Download PDF

Chinese Science Bulletin

, Volume 57, Issue 34, pp 4394–4399 | Cite as

Recent progress in theoretical studies of nuclear magnetic moments

Open Access
Progress Nuclear Physics
First Online:
Received:
Accepted:

Abstract

Nuclear magnetic moment is highly sensitive to the underlying structure of atomic nuclei and therefore serves as a stringent test of nuclear models. The advanced nuclear structure models have been successful in analyzing many nuclear structure properties, but they still cannot provide a satisfactory description of nuclear magnetic moments. Recently attempts to summarize the present understanding on nuclear magnetic moments in both relativistic and non-relativistic theoretical models have been made. The detailed contents are covered in the issue entitled “Nuclear magnetic moments and related topics” (in Sci China Phys Mech Astron, Vol. 54, No. 2, 2011). In this paper some of the related achievements will be highlighted.

Keywords

nuclear magnetic moments status and progress relativistic and non-relativistic many-body models 
Download to read the full article text

References

  1. 1.
    Arima A. A short history of nuclear magnetic moments and GT transitions. Sci China Phys Mech Astron, 2011, 54: 188–193CrossRefGoogle Scholar
  2. 2.
    Schmidt T. On the magnetic moments of atomic nuclei. Zeits f Physik, 1937, 106: 358CrossRefGoogle Scholar
  3. 3.
    Blin-Stoyle R J. The magnetic moments of spin 1/2 nuclei. Phys Soc A, 1953, 66: 1158–1161CrossRefGoogle Scholar
  4. 4.
    Miyazawa H. Deviations of nuclear magnetic moments from the Schmidt lines. Prog Theor Phys, 1951, 6: 801–814CrossRefGoogle Scholar
  5. 5.
    Villars F. Exchange current effects in the deuteron. Phys Rev, 1952, 86: 476–483CrossRefGoogle Scholar
  6. 6.
    Arima A, Horie H. Configuration mixing and magnetic moments of nuclei. Prog Theor Phys, 1954, 11: 509–511CrossRefGoogle Scholar
  7. 7.
    Arima A, Horie H. Configuration mixing and magnetic moments of odd nuclei. Prog Theor Phys, 1954, 12: 623–641CrossRefGoogle Scholar
  8. 8.
    Rho M. Quenching of axial-vector coupling constant in β-decay and pion-nucleus optical potential. Nucl Phys A, 1974, 231: 493–503CrossRefGoogle Scholar
  9. 9.
    Knüpfer W, Dillig M, Richter A. 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, 1980, 95: 349–354CrossRefGoogle Scholar
  10. 10.
    Oset E, Rho M. Axial currents in nuclei: The Gamow-Teller matrix element. Phys Rev Lett, 1979, 42: 47–50CrossRefGoogle Scholar
  11. 11.
    Serot B D, Walecka J D. The relativistic nuclear many-body problem. Adv Nucl Phys, 1986, 16: 1–327Google Scholar
  12. 12.
    Ring P. Relativistic mean field theory in finite nuclei. Prog Part Nucl Phys, 1996, 37: 193–263CrossRefGoogle Scholar
  13. 13.
    Vretenar D, Afanasjev A, Lalazissis G, et al. Relativistic Hartree-Bogoliubov theory: Static and dynamic aspects of exotic nuclear structure. Phys Rep, 2005, 409: 101–259CrossRefGoogle Scholar
  14. 14.
    Meng J, Toki H, Zhou S, et al. Relativistic continuum Hartree Bogoliubov theory for ground-state properties of exotic nuclei. Prog Part Nucl Phys, 2006, 57: 470–563CrossRefGoogle Scholar
  15. 15.
    Meng J, Guo J Y, Li J, et al. Covariant density functional theory in nuclear physics. Prog Phys, 2011, 31: 199–336Google Scholar
  16. 16.
    Ohtsubo H, Sano M, Morita M. Relativistic corrections to nuclear magnetic moments and Gamow-Teller matrix elements of beta decay. Prog Theor Phys, 1973, 49: 877CrossRefGoogle Scholar
  17. 17.
    Miller L D. Relativistic single-particle potentials for nuclei. Ann Phys, 1975, 91: 40CrossRefGoogle Scholar
  18. 18.
    Bawin M, Hughes C A, Strobel G L. Magnetic tests for nuclear Dirac wave functions. Phys Rev C, 1983, 28: 456–457CrossRefGoogle Scholar
  19. 19.
    Bouyssy A, Marcos S, Mathiot J F. Single-particle magnetic moments in a relativistic shell model. Nucl Phys A, 1984, 415: 497–519CrossRefGoogle Scholar
  20. 20.
    Kurasawa H, Suzuki T. Effective mass and particle-vibration coupling in the relativistic σ — ω model. Phys Lett B, 1985, 165: 234–238CrossRefGoogle Scholar
  21. 21.
    Yao J M, Mei H, Meng J, et al. Magnetic moment in relativistic mean field theory. High Energ Phys Nucl, 2006, 30(suppl. 2): 42–44Google Scholar
  22. 22.
    Li J, Meng J, Ring P, et al. Relativistic description of second-order correction to nuclear magnetic moments with point-coupling residual interaction. Sci China Phys Mech Astron, 2011, 54: 204–209CrossRefGoogle Scholar
  23. 23.
    Wolf A, Casten R F. Effective valence proton and neutron numbers in transitional A∼150 nuclei from B(E2) and g-factor data. Phys Rev C, 1987, 36: 851CrossRefGoogle Scholar
  24. 24.
    Zhang J Y, Casten R F, Wolf A, et al. Consistent interpretation of B(E2) values and g factors in deformed nuclei. Phys Rev C, 2006, 73: 037301CrossRefGoogle Scholar
  25. 25.
    Terasaki J, Engel J, Nazarewicz W, et al. Anomalous behavior of 21+ excitations around 132Sn. Phys Rev C, 2002, 66: 054313CrossRefGoogle Scholar
  26. 26.
    Bonneau L, Le Bloas J, Quentin P, et al. Effects of core polarization and pairing correlations on some ground-state properties of deformed odd-mass nuclei within the higher Tamm-Dancoff approach. Int JMod Phys E, 2011, 20: 252–258CrossRefGoogle Scholar
  27. 27.
    Jia L Y, Zhang H, Zhao Y M. Systematic calculations of low-lying states of even-even nuclei within the nucleon pair approximation. Phys Rev C, 2007, 75: 034307CrossRefGoogle Scholar
  28. 28.
    Forssen C, Caurier E, Navratil P. Charge radii and electromagnetic moments of Li and Be isotopes from the ab initio no-core shell model. Phys Rev C, 2009, 79: 021303CrossRefGoogle Scholar
  29. 29.
    Honma M, Otsuka T, Brown B A, et al. New effective interaction for pf-shell nuclei and its implications for the stability of the N = Z = 28 closed core. Phys Rev C, 2004, 69: 034335CrossRefGoogle Scholar
  30. 30.
    Brown B A, Stone N J, Stone J R, et al. Magnetic moments of the 21+ states around 132Sn. Phys Rev C, 2005, 71: 044317CrossRefGoogle Scholar
  31. 31.
    Shimizu N, Otsuka T, Mizusaki T, et al. Anomalous properties of quadrupole collective states in 136Te and beyond. Phys Rev C, 2006, 74: 059903CrossRefGoogle Scholar
  32. 32.
    Marcucci L E, Pervin M, Pieper S C, et al. Quantum Monte Carlo calculations of magnetic moments and M1 transitions in A ⩾ 7 nuclei including meson-exchange currents. Phys Rev C, 2008, 78: 065501CrossRefGoogle Scholar
  33. 33.
    Bian B A, Di Y M, Long G L, et al. Systematics of g factors of 21+ states in even-even nuclei from Gd to Pt: A microscopic description by the projected shell model. Phys Rev C, 2007, 75: 014312CrossRefGoogle Scholar
  34. 34.
    Alder K, Steffen R M. Electromagnetic moments of excited nuclear states. Ann Rev Nucl Sci, 1964, 14: 403–482CrossRefGoogle Scholar
  35. 35.
    Hill J C, Wohn F K, Wolf A, et al. Study of magnetic moments of nuclear excited states at Tristan. Hyperfine Interactions, 1985, 22: 449–457CrossRefGoogle Scholar
  36. 36.
    Benczer-Koller N, Kumbartzki G J, Gurdal G, et al. Measurement of g factors of excited states in radioactive beams by the transient field technique: 132Te. Phys Lett B, 2008, 664: 241–245CrossRefGoogle Scholar
  37. 37.
    Benczer-Koller N, Kumbartzki G J. Magnetic moments of short-lived excited nuclear states: Measurements and challenges. J Phys G, 2007, 34: R321CrossRefGoogle Scholar
  38. 38.
    Zheng Y N, Zhou D M, Yuan D Q, et al. Nuclear structure and magnetic moment of the unstable 12B-12N mirror pair. Chin Phys Lett, 2010, 27: 022102CrossRefGoogle Scholar
  39. 39.
    Yuan D Q, Fang P, Zheng Y N, et al. Study of dependence of quasiparticle alignment on proton and neutron numbers in A = 80 region through g-factor measurements. Hyperfine Interactions, 2010, 198: 129CrossRefGoogle Scholar
  40. 40.
    Yuan D, Zheng Y, Zuo Y, et al. The g-factors and magnetic rotation in 82Rb. Chin Phys B, 2010, 19: 062701CrossRefGoogle Scholar
  41. 41.
    Noya H, Arima A, Horie H. Nuclear moments and configuration mixing. Prog Theor Phys Suppl, 1958, 8: 33–112CrossRefGoogle Scholar
  42. 42.
    Chemtob M. Two-body interaction currents and nuclear magnetic moments. Nucl Phys A, 1969, 123: 449–470CrossRefGoogle Scholar
  43. 43.
    Shimizu K, Ichimura M, Arima A. Magnetic moments and GT type beta decay matrix elements in nuclei with a LS doubly closed shell plus or minus one nucleon. Nucl Phys A, 1974, 226: 282–318CrossRefGoogle Scholar
  44. 44.
    Towner I S, Khanna F C. Corrections to the single-particle M1 and Gamow-Teller matrix elements. Nucl Phys A, 1983, 399: 334–364CrossRefGoogle Scholar
  45. 45.
    Towner I S. Quenching of spin matrix elements in nuclei. Phys Rep, 1987, 155: 263–377CrossRefGoogle Scholar
  46. 46.
    Arima A, Shimizu K, Bentz W, et al. Nuclear magnetic properties and Gamow-Teller transitions. Adv Nucl Phys, 1987, 18: 1–106Google Scholar
  47. 47.
    Sun B H, Montes F, Geng L S, et al. Application of the relativistic mean-field mass model to the r-process and the influence of mass uncertainties. Phys Rev C, 2008, 78: 025806CrossRefGoogle Scholar
  48. 48.
    Sun B H, Meng J. Challenge on the astrophysical r-process calculation with nuclear mass models. Chin Phys Lett, 2008, 25: 2429CrossRefGoogle Scholar
  49. 49.
    Niu Z M, Sun B H, Meng J. Influence of nuclear physics inputs and astrophysical conditions on the Th/U chronometer. Phys Rev C, 2009, 80: 065806CrossRefGoogle Scholar
  50. 50.
    Zhang W H, Niu Z M, Wang F, et al. Uncertainties of nucleochronometers from nuclear physics inputs. Acta Phys Sin, 2012, 61: 112601Google Scholar
  51. 51.
    Meng J, Li Z P, Liang H Z, et al. Covariant density functional theory for nuclear structure and application in astrophysics. Nucl Phys A, 2010, 834: 436c–439cCrossRefGoogle Scholar
  52. 52.
    Meng J, Niu Z M, Liang H Z, et al. Selected issues at the interface between nuclear physics and astrophysics as well as the standard model. Sci China Phys Mech Astron, 2011 (suppl. 1), 54: 119–123CrossRefGoogle Scholar
  53. 53.
    Li Z, Niu Z M, Sun B H, et al. WLW mass model in nuclear r-process calculations. Acta Phys Sin, 2012, 61: 072601Google Scholar
  54. 54.
    Shepard J R, Rost E, Cheung C Y, et al. Magnetic response of closedshell ±1 nuclei in Dirac-Hartree approximation. Phys Rev C, 1988, 37: 1130–1141CrossRefGoogle Scholar
  55. 55.
    Ichii S, Bentz W, Arima A. Isoscalar currents and nuclear magnetic moments. Nucl Phys A, 1987, 464: 575–602CrossRefGoogle Scholar
  56. 56.
    Bentz W, Arima A, Hyuga H, et al. Ward identity in the many-body system and magnetic moments. Nucl Phys A, 1985, 436: 593CrossRefGoogle Scholar
  57. 57.
    McNeil J A, Amado R D, Horowitz C J, et al. Resolution of the magnetic moment problem in relativistic theories. Phys Rev C, 1986, 34: 746–749CrossRefGoogle Scholar
  58. 58.
    Hofmann U, Ring P. A new method to calculate magnetic moments in relativistic mean field theories. Phys Lett B, 1988, 214: 307–311CrossRefGoogle Scholar
  59. 59.
    Furnstahl R J, Price C E. Relativistic Hartree calculations of odd-A nuclei. Phys Rev C, 1989, 40: 1398–1413CrossRefGoogle Scholar
  60. 60.
    Li J, Zhang Y, Yao J M, et al. Magnetic moments of 33Mg in time-odd relativistic mean field approach. Sci China Ser G: Phys Mech Astron, 2009, 52: 1586–1592CrossRefGoogle Scholar
  61. 61.
    Yao J M, Chen H, Meng J. Time-odd triaxial relativistic mean field approach for nuclear magnetic moments. Phys Rev C, 2006, 74: 024307CrossRefGoogle Scholar
  62. 62.
    Nikšić T, Vretenar D, Ring P. Beyond the relativistic mean-field approximation: Configuration mixing of angular-momentum-projected wave functions. Phys Rev C, 2006, 73: 034308CrossRefGoogle Scholar
  63. 63.
    Yao J M, Meng J, Arteaga D P, et al. Three-dimensional angular momentum projected relativistic point-coupling approach for low-lying excited states in 24Mg. Chin Phys Lett, 2008, 25: 3609–3612CrossRefGoogle Scholar
  64. 64.
    Yao J M, Meng J, Ring P, et al. Three-dimensional angular momentum projection in relativistic mean-field theory. Phys Rev C, 2009, 79: 044312CrossRefGoogle Scholar
  65. 65.
    Yao J M, Meng J, Ring P, et al. Configuration mixing of angularmomentum projected triaxial relativistic mean-field wave functions. Phys Rev C, 2010, 81: 044311CrossRefGoogle Scholar
  66. 66.
    Yao J M, Mei H, Chen H, et al. Configuration mixing of angularmomentum projected triaxial relativistic mean-field wave functions. II. Microscopic analysis of low-lying states in magnesium isotopes. Phys Rev C, 2011, 83: 014308CrossRefGoogle Scholar
  67. 67.
    Morse T M, Price C E, Shepard J R. Meson exchange current corrections to magnetic moments in quantum hadro-dynamics. Phys Lett B, 1990, 251: 241–244CrossRefGoogle Scholar
  68. 68.
    Li J, Yao J M, Meng J, et al. One-pion exchange current corrections for nuclear magnetic moments in relativistic mean field theory. Prog Theor Phys, 2011, 125: 1185–1192CrossRefGoogle Scholar
  69. 69.
    Bentz W, Arima A. The orbital g-factor and related sum rules. Sci China Phys Mech Astron, 2011, 54: 194–197CrossRefGoogle Scholar
  70. 70.
    Zhao YM, Lei Y, Xu Z Y, et al. The nucleon pair approximation (NPA) of the shell model. Sci China Phys Mech Astron, 2011, 54: 215–221CrossRefGoogle Scholar
  71. 71.
    Yao J M, Peng J, Meng J, et al. g factors of nuclear low-lying states: A covariant description. Sci China Phys Mech Astron, 2011, 54: 198–203CrossRefGoogle Scholar
  72. 72.
    Iachello F. Dynamic symmetries at the critical point. Phys Rev Lett, 2000, 85: 3580–3583CrossRefGoogle Scholar
  73. 73.
    Iachello F. Analytic description of critical point nuclei in a sphericalaxially deformed shape phase transition. Phys Rev Lett, 2001, 87: 052502CrossRefGoogle Scholar
  74. 74.
    Casten R F, McCutchan E A. Quantum phase transitions and structural evolution in nuclei. J Phys G: Nucl Part Phys, 2007, 34: R285CrossRefGoogle Scholar
  75. 75.
    Cejnar P, Jolie J. Quantum phase transitions in the interacting boson model. Prog Part Nucl Phys, 2009, 62: 210CrossRefGoogle Scholar
  76. 76.
    Cejnar P, Jolie J, Casten R F. Quantum phase transitions in the shapes of atomic nuclei. Rev Mod Phys, 2010, 82: 2155–2212CrossRefGoogle Scholar
  77. 77.
    Zhang Y, Liu Y X, Hou Z F, et al. Relation between the E(5) symmetry and the interacting boson model beyond the mean-field approximation. Sci China Phys Mech Astron, 2011, 54: 227–230CrossRefGoogle Scholar
  78. 78.
    Meng J, Zhang W, Zhou S G, et al. Shape evolution for Sm isotopes in relativistic mean-field theory. Eur Phys J A, 2005, 25: 23CrossRefGoogle Scholar
  79. 79.
    Sheng Z Q, Guo J Y. Systematic analysis of critical point nuclei in the rare-earth region with relativistic mean field theory. Mod Phys Lett A, 2005, 20: 2711CrossRefGoogle Scholar
  80. 80.
    Li Z P, Nikšić T, Vretenar D, et al. Microscopic analysis of order parameters in nuclear quantum phase transitions. Phys Rev C, 2009, 80: 061301 (R)Google Scholar
  81. 81.
    Song C Y, Li Z P, Vretenar D, et al. Microscopic analysis of spherical to γ-soft shape transitions in Zn isotopes. Sci China Phys Mech Astron, 2011, 54: 222–226CrossRefGoogle Scholar
  82. 82.
    Mei H, Xiang J, Yao J M, et al. Rapid structural change in lowlying states of neutron-rich Sr and Zr isotopes. Phys Rev C, 2012, 85: 034321CrossRefGoogle Scholar
  83. 83.
    Faisal J Q, Hua H, Li X Q, et al. Shape evolution in the neytron-rich Ru isotopes. Phys Rev C, 2010, 82: 014321CrossRefGoogle Scholar
  84. 84.
    Luo Y A, Zhang Y, Meng X F, et al. Quantum phase transitional patterns in the SD-pair shell model. Phys Rev C, 2009, 80: 014311CrossRefGoogle Scholar
  85. 85.
    Zhang Y, Pan F, Liu Y X, et al. analytical description of odd-A nuclei near the critical point of the spherical to axially deformed shape transition. Phys Rev C, 2010, 82: 034327CrossRefGoogle Scholar
  86. 86.
    Zhang Y, Pan F, Liu Y X, et al. Simple description of odd-A nuclei around the critical point of the spherical to axially deformed shape phase transition. Phys Rev C, 2011, 84: 034306CrossRefGoogle Scholar
  87. 87.
    Zhang Y, Pan F, Liu Y X, et al. Critical point symmetries in deformed odd-A nuclei. Phys Rev C, 2011, 84: 054319CrossRefGoogle Scholar
  88. 88.
    Lunney D, Pearson J M, Thibault C. Recent trends in the determination of nuclear masses. Rev Mod Phys, 2003, 75: 1021–1082CrossRefGoogle Scholar
  89. 89.
    Liang Z Y, Liu J H, Liu M, et al. Study on ground state properties of nuclei with Weizsaecher-Skyrme nuclear mass formula. Nucl Phys Rev, 2011, 28: 257Google Scholar
  90. 90.
    Liu M, Wang N, Deng Y G, et al. Further improvements on a global nuclear mass model. Phys Rev C, 2011, 84: 014333CrossRefGoogle Scholar
  91. 91.
    Sun B H, Zhao P W, Meng J. Mass prediction of proton-rich nuclides with the Coulomb displacement energies in the relativistic pointcoupling model. Sci China Phys Mech Astron, 2011, 54: 210–214CrossRefGoogle Scholar
  92. 92.
    Jiang H, Fu G J, Zhao Y M, et al. Nuclear mass relations based on systematics of proton-neutron interactions. Phys Rev C, 2010, 82: 054317CrossRefGoogle Scholar
  93. 93.
    Fu G J, Lei Y, Jiang H, et al. Description and evaluation of nuclear masses based on residual proton-neutron interactions. Phys Rev C, 2011, 84: 034311CrossRefGoogle Scholar
  94. 94.
    Jiang H, Fu G J, Sun B, et al. Predictions of unknown masses and their applications. Phys Rev C, 2012, 85: 054303CrossRefGoogle Scholar
  95. 95.
    Wang N, Liu M. Nuclear mass predictions with a radial basis function approach. Phys Rev C, 2011, 84: 051303 (R)Google Scholar
  96. 96.
    Zhang S S, Lombardo U, Zhao E G. Comparison between microscopic and phenomenological nuclear pairing calculations. Sci China Phys Mech Astron, 2011, 54: 236–239CrossRefGoogle Scholar
  97. 97.
    Margueron J, Sagawa H, Hagino K. Effective pairing interactions with isospin density dependence. Phys Rev C, 2008, 77: 054309CrossRefGoogle Scholar
  98. 98.
    Zhang S S, Cao L G, Lombardo U, et al. Isospin-dependent pairing interaction from nuclear matter calculations. Phys Rev C, 2010, 81: 044313CrossRefGoogle Scholar
  99. 99.
    Che J Q. Nucleon-pair shell model: Formalism and special cases. Nucl Phys A, 1997, 626: 686CrossRefGoogle Scholar
  100. 100.
    Zhao Y M, Yoshinaga N, Yamaji S, et al. Nucleon-pair approximation of the shell model: Unified formalism for both odd and even systems. Phys Rev C, 2000, 62: 014304CrossRefGoogle Scholar
  101. 101.
    Lei Y, Xu Z Y, Zhao Y M, et al. SD-pair structure in the pair approximation of the nuclear shell model. Sci China Phys Mech Astron, 2010, 53: 1460CrossRefGoogle Scholar
  102. 102.
    Jiang H, Zhao Y M. Low-lying states of Hg isotopes within the nucleo pair approximation. Sci China Phys Mech Astron, 2011, 54: 1461CrossRefGoogle Scholar
  103. 103.
    Jiang H, Fu G J, Zhao Y M, et al. Low-lying structure of neutron-rich Zn and Ga isotopes. Phys Rev C, 2011, 84: 034302 (R)CrossRefGoogle Scholar
  104. 104.
    Zhang L H, Jiang H, Zhao Y M. Studies of low-lying states of eveneven Xe isotopes within the nucleo pair approximation. Sci China Phys Mech Astron, 2011, 54(suppl. 1): 103–108CrossRefGoogle Scholar
  105. 105.
    Luo Y A, Ning P Z. Nucleon-pair shell model: Magnetic excitations for ba isotopes. Commun Theor Phys, 2002, 37: 331Google Scholar
  106. 106.
    Luo Y A, Pan F, Ning P Z, et al. Sueface delta-interaction in nucleonpair shell model. Commun theor Phys, 2004, 42: 397Google Scholar
  107. 107.
    Luo Y A, Pan F, Ning P Z, et al. SD-pair shell model for identical nuclear systems. Chin Phys Lett, 2005, 22: 1366CrossRefGoogle Scholar
  108. 108.
    Wang F R, Liu L, Luo Y A, et al. U(5)-O(6) phase transition in SD-pair shell model. Chin Phys Lett, 2008, 25: 2432CrossRefGoogle Scholar
  109. 109.
    Zhou S G, Meng J, Yamaji S, et al. Deformed relativistic Hartree theory in coordinate space and in harmonic oscillator basis. Chin Phys Lett, 2000, 17: 717CrossRefGoogle Scholar
  110. 110.
    Zhou S G, Meng J, Ring P. Deformed relativistic Hartree-Bogoliubov model for exotic nuclei. In: Physics of Unstable Nuclei. Singapore: World Scientific Press, 2008. 402–408Google Scholar
  111. 111.
    Zhou S G, Meng J, Ring P, et al. Neutron halo in deformed nuclei. Phys Rev C, 2010, 82: 011301 (R)Google Scholar
  112. 112.
    Li L L, Meng J, Ring P, et al. Deformed relativistic Hartree-Bogoliubov theory in continuum. Phys Rev C, 2012, 85: 024312CrossRefGoogle Scholar
  113. 113.
    Li L L, Meng J, Ring P, et al. Odd Systems in deformed relativistic Hartree-Bogoliubov theory in continuum. Chin Phys Lett, 2012, 29: 042101.CrossRefGoogle Scholar
  114. 114.
    Zhang Y, Liang H Z, Meng J. Solving the Dirac equation with nonlocal potential by imaginary time step method. Chin Phys Lett, 2009, 26: 092401CrossRefGoogle Scholar
  115. 115.
    Li F Q, Zhang Y, Liang H Z, et al. Optimization of the imaginary time step evolution for the Dirac equation. Sci China Phys Mech Astron, 2011, 54: 231–235CrossRefGoogle Scholar
  116. 116.
    Meng J, Liu Y X, Zhou S G. Editoral. Sci China Ser G: Phys Mech Astron, 2009, 52: 1449Google Scholar
  117. 117.
    Cao Z X, Ye Y L. Study of the structure of unstable nuclei through the reaction experiments. Sci China Phys Mech Astron, 2011, 54(suppl. 1): 1–5CrossRefGoogle Scholar
  118. 118.
    Zhao E G, Wang F. Recent progresss in theoretical nuclear physics related to large-scale scientific facilities. Chin Sci Bull, 2011, 56: 3797–3802CrossRefGoogle Scholar

Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Institute of Theoretical PhysicsChinese Academy of SciencesBeijingChina
  2. 2.Center of Theoretical Nuclear PhysicsNational Laboratory of Heavy Ion AcceleratorLanzhouChina

Personalised recommendations