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Possibility of deformed dual bubble-like structure in light nuclei

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Abstract

The nuclei with a depressed central nucleonic density (bubble nuclei) are studied. The relativistic Hartree-Bogoliubov model with density-dependent meson-exchange interaction has been used to explore the possibility of deformed dual bubble-like structures in light nuclei, which are experimentally accessible. In dual bubble nuclei, the central densities for both proton and neutron deplete simultaneously. The unoccupancy of low angular momentum states for proton and neutron orbitals plays a vital role in the formation of bubble structures. We find favorable candidates around N or/and Z = 14 exhibiting a deformed dual bubble-like structure.

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This manuscript has no associated data or the data will not be deposited. [Authors’ comment: The data underlying the results are available as part of this published article.]

References

  1. H.A. Wilson, A spherical shell nuclear model. Phys. Rev. 69(9–10), 538 (1946)

    Article  ADS  Google Scholar 

  2. K.T.R. Davies, C.Y. Wong, S.J. Krieger, Hartree-Fock calculations of bubble nuclei. Phys. Lett. B 41(4), 455–457 (1972)

    Article  ADS  Google Scholar 

  3. X. Campi, D.W.L. Sprung, Possible bubble nuclei-36Ar and 200Hg. Phys. Lett. B 46(3), 291–295 (1973)

    Article  ADS  Google Scholar 

  4. J.M. Cavedon, B. Frois, D. Goutte, M. Huet, C.N. Ph Leconte, X.-H. Phan, S.K. Papanicolas, S. Platchkov, S. Williamson, W. Boeglin, Is the shell-model concept relevant for the nuclear interior? Phys. Rev. Lett. 49(14), 978 (1982)

    Article  ADS  Google Scholar 

  5. E. Khan, M. Grasso, J. Margueron, G. Van Nguye, Detecting bubbles in exotic nuclei. Nucl. Phys. A 800(1–4), 37–46 (2008)

    Article  ADS  Google Scholar 

  6. M. Grasso, L. Gaudefroy, E. Khan, T. Nikšić, J. Piekarewicz, O. Sorlin, G. Van Nguyen, V. Dario, Nuclear “bubble” structure in Si 34. Phys. Rev. C 79(3), 034318 (2009)

    Article  ADS  Google Scholar 

  7. Y. Chu, Z. Ren, Z. Wang, T. Dong et al., Central depression of nuclear charge density distribution. Phys. Rev. C 82(2), 024320 (2010)

    Article  ADS  Google Scholar 

  8. Y.Z. Wang, J.Z. Gu, X.Z. Zhang, J.M. Dong et al., Tensor effects on the proton sd states in neutron-rich Ca isotopes and bubble structure of exotic nuclei. Phys. Rev. C 84(4), 044333 (2011)

    Article  ADS  Google Scholar 

  9. J.-M. Yao, S. Baroni, M. Bender, P.-H. Heenen, Beyond-mean-field study of the possible “bubble” structure of 34 Si. Phys. Rev. C 86(1), 014310 (2012)

    Article  ADS  Google Scholar 

  10. J.M. Yao, H. Mei, Z.P. Li, Does a proton “bubble” structure exist in the low-lying states of 34Si? Phys. Lett. B 723(4–5), 459–463 (2013)

    Article  ADS  Google Scholar 

  11. T. Duguet, V. Somà, S. Lecluse, C. Barbieri, P. Navrátil, Ab initio calculation of the potential bubble nucleus Si 34. Phys. Rev. C 95(3), 034319 (2017)

    Article  ADS  Google Scholar 

  12. G. Saxena, M. Kumawat, M. Kaushik, S.K. Jain, M. Aggarwal, Bubble structure in magic nuclei. Phys. Lett. B 788, 1–6 (2019)

    Article  ADS  Google Scholar 

  13. G. Saxena, M. Kumawat, B.K. Agrawal, M. Aggarwal, Anti-bubble effect of temperature & deformation: a systematic study for nuclei across all mass regions between A= 20–300. Phys. Lett. B 789, 323–328 (2019)

    Article  ADS  Google Scholar 

  14. J. Dechargé, J.-F. Berger, K. Dietrich, M.S. Weiss, Superheavy and hyperheavy nuclei in the form of bubbles or semi-bubbles. Phys. Lett. B 451(3–4), 275–282 (1999)

    Article  ADS  Google Scholar 

  15. A.V. Afanasjev, S. Frauendorf, Central depression in nuclear density and its consequences for the shell structure of superheavy nuclei. Phys. Rev. C 71(2), 024308 (2005)

    Article  ADS  Google Scholar 

  16. A. Sobiczewski, K. Pomorski, Description of structure and properties of superheavy nuclei. Prog. Part. Nucl. Phys. 58(1), 292–349 (2007)

    Article  ADS  Google Scholar 

  17. S.K. Singh, M. Ikram, S.K. Patra, Ground state properties and bubble structure of synthesized superheavy nuclei. Int. J. Mod. Phys. E 22(01), 1350001 (2013)

    Article  ADS  Google Scholar 

  18. M. Bender, P.H. Heenen, Structure of superheavy nuclei. In Journal of Physics: Conference Series, 420, 012002. IOP Publishing, (2013)

  19. A. Mutschler, A. Lemasson, O. Sorlin, D. Bazin, C. Borcea, R. Borcea, Z. Dombrádi, J.-P. Ebran, A. Gade, H. Iwasaki et al., A proton density bubble in the doubly magic 34Si nucleus. Nat. Phys. 13(2), 152–156 (2017)

    Article  Google Scholar 

  20. W. Yan-Zhao, Z. Xi-Zhen, G. Jian-Zhong, D. Jian-Min, Tensor effect on bubble nuclei. Chin. Phys. Lett. 28(10), 102101 (2011)

    Article  ADS  Google Scholar 

  21. H. Nakada, K. Sugiura, J. Margueron, Tensor-force effects on single-particle levels and proton bubble structure around the Z or N= 20 magic number. Phys. Rev. C 87(6), 067305 (2013)

    Article  ADS  Google Scholar 

  22. X.Y. Wu, J.M. Yao, Z.P. Li et al., Low-energy structure and anti-bubble effect of dynamical correlations in 46 Ar. Phys. Rev. C 89(1), 017304 (2014)

    Article  ADS  Google Scholar 

  23. A. Shukla, S. Åberg, Deformed bubble nuclei in the light-mass region. Phys. Rev. C 89(1), 014329 (2014)

    Article  ADS  Google Scholar 

  24. S. Åberg, A. Yadav, A. Shukla, Possible dual bubble-like structure predicted by the relativistic Hartree-Bogoliubov model. Int. J. Mod. Phys. E 29(09), 2050073 (2020)

    Article  ADS  Google Scholar 

  25. B. Schuetrumpf, W. Nazarewicz, P.-G. Reinhard, Central depression in nucleonic densities: trend analysis in the nuclear density functional theory approach. Phys. Rev. C 96(2), 024306 (2017)

    Article  ADS  Google Scholar 

  26. J. Meng, S.-G. Zhou, I. Tanihata, The relativistic continuum Hartree-Bogoliubov description of charge-changing cross section for C, N, O and F isotopes. Phys. Lett. B 532(3–4), 209–214 (2002)

    Article  ADS  Google Scholar 

  27. J. Meng, H. Toki, J.Y. Zeng, S.Q. Zhang, S.-G. Zhou, Giant halo at the neutron drip line in Ca isotopes in relativistic continuum Hartree-Bogoliubov theory. Phys. Rev. C 65(4), 041302 (2002)

    Article  ADS  Google Scholar 

  28. V. Thakur, P. Kumar, S. Thakur, S. Thakur, V. Kumar, S.K. Dhiman, Microscopic study of the shell structure evolution in isotopes of light to middle mass range nuclides. Nucl. Phys. A 1002, 121981 (2020)

    Article  Google Scholar 

  29. P. Kumar, S.K. Dhiman, Microscopic study of shape evolution and ground state properties in even-even Cd isotopes using covariant density functional theory. Nucl. Phys. A 1001, 121935 (2020)

    Article  Google Scholar 

  30. P. Kumar, V. Thakur, S. Thakur, V. Kumar, S.K. Dhiman, Nuclear shape evolution and shape coexistence in Zr and Mo isotopes. Eur. Phys. J. A 57(1), 1–13 (2021)

    Article  ADS  Google Scholar 

  31. G.A. Lalazissis, T. Nikšić, D. Vretenar, P. Ring, New relativistic mean-field interaction with density-dependent meson-nucleon couplings. Phys. Rev. C 71(2), 024312 (2005)

    Article  ADS  Google Scholar 

  32. M. Bender, P.-H. Heenen, P.-G. Reinhard, Self-consistent mean-field models for nuclear structure. Rev. Mod. Phys. 75(1), 121 (2003)

    Article  ADS  Google Scholar 

  33. G.A. Lalazissis, Relativistic Hartree-Bogoliubov theory and the isospin dependence of the effective nuclear force. Prog. Part. Nucl. Phys. 59, 277–284 (2007)

    Article  ADS  Google Scholar 

  34. S. Typel, H.H. Wolter, Relativistic mean field calculations with density-dependent meson-nucleon coupling. Nucl. Phys. A 656(3–4), 331–364 (1999)

    Article  ADS  Google Scholar 

  35. F. Hofmann, C.M. Keil, H. Lenske, Density dependent hadron field theory for asymmetric nuclear matter and exotic nuclei. Phys. Rev. C 64(3), 034314 (2001)

    Article  ADS  Google Scholar 

  36. T. Nikšić, D. Vretenar, P. Finelli, P. Ring, Relativistic Hartree-Bogoliubov model with density-dependent meson-nucleon couplings. Phys. Rev. C 66(2), 024306 (2002)

    Article  ADS  Google Scholar 

  37. F. De Jong, H. Lenske, Asymmetric nuclear matter in the relativistic Brueckner-Hartree-Fock approach. Phys. Rev. C 57(6), 3099 (1998)

    Article  ADS  Google Scholar 

  38. Y. Tian, Z.Y. Ma, P. Ring, A finite range pairing force for density functional theory in superfluid nuclei. Phys. Lett. B 676(1–3), 44–50 (2009)

    Article  ADS  Google Scholar 

  39. T. Nikšić, P. Ring, D. Vretenar, Y. Tian, Z.-Y. Ma, 3D relativistic Hartree-Bogoliubov model with a separable pairing interaction: triaxial ground-state shapes. Phys. Rev. C 81(5), 054318 (2010)

    Article  ADS  Google Scholar 

  40. T. Nikšić, N. Paar, D. Vretenar, P. Ring, DIRHB-A relativistic self-consistent mean-field framework for atomic nuclei. Comput. Phys. Commun. 185(6), 1808–1821 (2014)

    Article  ADS  MATH  Google Scholar 

  41. Y. Tian, Z.-Y. Ma, P. Ring, Separable pairing force for relativistic quasiparticle random-phase approximation. Phys. Rev. C 79(6), 064301 (2009)

    Article  ADS  Google Scholar 

  42. Y. Tian, Z.-Y. Ma, P. Ring, Axially deformed relativistic Hartree Bogoliubov theory with a separable pairing force. Phys. Rev. C 80(2), 024313 (2009)

    Article  ADS  Google Scholar 

  43. T. Nikšić, D. Vretenar, P. Ring, Relativistic nuclear energy density functionals: mean-field and beyond. Prog. Part. Nucl. Phys. 66(3), 519–548 (2011)

    Article  ADS  Google Scholar 

  44. J. Dechargé, J.-F. Berger, M. Girod, K. Dietrich, Bubbles and semi-bubbles as a new kind of superheavy nuclei. Nucl. Phys. A 716, 55–86 (2003)

    Article  ADS  Google Scholar 

  45. J.-P. Delaroche, M. Girod, J. Libert, H. Goutte, S. Hilaire, S. Péru, N. Pillet, G.F. Bertsch, Structure of even-even nuclei using a mapped collective Hamiltonian and the D1S Gogny interaction. Phys. Rev. C 81(1), 014303 (2010)

    Article  ADS  Google Scholar 

  46. M. Wang, G. Audi, F.G. Kondev, W.J. Huang, S. Naimi, X. Xu, The AME2016 atomic mass evaluation (II). Tables, graphs and references. Chin. Phys. C 41(3), 030003 (2017)

    Article  ADS  Google Scholar 

  47. B. Pritychenko, M. Birch, B. Singh, M. Horoi, Tables of E2 transition probabilities from the first 2+ states in even-even nuclei. At. Data Nucl. Data Tables 107, 1–139 (2016)

    Article  ADS  Google Scholar 

  48. I. Angeli, K.P. Marinova, Table of experimental nuclear ground state charge radii: an update. At. Data Nucl. Data Tables 99(1), 69–95 (2013)

    Article  ADS  Google Scholar 

  49. P. Möller, A.J. Sierk, T. Ichikawa, H. Sagawa, Nuclear ground-state masses and deformations: FRDM (2012). At. Data Nucl. Data Tables 109, 1–204 (2016)

    Article  ADS  Google Scholar 

  50. N. Bezginov, T. Valdez, M. Horbatsch, A. Marsman, A.C. Vutha, E.A. Hessels, A measurement of the atomic hydrogen Lamb shift and the proton charge radius. Science 365(6457), 1007–1012 (2019)

    Article  ADS  Google Scholar 

  51. A. Ong, J.C. Berengut, V.V. Flambaum, Effect of spin-orbit nuclear charge density corrections due to the anomalous magnetic moment on halonuclei. Phys. Rev. C 82(1), 014320 (2010)

    Article  ADS  Google Scholar 

  52. S. Karatzikos, A.V. Afanasjev, G.A. Lalazissis, P. Ring, The fission barriers in Actinides and superheavy nuclei in covariant density functional theory. Phys. Lett. B 689(2–3), 72–81 (2010)

    Article  ADS  Google Scholar 

  53. A. Ozawa, T. Suzuki, I. Tanihata, Nuclear size and related topics. Nucl. Phys. A 693(1–2), 32–62 (2001)

    Article  ADS  Google Scholar 

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Acknowledgements

PK would like to acknowledge the financial support provided by Council of Scientific and Industrial Research (CSIR), New Delhi under Senior Research Fellowship scheme vide Reference No. 09/237(0165)/2018-EMR-I.

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Kumar, P., Thakur, V., Kumar, V. et al. Possibility of deformed dual bubble-like structure in light nuclei. Eur. Phys. J. Plus 136, 1027 (2021). https://doi.org/10.1140/epjp/s13360-021-02036-0

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