Nuclear magnetic moments in covariant density functional theory

Abstract

Nuclear magnetic moment is an important physical variable and serves as a useful tool for the stringent test of nuclear models. For the past decades, the covariant density functional theory and its extension have been proved to be successful in describing the nuclear ground-states and excited states properties. However, a long-standing problem is its failure to predict magnetic moments. This article reviews the recent progress in the description of the nuclear magnetic moments within the covariant density functional theory. In particular, the magnetic moments of spherical odd-Anuclei with doubly closed shell core plus or minus one nucleon and deformed odd-Anuclei.

Keywords

nuclear magnetic moment / covariant density functional theory / meson exchange current / configuration mixing

References

[1] A. Arima, M. Harvey, and K. Shimizu, Pseudo LScoupling and pseudo SU3 coupling schemes, Phys. Lett. B 30(8), 517 (1969)

[2] J. Meng, K. Sugawara-Tanabe, S. Yamaji, P. Ring, and A. Arima, Pseudospin symmetry in relativistic mean field theory, Phys. Rev. C 58(2), R628 (1998)

[3] J. Meng, K. Sugawara-Tanabe, S. Yamaji, and A. Arima, Pseudospin symmetry in Zr and Sn isotopes from the proton drip line to the neutron drip line, Phys. Rev. C 59(1), 154 (1999)

[4] H. Liang, J. Meng, and S.-G. Zhou, Hidden pseudospin and spin symmetries and their origins in atomic nuclei, Phys. Rep. 570, 1 (2015)

[5] A. Arima, K. Shimizu, W. Bentz, and H. Hyuga, Nuclear magnetic properties and gamow-teller transitions, Adv. Nucl. Phys. 18, 1 (1987)

[6] A. Arima and H. Horie, Configuration mixing and magnetic moments of nuclei, Prog. Theor. Phys. 11(4), 509 (1954)

[7] H. Horie and A. Arima, Configuration mixing and quadrupole moments of odd nuclei, Phys. Rev. 99(3), 778 (1955)

[8] K. Shimizu, M. Ichimura, and A. Arima, Magnetic moments and GT-type β-decay matrix elements in nuclei with a LSdoubly closed shell plus or minus one nucleon, Nucl. Phys. A 226(2), 282 (1974)

[9] J. Li, J. M. Yao, J. Meng, and A. Arima, One-pion exchange current corrections for nuclear magnetic moments in relativistic mean field theory, Prog. Theor. Phys. 125(6), 1185 (2011)

[10] J. Li, J. Meng, P. Ring, J. M. Yao, and A. Arima, Relativistic description of second-order correction to nuclear magnetic moments with point-coupling residual interaction, Sci. China Phys. Mech. Astron. 54(2), 204 (2011)

[11] J. Li, Y. Zhang, J. M. Yao, and J. Meng, Magnetic moments of ³³Mg in the time-odd relativistic mean field approach, Sci. China Ser. G 52(10), 1586 (2009)

[12] J. Wei, J. Li, and J. Meng, Relativistic descriptions of nuclear magnetic moments, Prog. Theor. Phys. Supp. 196, 400 (2012)

[13] J. Li, J. X. Wei, J. N. Hu, P. Ring, and J. Meng, Relativistic description of magnetic moments in nuclei with doubly closed shells plus or minus one nucleon, Phys. Rev. C 88(6), 064307 (2013)

[14] R. J. Blin-Stoyle, Theories of nuclear moments, Rev. Mod. Phys. 28(1), 75 (1956)

[15] A. Arima, Nuclear magnetic moments and gamow-teller matrix elements — configuration mixing vs. mesonic effects, Prog. Part. Nucl. Phys. 1, 41 (1978)

[16] A. Arima, Nuclear magnetic properties and gamowteller transitions, Prog. Part. Nucl. Phys. 11, 53 (1984)

[17] I. S. Towner, Quenching of spin matrix elements in nuclei, Phys. Rep. 155(5), 263 (1987)

[18] B. Castel and I. S. Towner, Modern Theories of Nuclear Moments, Oxford University Press, USA, 1990

[19] I. Talmi, 55 years of the shell model: A challenge to nuclear many-body theory, Int. J. Mod. Phys. E 14(06), 821 (2005)

[20] T. Schmidt, Über die magnetischen Momente der Atomkerne, Z. Phys. A 106(5–6), 358 (1937)

[21] R. J. Blin-Stoyle, The magnetic moments of spin 1/2 Nuclei, Proc. Phys. Soc. A 66(12), 1158 (1953)

[22] R. J. Blin-Stoyle and M. A. Perks, The deviations of nuclear magnetic moments from the schmidt lines, Proc. Phys. Soc. A 67(10), 885 (1954)

[23] A. Arima and H. Horie, Configuration mixing and magnetic moments of odd nuclei, Prog. Theor. Phys. 12(4), 623 (1954)

[24] H. Noya, A. Arima, and H. Horie, Nuclear moments and configuration mixing, Prog. Theor. Phys. Suppl. 8, 33 (1958)

[25] H. Miyazawa, Deviations of nuclear magnetic moments from the Schmidt lines, Prog. Theor. Phys. 6(5), 801 (1951)

[26] F. Villars, Exchange current effects in the Deuteron, Phys. Rev. 86(4), 476 (1952)

[27] M. Chemtob, Two-body interaction currents and nuclear magnetic moments, Nucl. Phys. A 123(2), 449 (1969)

[28] H. Hyuga, A. Arima, and K. Shimizu, Exchange magnetic moments, Nucl. Phys. A 336(3), 363 (1980)

[29] M. Ichimura, The magnetic moments of nuclei with a closed shell plus or minus one nucleon, Nucl. Phys. 63(3), 401 (1965)

[30] H. Mavromatis, First and second order corrections to the magnetic moments of nuclei using realistic interactions, Nucl. Phys. 80(3), 545 (1966)

[31] H. Mavromatis, Magnetic moments of nuclei with closed j–jshells plus or minus one nucleon, Nucl. Phys. A 104(1), 17 (1967)

[32] I. S. Towner and F. C. Khanna, Corrections to the single-particle M1 and gamow-teller matrix elements, Nucl. Phys. A 399(2), 334 (1983)

[33] A. Arima, A short history of nuclear magnetic moments and GT transitions, Sci. China Phys. Mech. Astron. 54(2), 188 (2011)

[34] N. J. Stone, D. Doran, M. Lindroos, J. Rikovska, M. Veskovic, et al., Magnetic moments of odd-ASb isotopes to ¹³³Sb: Significant evidence for mesonic exchange current contributions and on core collective gfactors, Phys. Rev. Lett. 78(5), 820 (1997)

[35] J. Rikovska, T. Giles, N. J. Stone, K. van Esbroeck, G. White, et al., First on-line beta-nMR on oriented nuclei: Magnetic dipole moments of the (νp_1/2)^–1 1/2^– ground state in ⁶⁷Ni and (πp_3/2)⁺¹ 3/2^– ground state in ⁶⁹Cu, Phys. Rev. Lett. 85(7), 1392 (2000)

[36] T. Ohtsubo, N. J. Stone, J. R. Stone, I. S. Towner, C. R. Bingham, et al., Magnetic dipole moment of the doubly-closed-shell plus one proton nucleus ⁴⁹Sc, Phys. Rev. Lett. 109(3), 032504 (2012)

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

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

[39] 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. 57(3), 470 (2006)

[40] J. Meng, J.-Y. Guo, J. Li, Z. P. Li, H. Z. Liang, W. H. Long, Y. F. Niu, Z. M. Niu, Y. Zhang, P. W. Zhao, and S. G. Zhou, Covariant density functional theory in nuclear physics, Prog. Phys. 31(4), 199 (2011)

[41] T. Nikšić, D. Vretenar, and P. Ring, Relativistic nuclear energy density functionals: Mean-field and beyond, Prog. Part. Nucl. Phys. 66(3), 519 (2011)

[42] J. Meng, Relativistic Density Functional for Nuclear Structure, World Scientific, Singapore, 2015

[43] M. M. Sharma, G. A. Lalazissis, and P. Ring, Rho meson coupling in the relativistic mean field theory and description of exotic nuclei, Phys. Lett. B 317(4), 9 (1993)

[44] S. G. Zhou, J. Meng, and P. Ring, Spin symmetry in the antinucleon spectrum, Phys. Rev. Lett. 91(3), 262501 (2003)

[45] W. Koepf and P. Ring, A relativistic description of rotating nuclei: The yrast line of ²⁰Ne, Nucl. Phys. A 493(1), 61 (1989)

[46] J. König and P. Ring, Identical bands in superdeformed nuclei: A relativistic description, Phys. Rev. Lett. 71(19), 3079 (1993)

[47] A. V. Afanasjev and P. Ring, Time-odd mean fields in the rotating frame: Microscopic nature of nuclear magnetism, Phys. Rev. C 62(3), 031302 (2000)

[48] A. V. Afanasjev and H. Abusara, Time-odd mean fields in covariant density functional theory: Rotating systems, Phys. Rev. C 82(3), 034329 (2010)

[49] 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 699(3), 181 (2011)

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

[51] 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. 8(1), 55 (2013)

[52] L. D. Miller, Relativistic single-particle potentials for nuclei, Ann. Phys. 91(1), 40 (1975)

[53] B. D. Serot, Elastic electron-nucleus scattering in a relativistic theory of nuclear structure, Phys. Lett. B 107(4), 263 (1981)

[54] J. A. McNeil, R. D. Amado, C. J. Horowitz, M. Oka, J. R. Shepard, and D. A. Sparrow, Resolution of the magnetic moment problem in relativistic theories, Phys. Rev. C 34(2), 746 (1986)

[55] S. Ichii, W. Bentz, A. Arima, and T. Suzuki, RPA type vertex corrections to isoscalar magnetic moments in the sigma-omega model, Phys. Lett. B 192(1–2), 11 (1987)

[56] J. R. Shepard, E. Rost, C.-Y. Cheung, and J. A. Mc Neil, Magnetic response of closed shell±1 nuclei in Dirac-Hartree approximation, Phys. Rev. C 37(3), 1130 (1988)

[57] U. Hofmann and P. Ring, A new method to calculate magnetic moments in relativistic mean field theories, Phys. Lett. B 214(3), 307 (1988)

[58] R. J. Furnstahl and C. E. Price, Relativistic Hartree calculations of odd-Anuclei, Phys. Rev. C 40(3), 1398 (1989)

[59] J. M. Yao, H. Chen, and J. Meng, Time-odd triaxial relativistic mean field approach for nuclear magnetic moments, Phys. Rev. C 74(2), 024307 (2006)

[60] T. M. Morse, C. E. Price, and J. R. Shepard, Meson exchange current corrections to magnetic moments in quantum hadro-dynamics, Phys. Lett. B 251(2), 241 (1990)

[61] R. J. Furnstahl and B. D. Serot, Nuclear currents in a relativistic mean field theory, Nucl. Phys. A 468(3–4), 539 (1987)

[62] 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 82(5), 054319 (2010)

[63] 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 65(4), 044308 (2002)

[64] T. Nikšić, D. Vretenar, and P. Ring, Random-phase approximation based on relativistic point-coupling models, Phys. Rev. C 72(1), 014312 (2005)

[65] J. Daoutidis and P. Ring, Continuum random-phase approximation for relativistic point coupling models, Phys. Rev. C 80(2), 024309 (2009)

[66] C. De Conti, A. P. Galeão, and F. Krmpotić, Relativistic RPA for isobaric analogue and Gamow–Teller resonances in closed shell nuclei, Phys. Lett. B 444(2), 14 (1998)

[67] N. Paar, T. Nikšić, D. Vretenar, and P. Ring, Quasiparticle random phase approximation based on the relativistic Hartree-Bogoliubov model (II): Nuclear spin and isospin excitations, Phys. Rev. C 69(5), 054303 (2004)

[68] H. Z. Liang, N. V. Giai, and J. Meng, Spin-isospin resonances: A self-consistent covariant description, Phys. Rev. Lett 101(12), 122502 (2008)

[69] B. D. Serot, Quantum hadrodynamics, Rep. Prog. Phys. 55(4), 1855 (1992)

[70] W. Bentz, A. Arima, H. Hyuga, K. Shimizu, and K. Yazaki, Ward identity in the many-body system and magnetic moments, Nucl. Phys. A 436(4), 593 (1985)

[71] R. J. Furnstahl, Convection currents in nuclei in a relativistic mean field theory, Phys. Rev. C 38(1), 370 (1988)

[72] H. Ito and L. S. Kisslinger, Nuclear magnetic moments in the hybrid quark-hadron model, Ann. Phys. 174(1), 169 (1987)

[73] W. H. Long, J. Meng, N. Van Giai, and S.-G. Zhou, New effective interactions in relativistic mean field theory with nonlinear terms and density-dependent mesonnucleon coupling, Phys. Rev. C 69(3), 034319 (2004)

[74] T. Yamazaki, T. Nomura, S. Nagamiya, and T. Katou, Anomalous orbital magnetism of proton deduced from the magnetic moment of the 11^– state of ²¹⁰Po, Phys. Rev. Lett. 25(8), 547 (1970)

[75] H. Horie and K. Sugimoto, Nuclear moments and nuclear structure, vol. 34 (J. Phys. Soc. Japan Suppl., 1973)

[76] A. Green, A. Kallio, and K. Kolltveit, Odd parity excitations of ¹⁶O with a realistic nucleon-nucleon interaction, Phys. Lett. 14(2), 142 (1965)

[77] V. Gillet, A. Green, and E. Sanderson, Particle-hole description of lead 208, Phys. Lett. 11(1), 44 (1964)

[78] Y. E. Kim and J. O. Rasmussen, Energy levels of ²¹⁰Bi and ²¹⁰Po and the shell-model residual force, Nucl. Phys. 47, 184 (1963)

[79] K. A. Brueckner and J. L. Gammel, Properties of Nuclear Matter, Phys. Rev. 109(4), 1023 (1958)

[80] T. Hamada and I. Johnston, A potential model representation of two-nucleon data below 315 MeV, Nucl. Phys. 34(2), 382 (1962)

[81] G. Bertsch, J. Borysowicz, H. McManus, and W. Love, Interactions for inelastic scattering derived from realistic potentials, Nucl. Phys. A 284(3), 399 (1977)

[82] A. Arima and L. J. Huang-Lin, Magnetic moments of odd-mass nuclei with simple configurations, Phys. Lett. B 41(4), 435 (1972)

[83] J. Blomqvist, N. Freed, and H. Zetterström, Magnetic moments of single particle states in ²⁰⁷Pb and ²⁰⁹Bi, Phys. Lett. 18(1), 47 (1965)

[84] P. Ring and E. Werner, Distribution of single-particle strengths in the nuclei ²⁰⁷Tl, ²⁰⁷Pb, ²⁰⁹Bi and ²⁰⁹Pb, Nucl. Phys. A 211, 198 (1973)

[85] V. Bernard and N. Van Giai, Effects of collective modes on the single-particle states and the effective mass in ²⁰⁸Pb, Nucl. Phys. A 348, 75 (1980)

[86] E. Litvinova and P. Ring, Covariant theory of particlevibrational coupling and its effect on the single-particle spectrum, Phys. Rev. C 73(4), 044328 (2006)

[87] P. Ring and E. Litvinova, Particle-vibrational coupling in covariant density-functional theory, Phys. At. Nucl. 72, 1285 (2009)

[88] N. Stone, Tech. Rep., International Atomic Energy Agency, International Nuclear Data Committee, Vienna, Austria, 2014

[89] G. Neyens, Nuclear magnetic and quadrupole moments for nuclear structure research on exotic nuclei, Rep. Prog. Phys. 66(4), 633 (2003)

[90] A. Bohr and B. R. Mottelson, Nuclear Structure Volume II: Nuclear Deformation, W. A. Benjamin, Inc., 1975

[91] 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(3), 1147 (1990)

[92] S. Nummela, F. Nowacki, P. Baumann, E. Caurier, J. Cederkäll, et al., Intruder features in the island of inversion: The case of ³³Mg, Phys. Rev. C 64(5), 054313 (2001)

[93] B. V. Pritychenko, T. Glasmacher, P. D. Cottle, R. W. Ibbotson, K. W. Kemper, L. A. Riley, A. Sakharuk, H. Scheit, M. Steiner, and V. Zelevinsky, Structure of the “island of inversion” nucleus ³³Mg, Phys. Rev. C 65(6), 061304 (2002)

[94] Z. Elekes, Z. Dombradi, A. Saito, N. Aoi, H. Baba, et al., Proton inelastic scattering studies at the borders of the “island of inversion”: The ^30,31Na and ^33,34Mg case, Phys. Rev. C 73(4), 044314 (2006)

[95] V. Tripathi, S. L. Tabor, P. F. Mantica, Y. Utsuno, P. Bender, et al., Intruder Configurations in the A= 33 isobars: ³³Mg and ³³Al, Phys. Rev. Lett. 101(14), 142504 (2008)

[96] D. T. Yordanov, M. Kowalska, K. Blaum, M. D. Rydt, K. T. Flanagan, P. Lievens, R. Neugart, G. Neyens, and H. H. Stroke, Spin and magnetic moment of ³³Mg: evidence for a negative-parity intruder ground State, Phys. Rev. Lett. 99(21), 212501 (2007)

[97] R. D. Lawson, Theory of the Nuclear Shell Model, Oxford University Press, Oxford, 1980

[98] M. Wang, G. Audi, F. Kondev, W. Huang, S. Naimi, and X. Xu, The AME2016 atomic mass evaluation (II): Tables, graphs and references, Chin. Phys. C 41(3), 030003 (2017)

[99] H. Lü, L. S. Geng, and J. Meng, Constrained relativistic mean field approach with fixed configurations, Eur. Phys. J. A 31(3), 273 (2007)

[100] E. Caurier, G. Martínez-Pinedo, F. Nowacki, A. Poves, and A. P. Zuker, The shell model as a unified view of nuclear structure, Rev. Mod. Phys. 77(2), 427 (2005)

[101] Y. M. Zhao and A. Arima, Nucleon-pair approximation to the nuclear shell model, Phys. Rep. 545, 1 (2014)

[102] B.-A. Bian, Y.-M. Di, G.-L. Long, Y. Sun, J.-Y. Zhang, and J. A. Sheikh, Systematics of g factors of 2⁺₁ states in even-even nuclei from Gd to Pt: A microscopic description by the projected shell model, Phys. Rev. C 75(1), 014312 (2007)

[103] R. Bauer, J. Speth, V. Klemt, P. Ring, E. Werner, and T. Yamazaki, Magnetic multipole moments and transition probabilities of single-particle states around ²⁰⁸Pb, Nucl. Phys. A 209(3), 535 (1973)

[104] M. Rho, Quenching of axial-vector coupling constant in β-decay and pion-nucleus optical potential, Nucl. Phys. A 231, 493 (1974)

[105] E. Oset and M. Rho, Axial currents in nuclei: The Gamow–Teller matrix element, Phys. Rev. Lett. 42(1), 47 (1979)

[106] W. Knüpfer, M. Dillig, and A. Richter, Quenching of the magnetic multipole strength distribution and of the anomalous magnetic moment in complex nuclei and mesonic renormalization of the nuclear spin current, Phys. Lett. B 95(3–4), 349 (1980)

[107] W. H. Long, N. Van Giai, and J. Meng, Densitydependent relativistic Hartree–Fock approach, Phys. Lett. B 640(4), 150 (2006)

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature