The low-lying spectra of7 Li and9Li are investigated within an ab initio Monte Carlo Shell Model（MCSM） employing a realistic potential obtained via the Unitary Correlation Operator Method（UCOM）. The MCSM calculations in a 4-major-shells model space for the binding energy and mass quadrupole moment of7, 9Li show good convergence when the MCSM dimension reaches 20. The excitation energy of the Jπ= 1/2-state for7 Li and the magnetic moments for7, 9Li ground states in the MCSM with a treatment of spurious center-of-mass motion are close to the experimental data. Correct level ordering of Jπ=3/2-and 1/2-states for7, 9Li can be reproduced due to the inclusion of three-body correlations in the MCSM＋UCOM. However, the excitation energy of Jπ=1/2-state for9 Li is not reproduced in the MCSM mainly due to the lack of larger model space.
Within the relativistic mean field （RMF） theory, the ground state properties of dysprosium isotopes are studied using the shell-model-like approach （SLAP）, in which pairing correlations are treated with particle- number conservation, and the Pauli blocking effects are taken into account exactly. For comparison, calculations of the Bardeen Cooper Schrieffer （BCS） model with the RMF are also performed. It is found that the RMF＋SLAP calculation results, as well as the RMF＋BCS ones, reproduce the experimental binding energies and one- and twoneutron separation energies quite well. However, the RMF＋BCS calculations give larger pairing energies than those obtained by the RMF＋SLAP calculations, in particular for nuclei near the proton and neutron drip lines. This deviation is discussed in terms of the BCS particle-number fluctuation, which leads to the sizable deviation of pairing energies between the RMF＋BCS and RMF＋SLAP models, where the fluctuation of the particle number is eliminated automatically.
The magnetic moment of 2＋1 state for 10Be are calculated and investigated in terms of single particle orbits for protons and neutrons under the framework of ab initio Monte Carlo shell model method in an emax=3 model space. The reduced matrix elements of orbital and spin angular momentum are evaluated. It is found that the orientations of orbital angular momentum in different single particle orbits are consistent. Conversely, the orientations of spin in different single particle orbits tend to be chaotic. The nuclear magnetic moment of 2＋1 state for 10Be is obtained as 1.006 ,UN and is discussed in regards to the contribution of orbital and spin angular momentum both for protons and neutrons. The corresponding g-factor is also given.
The unitary correlation operator method （UCOM） and the similarity renormalization group theory （SRG） are compared and discussed in the framework of the no-core Monte Carlo shell model （MCSM） calculations for ^3H and ^4He. The treatment of spurious center-of-mass motion by Lawson＇s prescription is performed in the MCSM calculations. These results with both transformed interactions show good suppression of spurious center-of-mass motion with proper Lawson＇s prescription parameter βc.m. values. The UCOM potentials obtain faster convergence of total energy for the ground state than that of SRG potentials in the MCSM calculations, which differs from the cases in the no-core shell model calculations （NCSM）. These differences are discussed and analyzed in terms of the truncation scheme in the MCSM and NCSM, as well as the properties of the potentials of SRG and UCOM.
本文介绍了协变密度泛函理论研究热原子核对关联的工作.该工作在协变密度泛函理论框架下,引入严格保持粒子数守恒的类壳模型方法来处理对关联.基于正则系综理论分析了^(162)Dy原子核的热力学性质,计算了该原子核的比热容,得到了随温度变化的"S"型曲线,发现对关联对此"S"型曲线至关重要.在保持粒子数守恒的条件下,对能隙随温度平滑变化,表明原子核从超流态转变到正常态.该工作还分析了不同辛弱数对热原子核的影响,发现温度在1 Me V以内,热原子核的性质主要由辛弱数为0,2和4的态所决定.
The effects of pairing correlation in Yb isotopes are investigated by covariant density functional theory with pairing correlations and blocking effects treated exactly by a shell model like approach （SLAP）. Experimental one- and two-neutron separation energies are reproduced quite well. The traditional BCS calculations always give larger pairing energies than those given by SLAP calculations, particularly for the nuclei near the proton and neutron drip lines. This may be caused because many of the single particle orbits above the Fermi surface are involved in the BCS calculations, but many of them are excluded in the SLAP calculations.
