Exploring effects of tensor force and its strength via neutron drops

The tensor-force effects on the evolution of spin-orbit splittings in neutron drops are investigated within the framework of the relativistic Hartree-Fock theory.For a fair comparison on the pure mean-field level,the results of the relativistic Brueckner-Hartree-Fock calculation with the Bonn A interaction are adopted as meta-data.Through a quantitative analysis,we certify that the π-psendovector(π-PV) coupling affects the evolutionary trend through the embedded tensor force.The strength of the tensor force is explored by enlarging the strength f_π of the π-PV coupling.It is found that weakening the density dependence of f_π is slightly better than enlarging it with a factor.We thus provide a semiquantitative support for the renormalization persistency of the tensor force within the framework of density functional theory.This will serve as important guidance for further development of relativistic effective interactions with particular focus on the tensor force.     

张量力对原子核性质的影响(英文)

最近一段时期, 对张量力性质研究成为原子核结构研究的热点之一。 基于自洽的Skyrme平均场理论讨论了张量力研究的最新进展。 同时, 讨论了张量力和Skyrme能量密度中的中心交换项对原子核单粒子态的演化以及多极巨共振的贡献。 发现考虑张量力贡献后,利用Skyrme平均场计算可以基本描述Z=50和N=82原子核单粒子态演化的实验结果。而张量力对于原子核电多极巨共振基本没有影响,只对其低能集体态有一定的影响。 张量力的引入使得原子核磁单极巨共振的能量和强度发生显著的改变。 通过对数值结果的分析,发现张量力会产生吸引的粒子-空穴剩余相互作用。The impact of the tensor force on the properties of finite nuclei is discussed by analyzing the spin orbit splittings and the multipole giant resonances in nuclei. It is found that the tensor force do plays an important role in nuclear structure. The experimental isospin dependence of the spin orbit splitting is very well depicted when the tensor force is included. The tensor force has a larger effect on the spin flip magnetic dipole states than on the natural parity isoscalar quadrupole(2+) states. By analyzing the modifications to the Hartree Fock mean field induced by the tensor terms,and the specific features of the residual particle hole tensor interaction,we find that the tensor force gives an attractive contribution to the particle hole matrix elements.     

Effect of tensor force on the density dependence of symmetry energy within the BHF framework

The effect of tensor force on the density dependence of nuclear symmetry energy has been investigated within the framework of the Brueckner-Hartree-Fock(BHF) approach. It is shown that the tensor force manifests its effect via the tensor 3 S D1channel. The density dependence of symmetry energy Esym turns out to be determined essentially by the tensor force from the π meson and ρ meson exchanges via the 3 S D1 coupled channel. Increasing the strength of the tensor component due to the ρ-meson exchange tends to enhance the repulsion of the equation of state of symmetric nuclear matter and leads to the reduction of symmetry energy. The present results confirm the dominant role played by the tensor force in determining nuclear symmetry energy and its density dependence within the microscopic BHF framework.     

Effect of tensor force on the density dependence of symmetryenergy within the BHF framework

The effect of tensor force on the density dependence of nuclear symmetry energy has been investigated within the framework of the Brueckner-Hartree-Fock (BHF) approach. It is shown that the tensor force manifests its effect via the tensor ³SD₁ channel. The density dependence of symmetry energy E_sym turns out to be determined essentially by the tensor force from the π meson and ρ meson exchanges via the ³SD₁ coupled channel. Increasing the strength of the tensor component due to the ρ-meson exchange tends to enhance the repulsion of the equation of state of symmetric nuclear matter and leads to the reduction of symmetry energy. The present results confirm the dominant role played by the tensor force in determining nuclear symmetry energy and its density dependence within the microscopic BHF framework.     

Evolution of N = 20, 28, 50 shell closures in the 20 ≤ Z ≤ 30 region in deformed relativistic Hartree-Bogoliubov theory in continuum

Magicity,or shell closure,plays an important role in our understanding of complex nuclear phenomena.In this work,we employ one of the state-of-the-art density functional theories,the deformed relativistic HartreeBogoliubov theory in continuum(DRHBc) with the density functional PC-PK1,to investigate the evolution of the N=20,28,50 shell closures in the 20 ≤Z ≤30 region.We show how these three conventional shell closures evolve from the proton drip line to the neutron drip line by studying the cha...     

张量力在16O+16O熔合动力学中的效应（英文）

利用时间相关Hartree-Fock 理论和完整Skyrme 有效相互作用研究了16O+16O 碰撞在库仑位垒附近的熔合动力学。数值计算是在没有任何对称性约束的三维笛卡尔基下完成。将时间相关Hartree-Fock 理论和冻结密度近似下的能量密度泛函方法给出的库仑位垒与实验结果进行了比较,发现同位旋标量的张量项能降低自旋饱和体系16O+16O的库仑位垒,而库仑位垒高度随着同位旋矢量的张量项的耦合常数减小而降低。并计算了包含和不包含张量力的16O+16O熔合截面,发现张量力对16O+16O碰撞在库仑位垒附近的熔合动力学影响较小。The fusion dynamics of 16O+16O around Coulomb barrier has been studied in the timedependent Hartree-Fock (TDHF) theory with the full Skyrme effective interaction. The calculations have been carried out in three-dimensional Cartesian basis without any symmetry restrictions. We have included the full tensor force and all the time-odd terms in Skyrme energy density functional (EDF). The Coulomb barrier obtained from the dynamical TDHF calculations and EDF with frozen density approximation has been compared with the available experimental data. The isoscalar tensor terms and the rearrangement of other terms are found to decrease the barrier height in the spin-saturated system 16O+16O, while the energy of Coulomb barrier tends to decrease as the isovector coupling constant decreases. The fusion cross section for 16O+16O collision has been calculated with and without the tensor force. We found that the tensor force has minor effect on the fusion dynamics of 16O+16O at the energies around Coulomb barrier.     

Restoration of pseudo-spin symmetry in N = 32 and N = 34 isotones described by relativistic Hartree-Fock theory

The restoration of pseudo-spin symmetry(PSS) along the N = 32 and N = 34 isotonic chains and the physics behind are studied by applying the relativistic Hartree-Fock theory with the effective Lagrangian PKA1. Taking the proton pseudo-spin partners(π2s_(1/2), π1d_(3/2)) as candidates, the systematic restoration of PSS along both isotonic chains is found from sulphur(S) to nickel(Ni), while an obvious PSS violation from silicon(Si) to sulphur is discovered near the drip lines. The effects of the tensor force components are investigated, introduced naturally by the Fock terms, which can only partially interpret the systematics from calcium to nickel, whereas they fail for the overall trends. Further analysis following the Schr?dinger-like equation of the lower component of Dirac spinor shows that contributions from the Hartree terms dominate the overall systematics of the PSS restoration. Such effects can be self-consistently interpreted by the evolution of the proton central density profiles along both isotonic chains. In particular, the PSS violation is found to tightly relate to the dramatic changes from the bubble-like density profiles in silicon to the central-bumped ones in sulphur.     

相对论小分量波函数对原子光电离截面的影响

利用相对论平均自洽场理论,　研究了相对论波函数的小分量对原子光电离截面的影响。原子核尺寸效应将使波函数小分量对原子光电离截面的影响减弱。由于波函数沿径向空间被压缩,　电子离核的平均半径较小,　波函数小分量对高离化态离子光电离截面的影响比对一般原子要强得多。波函数小分量反映了相对论效应的基本特征,　从而也定性地说明了光电离过程中相对论效应的强弱。The effects of relativistic small radial component on atomic photoionization cross sections have been studied within relativistic average self consistent field theory. Relativistic effects are relatively unimportant for low photon energy, along with a review of high energy photoionization the relativistic effects are quite important. The effects of relativistic small radial component on photoionization process should show breakdown when the nuclear finite size effects is taken into account. The compression of wavefunction into the space near nucleus is so strong in highly charged ions that the electronic radius greatly decreases, and the effects of relativistic small radial component on photoionization cross sections turn to stronger than ordinary atoms. Since relativistic effects are extremely sensitive to the behavior of small radial component, the results are in good agreement with relativistic effects on photoionization cross section.     

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.     

Proton Fraction in Neutron Star Matter and Three-Body Force Effects

The three-body force effects on the equation of state and its iso-spin dependence of asymmetric nuclear matter and on the proton fraction in neutron star matter have been investigated[1] within Brueckner Hartree-Fock (BHF) approach by using a microscopic three-body force. It is shown that, even in the presence of the three-body force, the empirical parabolic law of the energy per nucleon vs. isospin asymmetry β=(N-Z)/A is fulfilled in the whole asymmetry range 0 ≤β ≤1 and also up to high density. The three-body force provides a strong enhancement of symmetry energy at high density in agreement with relativistic approaches. Thecalculated proton fraction in β stable neutron star matter is given in Fig.l, where the thick solid line is the BHF prediction using AV18 TBF, while the dotted one is the BHF result using AVis. The thin solid line is the prediction of the Dirac-Brueckner approach taken from Ref.[2]. The results extracted according to the phenomenological paramete rizations of the symmetry energy suggested in Ref.[3] are also plotted. It is seen from     

Nucleon momentum distribution of ~(56)Fe from the axially deformed relativistic mean-field model with nucleon-nucleon correlations

Nucleon momentum distribution(NMD), particularly its high-momentum components, is essential for understanding the nucleonnucleon(NN) correlations in nuclei. Herein, we develop the studies of NMD of ~(56)Fe from the axially deformed relativistic mean-field(RMF) model. Moreover, we introduce the effects of NN correlation into the RMF model from phenomenological models basing on deuteron and nuclear matter. For the region k k_F, the effects of deformation on the NMD of the RMF model are investigated using the total and single-particle NMDs. For the region k k_F, the high-momentum components of the RMF model are modified by the effects of NN correlation, which agree with the experimental data. Comparing the NMD of relativistic and non-relativistic mean-field models, the relativistic effects on nuclear structures in momentum space are analyzed. Finally, by analogizing the tensor correlations in deuteron and Jastrow-type correlations in nuclear matter, the behaviors and contributions of NN correlations in ~(56)Fe are further analyzed, which helps clarify the effects of the tensor force on the NMD of heavy nuclei.     

Nuclear relativistic Hartree-Fock approximation with weakened pion tensor force

Properties linked to the single-particle energies, as nuclear spectra, spin-orbit splittings and shell gaps are investigated in the framework of the relativistic Hartree-Fock approximation with pseudovector coupling for the πN vertex. The role of an effective mass of pions moving in the nuclear medium and its relationship with the strength of pion tensor force is discussed. A simple method to reduce the contribution of this tensor force that considerably improves the single-particle spectrum of nuclei is proposed.     

Calculation of the ground state properties of even-even Sn isotopes

We investigate the ground-state properties of even-even Sn isotopes using the Skyrme-Hartree-Fock (SHF) and Skyrme-Hartree-Fock-Bogolyubov (SHFB) methods with SKM* and SLy4 force parameters. We focus on isotopes of even-even Sn because these isotopes are vital to the structural studies of unstable nuclei taking place at the electron radioactive-ion collider at RIKEN. In the present paper, we calculate the binding energies per particle, the rms nuclear charge radii, the rms nuclear proton density radii, and the rms nuclear neutron density radii, for even-even Sn isotopes, using the SHF and SHFB methods. We compare our results with experimental data and with the results of relativistic mean-field theory. Notably, we fit our calculated binding energies per particle to experimental results, using the aforementioned SHF methods with SKM* and SLy4 parameters     

A generalized quantum kinetic equation for models of relativistic nuclear dynamics

Zubarev’s method of non-equilibrium statistical operator is applied to problems of relativistic kinetic theory. Within this method, a generalized relativistic quantum kinetic equation for the relativistic Wigner function is derived with taking into account the drift term of the Vlasov type and the collision integral of the second order in particle interaction. It is shown that this result holds as well for gauge invariant theories in the case of slowly changing fields. An advantage of the developed approach is exemplified by the consideration of relativistic nuclear matter within the Walecka and Nambu-Jona-Lasinio models. Typical relativistic effects like retardation, spin degrees of freedom and antiparticle evolution are taken into consideration.     

The nuclear symmetry energy from relativistic Brueckner-Hartree-Fock model

The microscopic mechanisms of the symmetry energy in nuclear matter are investigated in the framework of the relativistic Brueckner-Hartree-Fock (RBHF) model with a high-precision realistic nuclear potential, pvCDBonn A. The kinetic energy and potential contributions to symmetry energy are decomposed. They are explicitly expressed by the nucleon self-energies, which are obtained through projecting the G-matrices from the RBHF model into the terms of Lorentz covariants. The nuclear medium effects on the nucleon self-energy and nucleon-nucleon interaction in symmetry energy are discussed by comparing the results from the RBHF model and those from Hartree-Fock and relativistic Hartree-Fock models. It is found that the nucleon self-energy including the nuclear medium effect on the single-nucleon wave function provides a largely positive contribution to the symmetry energy, while the nuclear medium effect on the nucleon-nucleon interaction, i.e., the effective G-matrices provides a negative contribution. The tensor force plays an essential role in the symmetry energy around the density. The scalar and vector covariant amplitudes of nucleon-nucleon interaction dominate the potential component of the symmetry energy. Furthermore, the isoscalar and isovector terms in the optical potential are extracted from the RBHF model. The isoscalar part is consistent with the results from the analysis of global optical potential, while the isovector one has obvious differences at higher incident energy due to the relativistic effect.     

Tensor optimized antisymmetrized molecular dynamics for relativistic nuclear matter

We apply a newly developed many-body theory, tensor optimized antisymmetrized molecular dynamics (TOAMD), to nuclear matter using a relativistic bare nucleon-nucleon interaction in the relativistic framework. It becomes evident that the tensor interaction plays an important role in nuclear many-body system due to the role of the pion in a strongly interacting system. We take the relativistic nuclear matter (RNM) wave function as a basic state and add tensor and short-range correlation operators in the form of pion and omega-meson correlation functions acting on the RNM wave function using the concept of TOAMD. We use the Monte Carlo (Metropolis) method based on the Gaussian integration and the second quantization method for antisymmetrization to calculate all the matrix elements of the many-body Hamiltonian. We write the whole formula of the TOAMD method for numerical calculations of the nuclear binding and saturation properties of nuclear matter using one-boson exchange potential.     

COMPARISON OF THE EFFECTIVE NUCLEAR INTERACTIONS IN NON-RELATIVISTIC AND RELATIVISTICM ICROSCOPIC CALCULATIONS

The microscopic calculations of the effective nuclear interactions in the Landav Fermi-Liquid theory were performed in the framework of both the nonrelativistic Brueckner theory and rela-tivistic mean-field theory. The Landau parameters obtained from the relativistic approach exhibit a strong density dependence.In the vicinity of the nuclear saturation density the strong density dependence of the scalar and isoscalar Landau parameter F₀ has somewhat eased up by the many-body force of nucleons.     

Ground state properties of 16O, 40Ca and 48Ca in a relativistic Hartree theory of nuclear matter

A relativistic field theory model of nuclear matter is solved in a Hartree approximation for finite nuclei. We show that the theory predicts small shell effects for the charge-density distributions in magic nuclei and is in agreement with recent electron scattering data. The effects of the small component of the relativistic wave function are investigated as well as the role of the isospin-dependent force generated by the rho field.