Global dynamical correlation energies in covariant density functional theory: Cranking approximation

Abstract

The global dynamical correlation energies for 575 even–even nuclei with proton numbers ranging from Z= 8 to Z= 108 calculated with the covariant density functional theory using the PC-PK1 parametrization are presented. The dynamical correlation energies include the rotational correction energies obtained with the cranking approximation and the quadrupole vibrational correction energies. The systematic behavior of the present correlation energies is in good agreement with that obtained from the projected generator coordinate method using the SLy4 Skyrme force although our values are systematically smaller. After including the dynamical correlation energies, the rootmean- square deviation predicted by the PC-PK1 for the 575 even-even nuclei masses is reduced from 2.58 MeV to 1.24 MeV.

Graphical abstract

Keywords

binding energies and masses / nuclear density functional theory and extensions

References

[1] I. Tanihata, H. Hamagaki, O. Hashimoto, Y. Shida, N. Yoshikawa, K. Sugimoto, O. Yamakawa, T. Kobayashi, and N. Takahashi, Measurements of interaction cross sections and nuclear radii in the light p-shell region, Phys. Rev. Lett., 1985, 55(24): 2676

[2] A. C. Mueller and B. M. Sherrill, Nucli at the limits of particle stability, Annu. Rev. Nucl. Part. Sci., 1993, 43(1): 529

[3] I. Tanihata, Nuclear structure studies from reaction induced by radioactive nuclear beams, Prog. Part. Nucl. Phys., 1995, 35: 505

[4] J. Meng and P. Ring, Relativistic Hartree–Bogoliubov description of the neutron halo in ¹¹Li, Phys. Rev. Lett., 1996, 77(19): 3963

[5] J. Meng and P. Ring, Giant halo at the neutron drip line, Phys. Rev. Lett., 1998, 80(3): 460

[6] O. Sorlin and M. G. Porquet, Nuclear magic numbers: New features far from stability, Prog. Part. Nucl. Phys., 2008, 61(2): 602

[7] A. Ozawa, T. Kobayashi, T. Suzuki, K. Yoshida, and I. Tanihata, New magic number, N = 16, near the neutron drip line, Phys. Rev. Lett., 2000, 84(24): 5493

[8] S. G. Zhou, J. Meng, P. Ring, and E. G. Zhao, Neutron halo in deformed nuclei, Phys. Rev. C, 2010, 82(1): 011301

[9] E.M. Burbidge, G. R. Burbidge, W. A. Fowler, and F. Hoyle, Synthesis of the elements in stars, Rev. Mod. Phys., 1957, 29(4): 547

[10] B. Sun, F. Montes, L. S. Geng, H. Geissel, Y. A. Litvinov, and J. Meng, Application of the relativistic mean-field mass model to the r-process and the influence of mass uncertainties, Phys. Rev. C, 2008, 78(2): 025806

[11] Z. M. Niu, B. Sun, and J. Meng, Influence of nuclear physics inputs and astrophysical conditions on the Th/U chronometer, Phys. Rev. C, 2009, 80(6): 065806

[12] Z. Li, Z. M. Niu, B. Sun, N. Wang, and J. Meng, WLW mass model in nuclear r-process calculations, Acta Phys. Sin., 2012, 61(7): 072601 (in Chinese)

[13] W. H. Zhang, Z. M. Niu, F. Wang, X. B. Gong, and B. H. Sun, Uncertainties of nucleo-chronometers from nuclear physics inputs, Acta Phys. Sin., 2012, 61(11): 112601(in Chinese)

[14] X. D. Xu, B. Sun, Z. M. Niu, Z. Li, Y. Z. Qian, and J. Meng, Reexamining the temperature and neutron density conditions for r-process nucleosynthesis with augmented nuclear mass models, Phys. Rev. C, 2013, 87(1): 015805

[15] Z. M. Niu, Y. F. Niu, H. Z. Liang, W. H. Long, T. Nikšić, D. Vretenar, and J. Meng, b-decay half-lives of neutron-rich nuclei and matter flow in the r-process, Phys. Lett. B, 2013, 723(1-3): 172

[16] P. Möller, J. R. Nix, W. D. Myers, and W. J. Swiatecki, Nuclear ground-state masses and deformations, At. Data Nucl. Data Tables, 1995, 59(2): 185

[17] H. A. Bethe and R. F. Bacher, Nuclear Physics A. Stationary states of nuclei, Rev. Mod. Phys., 1936, 8(2): 82

[18] N. Wang, Z. Liang, M. Liu, and X. Wu, Mirror nuclei constraint in nuclear mass formula, Phys. Rev. C, 2010, 82(4): 044304

[19] M. Liu, N. Wang, Y. Deng, and X. Wu, Further improvements on a global nuclear mass model, Phys. Rev. C, 2011, 84(1): 014333

[20] J. Duflo and A. P. Zuker, Microscopic mass formulas, Phys. Rev. C, 1995, 52(1): R23

[21] H. Koura, T. Tachibana, M. Uno, and M. Yamada, Nuclidic mass formula on a spherical basis with an improved even– odd term, Prog. Theor. Phys., 2005, 113(2): 305

[22] M. Bender, G. F. Bertsch, and P. H. Heenen, Systematics of quadrupolar correlation energies, Phys. Rev. Lett., 2005, 94(10): 102503

[23] M. Bender, G. F. Bertsch, and P. H. Heenen, Global study of quadrupole correlation effects, Phys. Rev. C, 2006, 73(3): 034322

[24] S. Goriely, N. Chamel, and J. M. Pearson, Skyrme–Hartree– Fock–Bogoliubov nuclear mass formulas: Crossing the 0.6 MeV accuracy threshold with microscopically deduced pairing, Phys. Rev. Lett., 2009, 102(15): 152503

[25] S. Goriely, N. Chamel, and J. M. Pearson, Further explorations of Skyrme–Hartree–Fock–Bogoliubov mass formulas. XII. Stiffness and stability of neutron-star matter, Phys. Rev. C, 2010, 82(3): 035804

[26] S. Goriely, S. Hilaire, M. Girod, and S. Péru, First Gogny– Hartree–Fock–Bogoliubov nuclear mass model, Phys. Rev. Lett., 2009, 102(24): 242501

[27] P. G. Reinhard, The relativistic mean-field description of nuclei and nuclear dynamics, Rep. Prog. Phys., 1989, 52(4): 439

[28] P. Ring, Relativistic mean field theory in finite nuclei, Prog. Part. Nucl. Phys., 1996, 37: 193

[29] D. Vretenar, A. V. Afanasjev, G. A. Lalazissis, and P. Ring, Relativistic Hartree–Bogoliubov theory: Static and dynamic aspects of exotic nuclear structure, Phys. Rep., 2005, 409(3-4): 101

[30] J. Meng, H. Toki, S. G. Zhou, S. Q. Zhang, W. H. Long, and L. S. Geng, Relativistic continuum Hartree Bogoliubov theory for ground-state properties of exotic nuclei, Prog. Part. Nucl. Phys., 2006, 57(2): 470

[31] D. Hirata, K. Sumiyoshi, I. Tanihata, Y. Sugahara, T. Tachibana, and H. Toki, A systematic study of even-even nuclei up to the drip lines within the relativistic mean field framework, Nucl. Phys. A, 1997, 616(1-2): 438

[32] G. A. Lalazissis, S. Raman, and P. Ring, Ground-state properties of even–even nuclei in the relativistic mean-field theory, At. Data Nucl. Data Tables, 1999, 71(1): 1

[33] L. S. Geng, H. Toki, and J. Meng, Masses, Deformations and charge radii – nuclear ground-state properties in the relativistic mean field model, Prog. Theor. Phys., 2005, 113(4): 785

[34] T. Nikšić, D. Vretenar, and P. Ring, Beyond the relativistic mean-field approximation. II. Configuration mixing of meanfield wave functions projected on angular momentum and particle number, Phys. Rev. C, 2006, 74(6): 064309

[35] J. M. Yao, J. Meng, P. Ring, and D. Pena Arteaga, Threedimensional angular momentum projected relativistic pointcoupling approach for low-lying excited states in 24 Mg, Chin. Phys. Lett., 2008, 25(10): 3609

[36] J. M. Yao, J. Meng, P. Ring, and D. Pena Arteaga, Threedimensional angular momentum projection in relativistic mean-field theory, Phys. Rev. C, 2009, 79(4): 044312

[37] 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, 2010, 81(4): 044311

[38] T. Nikšić, Z. P. Li, D. Vretenar, L. Próchniak, J. Meng, and P. Ring, Beyond the relativistic mean-field approximation. III. Collective Hamiltonian in five dimensions, Phys. Rev. C, 2009, 79(3): 034303

[39] Z. P. Li, T. Nikšić, D. Vretenar, J. Meng, G. A. Lalazissis, and P. Ring, Microscopic analysis of nuclear quantum phase transitions in the N≈90 region, Phys. Rev. C, 2009, 79(5): 054301

[40] Z. M. Niu, Y. F. Niu, Q. Liu, H. Z. Liang, and J. Y. Guo, Nuclear β+/EC decays in covariant density functional theory and the impact of isoscalar proton–neutron pairing, Phys. Rev. C, 2013, 87(5): 051303(R)

[41] 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, 2011, 83(1): 014308

[42] P. W. Zhao, Z. P. Li, J. M. Yao, and J. Meng, New parametrization for the nuclear covariant energy density functional with a point-coupling interaction, Phys. Rev. C, 2010, 82(5): 054319

[43] P. W. Zhao, S. Q. Zhang, J. Peng, H. Z. Liang, P. Ring, and J. Meng, Novel structure for magnetic rotation bands in ⁶⁰Ni, Phys. Lett. B, 2011, 699(3): 181

[44] P. W. Zhao, J. Peng, H. Z. Liang, P. Ring, and J. Meng, Antimagnetic rotation band in nuclei: A microscopic description, Phys. Rev. Lett., 2011, 107(12): 122501

[45] J. Xiang, Z. P. Li, Z. X. Li, J. M. Yao, and J. Meng, Covariant description of shape evolution and shape coexistence in neutron-rich nuclei at N≈ 60, Nucl. Phys. A, 2012, 873: 1

[46] Z. P. Li, C. Y. Li, J. Xiang, J. M. Yao, and J. Meng, Enhanced collectivity in neutron-deficient Sn isotopes in energy functional based collective Hamiltonian, Phys. Lett. B, 2012, 717(4-5): 470

[47] X. M. Hua, T. H. Heng, Z. M. Niu, B. Sun, and J. Y. Guo, Comparative study of nuclear masses in the relativistic mean-field model, Sci. China Phys. Mech. Astron., 2012, 55(12): 2414

[48] P. W. Zhao, L. S. Song, B. Sun, H. Geissel, and J. Meng, Crucial test for covariant density functional theory with new and accurate mass measurements from Sn to Pa, Phys. Rev. C, 2012, 86(6): 064324

[49] J. Meng, J. Peng, S. Q. Zhang, and P. W. Zhao, Progress on tilted axis cranking covariant density functional theory for nuclear magnetic and antimagnetic rotation, Front. Phys., 2013, 8(1): 55

[50] X. Y. Qu, Y. Chen, S. Q. Zhang, P. W. Zhao, I. J. Shin, Y. Lim, Y. Kim, and J. Meng, Extending the nuclear chart by continuum: From oxygen to titanium, Sci. China Phys. Mech. Astron., 2013, 56(11): 2031

[51] T. Bürvenich, D. G. Madland, J. A. Maruhn, and P. G. Reinhard, Nuclear ground state observables and QCD scaling in a refined relativistic point coupling model, Phys. Rev. C, 2002, 65(4): 044308

[52] S. Goriely, M. Samyn, J. M. Pearson, and M. Onsi, Further explorations of Skyrme–Hartree–Fock–Bogoliubov mass formulas. IV: Neutron-matter constraint, Nucl. Phys. A, 2005, 750(2-4): 425

[53] N. Chamel, S. Goriely, and J. M. Pearson, Further explorations of Skyrme–Hartree–Fock–Bogoliubov mass formulas. IX: Constraint of pairing force to S01 neutron-matter gap, Nucl. Phys. A, 2008, 812(1-4): 72

[54] D. Inglis, Nuclear moments of inertia due to nucleon motion in a rotating well, Phys. Rev., 1956, 103(6): 1786

[55] S. Belyaev, Concerning the calculation of the nuclear moment of inertia, Nucl. Phys. A, 1961, 24: 322

[56] See Supplemental files for the detailed results.

[57] R. R. Rodríguez-Guzmán, J. L. Egido, and L. M. Robledo, Angular momentum projected analysis of quadrupole collectivity in Mg30,32,34 and Si32,34,36,38 with the Gogny interaction, Phys. Lett. B2000, 474(1-2): 15

[58] Z. P. Li, J. M. Yao, D. Vretenar, T. Nikšić, H. Chen, and J. Meng, Energy density functional analysis of shape evolution in N=28 isotones, Phys. Rev. C, 2011, 84(5): 054304

[59] K. Heyde and J. L. Wood, Shape coexistence in atomic nuclei, Rev. Mod. Phys., 2011, 83(4): 1467

[60] G. Audi, A. H. Wapstra, and C. Thibault, The Ame2003 atomic mass evaluation, Nucl. Phys. A, 2003, 729(1): 337

[61] T. R. Rodríguez and J. L. Egido, Multiple shape coexistence in the nucleus, Phys. Lett. B, 2011, 705(3): 255

[62] Y. Fu, H. Mei, J. Xiang, Z. P. Li, J. M. Yao, and J. Meng, Beyond relativistic mean-field studies of low-lying states in neutron-deficient krypton isotopes, Phys. Rev. C, 2013, 87(5): 054305

[63] E. Wigner, On the consequences of the symmetry of the nuclear hamiltonian on the spectroscopy of nuclei, Phys. Rev., 1937, 51(2): 106

[64] S. Goriely, M. Samyn, P. H. Heenen, J. M. Pearson, and F. Tondeur, Hartree–Fock mass formulas and extrapolation to new mass data, Phys. Rev. C, 2002, 66(2): 024326

[65] P. Möller, R. Bengtsson, B. G. Carlsson, P. Olivius, and T. Ichikawa, Global calculations of ground-state axial shape asymmetry of nuclei, Phys. Rev. Lett., 2006, 97(16): 162502

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