Journal of Low Temperature Physics

, Volume 192, Issue 1–2, pp 117–132 | Cite as

Scattering Properties of Ground-State 23Na Vapor Using Generalized Scattering Theory

  • A. A. Al-Harazneh
  • A. S. Sandouqa
  • B. R. Joudeh
  • H. B. Ghassib


The scattering properties of ground-state 23Na vapor are investigated within the framework of the Galitskii–Migdal–Feynman formalism. Viewed as a generalized scattering theory, this formalism is used to calculate the medium phase shifts. The scattering properties of the system—the total, viscosity, spin-exchange, and average cross sections—are then computed using these phase shifts according to standard recipes. The total cross section is found to exhibit the Ramsauer–Townsend effect as well as resonance peaks. These peaks are caused by the large difference between the potentials for electronic spin-singlet and spin-triplet states. They represent quasi-bound states in the system. The results obtained for the complex spin-exchange cross sections are particularly highlighted because of their importance in the spectroscopy of the Na2 dimer. So are the results for the scattering lengths pertaining to both singlet and triplet states. Wherever possible, comparison is made with other published results.


The total Viscosity Spin-exchange and average cross sections Hulburt–Hirshfelder (HH) potential Galitskii–Migdal–Feynman formalism 



One of the authors (H. B. Ghassib) is grateful to The University of Jordan for granting him a sabbatical leave in the academic year 2017–2018, during which this work was completed.


  1. 1.
    F.H. Mies, P.S. Julienne, The thermodynamic properties of diatomic molecules at elevated temperatures: role of continuum and metastable states. J. Chem. Phys. 77, 6162 (1982)ADSCrossRefGoogle Scholar
  2. 2.
    P.M. Holland, Calculation of the thermophysical properties of ground state sodium atoms. J. Chem. Phys. 87, 2 (1987)CrossRefGoogle Scholar
  3. 3.
    A.L. Fetter, J.D. Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill, New York, 1971)Google Scholar
  4. 4.
    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)ADSCrossRefGoogle Scholar
  5. 5.
    R.F. Bishop, H.B. Ghassib, M.R. Strayer, Composite pairs and effective two- body scattering in a many-body medium. Phys. Rev. A 13(4), 1570–1580 (1976)ADSCrossRefGoogle Scholar
  6. 6.
    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)ADSCrossRefGoogle Scholar
  7. 7.
    A.S. Sandouqa, H.B. Ghassib, B.R. Joudeh, A Ramsauer–Townsend effect in liquid 3He. Chem. Phys. Lett. 490, 172–175 (2010)CrossRefGoogle Scholar
  8. 8.
    B.R. Joudeh, A.S. Sandouqa, H.B. Ghassib, M.K. Al-Sugheir, 3He–3He and 4He–4He cross sections in matter at low temperature. J. Low Temp. Phys. 161, 348–366 (2010)ADSCrossRefGoogle Scholar
  9. 9.
    B.R. Joudeh, A.S. Sandouqa, M.K. Al-Sugheir, H.B. Ghassib, T-matrix and effective scattering in spin-polarized atomic deuterium (↓D). Phys. B 404, 1847–1851 (2009)ADSCrossRefzbMATHGoogle Scholar
  10. 10.
    A.S. Sandouqa, M.K. Al-Sugheir, H.B. Ghassib, Phys. Scr. 74, 5–11 (2006)ADSCrossRefGoogle Scholar
  11. 11.
    B.V. Yakshinskiy, T.E. Madey, Thermal desorption of sodium atoms from thin SiO2 films. Surf. Rev. Lett. 7, 75–87 (1999)CrossRefGoogle Scholar
  12. 12.
    H. Stein, K. Morawetz, G. Röpke, Medium modification of two-particle scattering in nonideal Bose systems. Phys. Rev. A 55, 3 (1997)CrossRefGoogle Scholar
  13. 13.
    C. Baumgarten, B. Braun, M. Capiluppi, G. Ciullo, B.F. Dalpiaz, H. Kolster, P. Lenisa, H. Marukyan, A. Nass, D. Reggiani, M. Stancari, E. Steffens, First measurement of the hydrogen spin-exchange collision cross section in the low temperature region. Eur. Phys. J. D 48, 343–350 (2008)ADSCrossRefGoogle Scholar
  14. 14.
    B. Bates, B. Bederson, Advances in Atomic and Molecular Physics, vol. 24 (Academic Press, San Diego, 1988)Google Scholar
  15. 15.
    L.W. Anderson, A.T. Ramsey, Study of the spin-relaxation times and the effects of spin-exchange collisions in an optically oriented sodium vapor. Phys. Rev. 132, 2 (1963)CrossRefGoogle Scholar
  16. 16.
    V.A. Kartoshkin, Spin exchange during collisions of two sodium atoms. Opt. Spectrosc. 116, 548 (2014)ADSCrossRefGoogle Scholar
  17. 17.
    A.G. Leonov, A.A. Rudenko, A.N. Starostin, M.D. Taran, D.I. Chekhov, I.I. Yakunin, Infrared absorption in dense sodium vapor. J. Exp. Theor. Phys. JETP 95, 242 (2002)ADSCrossRefGoogle Scholar
  18. 18.
    E. Tiesinga, A.J. Moerdijk, B.J. Verhaar, H.T.C. Stoof, Conditions for Bose–Einstein condensation in magnetically trapped atomic cesium. Phys. Rev. A 46, R1167 (1992)ADSCrossRefGoogle Scholar
  19. 19.
    K.B. Davis, M.O. Mewes, M.A. Joffe, M.R. Andrews, W. Ketterle, Evaporative cooling of sodium atoms. Phys. Rev. Lett. 74, 5202–5205 (1995)ADSCrossRefGoogle Scholar
  20. 20.
    K.B. Davis, M.O. Mewes, M.R. Andrews, N.J. van Druten, D.S. Durfee, D.M. Kurn, W. Ketterle, Bose–Einstein condensation in a gas of sodium atoms. Phys. Rev. Lett. 75, 3969–3972 (1995)ADSCrossRefGoogle Scholar
  21. 21.
    W. Ketterle, Experimental studies of Bose–Einstein condensates in sodium, in Bose Einstein Condensates and Atom Lasers, Proceedings of the International School of Quantum Electronics, 27th Course, Erice, 1999, Sicily, Italy, p. 1-29Google Scholar
  22. 22.
    W. Ketterle, D.S. Durfee, and D.M. Stamper-Kurn: Making, probing and understanding Bose–Einstein condensates, in Bose–Einstein condensation in atomic gases, Proceedings of the International School of Physics “Enrico Fermi”, Course CXL, ed by M. Inguscio, S. Stringari and C.E. Wieman (IOS Press, Amsterdam, 1999) p. 67–176Google Scholar
  23. 23.
    W. Ketterle, Experimental studies of Bose–Einstein condensation. Phys. Today 52(12), 30–35 (1999)ADSCrossRefGoogle Scholar
  24. 24.
    M.J. Jamieson, A. Dalgarno, J.N. Yukich, Elastic scattering of hydrogen atoms at low temperatures. Phys. Rev. A 46, 6956 (1992)ADSCrossRefGoogle Scholar
  25. 25.
    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 (1981)ADSCrossRefGoogle Scholar
  26. 26.
    R. Cote, A. Dalgarno, M.J. Jamieson, Elastic scattering of two 7Li atoms. Phys. Rev. A 50, 399 (1994)ADSCrossRefGoogle Scholar
  27. 27.
    A. Dalgarno, M.R.H. Rudge, Spin-change cross- sections for collisions between alkali atoms. Proc. R. Soc. Lond. Ser. A 286, 519–524 (1965)ADSCrossRefGoogle Scholar
  28. 28.
    V.A. Kartoshkin, Complex cross sections of spin exchange in collisions of sodium and potassium atoms in the ground state. Opt. Spectrosc. 109, 674–679 (2010)ADSCrossRefGoogle Scholar
  29. 29.
    R.H. Landau, Quantum mechanics II, 2nd edn. (Wiley, New York, 1996)zbMATHGoogle Scholar
  30. 30.
    R.F. Bishop, H.B. Ghassib, M.R. Strayer, Composite pairs and effective two-body scattering in a many-body medium. Phys. Rev. A 13(4), 1570–1580 (1976)ADSCrossRefGoogle Scholar
  31. 31.
    H.B. Ghassib, J.M. Irvine, R.H. Ibarra, A study of liquid 3He in the Brueckner–Goldstone formalism. Ann. Phys. 85(2), 378–409 (1974)ADSCrossRefGoogle Scholar
  32. 32.
    H.B. Ghassib, J.M. Irvine, An “Exact” self-consistent Brueckner calculation for liquid 3He. J. Low Temp. Phys. 18(3–4), 201–217 (1975)ADSCrossRefGoogle Scholar
  33. 33.
    H.T. Stoof, M. Bijlsma, M. Houbiers, Theory of interacting quantum gases. J. Res. Nat. Inst. Stand. Technol. 101(4), 443–455 (1996)CrossRefGoogle Scholar
  34. 34.
    C. Kittel, H. Kroemer, Thermal Physics (Freeman, New York, 1980)Google Scholar
  35. 35.
    H.M. Hulburt, J.O. Hirschfelder, Potential energy functions for diatomic molecules. J. Chem. Phys. 9, 61 (1941)ADSCrossRefGoogle Scholar
  36. 36.
    D.D. Konowalow, M.E. Rosenkrantz, M.L. Olson, The molecular electronic structure of the lowest\( {}^{1}\sum\nolimits_{g}^{ + } {} \),\( {}^{3}\sum\nolimits_{u}^{ + } {} \) ,\( {}^{1}\sum\nolimits_{u}^{ + } {} \),\( {}^{3}\sum\nolimits_{g}^{ + } {} \),\( {}^{1}\varPi_{u} \), \( {}^{1}\varPi_{g} \),\( {}^{3}\varPi_{u} \), and \( {}^{3}\varPi_{g} \) states of Na2. J. Chem. Phys. 72, 4 (1979)Google Scholar
  37. 37.
    H. Goldstein, C. Poole, J. Safko, Classical Mechanics, 3rd edn. (Addison-Wesley, Reading, 2001)zbMATHGoogle Scholar
  38. 38.
    C. Samuelis, E. Tiesinga, T. Laue, M. Elbs, H. Knökel, E. Tiemann, Cold atomic collisions studied by molecular spectroscopy. Phys. Rev. A 63, 012710 (2000)ADSCrossRefGoogle Scholar
  39. 39.
    A.J. Moerdijk, B.J. Verhaar, Prospects for Bose–Einstein condensation in atomic 7Li and 23Na. Phys. Rev. Lett. 73(4), 518–521 (1994)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • A. A. Al-Harazneh
    • 1
  • A. S. Sandouqa
    • 2
  • B. R. Joudeh
    • 3
    • 4
  • H. B. Ghassib
    • 5
  1. 1.Ministry of EducationAL-KarakJordan
  2. 2.Department of Physics and Basic Sciences, Faculty of Engineering TechnologyAl-Balqa Applied UniversityAmmanJordan
  3. 3.Applied Physics DepartmentTafila Technical UniversityTafilaJordan
  4. 4.Department of Computer Science, College of Shari’a and Islamic Studies in Al AhsaaAl Imam Mohammad Ibn Saud Islamic University (IMSIU)RiyadhSaudi Arabia
  5. 5.Department of Physics, Faculty of ScienceThe University of JordanAmmanJordan

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