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Multipole polarizabilities for hydrogen-like atoms in Hulthén potential with and without spherical confinement

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Abstract

The multipole polarizabilities for hydrogen-like atoms with Hulthén potential are calculated with the sum-over-states formalism where the system bound and pseudocontinuum states are produced by employing the generalized pseudospectral method. Energies for nonzero angular momentum states, transition oscillator strengths, and dipole polarizabilities for the ground state of H atom with HP are calculated with high accuracy and compared with previous calculations. Quadrupole, octupole, and hexadecapole polarizabilities for both the ground and excited states are reported for the first time. The combined effect of Hulthén potential and impenetrable sphere on the polarizabilities is investigated, and the relation of such system with the confined H atom and particle in a box is discussed. Further comparison among Hulthén, screened Coulomb, and exponential cosine screened Coulomb potentials reveals that although the ground state energies follow the comparison theorem very well, their first-order energy corrections show complicated variations.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: All relevant data are included in the paper.]

References

  1. A.N. Sil, S. Canuto, P.K. Mukherjee, Adv. Quantum Chem. 58, 115 (2009)

    Article  Google Scholar 

  2. R.K. Janev, S.B. Zhang, J.G. Wang, Matter Radiat. Extrem. 1, 237 (2016)

    Article  Google Scholar 

  3. Y.D. Kwon, Phys. Rev. B 73, 165210 (2006)

    Article  ADS  Google Scholar 

  4. C.R. Stillman, P.M. Nilson, S.T. Ivancic, I.E. Golovkin, C. Mileham, I.A. Begishev, D.H. Froula, Phys. Rev. E 95, 063204 (2017)

    Article  ADS  Google Scholar 

  5. P. Beiersdorfer, G.V. Brown, A. McKelvey, R. Shepherd, D.J. Hoarty, C.R.D. Brown, M.P. Hill, L.M.R. Hobbs, S.F. James, J. Morton, L. Wilson, Phys. Rev. A 100, 012511 (2019)

    Article  ADS  Google Scholar 

  6. J. Weisheit, Chap. 82: Atoms in Plasmas, in Atomic, Molecular, and Optical Physics Handbook, ed. by W.F. Drake (American Institute of Physics, New York, 1996)

    Google Scholar 

  7. D. Salzman, Atomic Physics in Hot Plasmas (Oxford University Press, Oxford, 1998)

    Google Scholar 

  8. P.K. Shukla, B. Eliasson, Phys. Lett. A 372, 2897 (2008)

    Article  ADS  Google Scholar 

  9. P.K. Shukla, B. Eliasson, Phys. Rev. Lett. 108, 165007 (2012)

    Article  ADS  Google Scholar 

  10. L. Hulthén, Ark. Mat. Astron. Fys. 28A, 5 (1942)

    MathSciNet  Google Scholar 

  11. L. Hulthén, Ark. Mat. Astron. Fys. 29B, 1 (1942)

    MathSciNet  Google Scholar 

  12. C.S. Lam, Y.P. Varshni, Phys. Rev. A 4, 1875 (1971)

    Article  ADS  Google Scholar 

  13. D. Durand, L. Durand, Phys. Rev. D 23, 1092 (1981)

    Article  ADS  Google Scholar 

  14. U. Laha, J. Bhoi, Phys. Rev. C 91, 034614 (2015)

  15. J. Bhoi, U. Laha, Phys. Atom. Nucl. 79, 62 (2016)

    Article  ADS  Google Scholar 

  16. P. Matthys, H.D. Meyer, Phys. Rev. A 38, 1168 (1988)

    Article  ADS  Google Scholar 

  17. Y.P. Varshni, Phys. Rev. A 41, 4682 (1990)

  18. C. Stubbins, Phys. Rev. A 48, 220 (1993)

    Article  ADS  Google Scholar 

  19. A.K. Roy, Pramana-J. Phys. 65, 1 (2005)

    Article  ADS  Google Scholar 

  20. O. Bayrak, G. Kocak, I. Boztosun, J. Phys. A: Math. Gen. 39, 11521 (2006)

    Article  ADS  Google Scholar 

  21. P. Pyykkö, J. Jokisaari, Chem. Phys. 10, 293 (1975)

    Article  Google Scholar 

  22. J.A. Olson, D.A. Micha, J. Chem. Phys. 68, 4352 (1978)

    Article  ADS  Google Scholar 

  23. J.H. Yoon, Y. Yun, J. Korean Phys. Soc. 37, 73 (2000)

    Google Scholar 

  24. A.D. Alhaidari, J. Phys. A: Math. Gen. 37, 5805 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  25. X.Y. Gu, J.Q. Sun, J. Math. Phys. 51, 022106 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  26. S.M. Ikhdair, R. Sever, J. Phys. A: Math. Theor. 44, 355301 (2011)

    Article  Google Scholar 

  27. M.C. Onyeaju, J.O.A. Idiodi, A.N. Ikot, M. Solaimani, H. Hassanabadi, Few-Body Syst. 57, 793 (2016)

    Article  ADS  Google Scholar 

  28. R.L. Hall, N. Saad, K.D. Sen, J. Math. Phys. 59, 122103 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  29. M.K. Bahar, A. Soylu, A. Poszwa, IEEE Trans. Plasma Sci. 44, 2297 (2016)

    Article  ADS  Google Scholar 

  30. E. Hocine, R. Yekken, R. Lombard, Eur. Phys. J. Plus 134, 561 (2019)

    Article  Google Scholar 

  31. S.L. Talwar, S. Lumb, K.D. Sen, V. Prasad, Phys. Scr. 95, 035404 (2020)

    Article  Google Scholar 

  32. A.K. Roy, Int. J. Quantum Chem. 116, 953 (2016)

    Article  Google Scholar 

  33. C. Yadav, S. Lumb, V. Prasad, Eur. Phys. J. D 75, 21 (2021)

    Article  ADS  Google Scholar 

  34. H.E. Montgomery Jr., V.I. Pupyshev, Phys. Scr. 92, 015401 (2017)

    Article  ADS  Google Scholar 

  35. A.K. Roy, Int. J. Quantum Chem. 115, 937 (2015)

    Article  Google Scholar 

  36. Y.P. Varshni, Mod. Phys. Lett. A 19, 2757 (2004)

    Article  ADS  Google Scholar 

  37. L. Zhu, Y.Y. He, L.G. Jiao, Y.C. Wang, Y.K. Ho, Phys. Plasmas 27, 072101 (2020)

    Article  ADS  Google Scholar 

  38. L.G. Jiao, Y.Y. He, Y.Z. Zhang, Y.K. Ho, J. Phys. B: At. Mol. Opt. Phys. (2021) (Article in press)

  39. G. Yao, S.I. Chu, Chem. Phys. Lett. 204, 381 (1993)

    Article  ADS  Google Scholar 

  40. S.I. Chu, D.A. Telnov, Phys. Rep. 390, 1 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  41. L. Zhu, Y.Y. He, L.G. Jiao, Y.C. Wang, Y.K. Ho, Int. J. Quantum Chem. 120, e26245 (2020)

    Google Scholar 

  42. A. Dalgarno, Adv. Phys. 11, 281 (1962)

    Article  ADS  Google Scholar 

  43. J. Mitroy, M.S. Safronova, C.W. Clark, J. Phys. B: At. Mol. Opt. Phys. 43, 202001 (2010)

    Article  ADS  Google Scholar 

  44. H.A. Bethe, E.E. Salpeter, Quantum Mechanics of One- and Two-Electron Atoms (Dover Publications, New York, 2008)

    MATH  Google Scholar 

  45. C. Laughlin, J. Phys. B: At. Mol. Opt. Phys. 37, 4085 (2004)

    Article  Google Scholar 

  46. L.G. Jiao, Y.K. Ho, Int. J. Quantum Chem. 115, 434 (2015)

    Article  Google Scholar 

  47. Y.Z. Zhang, Y.C. Gao, L.G. Jiao, F. Liu, Y.K. Ho, Int. J. Quantum Chem. 120, e26136 (2020)

    Google Scholar 

  48. K.D. Sen (ed.), Electronic Structure of Quantum Confined Atoms and Molecules (Springer International Publishing, Switzerland, 2014)

    MATH  Google Scholar 

  49. R.A. Buckingham, Proc. Roy. Soc. A 160, 94 (1937)

    ADS  Google Scholar 

  50. P.W. Fowler, Mol. Phys. 53, 865 (1984)

    Article  ADS  Google Scholar 

  51. R.A. Rojas, N. Aquino, A. Flores-Riveros, Int. J. Quantum Chem. 118, e25584 (2018)

    Article  Google Scholar 

  52. X.R. Wang, Phys. Rev. A 46, 7295 (1992)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

Financial support from the National Natural Science Foundation of China (Grant Nos. 11504128, 11774131, and 91850114) is greatly acknowledged.

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Correspondence to Li Guang Jiao.

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He, Y.Y., Jiao, L.G., Liu, A. et al. Multipole polarizabilities for hydrogen-like atoms in Hulthén potential with and without spherical confinement. Eur. Phys. J. D 75, 126 (2021). https://doi.org/10.1140/epjd/s10053-021-00141-4

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  • DOI: https://doi.org/10.1140/epjd/s10053-021-00141-4

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