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Mobility tensor of negative ions in superfluid 3He-A

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The mobility tensor of negative ions in the A phase of superfluid 3He is calculated for temperatures close to T c . In this regime the scattering of superfluid quasiparticles from an electron bubble is practically elastic and the mobility tensor is expressed in terms of momentum transfer cross sections for an ion at rest. These generalized transport cross sections are obtained from the quasiparticle-ion scattering T-matrix, which we evaluate in terms of the normal state scattering amplitude. The p-wave pairing correlations in the intermediate states result in important interference effects among all partial waves in the scattering process, and, in addition, for the low-energy quasiparticles they lead to resonant states below the gap edge. These phenomena modify the scattering amplitude in the superfluid in an essential way and the differential quasiparticle-ion cross section is found to display strongly anisotropic, energy-dependent variations on the scale of the superfluid energy gap. We find that, in contrast to simple approximations, for low quasiparticle energies the parallel and perpendicular momentum transfer cross sections are very different from one another. Close to T c , the calculated mobility remains rather isotropic, but at lower temperatures the anisotropy is considerably larger than predicted by simple approximations for the cross section. The computed results are compared with the available measurements.

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References

  1. R. A. Ferrell, Phys. Rev. 108, 167 (1957).

    Google Scholar 

  2. C. G. Kuper, Phys. Rev. 122, 1007 (1961).

    Google Scholar 

  3. G. Baym, C. J. Pethick, and M. Salomaa, Phys. Rev. Lett. 38, 845 (1977).

    Google Scholar 

  4. G. Baym, C. J. Pethick, and M. Salomaa, J. Low Temp. Phys. 36, 431 (1979).

    Google Scholar 

  5. M. Salomaa, C. J. Pethick, and G. Baym, Phys. Rev. Lett. 44, 998 (1980).

    Google Scholar 

  6. A. C. Anderson, M. Kuchnir, and J. C. Wheatley, Phys. Rev. 168, 261 (1968); M. Kuchnir, P. R. Roach, and J. B. Ketterson, Phys. Rev. A 2, 262 (1970); P. V. E. McClintock, J. Low Temp. Phys. 11, 277 (1973).

    Google Scholar 

  7. A. I. Ahonen, J. Kokko, O. V. Lounasmaa, M. A. Paalanen, R. C. Richardson, W. Schoepe, and Y. Takano, Phys. Rev. Lett. 37, 511 (1976).

    Google Scholar 

  8. P. D. Roach, J. B. Ketterson, and P. R. Roach, in Quantum Fluids and Solids, S. B. Trickey, E. D. Adams, and J. W. Dufty, eds. (Plenum Press, New York, 1977), p. 259.

    Google Scholar 

  9. A. I. Ahonen, J. Kokko, M. A. Paalanen, R. C. Richardson, W. Schoepe, and Y. Takano, J. Low Temp. Phys. 30, 205 (1978).

    Google Scholar 

  10. A. I. Ahonen, in Physics at Ultralow Temperatures, T. Sugawara, ed. (The Physical Society of Japan, Tokyo, 1978), p. 23; W. Schoepe, J. Phys. (Paris) 39, C6–1290 (1978).

    Google Scholar 

  11. B. D. Josephson and J. Lekner, Phys. Rev. Lett. 23, 111 (1969).

    Google Scholar 

  12. P. D. Roach, J. B. Ketterson, and P. R. Roach, Phys. Rev. Lett. 39, 626 (1977).

    Google Scholar 

  13. R. M. Bowley, J. Phys. C 9, L151 (1976); 10, 4033 (1977).

    Google Scholar 

  14. A. L. Fetter and J. Kurkijärvi, Phys. Rev. B 15, 4272 (1977).

    Google Scholar 

  15. T. Soda, Prog. Theor. Phys. 58, 1096 (1977).

    Google Scholar 

  16. D. J. Bromley, Bull. Am. Phys. Soc. 23, 50(A) (1978); A. L. Fetter, private communications.

    Google Scholar 

  17. P. W. Anderson and P. Morel, Phys. Rev. 123, 1911 (1961); P. W. Anderson and W. F. Brinkman, Phys. Rev. Lett. 30, 1108 (1973).

    Google Scholar 

  18. W. F. Brinkman, J. W. Serene, and P. W. Anderson, Phys. Rev. A 10, 2386 (1974).

    Google Scholar 

  19. W. P. Halperin, C. N. Archie, F. B. Rasmussen, T. A. Alvesalo, and R. C. Richardson, Phys. Rev. B 13, 2124 (1976); W. P. Halperin, F. B. Rasmussen, C. N. Archie, and R. C. Richardson, J. Low Temp. Phys. 31, 617 (1978).

    Google Scholar 

  20. A. I. Ahonen, M. Krusius, and M. A. Paalanen, J. Low Temp. Phys. 25, 421 (1976).

    Google Scholar 

  21. L. P. Kadanoff and G. Baym, Quantum Statistical Mechanics (Benjamin, New York, 1962).

    Google Scholar 

  22. P. W. Anderson and W. F. Brinkman, in Physics of Liquid and Solid Helium, Vol. II, K. H. Bennemann and J. B. Ketterson, eds. (Wiley, New York, 1978), p. 177.

    Google Scholar 

  23. A. J. Leggett, Rev. Mod. Phys. 47, 331 (1975).

    Google Scholar 

  24. D. Rainer and M. Vuorio, J. Phys. C 10, 3093 (1977).

    Google Scholar 

  25. G. E. Brown, Unified Theory of Nuclear Models and Forces (North-Holland, Amsterdam, 1971), Chapter XI.

    Google Scholar 

  26. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).

    Google Scholar 

  27. V. N. Bondarev, Pis'ma Zh. Eksp. Tear. Fiz. 18, 693 (1973) [JETP Lett. 18, 405 (1973)]; V. N. Bondarev, Zh. Eksp. Tear. Fiz. 75, 913 (1978) [Sov. Phys.—JETP 48, 462 (1978)].

    Google Scholar 

  28. R. Combescot, J. Low Temp. Phys. 18, 537 (1975).

    Google Scholar 

  29. P. Wölfle and V. E. Koch, J. Low Temp. Phys. 30, 61 (1978).

    Google Scholar 

  30. D. D. Osheroff and P. W. Anderson, Phys. Rev. Lett. 33, 686 (1974).

    Google Scholar 

  31. R. A. Webb, T. J. Greytak, R. T. Johnson, and J. C. Wheatley, Phys. Rev. Lett. 30, 210 (1973); J. C. Wheatley, Rev. Mod. Phys. 47, 415 (1975).

    Google Scholar 

  32. D. N. Paulson, M. Krusius, and J. C. Wheatley, J. Low Temp. Phys. 26, 73 (1977).

    Google Scholar 

  33. D. N. Paulson, M. Krusius, J. C. Wheatley, R. S. Safrata, M. Koláč, T. Těthal, K. Svec, and J. Matas, J. Low Temp. Phys. 34, 63 (1979); 36, 721 (E) (1979).

    Google Scholar 

  34. D. Rainer and J. W. Serene, Phys. Rev. B 13, 4745 (1976).

    Google Scholar 

  35. P. Wölfle, W. Götze, J. Kurkijärvi, and H. Smith, J. Phys. C 13, 2461 (1980).

    Google Scholar 

  36. P. Bhattacharyya, T. L. Ho, and N. D. Mermin, Phys. Rev. Lett. 39, 1290 (1977); A. L. Fetter, Phys. Rev. Lett. 40, 1656 (1978); H. Kleinert, Y. R. Lin-Liu, and K. Maki, Phys. Lett. 70A, 27 (1979).

    Google Scholar 

  37. M. Salomaa, J. Phys. (Paris) 39, C6–24 (1978).

    Google Scholar 

  38. P. D. B. Collins and E. J. Squires, in Regge Poles in Particle Physics (Springer Tracts in Modern Physics, Vol. 45), G. Höhler, ed. (Springer-Verlag, Heidelberg, (1968), p. 42.

    Google Scholar 

  39. G. Baym, Lectures on Quantum Mechanics (Benjamin, New York, 1969), Chapter XVII.

    Google Scholar 

  40. W. Gröbner and N. Hofreiter, Integraltafel, Vol. I (Springer-Verlag, Vienna, 1965), p. 45.

    Google Scholar 

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Supported in part by U.S. National Science Foundation Grants DMR78-21068 and DMR78-21069.

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Salomaa, M., Pethick, C.J. & Baym, G. Mobility tensor of negative ions in superfluid 3He-A. J Low Temp Phys 40, 297–356 (1980). https://doi.org/10.1007/BF00117121

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