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Neutron skin thickness for Pbnat and Tb159, and effects of deformation on matter radii for Mg, Na, and Ar isotopes

Shingo Tagami

Takaykui Myo

Masanobu Yahiro*

  • *Contact author: orion093g@gmail.com
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Phys. Rev. C 112, 014622 – Published 24 July, 2025

DOI: https://doi.org/10.1103/pnrl-pwky

Abstract

Background: Data on reaction cross section σR of proton scattering are available for Pbnat (natural lead) and Tb159. In addition, data on σR and/or interaction ones σI are available for Mg, Na, and Ar isotopes.

Purpose: Our aim is to determine neutron skin thickness rskin for Pbnat and Tb159 and to investigate effects of deformation for Mg, Na, and Ar isotopes.

Methods: We use the chiral (Kyushu) g-matrix folding model for lower energies and the folding model based on the Love-Franey (LF) t-matrix for higher energies.

Results: For Tb159, our skin value is rskin=0.273±0.073 fm. As for Mg24, our matter radius rm(σR)=3.03±0.08 fm determined from σR includes effects of deformation, whereas the corresponding rm(σI)=2.79±0.15 fm does not. Effects of deformation are seen for Mg isotopes, Na21,23, and Ar40.

Conclusion: Our result rskin=0.271±0.008 fm for Pbnat agrees with rskin208(PREX−II)=0.283±0.071 fm for Pb208, where we assume A=208 for Pbnat.

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References (55)

  1. C. J. Horowitz, S. J. Pollock, P. A. Souder, and R. Michaels, Parity violating measurements of neutron densities, Phys. Rev. C 63, 025501 (2001).
  2. D. Adhikari et al. (PREX Collaboration), Accurate determination of the neutron skin thickness of Pb208 through parity-violation in electron scattering, Phys. Rev. Lett. 126, 172502 (2021).
  3. D. Adhikari et al. (CREX Collaboration), Precision determination of the neutral weak form factor of Ca48, Phys. Rev. Lett. 129, 042501 (2022).
  4. B. A. Brown, Constraints on the Skyrme equations of state from properties of doubly magic nuclei, Phys. Rev. Lett. 111, 232502 (2013).
  5. I. Angeli and K. P. Marinova, Table of experimental nuclear ground state charge radii: An update, At. Data Nucl. Data Tables 99, 69 (2013).
  6. S. Tagami, T. Wakasa, J. Matsui, M. Yahiro, and M. Takechi, Neutron skin thickness of Pb208 determined from the reaction cross section for proton scattering, Phys. Rev. C 104, 024606 (2021).
  7. M. Toyokawa, M. Yahiro, T. Matsumoto, and M. Kohno, Effects of chiral three-nucleon forces on He4-nucleus scattering in a wide range of incident energies, Progr. Theor. Exp. Phys. 2018, 023D03 (2018).
  8. S. Tagami, M. Tanaka, M. Takechi, M. Fukuda, and M. Yahiro, Chiral g-matrix folding-model approach to reaction cross sections for scattering of Ca isotopes on a C target, Phys. Rev. C 101, 014620 (2020).
  9. S. Tagami, T. Wakasa, and M. Yahiro, Neutron skin thickness of Sn116,118,120,122,124 determined from reaction cross sections of proton scattering, Results Phys. 46, 106296 (2023).
  10. F. S. Dietrich et al., Proton reaction cross sections measured in the BNL/AGS E943 experiment, J. Nucl. Sci. Technol. 39, 269 (2002).
  11. P. U. Renberg, D. F. Measday, M. Pepin, P. Schwaller, B. Favier, and C. Richard-Serre, Reaction cross sections for protons in the energy range 220–570 MeV, Nucl. Phys. A 183, 81 (1972).
  12. J. M. Cassels and J. D. Lawson, Absorption cross sections for 134 MeV protons, Proc. Phys. Soc. Sec. A 67, 125 (1954).
  13. P. Kirkby and W. T. Link, Faraday-cup measurement of proton total reaction cross sections at 100 MeV, Can. J. Phys. 44, 1847 (1966).
  14. R. Goloskie and K. Strauch, Measurement of proton inelastic cross sections, Nucl. Phys. 29, 474 (1962).
  15. V. Meyer, R. M. Eisberg, and R. F. Carlson, Total reaction cross sections of several nuclei for protons, Phys. Rev. 117, 1334 (1960).
  16. T. Gooding, Proton total reaction cross sections at 34 MeV, Nucl. Phys. 12, 241 (1959).
  17. R. Abegg, J. Birchall, N. Davison, M. de Jong, D. Ginther, D. Hasell, T. Nasr, W. van Oers, R. Carlson, and A. Cox, Measurement of the proton total reaction cross section for Tb159, Ta181 and Au197 between 20 and 48 MeV, Nucl. Phys. A 324, 109 (1979).
  18. T. Suzuki et al., Neutron skin of Na isotopes studied via the interaction cross-sections, Phys. Rev. Lett. 75, 3241 (1995).
  19. T. Suzuki et al., Nuclear radii of Na and Mg isotopes, Nucl. Phys. A 630, 661 (1998).
  20. G. Huber et al., Spins, magnetic moments, and isotope shifts of 21−31Na by high resolution laser spectroscopy of the atomic D1 line, Phys. Rev. C 18, 2342 (1978); ; Erratum: 20, 2457(E) (1979).
  21. H. Zhang, W. Shen, Z. Ren, Y. Ma, W. Jiang, Z. Zhu, X. Cai, D. Fang, C. Zhong, L. Yu, Y. Wei, W. Zhan, Z. Guo, G. Xiao, J. Wang, J. Wang, Q. Wang, J. Li, M. Wang, and Z. Chen, Measurement of reaction cross section for proton-rich nuclei (A<30) at intermediate energies, Nucl. Phys. A 707, 303 (2002).
  22. A. Ozawa, T. Suzuki, and I. Tanihata, Nuclear size and related topics, Nucl. Phys. A 693, 32 (2001).
  23. A. Ozawa et al., Measurements of the interaction cross sections for Ar and Cl isotopes, Nucl. Phys. A 709, 60 (2002); ; Erratum: 727, 465 (2003).
  24. M. Takechi, S. Suzuki, D. Nishimura, M. Fukuda, T. Ohtsubo, M. Nagashima, T. Suzuki, T. Yamaguchi, A. Ozawa, T. Moriguchi, H. Ohishi, T. Sumikama, H. Geissel, N. Aoi, R.-J. Chen, D.-Q. Fang, N. Fukuda, S. Fukuoka, H. Furuki, N. Inabe et al., Evidence of halo structure in Mg37 observed via reaction cross sections and intruder orbitals beyond the island of inversion, Phys. Rev. C 90, 061305 (2014).
  25. S. Watanabe et al., Ground-state properties of neutron-rich Mg isotopes, Phys. Rev. C 89, 044610 (2014).
  26. S. Tagami, T. Wakasa, and M. Yahiro, C12+C12 scattering as the reference system for reaction cross section, Results Phys. 51, 106675 (2023).
  27. T. Wakasa, M. Takechi, S. Tagami, and M. Yahiro, Matter radii and skins of He6,8 from reaction cross section of proton+He6,8 scattering based on the Love–Franey t-matrix model, Results Phys. 35, 105329 (2022).
  28. M. Takechi, M. Fukuda, M. Mihara, K. Tanaka, T. Chinda, T. Matsumasa, M. Nishimoto, R. Matsumiya, Y. Nakashima, H. Matsubara, K. Matsuta, T. Minamisono, T. Ohtsubo, T. Izumikawa, S. Momota, T. Suzuki, T. Yamaguchi, R. Koyama, W. Shinozaki, M. Takahashi et al., Reaction cross sections at intermediate energies and Fermi-motion effect, Phys. Rev. C 79, 061601(R) (2009).
  29. T. Wakasa, S. Tagami, J. Matsui, M. Takechi, and M. Yahiro, Neutron-skin values and matter and neutron radii determined from reaction cross sections of proton scattering, Phys. Rev. C 107, 024608 (2023).
  30. W. G. Love and M. A. Franey, Effective nucleon-nucleon interaction for scattering at intermediate energies, Phys. Rev. C 24, 1073 (1981).
  31. M. Takechi, T. Ohtsubo, M. Fukuda, D. Nishimura, T. Kuboki, T. Suzuki, T. Yamaguchi, A. Ozawa, T. Moriguchi, H. Ooishi, D. Nagae, H. Suzuki, S. Suzuki, T. Izumikawa, T. Sumikama, M. Ishihara, H. Geissel, N. Aoi, R.-J. Chen, D.-Q. Fang et al., Interaction cross sections for Ne isotopes towards the island of inversion and halo structures of 29Ne and 31Ne, Phys. Lett. B 707, 357 (2012).
  32. K. Minomo, T. Sumi, M. Kimura, K. Ogata, Y. R. Shimizu, and M. Yahiro, Determination of the structure of Ne31 by a fully microscopic framework, Phys. Rev. Lett. 108, 052503 (2012).
  33. T. Sumi, K. Minomo, S. Tagami, M. Kimura, T. Matsumoto, K. Ogata, Y. R. Shimizu, and M. Yahiro, Deformation of Ne isotopes in the region of the island of inversion, Phys. Rev. C 85, 064613 (2012).
  34. M. Tanaka et al., Swelling of doubly magic Ca48 core in Ca isotopes beyond N=28, Phys. Rev. Lett. 124, 102501 (2020).
  35. M. Takechi, T. Wakasa, S. Tagami, J. Matsui, and M. Yahiro, Reanalyzes for Ca42−51 scattering on a C12 target at 280 meV/nucleon based on chiral g folding mode with Gogny-D1S Hartree–Fock–Bogoliubov densities, Results Phys. 31, 104923 (2021).
  36. E. Chabanat, P. Bonche, P. Haensel, J. Meyer, and R. Schaeffer, A Skyrme parametrization from subnuclear to neutron star densities Part II. Nuclei far from stablities, Nucl. Phys. A 635, 231 (1998); ; Erratum: 643, 441 (1998).
  37. N. Schunck et al., Solution of the Skyrme-Hartree–Fock–Bogolyubovequations in the Cartesian deformed harmonic-oscillator basis. (VIII) hfodd (v2.73y): A new version of the program, Comput. Phys. Commun. 216, 145 (2017).
  38. M. Matsuzaki, S. Tagami, and M. Yahiro, Neutron skin thickness of Pb208,Sn116,120,124, and Ca40 determined from reaction cross sections of He4 scattering, Phys. Rev. C 104, 054613 (2021).
  39. R. Carlson, A. Cox, T. Nasr, M. De Jong, D. Ginther, D. Hasell, A. Sourkes, W. van Oers, and D. Margaziotis, Measurements of proton total reaction cross sections, Nucl. Phys. A 445, 57 (1985).
  40. F. A. Brieva and J. Rook, Nucleon-nucleus optical model potential: (1). Nuclear matter approach, Nucl. Phys. A 291, 299 (1977).
  41. K. Amos, P. J. Dortmans, H. V. von Geramb, S. Karataglidis, and J. Raynal, Advances in Nuclear Physics, edited by J. W. Negele and E. Vogt (Plenum, New York, 2000), Vol. 25, p. 275
  42. T. Furumoto, Y. Sakuragi, and Y. Yamamoto, New complex G-matrix interactions derived from two- and three-body forces and application to proton-nucleus elastic scattering, Phys. Rev. C 78, 044610 (2008).
  43. M. Toyokawa, K. Minomo, and M. Yahiro, Mass-number and isotope dependence of local microscopic optical potentials for polarized proton scattering, Phys. Rev. C 88, 054602 (2013).
  44. K. Egashira, K. Minomo, M. Toyokawa, T. Matsumoto, and M. Yahiro, Microscopic optical potentials for He4 scattering, Phys. Rev. C 89, 064611 (2014).
  45. M. Toyokawa, K. Minomo, M. Kohno, and M. Yahiro, Roles of chiral three-nucleon forces in nucleon–nucleus scattering, J. Phys. G 42, 025104 (2015); Erratum: 44, 079502 (2017).
  46. M. Toyokawa, M. Yahiro, T. Matsumoto, K. Minomo, K. Ogata, and M. Kohno, Microscopic calculations based on chiral two- and three-nucleon forces for proton- and He4-nucleus scattering, Phys. Rev. C 92, 024618 (2015); Erratum: 96, 059905(E) (2017).
  47. G. R. Satchler and W. G. Love, Folding model potentials from realistic interactions for heavy-ion scattering, Phys. Rep. 55, 183 (1979).
  48. M. Kohno, Nuclear and neutron matter G-matrix calculations with a chiral effective field theory potential including effects of three-nucleon interactions, Phys. Rev. C 88, 064005 (2013).
  49. J. Fujita and H. Miyazawa, Pion theory of three-body forces, Prog. Theor. Phys. 17, 360 (1957).
  50. H.V. vonGeramb, K. Amos, L. Berge, S. Brautigam, H. Kohlhoff, and A. Ingemarsson, Parametrization scheme for effective interactions, Phys. Rev. C 44, 73 (1991).
  51. P. J. Dortmans and K. Amos, Density-dependent effective interactions, Phys. Rev. C 49, 1309 (1994).
  52. K. Minomo, K. Ogata, M. Kohno, Y. R. Shimizu, and M. Yahiro, The Brieva-Rook localization of the microscopic nucleon-nucleus potential, J. Phys. G 37, 085011 (2010).
  53. N. Yamaguchi, S. Nagata, and T. Matsuda, Optical model potential in the lowest order Brueckner theory and complex effective N-N interaction, Prog. Theor. Phys. 70, 459 (1983).
  54. H. De Vries, C. W. de Jager, and C. de Vries, Nuclear charge-density-distribution parameters, At. Data Nucl. Data Tables 36, 495 (1987).
  55. S. Tagami, T. Myo, and M. Yahiro, Neutron skin thickness of Pb208 from total cross sections of neutron scattering at 14.137 MeV and neutron skin thickness of Ca48, O, N, and C isotopes from reaction and interaction cross sections, Phys. Rev. C 110, 064610 (2024).

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Phys. Rev. C 112, 014622– Published 24 July, 2025
  • Received 6 January 2025
  • Revised 14 April 2025
  • Accepted 2 June 2025
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