Pion tensor force and nuclear binding energy in the relativistic Hartree-Fock formalism

The binding energies of several isotopic families are studied within the relativistic Hartree-Fock approximation with the pseudovector coupling for the πN vertex, to find out a suitable strength for the effective pion tensor force (EPTF). An approximation for determining separately the contributions of the central and tensor forces generated by pion is considered. The results for heavy nuclei indicate that a realistic strength for the EPTF is smaller than a half of that appearing in the OPEP. This conclusion also applies to the results for the single-particle energies. Besides, it has been found that there is a genuine relativistic contribution of the EPTF in nuclear matter which is small but significant.     

协变密度泛函理论中的张量力效应

张量力是核子-核子相互作用的重要成分,被认为是理解奇特原子核中壳结构演化规律的关键要素。然而,目前对于核介质中的张量力及其效应的定量认识,仍存在很多亟待解决的关键问题。着重梳理了在原子核密度泛函理论框架下,研究有效相互作用中的张量力成分以及相应的张量力效应的相关工作,重点包括:基于相对论Hartree-Fock理论,以同位素链中的质子幻数壳演化为例,定量提取与分析其中的张量力效应;以及基于第一性原理的相对论Brueckner-Hartree-Fock理论,以中子滴单粒子能谱中的自旋-轨道劈裂演化为例,提出与张量力效应相关联的"准实验数据"。最后,展望原子核密度泛函理论今后可能的发展策略。Tensor force is one of the most important components of the nucleon-nucleon interaction. It plays a critical role in understanding the shell evolution in exotic nuclei. However, there are still several puzzles concerning the tensor force and its effects in the nuclear medium. In this paper, we mainly focus on the studies of tensor force in the effective interactions and its effects in finite nuclear systems within the scheme of nuclear density functional theory. In particular, we highlight the recent developments, including the quantitative analysis of tensor effects in the relativistic Hartree-Fock theory by taking the evolution of proton magic shells in the isotopic chains as an example, and the "meta-data" of tensor effects provided by the ab initio relativistic Brueckner-Hartree-Fock theory by taking the evolution of spin-orbit splitting in the single-particle spectra of neutron drops as an example. Perspectives are focused on the possible strategies for the future developments of nuclear density functional theory.     

An investigation of the tensor force effects on the spin-orbit splitting in spherical and very deformed nuclei

A contribution of the tensor force to the phenomenological spin-orbit (SO) potential in the single-particle Hamiltonian is studied for spherical and deformed rare-earth and actinide nuclei. It is found that the deformation dependence of the SO coupling constant, suggested by the second order tensor force contribution, enables to explain the observed single particle (s.p.) states in the second minimum of²³⁷Pu and²³⁹Pu using a SO strength weaker than usually applied. Consequences of the tensor contributions for the stability of theZ=114 superheavy nucleus are studied.     

Symmetry energy,unstable nuclei and neutron star crusts

We present an upgraded review of our microscopic investigation on the single-particle properties and the EOS of isospin asymmetric nuclear matter within the framework of the Brueckner theory extended to include a microscopic three-body force. We pay special attention to the discussion of the three-body force effect and the comparison of our results with the predictions by other ab initio approaches. Three-body force is shown to be necessary for reproducing the empirical saturation properties of symmetric nuclear matter within nonrelativistic microscopic frameworks, and also for extending the hole-line expansion to a wide density range. The three-body force effect on nuclear symmetry energy is repulsive, and it leads to a significant stiffening of the density dependence of symmetry energy at supra-saturation densities. Within the Brueckner approach, the three-body force affects the nucleon s.p. potentials primarily via its rearrangement contribution which is strongly repulsive and momentum-dependent at high densities and high momenta. Both the rearrangement contribution induced by the three-body force and the effect of ground-state correlations are crucial for predicting reliably the single-particle properties within the Brueckner framework.     

A complex effective force for heavy-ion collisions

A local, complex, density and kinetic energy density-dependent effective force is derived from the G-matrix corresponding to two colliding nuclear matters. The Bethe-Goldstone equation uses the Reid soft-core interaction as input. The auxiliary single-particle potential is chosen self-consistently for all momenta. The results are presented in parametrized form.     

One-body nuclear friction

We have calculated the velocity dependent forces acting between two nuclei that arise due to one-body mechanism of nuclear excitation when they are dragged against one another with constant velocity. The nuclear friction coefficients are then extracted from the velocity dependence of these forces which is found to be strongly linear. The one-body force is calculated by solving the time-dependent Schrödinger equation for all the occupied single-particle states of a nuclear system in a central collision. Each nucleus in this model is assumed to be described by a single-particle Woods-Saxon potential filled with 40 nucleons each. The magnitude of the resulting one-body friction is found to be in between the proximity and surface frictions. The proximity-friction is too small by about an order of magnitude. To check this result, we calculated the one-sided flux from one nucleus to the other. The friction force connected to this flux (i.e. the one-body exchange friction) turns out to be about half or less than the one body friction. We conclude that theproximity-friction grossly underestimates the one-body exchange friction. Furthermore,inelastic excitations are at least as important for one-body dissipation at distances beyond the touching point as is particle exchange.     

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.     

Mean-field and RPA approaches to stable and unstable nuclei with semi-realistic interactions

We have developed semi-realistic NN interactions by modifying the M3Y interaction that was derived from the G -matrix. The modification has been made so that the saturation and the spin-orbit splittings should be reproduced. After viewing nuclear-matter properties, the semi-realistic M3Y-P5 interaction, which includes realistic tensor channels, is applied to finite nuclei in the mean-field and the random-phase approximations. In comparison with the results with widely used phenomenological interactions, we find that notable interaction dependence could remain in several Landau-Migdal parameters in the nuclear matter, in the N -dependence of proton single-particle levels in the Sn isotopes, and in the M1 strength distribution in ²⁰⁸Pb . Having microscopic origin in part, the semi-realistic interaction describes all these properties to reasonable accuracy. We confirm that the tensor force plays a crucial role in the single-particle levels and in the M1 distribution. Applying the semi-realistic interaction, we give prediction for a ground-state property of ⁶⁰Ca , for the magic nature of N = 32 and 34 in the neutron-rich region, and for the property of the first excited state of ²⁴O .     

Calculated ground-state properties of heavy nuclei

Ground-state distortions and single-particle corrections are calculated fornuclei with $\text{Z ≧ 68}\text{and}\text{N ≧ 106}$ by use of the macroscopic-microscopic method as developed by Strutinsky. The microscopic part is calculated primarily by use of the folded Yukawa single-particle potential. Its parameters are redetermined to fit a actinide data. The modified oscillator potential is also used in some of the studies. Two methods for calculating the macroscopic energy are investigated. One is the droplet model of Myers and Swiatecki, and other is a modified liquid-drop model in which the surface-energy term is modified to take into account the finite range of the nuclear force. Single-particle level diagrams for the folded Yukawa potential are also presented. They are plotted as functions of the distortion parameters ?, ?₄ and ?₆. Theoretical and experimental single-particle levels at the ground state for actinide nuclei are also compared.     

Evolution of nuclear shells due to the tensor force

The monopole effect of the tensor force is presented, exhibiting how spherical single-particle energies are shifted as protons or neutrons occupy certain orbits. An analytic relation for such shifts is shown, and their general features are explained intuitively. Single-particle levels are shown to change in a systematic and robust way, by using the pi + rho meson exchange tensor potential, consistently with the chiral perturbation idea. Several examples are compared with experiments.     

Tensor coupling effect on relativistic symmetries

The similarity renormalization group is used to transform the Dirac Hamiltonian with tensor coupling into a diagonal form. The upper(lower) diagonal element becomes a Schr¨odinger-like operator with the tensor component separated from the original Hamiltonian.Based on the operator, the tensor effect of the relativistic symmetries is explored with a focus on the single-particle energy contributed by the tensor coupling. The results show that the tensor coupling destroying(improving) the spin(pseudospin) symmetry is mainly attributed to the coupling of the spin-orbit and the tensor term, which plays an opposite role in the single-particle energy for the(pseudo-) spin-aligned and spin-unaligned states and has an important influence on the shell structure and its evolution.     

Role of Tensor Force in Light Nuclei with Tensor-Optimized Shell Model

We propose a new theoretical approach to describe nucleus using bare nuclear interaction, in which the tensor and short-range correlations are described with the tensor-optimized shell model (TOSM) and the unitary correlation operator method (UCOM), respectively. We use a bare nucleon–nucleon interaction AV8′ and show the spectroscopic results of the He and Li isotopes with TOSM+UCOM, such as the importance of the pn pair correlated by the tensor force and the corresponding high momentum components.     

Role of Tensor Force in He and Li Isotopes with Tensor Optimized Shell Model

We propose a new theoretical approach to describe nucleus using bare nuclear interaction, in which the tensor and short-range correlations are described with the tensor optimized shell model (TOSM) and the unitary correlation operator method (UCOM), respectively. We show the obtained results of He and Li isotopes using TOSM + UCOM, such as the importance of the pn-pair correlated by the tensor force, and the structure differences in the 3/2^? and 1/2^? states of ⁵He.     

Energy- andN-averagings in the shell correction method

It is shown that a difference exists between the mean values of the total single-particle energies obtained by averaging over the nucleon numberN and over the phase-space distributions (the energy-averaging) due to the symmetry of the single-particle Hamiltonian. This difference could lead to significant corrections in fitting the nuclear masses involving the droplet model.     

The tensor force in nuclear saturation

One-term separable potentials in the ³S-³D channel are constructed which fit the following low-energy nucleon-nucleon data: the triplet effective range and scattering length, deuteron binding energy and quadrupole moment. They also yield ³D₁ phase shifts which have the correct sign. These potentials differ, however, in the amount of deuteron D-state probability, P_D, which they predict, where P_D ranges from 1 % to 9 %. Binding energy calculations of infinite nuclear matter and ⁴He are performed in order to test the effect of the tensor force on nuclear saturation properties. It is found that the larger the D-state probability, the smaller the energy per particle and saturation density. Detailed comparisons with local potentials in nuclear matter are also presented.

In nuclear matter no single-particle potential in intermediate states is used; in ⁴He, , where f is varied such that the absolute value of the diagram with a single potential insertion in a particle line is minimized. It is found in ⁴He that f= 0.75 and that this result is almost independent of both the potential employed and of ω. Furthermore, for 0 f 1.5, the total energy is independent of f.     

Single-particle potential in a relativistic Hartree-Fock mean field approximation

A relativistic Hartree-Fock mean field approximation is investigated in a model in which the nucléon field interacts with scalar and vector meson fields. The Hartree-Fock potential felt by individual nucléons enters in a relativistic Dirac single-particle equation. It is shown that in the case of symmetric nuclear matter one can always find a potential which is fully equivalent to the most general mean field and which is only the sum of a Lorentz scalar, of one component of a Lorentz tensor and of the fourth component of a Lorentz vector. A non-relativistic potential is derived which yields exactly the same single-particle energies and elastic scattering phase shifts as the relativistic Hartree-Fock potential. Analytical results are presented in the case of nuclear matter. A local density approximation is constructed which enables one to consider finite nuclei. The input parameters of the model can be chosen in such a way that the empirical saturation properties of nuclear matter are well reproduced. Good agreement is obtained between the calculated non-relativistic potential and the empirical value of the real part of the optical-model potential at low and at intermediate energy. At intermediate energy, the wine-bottle bottom shape which had previously been found for the potential in the framework of the relativistic Hartree approximation is maintained when the Fock contribution is included.     

Nuclear properties of Z=114 isotopes and shell structure of ~(298)114

The two-neutron separation energies(S_(2n)) and α-decay energies(Q_α) of the Z=114 isotopes are calculated by the deformed Skyrme-Hartree-Fock-Bogoliubov(SHFB) approach with the SLy5,T22,T32 and T43 interactions.It is found that the tensor force effect on the bulk properties is weak and the shell closure at N=184 is seen evidently with these interactions by analyzing the S_(2n) and Q_α evolutions with neutron number N.Meanwhile,the single-particle energy spectra of ~(298)114 are studied using the spherical SHFB approach with these interactions to furthermore examine the shell structure of the magic nucleus ~(298)114.It is shown that the shell structure is almost not changed by the inclusion of the tensor force in the Skyrme interactions.Finally,by examining the energy splitting of the three pairs of pseudospin partners for the protons and neutrons of ~(298)114,it is concluded that the pseudospin symmetry of the neutron states is preserved better than that of the proton states and not all of the pseudospin symmetries of the proton and neutron states are influenced by the tensor force.     

The systematics of nuclear single-particle states (I). The region 35 ≦ A ≦ 65

The energies of single-particle states in nuclei with 35 ≦ A ≦ 65 are obtained as eigenvalues of a local Saxon-Woods potential with depth depending linearly on A and on the nuclear symmetry parameter.     

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.