implementation of this correction in Ref., the 3 He effective mass is taken to be one third of its actual value, and therefore the effects of recoil are overestimated.
19. 3 becomes sufficiently small, the 3 He no longer provides the mechanism for absorbing momentum from the phonons, and rather the phonon thermal conductivity becomes limited by viscous transfer of momentum from the phonons to the container walls.
20. C. Boghosian and H. Meyer, Phys. Lett. A PYLAAG 0375-9601 10.1016/0375-9601(67)90693-7 25, 352 (1967).
21. G. E. Watson, J. D. Reppy, and R. C. Richardson, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.188.384 188, 384 (1969).
22. B. M. Abraham, C. G. Brandt, Y. Eckstein, J. Munarin, and G. Baym, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.188.309 188, 309 (1969).
23. In fact, the viscosity for flow in a circular pipe plays a role only in a thin boundary layer, which for the concentrations and temperatures under consideration is of order millimeters thick.
24. D. S. Greywall, Phys. Rev. B PRBMDO 1098-0121 10.1103/PhysRevB.23.2152 23, 2152 (1981).
25. PDE Solutions Inc., Spokane Valley, WA 99206, USA.
26. We note that the analysis here must be extended for the lower temperatures in the experiment to include scattering from the walls. For example, the phonon mean free path is larger than the diameter of the pipe for temperatures below about 0.37 K.
27. We are grateful to M. Hayden, private communication, for the details of the geometry.
28. C. B. Satterthwaite, Phys. Rev. PHRVAO 0031-899X 10.1103/PhysRev.125.873 125, 873 (1962);
29. R. M. Mueller, C. Buchal, T. Oversluizen, and F. Pobell, Rev. Sci. Instrum. 10.1063/1.1135452 49, 515 (1978) (Pubitemid 8596408)
30. and references therein.