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4He Gas in the Temperature-Range 1 mK–5 K: Thermodynamic Properties from the Quantum Second Virial Coefficient

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Abstract

The quantum second virial coefficient Bq of low-dense 4He gas is calculated over the temperature range 1 mK–5 K. This is the first step in determining, according to standard expressions, the thermodynamic properties of the system, namely, the virial equation of state, compressibility factor, total internal energy, specific heat capacity, and entropy. These are compared to previous results wherever available. A large negative Bq is obtained. It is argued that this is intimately related to the formation of small clusters. Based on the semi-quantitative analysis, the cluster formation is predicted to occur in the present system at a fairly low temperature ~ 0.049 to 2.254 K. It is found that: (1) as the temperature decreases, the second virial coefficient deviates more and more from the classical behavior, thanks to quantum effects; and (2) from the pressure (P)-temperature (T) behavior, it is deduced that P is negative in the T-range 0.04 K < T < 0.17 K. In the negative-P regime, the system becomes unstable.

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References

  1. O.T. Al-Obeidat, A.S. Sandouqa, B.R. Joudeh, H.B. Ghassib, M.M. Hawamdeh, Can. J. Phys. 95(12), 1208 (2017)

    Article  ADS  Google Scholar 

  2. R.A. Aziz, V.P.S. Nain, J.S. Carley, W.L. Taylor, G.T. McConville, J. Chem. Phys. 70, 4330–4341 (1979)

    Article  ADS  Google Scholar 

  3. R.A. Aziz, A.R. Janzen, Metrologia 25, 57–58 (1988)

    Article  ADS  Google Scholar 

  4. R.F. Bishop, H.B. Ghassib, M.R. Strayer, Phys. Rev. A 13, 1570 (1976)

    Article  ADS  Google Scholar 

  5. U.K. Deiters, R.J. Sadus, J. Chem. Phys. 150, 134504 (2019)

    Article  ADS  Google Scholar 

  6. J. van Rijssel, V.F.D. Peters, J.D. Meeldijk, R.J. Kortschot, R.J.A. van Dijk-Moes, A.V. Petukhov, B.H. Erné, A.P. Philips, J. Phys. Chem. B. 118, 11000 (2014)

    Article  Google Scholar 

  7. H.B. Ghassib, A.S. Sandouqa, B.R. Joudeh, S.M. Mosameh, Can. J. Phys. 92(9), 997–1001 (2014)

    Article  ADS  Google Scholar 

  8. A.S. Sandouqa, Chem. Phys. Lett. 703, 29 (2018)

    Article  ADS  Google Scholar 

  9. H.B. Ghassib, Zeitschrift für Physik B-Condensed Matter 56, 91 (1984)

    Article  ADS  Google Scholar 

  10. R.E. Grisenti, W. Scohöllkopf, J.P. Toennies, Phys. Rev. Lett. 85, 2284 (2000)

    Article  ADS  Google Scholar 

  11. T.R. Prisk, M.S. Bryan, P.E. Sokol, G.E. Granroth, S. Moroni, M. Boninsegni, J. Low Temp. Phys. 189, 158 (2017)

    Article  ADS  Google Scholar 

  12. S. Zeller, M. Kunitski, J. Voigtsberger, A. Kalinin, A. Schottelius, C. Schober, M. Waitz, H. Sann, A. Hartung, T. Bauer, M. Pitzer, F. Trinter, C. Goihl, C. Jankea, M. Richtera, G. Kastirkea, M. Weller, A. Czasch, M. Kitzler, M. Braune, R.E. Grisenti, W. Schoollkopf, LPh.H. Schmidt, M.S. Schooffler, J.B. Williams, T. Jahnke, R. Doorner, Proc. Natl. Acad. Sci. USA 113, 14651 (2016). https://doi.org/10.1073/pnas.1610688113

    Article  ADS  Google Scholar 

  13. J. Voigtsberger, S. Zeller, J. Becht, N. Neumann, F. Sturm, H.-K. Kim, M. Waitz, F. Trinter, M. Kunitski, A. Kalinin, J. Wu, W. Schoollkopf, D. Bressanini, A. Czasch, J.B. Williams, K. Ullmann-Pfleger, L. Ph, H. Schmidt, M.S. Schooffler, R.E. Grisenti, T. Jahnke, R. Dooner, Nat. Commun. 5, 5765 (2014). https://doi.org/10.1038/ncomms6765

    Article  ADS  Google Scholar 

  14. E. Hiyama, M. Kamimura, Phys. Rev. A. 85, 022502 (2012)

    Article  ADS  Google Scholar 

  15. R.L. Johnston, Atomic and Molecular Clusters (Taylor & Francis, London, 2002)

    Book  Google Scholar 

  16. V. Efimov, Phys. Lett. B. 33, 563 (1970)

    Article  ADS  Google Scholar 

  17. M. Hartmann, R.E. Miller, J.P. Toennies, A. Vilesov, Phys. Rev. Lett. 75, 1566 (1995)

    Article  ADS  Google Scholar 

  18. M.V. Rama Krishna, K.B. Whaley, Phys. Rev. Lett. 54, 1126 (1990)

    Article  ADS  Google Scholar 

  19. M.V. Rama Krishna, K.B. Whaley, J. Chem. Phys. 93, 746 (1990)

    Article  ADS  Google Scholar 

  20. G.E. Uhlenbeck, E. Beth, Physica 3, 729 (1936)

    Article  ADS  Google Scholar 

  21. E. Beth, G.E. Uhlenbeck, Physica 4, 915 (1937)

    Article  ADS  Google Scholar 

  22. V.L. Seguin, H. Guignes, C. Lhuillier, Phys. Rev. B. 36, 141 (1987)

    Article  ADS  Google Scholar 

  23. S.M. Mosameh, A.S. Sandouqa, H.B. Ghassib, B.R. Joudeh, J. Low Temp. Phys. 175, 523 (2014)

    Article  ADS  Google Scholar 

  24. I.F. Al-Maaitah, B.R. Joudeh, A.S. Sandouqa, H.B. Ghassib, Acta Phys. Pol. A 129, 1131 (2016)

    Article  ADS  Google Scholar 

  25. A.S. Sandouqa, B.R. Joudeh, Phys. Scr. 93, 095401 (2018)

    Article  ADS  Google Scholar 

  26. B.R. Joudeh, A.S. Sandouqa, J. Low Temp. Phys. 190, 101 (2018)

    Article  ADS  Google Scholar 

  27. A.N. Akour, A.S. Sandouqa, B.R. Joudeh, H.B. Ghassib, Chin. J. Phys. 56, 411 (2018)

    Article  Google Scholar 

  28. A.F. Al-Maaitah, A.S. Sandouqa, B.R. Joudeh, O.T. Al-Obeidat, Chin. J. Phys. 62, 194 (2019)

    Article  Google Scholar 

  29. O.T. Al-Obeidat, A.S. Sandouqa, B.R. Joudeh, M.M. Hawamdeh, H.B. Ghassib, Phys. Scr. 95, 015401 (2020)

    Article  ADS  Google Scholar 

  30. A.S. Sandouqa, B.R. Joudeh, O.T. Al-Obeidat, M.M. Hawamdeh, H.B. Ghassib, Eur. Phys. J Plus. 135, 161 (2020)

    Article  Google Scholar 

  31. M.M. Hawamdeh, A.S. Sandouqa, B.R. Joudeh, O.T. Al-Obeidat, H.B. Ghassib, Eur. Phys. J Plus. 137, 1025 (2022)

    Article  Google Scholar 

  32. P. Czachorowski, M. Przybytek, M. Lesiuk, M. Puchalski, and B. Jeziorski Phys. Rev. A 102, 042810 (2020)

    Article  ADS  Google Scholar 

  33. W. Cencek, M. Przybytek, J. Komasa, J.B. Mehl, B. Jeziorski, K. Szalewicz, J. Chem. Phys. 136, 224303 (2012)

    Article  ADS  Google Scholar 

  34. R.F. Bishop, H.B. Ghassib, M.R. Strayer, J. Low Temp. Phys. 26, 669 (1977)

    Article  ADS  Google Scholar 

  35. E.V.L. Mello, J.J. Rehr, O.E. Vilches, Phys. Rev. B. 28(7), 3759 (1983)

    Article  ADS  Google Scholar 

  36. R.T. Pack, J. Chem, Phys. 78, 7217 (1983)

    Google Scholar 

  37. H.B. Ghassib, R.F. Bishop, M.R. Strayer, J. Low Temp. Phys. 23, 393 (1976)

    Article  ADS  Google Scholar 

  38. B. Song, P. Xu, M. He, Mol. Phys. 119, e1802525 (2021). https://doi.org/10.1080/00268976.2020.1802525

    Article  ADS  Google Scholar 

  39. H. Maris, S. Balibar, Phys. Today 53(2), 29 (2000)

    Article  Google Scholar 

  40. M. D’Agostino, F. Gulminelli, Ph. Chomaz, M. Bruno, F. Cannata, R. Bougault, F. Gramegna, I. Iori, N. Le Neindre, G.V. Margagliotti, A. Moroni, G. Vannini, Phys. Lett B. 473, 219 (2000)

    Article  ADS  Google Scholar 

  41. A.F. Al-Maaitah, A.S. Sandouqa, B.R. Joudeh, H.B. Ghassib, Int. J. of Mod. Phys. B 31, 17502021–175020211 (2017)

    Article  Google Scholar 

  42. A.A. Al-Harazneh, A.S. Sandouqa, B.R. Joudeh, H.B. Ghassib, J. Low Temp. Phys. 192, 117–132 (2018)

    Article  ADS  Google Scholar 

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Authors and Affiliations

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

    B. R. Joudeh

  2. Department of Physics, Faculty of Science, Al-Balqa Applied University, Al-Sult, Jordan

    A. S. Sandouqa

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

    O. T. Al-Obeidat

  4. Department of Physics, Mu’tah University, Al-Karak, Jordan

    A. F. Al-Maaitah

  5. Professor Emeritus of Physics, School of Science, The University of Jordan, Amman, 11942, Jordan

    H. B. Ghassib

Authors
  1. B. R. Joudeh
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  2. A. S. Sandouqa
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  3. O. T. Al-Obeidat
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  4. A. F. Al-Maaitah
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  5. H. B. Ghassib
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Contributions

Both B. R. Joudeh and A. S. Sandouqa performed the computations. Al-Obeidat and A. F. Al-Maaitah discussed the results. All authors and contributed to the final manuscript. H. B. Ghassib supervised the project.

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Correspondence to B. R. Joudeh.

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Joudeh, B.R., Sandouqa, A.S., Al-Obeidat, O.T. et al. 4He Gas in the Temperature-Range 1 mK–5 K: Thermodynamic Properties from the Quantum Second Virial Coefficient. J Low Temp Phys 213, 28–41 (2023). https://doi.org/10.1007/s10909-023-02986-y

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