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Study of the van der Waals Rare Gas Trimers \(\hbox {Ne}_3\), \(\hbox {Ar}_3\), \(\hbox {Kr}_3\), and \(\hbox {Xe}_3\) Using Hyperspherical Coordinates

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Abstract

We study the bosonic van der Waals rare gas trimers \(\hbox {Ne}_3\), \(\hbox {Ar}_3\), \(\hbox {Kr}_3\), and \(\hbox {Xe}_3\) in zero total angular momentum, \(J=0\), states. The three-body Schrödinger equation in hyperspherical coordinates is solved using the slow variable discretization approach. We calculate the \(J=0\) trimer bound state energy levels as well as their average root-mean-square radii. The adiabatic hyperspherical potential curves converging near the three-body dissociation threshold are also studied.

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References

  1. M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, ninth dover printing, tenth gpo, printing edn. (Dover, New York, 1964)

    MATH  Google Scholar 

  2. I. Baccarelli, F.A. Gianturco, T. Gonzlez-Lezana, G. Delgado-Barrio, S. Miret-Arts, P. Villarreal, Bound-state energies in argon trimers via a variational expansion: the effects from many-body corrections. J. Chem. Phys. 122(14), 144,319 (2005). https://doi.org/10.1063/1.1879972

    Article  Google Scholar 

  3. I. Baccarelli, F.A. Gianturco, T. Gonzlez-Lezana, G. Delgado-Barrio, S. Miret-Arts, P. Villarreal, A complete configurational study for the bound states of ne trimers. J. Chem. Phys. 122(8), 084,313 (2005). https://doi.org/10.1063/1.1850096

    Article  Google Scholar 

  4. D. Blume, C.H. Greene, B.D. Esry, Comparative study of he3, ne3, and ar3 using hyperspherical coordinates. J. Chem. Phys. 113(6), 2145–2158 (2000). https://doi.org/10.1063/1.482027

    Article  ADS  Google Scholar 

  5. C. de Boor, A Practical Guide to Splines (Springer, New York, 1978)

    Book  Google Scholar 

  6. V. Efimov, Energy levels arising from resonant two-body forces in a three-body system. Phys. Lett. B 33(8), 563–564 (1970). https://doi.org/10.1016/0370-2693(70)90349-7

    Article  ADS  Google Scholar 

  7. V. Efimov, Energy levels of three resonantly interacting particles. Nucl. Phys. A 210(1), 157–188 (1973). https://doi.org/10.1016/0375-9474(73)90510-1

    Article  ADS  Google Scholar 

  8. B.D. Esry, C.D. Lin, C.H. Greene, Adiabatic hyperspherical study of the helium trimer. Phys. Rev. A 54, 394–401 (1996). https://doi.org/10.1103/PhysRevA.54.394

    Article  ADS  Google Scholar 

  9. E.A. Kolganova, A.K. Motovilov, W. Sandhas, The \(^4\text{ He }\) trimer as an efimov system. Few-Body Syst. 51(2), 249 (2011). https://doi.org/10.1007/s00601-011-0233-x

    Article  ADS  Google Scholar 

  10. E.A. Kolganova, A.K. Motovilov, W. Sandhas, The \(^4\text{ He }\) trimer as an efimov system: latest developments. Few-Body Syst. 58(2), 35 (2017). https://doi.org/10.1007/s00601-016-1181-2

    Article  ADS  Google Scholar 

  11. A.A. Korobitsin, E.A. Kolganova, Two-body and three-body rare-gas clusters. Phys. Part. Nucl. 48(6), 900–905 (2017). https://doi.org/10.1134/S1063779617060284

    Article  Google Scholar 

  12. T. Kraemer, M. Mark, P. Waldburger, J.G. Danzl, C. Chin, B. Engeser, A.D. Lange, K. Pilch, A. Jaakkola, H.C. Nägerl, R. Grimm, Evidence for efimov quantum states in an ultracold gas of caesium atoms. Nature 440, 315–318 (2006)

    Article  ADS  Google Scholar 

  13. M. Kunitski, S. Zeller, J. Voigtsberger, A. Kalinin, L.P.H. Schmidt, M. Schöffler, A. Czasch, W. Schöllkopf, R.E. Grisenti, T. Jahnke, D. Blume, R. Dörner, Observation of the efimov state of the helium trimer. Science 348(6234), 551–555 (2015). https://doi.org/10.1126/science.aaa5601

    Article  ADS  Google Scholar 

  14. C. Lin, Hyperspherical coordinate approach to atomic and other coulombic three-body systems. Phys. Rep. 257(1), 1–83 (1995). https://doi.org/10.1016/0370-1573(94)00094-J

    Article  ADS  Google Scholar 

  15. M. Mrquez-Mijares, R. Prez de Tudela, T. Gonzlez-Lezana, O. Roncero, S. Miret-Arts, G. Delgado-Barrio, P. Villarreal, I. Baccarelli, F.A. Gianturco, J. Rubayo-Soneira, A theoretical investigation on the spectrum of the ar trimer for high rotational excitations. J. Chem. Phys. 130(15), 154,301 (2009). https://doi.org/10.1063/1.3115100

    Article  Google Scholar 

  16. T.N. Rescigno, C.W. McCurdy, Numerical grid methods for quantum-mechanical scattering problems. Phys. Rev. A 62, 032,706 (2000). https://doi.org/10.1103/PhysRevA.62.032706

    Article  Google Scholar 

  17. M. Salci, S.B. Levin, N. Elander, E. Yarevsky, A theoretical study of the rovibrational levels of the bosonic van der waals neon trimer. J. Chem. Phys. 129(13), 134,304 (2008). https://doi.org/10.1063/1.2955736

    Article  Google Scholar 

  18. H. Suno, Hyperspherical slow variable discretization method for weakly bound triatomic molecules. J Chem. Phys. 134(6), 064,318 (2011). https://doi.org/10.1063/1.3554329

    Article  Google Scholar 

  19. H. Suno, A theoretical study of \(\text{ Ne }_3\) using hyperspherical coordinates and a slow variable discretization approach. J. Chem. Phys. 135(13), 134,312 (2011). https://doi.org/10.1063/1.3645183

    Article  Google Scholar 

  20. H. Suno, Geometrical structure of helium triatomic systems: comparison with the neon trimer. J. Phys. B At. Mol. Opt. Phys. 49(1), 014,003 (2016)

    Article  Google Scholar 

  21. H. Suno, B.D. Esry, Adiabatic hyperspherical study of triatomic helium systems. Phys. Rev. A 78, 062,701 (2008). https://doi.org/10.1103/PhysRevA.78.062701

    Article  Google Scholar 

  22. H. Suno, B.D. Esry, C.H. Greene, J.P. Burke, Three-body recombination of cold helium atoms. Phys. Rev. A 65, 042,725 (2002). https://doi.org/10.1103/PhysRevA.65.042725

    Article  Google Scholar 

  23. K.T. Tang, J.P. Toennies, The van der waals potentials between all the rare gas atoms from he to rn. J. Chem. Phys. 118(11), 4976–4983 (2003). https://doi.org/10.1063/1.1543944

    Article  ADS  Google Scholar 

  24. O.I. Tolstikhin, S. Watanabe, M. Matsuzawa, Slow’ variable discretization: a novel approach for hamiltonians allowing adiabatic separation of variables. J. Phys. B At. Mol. Opt. Phys. 29(11), L389 (1996)

    Article  ADS  Google Scholar 

  25. R.C. Whitten, F.T. Smith, Symmetric representation for threebody problems. ii. motion in space. J. Math. Phys. 9(7), 1103–1113 (1968). https://doi.org/10.1063/1.1664683

    Article  ADS  Google Scholar 

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Acknowledgments

This work was carried out at RIKEN Advanced Institute for Computational Science from 2016 to 2017.

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Authors and Affiliations

  1. CCSE, Japan Atomic Energy Agency, 178-4-4 Wakashiba, Kashiwa-shi, 277-0871, Japan

    Hiroya Suno

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  1. Hiroya Suno
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Suno, H. Study of the van der Waals Rare Gas Trimers \(\hbox {Ne}_3\), \(\hbox {Ar}_3\), \(\hbox {Kr}_3\), and \(\hbox {Xe}_3\) Using Hyperspherical Coordinates. Few-Body Syst 60, 6 (2019). https://doi.org/10.1007/s00601-018-1475-7

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