The convergence for the Imaginary Time Step (ITS) evolution with time step is investigated by performing the ITS evolution for the Schrdinger-like equation and the charge-conjugate Schrdinger-like equation deduced from Dirac equation for the single proton levels of 12C in both the Fermi and Dirac seas. For the guaranteed convergence of the ITS evolution to the "exact" results,the time step should be smaller than a "critical" time step Δtc for a given single-particle level. The "critical" time step Δtc is more sensitive to the quantum numbers |κ| than to the energy of the single-particle level. For the single-particle levels with the same κ,their "critical" time steps are in the same order. For the single-particle levels with similar energy,a relatively small (large) "critical" time step for larger (smaller) |κ| is needed. These conclusions can be used in the future self-consistent calculation to optimize the evolution procedure.
LI FangQiong1,ZHANG Ying2 & MENG Jie2,3,4 1Guizhou University for Nationalities,Guiyang 550025,China
The density functional theory (DFT) with a minimal number of parameters allows a very successful phenomenological description of ground state properties of nuclei all over the periodic table. The recent developments on the application of the covariant density functional theory as well as its extensions by the group in Beijing for a series of interests and hot topics in nuclear astrophysics and nuclear structure are reviewed, including the rapid neutron-capture process, Th/U chronometer, and isospin corrections for superallowed β transitions.
MENG Jie1,2,3, NIU ZhongMing1, LIANG HaoZhao1 & SUN BaoHua2,4 1State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871, China
The g factors and spectroscopic quadrupole moments of low-lying excited states 2+1,…,81+ in 24Mg are studied in a covariant density functional theory.The wave functions are constructed by configuration mixing of axially deformed mean-field states projected on good angular momentum.The mean-field states are obtained from the constraint relativistic point-coupling model plus BCS calculations using the PC-F1 parametrization for the particle-hole channel and a density-independent delta-force for the particle-particle channel.The available experimental g factor and spectroscopic quadrupole moment of 21+ state are reproduced quite well.The angular momentum dependence of g factors and spectroscopic quadrupole moments,as well as the effects of pairing correlations are investigated.
Using the single particle states and the residual interaction derived from the relativistic point-coupling model with the PC-F1 parameter set,the second-order core polarization corrections to nuclear magnetic moments of LS closed shell nuclei ±1 nucleon with A = 15,17,39 and 41 are studied and compared with previous non-relativistic results.It is found that the second-order corrections are significant.With these corrections,the isovector magnetic moments of the concerned nuclei are well reproduced,especially those for A = 17 and A = 41.
The rapid transition between spherical and γ-soft shapes in Zn isotopes in the mass A 70 region,is analyzed using excitation spectra and collective wave functions obtained by diagonalization of a five-dimensional Hamiltonian for quadrupole vibrational and rotational degrees of freedom,with parameters determined by constrained self-consistent relativistic mean-field calculations for triaxial shapes.The microscopic potential energy surfaces,together with the characteristic collective observables,illustrate a rapid transition from near spherical shape at the N = 40 subshell,to γ-soft deformed shapes for lighter isotopes.The calculated spectra display fingerprints of a second-order shape phase transition that can be approximately described by the E(5) analytic solution.
Taking the single neutron levels of 12C in the Fermi sea as examples,the optimization of the imaginary time step(ITS) evolution with the box size and mesh size for the Dirac equation is investigated.For the weakly bound states,in order to reproduce the exact single-particle energies and wave functions,a relatively large box size is required.As long as the exact results can be reproduced,the ITS evolution with a smaller box size converges faster,while for both the weakly and deeply bound states,the ITS evolutions are less sensitive to the mesh size.Moreover,one can find a parabola relationship between the mesh size and the corresponding critical time step,i.e.,the largest time step to guarantee the convergence,which suggests that the ITS evolution with a larger mesh size allows larger critical time step,and thus can converge faster to the exact result.These conclusions are very helpful for optimizing the evolution procedure in the future self-consistent calculations.
LI FangQiong1,ZHANG Ying2,LIANG HaoZhao2,3 & MENG Jie4,2,5 1Guizhou University for Nationalities,Guiyang 550025,China
With experimental masses updated from AME11,the predictive power of relativistic mean-field(RMF) mass model is carefully examined and compared with HFB-17,FRDM,WS*,and DZ28 mass models.In the relativistic mean-field model,the calculation with the PC-PK1 has improved significantly in describing masses compared to the TMA,especially for the neutron-deficient nuclei.The corresponding rms deviation with respect to the known masses falls to 1.4 MeV.Furthermore,it is found that the RMF mass model better describes the nuclei with large deformations.The rms deviation for nuclei with the absolute value of quadrupole deformation parameter greater than 0.25 falls to 0.93,crossing the 1 MeV accuracy threshold for the PC-PK1,which may indicate the new model is more suitable for those largely-deformed nuclei.In addition,the necessity of new high-precision experimental data to evaluate and develop the nuclear mass models is emphasized as well.
