Skip to main content
SpringerLink
Log in

3He-3He and 4He-4He Cross Sections in Matter at Low Temperature

  • Published:
Journal of Low Temperature Physics Aims and scope Submit manuscript

Abstract

The Galitskii-Migdal-Feynman (GMF) formalism is applied to liquid 3He and (for the first time) to liquid 4He. The effective total, diffusion and viscosity cross sections, as well as the effective scattering length and the effective range, are calculated. For liquid 3He, it is found that S-wave scattering dominates for wave number k<0.5 Å−1. At the Fermi momentum k F, the effective partial cross section σ ℓ (and thus the total cross section σ T) has a singularity (virtual state). This singularity may be interpreted as a signature of superfluidity or a quasi-bound state. For k>2 Å−1, the effective total cross section is nearly constant. On the other hand, it is found in liquid 4He that S-wave scattering dominates for k<0.3 Å−1, and a peak exists in σ T arising from a peak in the effective D-wave cross section. This resonance corresponds to a quasi-bound state trapped by the ℓ=2 centrifugal barrier. The most prominent features of our calculations are a resonance and a Ramsauer-Townsend minimum in the matter cross section at low temperatures. This effect is absent in the 3He gas. It is, therefore, a purely many-body effect in liquid 3He. With increasing energies, the matter results approach the vacuum results. This indicates that the high-energy behavior is dominated by the self-energy contribution; the many-body effects can be neglected.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. C.J. Joachain, Quantum Collisions Theory, vol. 2 (Longman, New York, 1979)

    Google Scholar 

  2. R. Feltgen, H. Pauly, F. Torello, H. Vehmeyer, Determination of the 4He-4He repulsive potential up to 0.14 eV inversion of high-resolution total-cross-section measurements. Phys. Rev. Lett. 30, 820–823 (1973)

    Article  ADS  Google Scholar 

  3. A.F. Borghesani, Electron mobility maximum in dense argon gas at low temperature. J. Electrost. 53, 89–106 (2001)

    Article  Google Scholar 

  4. W.A. Kampe, D.E. Oates, W. Schrader, H.G. Bennewitz, Observation of the atomic Ramsauer-Townsend effect in 4He-4He scattering. Chem. Phys. Lett. 18, 323–324 (1973)

    Article  ADS  Google Scholar 

  5. T.K. Lim, S.Y. Larsen, The Ramsauer-Townsend effect in molecular systems of electron-spin-polarized hydrogen and helium and their isotopes. J. Chem. Phys. 74, 4997–4999 (1981)

    Article  ADS  Google Scholar 

  6. R.S. Grace, W.M. Pope, D.L. Johson, J.G. Skofronick, Ramsauer-Townsend effect in the total cross section of 4He-4He and 3He-3He. Phys. Rev. A 14, 1006–1008 (1976)

    Article  ADS  Google Scholar 

  7. R.F. Bishop, H.B. Ghassib, M.R. Strayer, Low-energy He-He interactions with phenomenological potentials. J. Low Temp. Phys. 26, 669–690 (1977)

    Article  ADS  Google Scholar 

  8. S.N. Ali, M.Sc. Thesis, The University of Jordan, available upon request (1997)

  9. M.K. Al-Sugheir, H.B. Ghassib, B.R. Joudeh, Fermi pairing in dilute 3He-HeII mixtures. Int. J. Mod. Phys. B 18, 2491–2504 (2006)

    Article  ADS  Google Scholar 

  10. A.S. Sandouqa, B.R. Joudeh, M.K. Al-Sugheir, H.B. Ghassib, Weak 3He Pairing in 3He-HeII Mixtures (2010, submitted for publication)

  11. A.S. Sandouqa, M.K. Al-Sugheir, H.B. Ghassib, Hole-Hole scattering in spin polarized 3He-HeII mixtures. Phys. Scr. 74, 5–11 (2006)

    Article  MATH  ADS  Google Scholar 

  12. B.R. Joudeh, A.S. Sandouqa, M.K. Al-Sugheir, H.B. Ghassib, T-matrix and effective scattering in spin-polarized atomic deuterium (↓D). Physica B 404, 1847–1851 (2009)

    Article  ADS  Google Scholar 

  13. H.T. Abu-Hamdeh, M.Sc. Thesis, The University of Jordan, available upon request (1999)

  14. R.A. Aziz, V.P.S. Nain, J. S Carley, W.L. Taylor, G.T. McConville, An accurate interatomic potential for helium. J. Chem. Phys. 70, 4330–4341 (1979)

    Article  ADS  Google Scholar 

  15. A.R. Janzen, R.A. Aziz, Modern He–He potentials: another look at binding energy,effective range theory, retardation, and Efimov states. J. Chem. Phys. 103, 9626–9830 (1995)

    Article  ADS  Google Scholar 

  16. G. Sposito, E. Hukoveh, The interatomic potential in liquid 4He. II. Fourier transform of the potential. J. Low Temp. Phys. 9, 495–498 (1972)

    Article  ADS  Google Scholar 

  17. F. Luo, C.F. Giese, W.R. Gentry, Direct measurement of the size of the helium dimer. J. Chem. Phys. 104, 1151–1154 (1996)

    Article  ADS  Google Scholar 

  18. H.B. Ghassib, On dimers and trimers in some helium fluids. Phys. B, Condens. Matter 56, 91–98 (1984)

    Article  ADS  Google Scholar 

  19. R.E. Grisenti, W. Scohöllkopf, J.P. Toennies, Determination of the bond length and length and binding energy and binding energy of the helium dimers by diffraction from a transmission grating. Phys. Rev. Lett. 85, 2284–2287 (2000)

    Article  ADS  Google Scholar 

  20. F.M. Pen’kov, One-parametric dependences of the spectra, scattering lengths, and recombination coefficients for a system of three bosons. J. Exp. Theor. Phys. 97, 485–492 (2003)

    Article  ADS  Google Scholar 

  21. W.G. Rellergert, S.B. Cahn, A. Garvan, J.C. Hanson, W.H. Lippincott, J.A. Nikkel, D.N. McKinsey, Detection and imaging of He2 molecules in superfluid helium. Phys. Rev. Lett. 100, 0253011–0253014 (2008)

    Article  Google Scholar 

  22. X. Wu, X. Hu, Y. Dai, C. Du, S. Chu, L. Hu, J. Deng, Y. Feng, Quantum Monte Carlo calculated potential energy curve for the helium dimer. J. Chem. Phys. 132, 204304–5 (2010)

    Article  ADS  Google Scholar 

  23. M. Jeziorska, B. Jeziorski, K. Szalewicz, Pair potential for helium from symmetry-adapted perturbation theory calculations and from supermolecular data. J. Chem. Phys. 127, 124303–13 (2007)

    Article  ADS  Google Scholar 

  24. P.A. Hilton, R.A. Cowley, R. Scherm, W.G. Stirling, Life time of zero sound in liquid helium. J. Phys. C, Solid State Phys. 13, L295–L299 (1980)

    Article  ADS  Google Scholar 

  25. W.G. Stirling, R. Scherm, P.A. Hilton, R.A. Cowley, Neutron inelastic scattering from liquid helium three. J. Phys. C, Solid State Phys. 9, 1643–1663 (1976)

    Article  ADS  Google Scholar 

  26. R.T. Azuah, W.G. Stirling, H.R. Glyde, M. Boninsegni, P.F. Sokol, S.M. Bennington, Condensate and final-state effects in superfluid 4He. Phys. Rev. B 56, 14620–14630 (1997)

    Article  ADS  Google Scholar 

  27. A.F. Wyatt, Evidence for a Bose–Einstein condensate in liquid 4He from quantum evaporation. Nature 391, 56–59 (1998)

    Article  ADS  Google Scholar 

  28. S. Moroni, G. Senatore, S. Fantoni, Momentum distribution of liquid helium. Phys. Rev. B 55, 1040–1049 (1997)

    Article  ADS  Google Scholar 

  29. B. Withers, H.R. Glyde, Quantum momentum distributions. J. Low Temp. Phys. 147, 633–643 (2007)

    Article  ADS  Google Scholar 

  30. J. Bossy, J.V. Pearce, H. Schober, H.R. Glyde, Excitations of nanoscale quantum liquids under pressure and the Bose glass phase. Phys. Rev. B 78, 224507 (2008)

    Article  ADS  Google Scholar 

  31. J.C. Mester, E.S. Meyer, M.W. Reynolds, T.E. Huber, Z. Zhao, B. Freedman, K. Kim, I.F. Silvera, Cold collisions of ground state 4He: giant S-wave scattering cross sections. Phys. Rev. Lett. 71, 1343–1346 (1993)

    Article  ADS  Google Scholar 

  32. E.S. Meyer, J.C. Mester, M.W. Reynolds, T.E. Huber, Z. Zhao, B. Freedman, J. Kim, I.F. Silvera, Observation of giant scattering cross sections in 4He. Physica B 194–196, 885–886 (1994)

    Article  Google Scholar 

  33. J.C. Mester, E. Meyer, T. Huber, M. Reynolds, I. Silvera, Low temperature scattering of helium and hydrogen. Physica B 194–196, 887–888 (1994)

    Article  Google Scholar 

  34. J.C. Mester, E.S. Meyer, T.E. Huber, M.W. Reynolds, I.F. Silvera, Measurements of giant cross sections in low temperature 4He-4He scattering. J. Low Temp. Phys. 89, 569–572 (1992)

    Article  ADS  Google Scholar 

  35. H.B. Ghassib, R.F. Bishop, M.R. Strayer, A study of the Galitskii-Feynman T-matrix for liquid 3He. J. Low Temp. Phys. 23, 393–401 (1976)

    Article  ADS  Google Scholar 

  36. H.T.C. Stoof, M. Bijlsma, M. Houbiers, Theory of interacting quantum gases. J. Res. Natl. Inst. Stand. Technol. 101, 443–455 (1996)

    Google Scholar 

  37. E. Merzbaucher, Quantum Mechanics, 3rd edn. (Wiley, New York, 1998)

    Google Scholar 

  38. S. Geltman, Topics in Atomic Collision Theory (Krieger, Florida, 1997)

    Google Scholar 

  39. H.R. Glyde, B. Fåk, N.H. Dijk, H. Godfrin, K. Guckelsberger, R. Scherm, Effective mass, spin fluctuations, and zero sound in liquid 3He. Phys. Rev. B 61, 1421–1432 (2000)

    Article  ADS  Google Scholar 

  40. T. Alm, T.G. Röpke, M. Schmidt, Critical enhancement of the in-medium nucleon- nucleon cross-section at low temperatures. Phys. Rev. C 50, 31–37 (1994)

    Article  ADS  Google Scholar 

  41. A. Bohm, Quantum Mechanics: Foundations and Applications, 1st edn. (Springer, New York, 1979). 3rd edn., second printing, 1994

    Google Scholar 

  42. W.H. Miller, Molecular-Ramsauer-Townsend effect in very low energy 4He-4He scattering. Chem. Phys. Lett. 10, 7–9 (1971)

    Article  ADS  Google Scholar 

  43. A. Rovenchak, Effective mass of atom and the excitation spectrum in liquid helium-4 at T=0 K. J. Low Temp. Phys. 29, 145–148 (2003)

    Google Scholar 

  44. J.P. Aldridge, R.H. Davis, Calculated Ramsauer-Townsend effect in 4He-4He. Phys. Rev. Lett. 19, 1001–1002 (1967)

    Article  ADS  Google Scholar 

  45. R. Feltgen, H. Krist, K.A. Kohler, H. Paul, F. Torello, Unique determination of the 2He ground state potential from experiment by use of a reliable potential model. J. Chem. Phys. 76(5), 2360–2376 (1982)

    Article  ADS  Google Scholar 

  46. M.J. Jamieson, A. Dalgarno, M. Kimura, Scattering lengths and effective ranges for He-He and spin-polarized H-H and D-D scattering. Phys. Rev. A 51, 2626–2629 (1995)

    Article  ADS  Google Scholar 

  47. G. Gutiérrez, M. de Llano, W.C. Stwalley, Accurate direct determination of effective-range expansion parameters for several central potentials. Phys. Rev. B 29, 5211–5212 (1984)

    Article  ADS  Google Scholar 

  48. M.J. Jamieson, Adiabatically corrected scattering lengths and effective ranges for collisions of helium atoms. Chem. Phys. Lett. 310, 222–224 (1999)

    Article  ADS  Google Scholar 

  49. R. Landau, Quantum Mechanics II, 2nd edn. (Wiley, New York, 1996)

    MATH  Google Scholar 

  50. S. Huber, Efimov states in 4He trimers by two-body effective-range and scattering-length analysis: A comparison with Fadeev calculations. Phys. Rev. A 31, 3981–3982 (1985)

    Article  ADS  Google Scholar 

  51. H.B. Ghassib, G.V. Chester, 4He n-mers and Bose-Einstein condensation in HeII. J. Chem. Phys. 81, 585–586 (1984)

    Article  ADS  Google Scholar 

  52. A.R. Janzen, R.A. Aziz, An accurate potential energy curve for helium based on ab initio calculations. J. Chem. Phys. 107, 914–919 (1997)

    Article  ADS  Google Scholar 

  53. A.S. Sandouqa, H.B. Ghassib, B.R. Joudeh, A Ramsauer-Townsend effect in liquid 3He. Chem. Phys. Lett. 490, 172–175 (2010)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Applied Physics Department, Tafila Technical University, Tafila, Jordan

    B. R. Joudeh

  2. Department of Applied Sciences, Faculty of Engineering Technology, Al-Balqa’ Applied University, Amman, Jordan

    A. S. Sandouqa

  3. Department of Physics, The University of Jordan, Amman, Jordan

    H. B. Ghassib

  4. Department of Physics, The Hashemite University, Zarqa, Jordan

    M. K. Al-Sugheir

Authors
  1. B. R. Joudeh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. S. Sandouqa
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. B. Ghassib
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. K. Al-Sugheir
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. R. Joudeh.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Joudeh, B.R., Sandouqa, A.S., Ghassib, H.B. et al. 3He-3He and 4He-4He Cross Sections in Matter at Low Temperature. J Low Temp Phys 161, 348–366 (2010). https://doi.org/10.1007/s10909-010-0211-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10909-010-0211-6

Keywords

Search

Navigation