10.57647/j.jtap.2025.1906.56

Study of the Electric Quadruple Moment of One-‎proton Halo Nucleus 8B by Using the Two-body ‎Model, the Collective Model and the Microscopic ‎Single-particle Shell Model

  1. Department of Physics, Mawlana Bhashani Science and Technology University, Santosh, Tangail, 1902, Bangladesh

Received: 2025-08-14

Revised: 2025-09-09

Accepted: 2025-10-17

Published in Issue 2025-12-31

How to Cite

1.
Mamun‎ MMA, Mia‎ MS, Islam T. Study of the Electric Quadruple Moment of One-‎proton Halo Nucleus 8B by Using the Two-body ‎Model, the Collective Model and the Microscopic ‎Single-particle Shell Model. J Theor Appl phys. 2025 Dec. 31;19(6). Available from: https://oiccpress.com/jtap/article/view/17996

PDF views: 192

Abstract

The nuclear electric quadruple moment of the proton-rich weakly bound Boron-8 (⁸B) halo nucleus is investigated using three theoretical approaches: the microscopic single-particle shell model, the collective model, and the two-body model. These approaches provide a reasonable prediction of the quadruple deformation that occurred due to the core polarization and many-body effects. These approaches also provide how the extended proton distribution influences the quadruple moment. The experimental value of electric quadruple moment (Q) of 8B is 6.45 efm². While the calculated value using the two-body model is 6.86 efm² and the collective model gives 5.83 efm² and the microscopic single particle shell model gives 4.03 efm². The ⁸B nucleus is a one-proton halo structure with a loosely bound valence proton outside a ⁷Be core, and it is an excellent candidate for studying nuclear deformation and quadruple effects near the proton drip-line. By comparing the predictions of these models with available experimental data, it can be measured their effectiveness in describing ⁸B’s structure. These predictions reveal the structure of the halo configuration that influences the quadruple properties of exotic nuclei.

Keywords

  • Nuclear electric quadruple moment,
  • Proton-rich,
  • Weakly bound,
  • Microscopic single-particle shell model,
  • Collective model,
  • Two-body model,
  • Proton drip-line

References

  1. . Sumikama et al., “Electric quadrupole moment of the proton halo nucleus 8B,” Phys. Rev. C, vol. 74, no. 2, p. 024327, Aug. 2006, doi: 10.1103/PhysRevC.74.02432
  2. . K. Azhibekov, V. V. Samarin, K. A. Kuterbekov, and M. A. Naumenko, “Shell model calculations for deformed Li isotopes,” Eurasian J. Phys. Funct. Mater., vol. 3, no. 4, pp. 307–318, Dec. 2019, doi: 10.29317/ejpfm.2019030403
  3. . A. Brown, “The nuclear shell model towards the drip lines,” Prog. Part. Nucl. Phys., vol. 47, no. 2, pp. 517–599, Jan. 2001, doi: 10.1016/S0146-6410(01)00159-
  4. . Shimizu, “Recent Progress of Shell-Model Calculations, Monte Carlo Shell Model, and Quasi-Particle Vacua Shell Model,” Physics (College. Park. Md)., vol. 4, no. 3, pp. 1081–1093, Sep. 2022, doi: 10.3390/physics403007
  5. . Navrátil, S. Quaglioni, I. Stetcu, and B. R. Barrett, “Recent developments in no-core shell-model calculations,” J. Phys. G Nucl. Part. Phys., vol. 36, no. 8, p. 083101, Aug. 2009, doi: 10.1088/0954-3899/36/8/08310
  6. . W. Moskowitz, K. E. Schmidt, M. A. Lee, and M. H. Kalos, “A new look at correlation energy in atomic and molecular systems. II. The application of the Green’s function Monte Carlo method to LiH,” J. Chem. Phys., vol. 77, no. 1, pp. 349–355, Jul. 1982, doi: 10.1063/1.44361
  7. . S. Hwash, “Nuclear Structure of the Heaviest Boron Isotope,” Eurasian Phys. Tech. J., vol. 19, no. 1 (39), pp. 113–118, Mar. 2022, doi: 10.31489/2022No1/113-11
  8. . F. Yang, S. J. Wang, S. G. Wilkins, and R. F. G. Ruiz, “Laser spectroscopy for the study of exotic nuclei,” Prog. Part. Nucl. Phys., vol. 129, p. 104005, Mar. 2023, doi: 10.1016/j.ppnp.2022.10400
  9. . Minamisono et al., “Giant quadrupole moment andproton halo discovered in 8B,” Hyperfine Interact., vol. 78, no. 1–4, pp. 165–168, 1993, doi: 10.1007/BF00568133
  10. D. C. Kean, “Measurement of quadrupole moments through Coulomb excitation,” in Nuclear Interactions, Berlin, Heidelberg: Springer Berlin Heidelberg, 2008, pp. 80–94. doi: 10.1007/3-540-09102-5_58
  11. C. A. Rouse, “Interior Structure of the Sun,” Nature, vol. 224, no. 5223, pp. 1009–1010, Dec. 1969, doi: 10.1038/2241009a
  12. I. Lopes and S. Turck-Chièze, “Detecting Gravity Modes in the Solar 8B Neutrino Flux,” Astrophys. J., vol. 792, no. 2, p. L35, Aug. 2014, doi: 10.1088/2041-8205/792/2/L3
  13. M. Agostini et al., “Comprehensive measurement of pp-chain solar neutrinos,” Nature, vol. 562, no. 7728, pp. 505–510, Oct. 2018, doi: 10.1038/s41586-018-0624-
  14. H. W. Barz, I. Rotter, and J. Höhn, “Coupled channels calculations in the continuum shell model with complicated configurations,” Nucl. Phys. A, vol. 275, no. 1, pp. 111–140, Jan. 1977, doi: 10.1016/0375-9474(77)90279-
  15. F. Winter et al., “First lattice QCD study of the gluonic structure of light nuclei,” Phys. Rev. D, vol. 96, no. 9, p. 094512, Nov. 2017, doi: 10.1103/PhysRevD.96.09451
  16. T. Naito, X. Roca-Maza, G. Colò, H. Liang, and H. Sagawa, “Isospin symmetry breaking in the charge radius difference of mirror nuclei,” Phys. Rev. C, vol. 106, no. 6, p. L061306, Dec. 2022, doi: 10.1103/PhysRevC.106.L06130
  17. P. J. Woods and C. N. Davids, “Nuclei Beyond the Proton DRIP-LINE,” Annu. Rev. Nucl. Part. Sci., vol. 47, no. 1, pp. 541–590, Dec. 1997, doi: 10.1146/annurev.nucl.47.1.54
  18. H. Esbensen and G. F. Bertsch, “Nuclear induced breakup of halo nuclei,” Phys. Rev. C, vol. 59, no. 6, pp. 3240–3245, Jun. 1999, doi: 10.1103/PhysRevC.59.324
  19. S. Shen, S. Elhatisari, D. Lee, U.-G. Meißner, and Z. Ren, “Ab Initio Study of the Beryllium Isotopes Be7 to Be12,” Phys. Rev. Lett., vol. 134, no. 16, p. 162503, Apr. 2025, doi: 10.1103/PhysRevLett.134.16250
  20. A. Bohr, B. R. Mottelson, and G. Breit, “Nuclear Structure, Vol. 1,” Phys. Today, vol. 23, no. 9, pp. 58–60, Sep. 1970, doi: 10.1063/1.302234
  21. T. Minamisono et al., “Proton halo of B8 disclosed by its giant quadrupole moment,” Phys. Rev. Lett., vol. 69, no. 14, pp. 2058–2061, 1992, doi: 10.1103/PhysRevLett.69.205
  22. Z. Dongmei et al., “Quadrupole moment and a proton halo structure in 17F (I π ≤ 5/2+),” J. Phys. G Nucl. Part. Phys., vol. 34, no. 3, pp. 523–528, 2007, doi: 10.1088/0954-3899/34/3/01
  23. G. A. Korolev et al., “Halo structure of 8B determined from intermediate energy proton elastic scattering in inverse kinematics,” Phys. Lett. B, vol. 780, pp. 200–204, May 2018, doi: 10.1016/j.physletb.2018.03.01
  24. G. Arfken and J. Mathews, Mathematical Methods for Physicists, ‎vol. 40, no. 4. Elsevier, 2013. doi: 10.1016/C2009-0-30629-7‎
  25. ‎M. L. Boas, “Mathematical methods in physical sciences,” ‎J. Symb. Log., vol. 57, no. 1, pp. 271–272, 1992, [Online]. ‎Available: https://www.cambridge.org/core/journals/journal-of-‎symbolic-logic
  26. ‎D. J. Griffiths and D. F. Schroeter, Introduction to Quantum ‎Mechanics, 3rd ed. Cambridge University Press, 2018. ‎
  27. ‎K. S. Krane and W. G. Lynch, “Introductory Nuclear ‎Physics,” Phys. Today, vol. 42, no. 1, pp. 78–78, Jan. 1989, ‎doi: 10.1063/1.2810884‎
  28. A. Bohr, B. R. Mottelson, G. Breit, and G. E. Brown, “Nuclear ‎Structure, Vol. 2: Nuclear Deformations,” Phys. Today, vol. 30, ‎no. 3, pp. 59–62, Mar. 1977, doi: 10.1063/1.3037453‎
  29. H. Kitagawa and H. Sagawa, “Quadrupole-moments in mirror ‎nuclei and proton halo,” Phys. Lett. B, vol. 299, no. 1–2, pp. 1–‎‎5, Jan. 1993, doi: 10.1016/0370-2693(93)90874-H.‎