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

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Abstract

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.

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References

  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)

    Article  ADS  Google Scholar 

  2. P.M. Holland, Calculation of the thermophysical properties of ground state sodium atoms. J. Chem. Phys. 87, 2 (1987)

    Article  Google Scholar 

  3. A.L. Fetter, J.D. Walecka, Quantum Theory of Many-Particle Systems (McGraw-Hill, New York, 1971)

    Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  MATH  Google Scholar 

  10. A.S. Sandouqa, M.K. Al-Sugheir, H.B. Ghassib, Phys. Scr. 74, 5–11 (2006)

    Article  ADS  Google Scholar 

  11. B.V. Yakshinskiy, T.E. Madey, Thermal desorption of sodium atoms from thin SiO2 films. Surf. Rev. Lett. 7, 75–87 (1999)

    Article  Google Scholar 

  12. H. Stein, K. Morawetz, G. Röpke, Medium modification of two-particle scattering in nonideal Bose systems. Phys. Rev. A 55, 3 (1997)

    Article  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  14. B. Bates, B. Bederson, Advances in Atomic and Molecular Physics, vol. 24 (Academic Press, San Diego, 1988)

    Google Scholar 

  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)

    Article  Google Scholar 

  16. V.A. Kartoshkin, Spin exchange during collisions of two sodium atoms. Opt. Spectrosc. 116, 548 (2014)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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. 1-29

  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. 67–176

  23. W. Ketterle, Experimental studies of Bose–Einstein condensation. Phys. Today 52(12), 30–35 (1999)

    Article  ADS  Google Scholar 

  24. M.J. Jamieson, A. Dalgarno, J.N. Yukich, Elastic scattering of hydrogen atoms at low temperatures. Phys. Rev. A 46, 6956 (1992)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  26. R. Cote, A. Dalgarno, M.J. Jamieson, Elastic scattering of two 7Li atoms. Phys. Rev. A 50, 399 (1994)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  29. R.H. Landau, Quantum mechanics II, 2nd edn. (Wiley, New York, 1996)

    MATH  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  33. H.T. Stoof, M. Bijlsma, M. Houbiers, Theory of interacting quantum gases. J. Res. Nat. Inst. Stand. Technol. 101(4), 443–455 (1996)

    Article  Google Scholar 

  34. C. Kittel, H. Kroemer, Thermal Physics (Freeman, New York, 1980)

    Google Scholar 

  35. H.M. Hulburt, J.O. Hirschfelder, Potential energy functions for diatomic molecules. J. Chem. Phys. 9, 61 (1941)

    Article  ADS  Google Scholar 

  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)

  37. H. Goldstein, C. Poole, J. Safko, Classical Mechanics, 3rd edn. (Addison-Wesley, Reading, 2001)

    MATH  Google Scholar 

  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)

    Article  ADS  Google Scholar 

  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)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

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.

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Authors and Affiliations

  1. Ministry of Education, AL-Karak, Jordan

    A. A. Al-Harazneh

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

    A. S. Sandouqa

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

    B. R. Joudeh

  4. Department of Computer Science, College of Shari’a and Islamic Studies in Al Ahsaa, Al Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia

    B. R. Joudeh

  5. Department of Physics, Faculty of Science, The University of Jordan, Amman, Jordan

    H. B. Ghassib

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  1. A. A. Al-Harazneh
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  2. A. S. Sandouqa
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  3. B. R. Joudeh
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  4. H. B. Ghassib
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Correspondence to A. S. Sandouqa.

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Al-Harazneh, A.A., Sandouqa, A.S., Joudeh, B.R. et al. Scattering Properties of Ground-State 23Na Vapor Using Generalized Scattering Theory. J Low Temp Phys 192, 117–132 (2018). https://doi.org/10.1007/s10909-018-1897-0

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