Probing Nuclear Radii of Exotic Nuclei with DRHBc Theory
"Explore the nuclear radii of exotic nuclei through the lens of deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc), considering deformation, pairing correlations, and continuum effects. Learn about charge radii, halo scales, and nuclear stability for a comprehensive understanding of these complex systems."
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The 29th International Nuclear Physics Conference (INPC 2025) May 25 - 30, 2025, Daejeon, Korea Nuclear radii of exotic nuclei in deformed relativistic Hartree-Bogoliubov theory in continuum Cong Pan ( ) School of Physics and Electronic Information, Anhui Normal University, China 2025/6/5 C. Pan - INPC2025 - Nuclear radii in DRHBc 1
Outline Introduction Theoretical framework Charge radii and deformation correlation Halo scales based on neutron radii Summary 2025/6/5 C. Pan - INPC2025 - Nuclear radii in DRHBc 2
Nuclear radius Nuclear radii are important properties for both exotic nuclei and stable nuclei. Neutron and proton halo Tanihata et al., PRL 55, 2676 (1985) Shell evolutions and new magic numbers Angeli, Marinova, JPG 42, 055108 (2015) Isomers Yordanov et al., PRL 116, 032501 (2016) Observed: NNDC Measured: ADNDT 99, 69 (2013) ADNDT 140, 101440 (2021) Predicted: ADNDT 144, 101488 (2022) 2025/6/5 C. Pan - INPC2025 - Nuclear radii in DRHBc 3
DRHBc theory To properly describe exotic nuclei, Zhou et al developed the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) by taking into account the effects of deformation, pairing correlations and continuum simultaneously. Zhou et al., PRC 82, 011301 (2010) Li et al., PRC 85, 024312 (2012) The DRHBc theory has been successfully applied in many studies on exotic nuclei. Prediction of new halos: 42,44Mg, 39Na, shape decoupling PRC 82, 011301 (2010); PRC 85, 024312 (2012); PRC 107, L041303 (2023) From X.H. Wu Interpretation of observed halos: 17,19B, 15,19,22C, 31Ne, 37Mg, PRL 126, 082501 (2021); PLB 844, 138112 (2023); PLB 849, 138422 (2024); PLB 855, 138792 (2024) Nuclear shapes and sizes PRC 105, 024306 (2022); PRC 108, 014319 (2023); PLB 847, 138298 (2023); PRC 110, 024310 (2024) Nuclear stability and radioactive decays PRC 104, L021301 (2021); PRC 104, 024331 (2021); PLB 845, 138160 (2023); PRC 109, 054310 (2024) For a review of DRHBc applications, see [Zhang, Pan, Wu, etc., AAPPS Bulletin, accepted (2025)] 2025/6/5 C. Pan - INPC2025 - Nuclear radii in DRHBc 4
DRHBc mass table https://drhbctable.jcnp.org/ In 2018, the DRHBc Mass Table Collaboration was established, aiming to provide a microscopic mass table that simultaneously includes the effects of deformation and continuum. Zhang et al., (DRHBc Mass Table Collaboration) PRC 102, 024314 (2020) Pan et al., (DRHBc Mass Table Collaboration) PRC 106, 014316 (2022) The even-Z part of the DRHBc mass table has been completed. Zhang et al., (DRHBc Mass Table Collaboration) ADNDT 144, 101488 (2022) Guo et al., (DRHBc Mass Table Collaboration) ADNDT 158, 101661 (2024) In this talk Systematics of charge radii and their deformation correlation Halo scales based on neutron radii and possible halo nuclei 2025/6/5 C. Pan - INPC2025 - Nuclear radii in DRHBc 5
Outline Introduction Theoretical framework Charge radii and deformation correlation Halo scales based on neutron radii Summary 2025/6/5 C. Pan - INPC2025 - Nuclear radii in DRHBc 6
Theoretical framework The mean fields and pairing correlations are self-consistently treated by the relativistic Hartree-Bogoliubov (RHB) equations: Kucharek and Ring, ZPA 339, 23 (1991) To properly consider continuum effect, the RHB equations are solved in a spherical Dirac Woods-Saxon (DWS) basis. Zhou et al., PRC, 68, 034323 (2003) For the nuclei with axial deformation and spatial reflection symmetry, the densities and potentials are expanded with Legendre polynomials: ( = 0, 2, 4, , max) Zhou et al., PRC 82, 011301 (2010) 2025/6/5 C. Pan - INPC2025 - Nuclear radii in DRHBc 7
Outline Introduction Theoretical framework Charge radii and deformation correlation Pan and Meng, arXiv:2504.13563 (2025) Halo scales based on neutron radii Summary 2025/6/5 C. Pan - INPC2025 - Nuclear radii in DRHBc 8
Charge radii Nuclear charge radius is one of the most fundamental properties in atomic nuclei, reflecting significant information. JPG 42, 055108 (2015) Exp: ADNDT 99, 69 (2013) ADNDT 140, 101440 (2021) DRHBc reproduces the Rchdata with = 0.033 fm, smaller than the = 0.036 fm from spherical calculations. ADNDT 121, 1 (2018) 2025/6/5 C. Pan - INPC2025 - Nuclear radii in DRHBc 9
Charge radii and deformation RCHB: Relativistic Continuum Hartree-Bogoliubov theory (Spherical calculations) For most nuclei, the deformation effect increases Rch. Near Z = 100, N = 240, the deformation effect decreases Rch. 2025/6/5 C. Pan - INPC2025 - Nuclear radii in DRHBc 10
Deformation dependence Empirical: Bohr, Mottelson, Nuclear Structure Vol I One cannot simply conclude the Rchas a monotonic function of the quadrupole deformation or total energy. 2025/6/5 C. Pan - INPC2025 - Nuclear radii in DRHBc 11
Outline Introduction Theoretical framework Charge radii and deformation correlation Halo scales based on neutron radii Pan et al, in preparation Summary 2025/6/5 C. Pan - INPC2025 - Nuclear radii in DRHBc 12
Halo scale Rnemp= r0A1/3 Based on neutron radii, the halo scales can be defined as: (m = 1 for one-neutron halo) Taken from PRC 108, L041301 (2023) 43,45Si A large Shaloindicates a possible neutron halo. 2025/6/5 C. Pan - INPC2025 - Nuclear radii in DRHBc 13
Si: Possible halos The Sndata of Si isotopes are reproduced with = 1.0 MeV. Provided by Prof. S.S. Zhang Signals for the one-neutron halos in 43,45Si are obtained by DRHBc. Method: PLB 849, 138422 (2024) 2025/6/5 C. Pan - INPC2025 - Nuclear radii in DRHBc 14
Outline Introduction Theoretical framework Charge radii and deformation correlation Halo scales based on neutron radii Summary 2025/6/5 C. Pan - INPC2025 - Nuclear radii in DRHBc 15
Summary and outlook Systematics of charge radii and their deformation correlation for even-Z nuclei are investigated based on DRHBc. Deformation effect improves the global descriptions of Rch. Rchis not a monotonic function of 2or Etot. Neutron halo scales of even-Z nuclei are studied. The one-neutron halos in 43,45Si are predicted. A complete DRHBc mass table including odd-Z nuclei will appear soon, enabling more comprehensive investigations for exotic nuclei. 2025/6/5 C. Pan - INPC2025 - Nuclear radii in DRHBc 16
Collaborators Peking University: Prof. J. Meng Beihang University: Prof. S.S. Zhang Ms. J.L. An Fuzhou University: Prof. X.H. Wu Mr. C.J. Lv Thank you for your attention! 2025/6/5 C. Pan - INPC2025 - Nuclear radii in DRHBc 17
DRHBc Mass Table Collaboration https://drhbctable.jcnp.org/ 2025/6/5 C. Pan - INPC2025 - Nuclear radii in DRHBc 18
Development of DRHBc 2010 Meson-exchange functional PRC 82, 011301; PRC 85, 024312 2012 DRHBc Mass Table Collaboration Density-dependent functional PRC 85, 067301 2018 Blocking effect CPL 29, 042101 Angular-momentum projection Sci. Bull. 66, 2072; PRC 104, 064319 2020 Point-coupling functional Finite-amplitude method PRC 105, 044312 PRC 102, 024314 2021 Collective Hamiltonian CPC 46, 064103 2022 Triaxial RHB in continuum PRC 108, L041301 Automatic blocking PRC 106, 014316 2023 Optimized basis PRC 106, 024302 2024 Time-odd DRHBc PLB 855, 138792 Glauber reaction PLB 849, 138422 2025/6/5 C. Pan - INPC2025 - Nuclear radii in DRHBc 19
Lagrangian The starting point of the relativistic density functional theory is a meson-exchange (ME) or point-coupling (PC) Lagrangian. A PC Lagrangian: Parameters , , , and are the coupling constants. Meng (Ed.), Relativistic Density Functional For Nuclear Structure (2016) 2025/6/5 C. Pan - INPC2025 - Nuclear radii in DRHBc 20
Neutron radii The sudden increase of Rnnear the neutron drip line may correspond to the neutron halo. 2025/6/5 C. Pan - INPC2025 - Nuclear radii in DRHBc 21
Si: Neutron densities 2025/6/5 C. Pan - INPC2025 - Nuclear radii in DRHBc 22
Si: Single-neutron levels 2025/6/5 C. Pan - INPC2025 - Nuclear radii in DRHBc 23
Si: Decomposition of neutron levels 2025/6/5 C. Pan - INPC2025 - Nuclear radii in DRHBc 24
