基于相对论平均场理论对超重核冷熔合反应截面的研究

在形变约束的相对论平均场理论框架下计算了合成Z=102—118元素的(可能)冷熔合反应中复合核及蒸发一或两个中子剩余核的位能曲面,得到了复合核和剩余核平衡点和鞍点的性质、静态裂变垒高度和冷熔合反应的最佳入射能;利用壳修正和对修正方法计算了平衡点和鞍点的壳修正能、对修正能和微观能.利用由此得到的壳结构信息,用简单的熔合蒸发唯象模型计算了相应反应的冷熔合截面.结果发现,TM1参数提供的结构性质给出了与实验接近的反应截面.     

Theoretical Study on N = 126 Shell Evolution

The nuclei around magic number N = 126 are investigated in the deformed relativistic mean field (RMF) model with effective interactions TMA. We focus investigations on the N = 126 isotonic chain. The N = 126 shell evolution is studied by analyzing the variations of two-neutron (proton) separation energies, quadruple deformations, single particle levels etc. The good agreement of two-neutron separation energies between experimental data and calculated values is reached. The RMF theory predicts that the sizes of N = 126 shell become smaller and smaller with the increasing of proton number Z. However, the N = 126 shell exists in our calculated region all along. According to the calculated two-proton separation energies, the RMF theory suggests ²²⁰Pu is a two-proton drip-line nucleus in the N = 126 isotonic chain.     

Ground-state properties of neutron magic nuclei

A systematic study of the ground-state properties of the entire chains of even–even neutron magic nuclei represented by isotones of traditional neutron magic numbers N = 8, 20, 40, 50, 82, and 126 has been carried out using relativistic mean-field plus Bardeen–Cooper–Schrieffer approach. Our present investigation includes deformation, binding energy, two-proton separation energy, single-particle energy, rms radii along with proton and neutron density profiles, etc. Several of these results are compared with the results calculated using nonrelativistic approach (Skyrme–Hartree–Fock method) along with available experimental data and indeed they are found with excellent agreement. In addition, the possible locations of the proton and neutron drip-lines, the (Z, N) values for the new shell closures, disappearance of traditional shell closures as suggested by the detailed analyzes of results are also discussed in detail.     

Properties of A = 7-9 Drip-Line Nuclei in RMF Theory

The relativistic mean-field （RMF） theory is used to calculate the properties of A =7-9 drip-line nuclei ^7Li, ^7;9Be, ^8;9B, and ^9C. Systematic deviations between experimental and theoretical binding energies are found. Possible reasons of these systematic deviations are discussed in terms of pairing energy. The root-mean-square （rms） radii of matter distributions for these nuclei agree with the experimental data quite well. The one-proton halo structure in ^8B is reproduced well, and the two-proton halo in ^9C is predicted. The calculations show that the RMF theory is valid in studying the properties of light drip-line nuclei.     

Particle number conserving BCS approach in the relativistic mean field model and its application to ~(32-74)Ca

A fixed particle number BCS(FBCS) approach is formulated in the relativistic mean field(RMF) model.It is shown that the RMF+FBCS model obtained can describe the weak pairing limit. We calculate the ground-state properties of the calcium isotopes ~(32-74)Ca and compare the results with those obtained from the usual RMF+BCS model. Although the results are quite similar to each other, we observe the interesting phenomenon that for ~(54)Ca,the FBCS approach can enhance the occupation probability of the 2p1/2 single particle level and slightly increases its radius, compared with the RMF+BCS model. This leads to the unusual scenario that although ~(54)Ca is more bound with a spherical configuration, the corresponding size is not the most compact. We anticipate that such a phenomenon might happen for other neutron-rich nuclei and should be checked by further more systematic studies.     

丰中子区幻数N=28消失的相对论平均场证明

提出了一种从理论上检验壳效应的方法. 即在考虑了BCS近似的相对论平均场理论框架内, 通过计算粒子数的涨落, 发现涨落的大小和核的壳结构有紧密的关系, 由此从理论上证明了在滴线附近的丰中子区, 传统幻数N=28已经消失.     

Ground State Properties of Ds Isotopes Within the Relativistic Mean Field Theory

The ground state properties of Ds (Z=110) isotopes (N=151-195) are studied in the framework of the relativistic mean field (RMF) theory with the effective interaction NL-Z2.The pairing correlation is treated within the conventional BCS approximation.The calculated binding energies are consistent with the results from finite-range droplet model (FRDM) and Macroscopic-microscopic method (MMM).The quadrupole deformation,α-decay energy,α-decay half-live,charge radius,two-neutron separation energy and single-particle spectra are analyzed for Ds isotopes to find new characteristics of superheavy nuclei (SHN).Among the calculated results it is rather distinct that the isotopic shift appears evidently at neutron number N=184.     

对关联对核基态和集体激发态性质的影响

基于相对论平均场和BCS理论,研究了共振连续对奇特核对关联性质的影响. 利用S矩阵方法，通过设定合理的散射态边界条件来得到单粒子共振态的能量和宽度. 通过引入连续态能级密度的方法来处理共振态宽度对核对关联的贡献. 计算结果显示合理地处理共振态对对关联性质的贡献在研究滴线附近核性质时很重要. 它可以影响中子的对隙、费米能级、对关联能以及总结合能. 其次,基于RMF+BCS基态,采用线性响应理论给出了描述开壳核集体激发态性质的准粒子相对论无规位相近似理论. 并且将该方法应用于开壳核120Sn的各种同位旋标量集体激发态性质的研究中. 研究表明：对关联对核的集体激发性质的影响主要表现在低能集体激发态上,考虑对关联后的相对论无规位相近似理论能够很好地再现低能集体激发的实验结果.     

Description of the New Nuclide 259Db and Its α-Decay Chain in Relativistic Mean Field Theory

The new nuclide ²⁵⁹Db and its α decay chain are systematically studied in the framework of the relativistic mean field (RMF) theory with NL3 and TM1 effective interactions. The nuclide ²⁵⁹Db and its α-decay daughter nuclei are calculated in a RMF framework with and without the pairing correlation. With the pairing gaps obtained from the RCHB, the deformed RMF+BCS has been carried out for these nuclei. It has been found that the DRMF+BCS well reproduces the data and implies that the new nuclide ²⁵⁹Db and its α decay daughter nuclei are highly deformed. The α-decay energy Q_α for different channel has been given and it seems that the ground state to ground state Q_α values from DRMF+BCS reproduce the data well. Furthermore the single particle levels of the α decay chain are studied carefully and the explanation for the stability is also presented.     

用相对论平均场理论研究近滴线区原子核传统幻数的消失和新幻数的产生

提出了一种从理论上检验壳效应的方法.在考虑了由Bardeen，Cooper和Schrieffer提出的金属超导理论(BCS方法)的相对论平均场理论框架内，通过计算粒子数的涨落，发现涨落的大小和核的壳结构有紧密的关系，进而研究了滴线区一些传统幻数的消失和新幻数的产生. 关键词： 相对论平均场理论 粒子数涨落 幻数 壳效应     

Superheavy nuclei in the RMF framework

The structure of superheavy even even nuclei is investigated using the self-consistent axially-deformed relativistic mean-field model (RMF) with BCS pairing. The isovector properties of the standard RMF ansatz are studied and the new RMF parameterization is tested with a better account for nuclei away of the line of stability. The heaviest even even nuclei are used as a benchmark to estimate the predictive power of the model.     

稀土区对关联经验参数公式的研究

在相对论平均场理论框架下， 采用不同对关联的参数公式对Ce, Gd和Yb稀土区同位素链进行了计算和研究。 理论计算表明: 尽管采用能隙经验参数公式和对力强度经验参数公式在能否表现出原子核的壳结构上有所区别， 但具体计算的其它物理量（如结合能、 双中子分离能等）趋向一致， 都能很好地反映原子核的基态性质。 In the framework of relativistic mean field (RMF)theory， we use BCS approximation to calculate Ce， Gd and Yb isotopic chains with different pairing parameters. And found whether they can show shell structure are different， but other physical quantities are similar by using different kinds of pairing parameters， both can correctly reproduce the experimental binding energies， two neutron separation energy and potential curves.     

Shell evolution at N=20 in the constrained relativistic mean field approach

The shell evolution at N = 20, a disappearing neutron magic number observed experimentally in very neutron-rich nuclides, is investigated in the constrained relativistic mean field (RMF) theory. The trend of the shell closure observed experimentally towards the neutron drip-line can be reproduced. The predicted two-neutron separation energies, neutron shell gap energies and deformation parameters of ground states are shown as well. These results are compared with the recent Hartree-Fock-Bogliubov (HFB-14) model and the available experimental data. The perspective towards a better understanding of the shell evolution is discussed.     

Shell evolution at N=20 in the constrained relativistic mean field approach

The shell evolution at N=20, a disappearing neutron magic number observed experimentally in very neutron-rich nuclides, is investigated in the constrained relativistic mean field (RMF) theory. The trend of the shell closure observed experimentally towards the neutron drip-line can be reproduced. The predicted two-neutron separation energies, neutron shell gap energies and deformation parameters of ground states are shown as well. These results are compared with the recent Hartree-Fock-Bogliubov (HFB-14) model and the available experimental data. The perspective towards a better understanding of the shell evolution is discussed.     

Effects of pairing correlation on neutron drop

In this work, the effects of the pairing correlation on the properties of neutron drops N=6-50 trapped in a harmonic oscillator potential with ω = 10 Me V are investigated by comparing the results given by the Skyrme Hartree-Fock and Hartree-FockBogoliubov theories with the density-dependent delta interaction(DDDI) pairing force. The results showed that the pairing correlation slightly made the neutron drops more bound, and increased the central neutron density, the spin-orbit and pseudo spin-orbit splittings. Thus, the pairing correlation must be accounted for to improve the Skyrme functional compared with the ab initio calculations. Furthermore, although the single-particle energy gaps with or without pairing were similar, the shell closures varied due to pair scattering. Here, the shell closures in neutron drops using the Sk M* parameter set and DDDI pairing force were found at N=8, 16, and 32.     

Properties and structure of N=Z nuclei within relativistic mean field theory

The axially deformed relativistic mean field theory with the force NLSH has been performed in the blocked BCS approximation to investigate the properties and structure of N=Z nuclei from Z=20 to Z=48.Some ground state quantities such as binding energies, quadrupole deformations, one/two-nucleon separation energies, root-mean-square (rms) radii of charge and neutron, and shell gaps have been calculated.The results suggest that large deformations can be found in medium-heavy nuclei with N=Z=38-42.The charge and neutron rms radii increase rapidly beyond the magic number N=Z=28 until Z=42 with increasing nucleon number, which is similar to isotope shift, yet beyond Z=42, they decrease dramatically as the structure changes greatly from Z=42 to Z=43.The evolution of shell gaps with proton number Z can be clearly observed.Besides the appearance of possible new shell closures, some conventional shell closures have been found to disappear in some region.In addition, we found that the Coulomb interaction is not strong enough to breakdown the shell structure of protons in the current region.