基于相对论平均场有效对力的中子物质BCS-BEC渡越

基于核物质的相对论Hartree-Bogoliubov（RHB）理论,采用相对论平均场单玻色子交换形式的有效对相互作用,研究了不同对力强度下双中子关联及其中的BCS-BEC渡越现象。通过引入有效衰减因子χ调节对力强度,定量分析费米面处中子对能隙和单粒子动能比值△_Fn/e_Fn及无量纲参数1/（k_Fna）随费米动量k_Fn的演化行为,发现双中子对在χ=0.51时进入BCS-BEC渡越区域,在χ=0.67时可达到幺正极限。进而分析了中子对能隙、中子对波函数及相干长度等物理量在相应临界点处的特征,并给出渡越时双中子短程关联概率的定量判据。发现当配对中子处于平均中子间距以内的概率P（d_n）?0.80时,双中子对从纯BCS耦合过渡到BCS-BEC渡越区域。Based on the relativistic Hartree-Bogoliubov theory in nuclear matter, the dineutron correlations and the crossover from Bardeen-Cooper-Schrieffer (BCS) region of neutron Cooper pairs to Bose-Einstein condensation (BEC) are investigated with the one-boson-exchange type of pairing force generated from the relativistic mean field (RMF) model. By introducing an effective factor χ in the RMF effective pairing interaction, the density dependence of the ratios between neutron pairing gap at Fermi surface and neutron Fermi kinetic energy △_Fn/e_Fn and the dimensionless parameter 1/(k_Fna) are analyzed quantitatively. Then the criteria where dineutron correlations exactly reach the threshold of BCS-BEC crossover or unitary limit are determined to be χ=0.51 or 0.67, respectively. In addition, features of neutron pairing gap, Cooper pair wave function and dineutron coherence length are illustrated, and the value of the probability for partner neutrons correlated within the average inter-neutron distance, namely P (d_n) ?0.80, is obtained as a criterion of BCS-BEC crossover.     

Neutron star equation of state in density dependent relativistic Hartree-Fock theory

The equation of state of neutron stars is studied in the newly developed density dependent relativistic Hartree-Fock (DDRHF) theory with the effective interaction PKO1 and applied to describe the properties of neutron stars. The results are compared with the recent observational data of compact stars and those calculated with the relativistic mean field (RMF) effective interactions. The maximum mass of neutron stars calculated with PKO1 is about 2.45 M_⊙, which consists with high pulsar mass from PSR B1516+02B recently reported. The influence of Fock terms on the cooling of neutron stars is discussed as well.     

适用于轻核区的相对论平均场理论新参数

考虑对关联和微观质心修正效应, 适用于轻核区的两组相对论平均场理论新参数被提出:包含σ, ω介子非线性自耦合项的NLLN和包含密度依赖的介子-核子耦合项的DDLN. 对于Z≤8轻核区β稳定线附近以及远离β稳定线的原子核, 新参数对结合能等基态性质给出了比已有参数更好的描述. 同时, 新参数给出O同位素的中子滴线核为²⁶O, ²⁴O中新幻数N=16的出现也能够被合理解释.     

基于实稳定方法求解单粒子共振态的Wigner函数

利用坐标空间的实稳定方法,求解了一维势场中单粒子散射态与其中共振态的本征值问题,由得到的单粒子本征波函数进一步给出相应的Wigner函数,分析了单粒子散射态与其中共振态的相空间分布特征.发现除了本征能量与本征波函数存在差异,Wigner函数在相空间的具体分布行为也可用于区分单粒子共振态与一般的散射态,在相关的量子测量实验中可能用作确定量子态的特征判据.     

一维谐振子势阱中二全同粒子的空间关联

针对一维谐振子势阱中由两个全同粒子组成的体系,假设其空间波函数分别具有以下3种交换对称性:1)没有交换对称性,2)对于交换是反对称情况,3)对于交换是对称情况,讨论了二粒子空间相对位置的分布概率.并由此将量子力学教材中自由粒子情况下的结论推广至一维谐振子束缚态情形,即两个全同粒子无论是处于自由态还是束缚态,在空间波函数交换对称的情况下,两个粒子靠拢的概率最大,而交换反对称情况下,两个粒子靠近(r→0)的概率趋于零.论文结论有助于加深对量子力学中全同粒子交换对称性及其物理效应的理解.     

Relativistic interpretation of the nature of the nuclear tensor force

The spin-dependent nature of the nuclear tensor force is studied in detail within the relativistic HartreeFock approach. The relativistic formalism for the tensor force is supplemented with an additional Lorentz-invariant tensor formalism in the a-scalar channel, so as to take into account almost fully the nature of the tensor force brought about by the Fock diagrams in realistic nuclei. Specifically, the tensor sum rules are tested for the spin and pseudospin partners with and without nodes, to further understand the nature of the tensor force within the relativistic model. It is shown that the interference between the two components of nucleon spinors causes distinct violations of the tensor sum rules in realistic nuclei, mainly due to the opposite signs on the κ quantities of the upper and lower components, as well as the nodal difference. However, the sum rules can be precisely reproduced if the same radial wave functions are taken for the spin/pseudo-spin partners in addition to neglecting the lower/upper components,revealing clearly the nature of the tensor force.     

核物质四阶对称能中的交换项相关物理

基于协变密度泛函（CDF）理论,核物质四阶对称能可以被分解为动能部分,同位旋单态势能部分以及同位旋三重态势能部分。交换项的引入明显改变了同位旋单态势能部分和同位旋三重态势能部分的密度行为,特别是来自同位旋标量介子-核子耦合道的交换项贡献提供了一个压制作用。作为一种有益的尝试,引入广义的对称能,可以更直观地统一描述核物质各阶对称能效应。The density dependence of nuclear fourth-order symmetry energy S₄ is studied within the covariant density functional (CDF) theory in terms of the kinetic energy, isospin-singlet, and isospin-triplet potential energy parts of the energy density functional. When the Fock diagram is introduced, it is found that both isospin-singlet and isospin-triplet components of the potential energy plays important roles in determining the fourth-order symmetry energy. Especially, an extra suppression, which comes from the Fock terms via isoscalar meson-nucleon coupling channels, is revealed in the isospin-triplet potential part of the fourth-order symmetry energy. As an useful attempt, the generalized symmetry energy is introduced to describe the various orders of nuclear symmetry energies in a visual and self-consistent way.     

Deformation Effect on the Center-of-Mass Correction Energy in Nuclei Ranging from Oxygen to Calcium

The microscopic c.m. correction energies for nuclei ranging from oxygen to calcium are systematically calculated by both spherical and axially deformed relativistic mean-field （RMF） models with the effective interaction PK1. The microscopic c.m. correction energies strongly depend on the isospin as well as deformation and deviate from the phenomenological ones. The deformation effect is discussed in detail by comparing the deformed with the spherical RMF calculation. It is found that the direct and exchange terms of the c.m. correction energies are strongly correlated with the density distribution of nuclei and are suppressed in the deformed case.     

RMF理论中Zr同位素链壳结构的形变依赖性

基于球形与轴对称形变的相对论平均场（Relativistic Mean Field, 简称RMF）理论模型, 分别计算了Zr同位素链的基态总能量, 并根据其差值提取了形变修正能后发现, Zr同位素链丰中子区的核具有大的长椭形变, 对应的形变修正能可达到10 MeV。 利用RMF理论计算的基态能量, 在扣除液滴模型计算的结合能后, 得到了Zr同位素链的壳修正能。 通过对壳修正能的分析后发现, 形变使N=50壳效应显著减弱。 特别是在丰中子区, 大形变导致了N=50壳结构的消失。 The total binding energy of nuclei for Zr isotopic chain is calculated by the spherical and axial deformed relativistic mean field(RMF) theory respectively, and the energy contribution due to the deformation(i.e., deformation correction energy) is extracted. It is found that the neutron rich nuclei in the isotopic chain have large prolate deformation, and corresponding deformation correction energy can be up to 10 MeV. The shell correction energy is obtained by the difference between the binding energies calculated by the liquid model and those by the RMF calculations. Detailed analysis indicates that the deformation weakens the shell effect of N=50 remarkably. Especially for the neutron rich nuclei, large deformation leads to disappearance of the N=50 shell structure.