2s1/2—1d3/2壳层原子核能谱的壳模型分析

本文对2s_1/2-1d_3/2壳层原子核(A=30—40)能谱作了系统分析,计算仅限于由2s_1/2和1d_3/2支壳层产生的情态,但考虑了它们之间的全部组态混合效应。计算是采用多粒子壳模型的Talmi方法,将二体矩阵元当作参数,其值由实验确定。文中详细分析了Si³⁰,Si³¹,P³⁰,P³¹,P³²,S³²,Ar³⁷,Ar³⁸,K³⁸等原子核能谱,理论与实验符合颇好。     

相对论平均场理论中的张量项对自旋-轨道劈裂的影响

在相对论平均场理论中引入同位旋标量-矢量介子ω张量项, 以²⁰⁸Pb为例,研究了张量项对原子核平均势场、介子场、自旋-轨道耦合势、单粒子能级的自旋-轨道劈裂和原子核壳层结构等的影响.结果发现张量项对核子平均势的影响主要表现在原子核的表面.随着张量耦合强度的增加, 自旋-轨道耦合势增强,单粒子能级的自旋-轨道劈裂增大,从而导致原子核单粒子能级的壳层结构发生很大变化,传统幻数所对应的主壳消失, 新的主壳出现.     

核电荷半径的同位旋相关性及其微观诠释

原子核电荷半径R_c所有的实验数据都表明, R_c系统偏离A^1/3律, 即随A增大R_c/A^1/3系统地递减, 而R_c/Z^1/3则比较接近于一个常量. 原子核巨单极共振能量E_x ∝ R^－1的大量实验数据也支持这一结论. 根本原因在于A^1/3律与同位旋无关, 而Z^1/3律已部分反映了同位旋的影响. 基于壳模型, 给出了Z^1/3律的微观诠释. 壳模型中质子和中子谐振子势强度参数ω_p和ω_n的差异, 可以用Z^1/3律说明. 基于与Wigner的原子核同位旋多重态质量公式(IMME)相似的理论考虑, 提出了核电荷半径改进的Z^1/3律.     

相对论平均场理论研究原子核的磁矩

采用球形以及三轴形变的相对论平均场理论研究了满壳附近质量数A=133, 207, 209的原子核的磁矩, 分析了相对论效应以及核芯极化对磁矩的影响. 计算结果表明用包含矢量介子空间分量(奇时间分量)的三轴的相对论平均场理论 可以很好的描述满壳附近重质量区原子核¹³³Sb以及²⁰⁹Bi的磁矩.     

C,Al,Cu,Sn,Pb等原子核对高能π+,K+介子及质子的吸收截面

在联合原子核研究所同步稳相加速器上,研究了高能π⁺、K⁺介子和原子核的相互作用。利用角度式气体契连科夫速度选择器,选择出纯度约达99％的K⁺介子束。测量了C,Al,Cu,Sn,Pb等原子核对动量为2.72,3.70,4.75Бэв/с的π⁺介子的吸收截面;C,Al,Cu等原子核对动量为4.75Бэв/с的K⁺介子的吸收截面;C,Sn,Pb等原子核对动量为2.72Бэв/с的质子的吸收截面。利用光学模型,对所得的数据进行了分析。根据π⁺介子数据得到的原子核半径公式,与T.Bowen根据π^-介子的测量数据所得结果不同,而和由低能中子散射工作所得结果(R=1.37A^1/3×10^-13厘米)相符。根据K⁺介子数据得到,高能K⁺介子与核子相互作用全截面的平均值应为σ_KN=16.5毫巴。     

形变核中的E2和M1强度:赝-SU(3)模型的应用

通过-SU(3)壳模型对¹⁶²Dy核的描述,揭示了原子核的复杂多体行为能通过简单的几何图像来解释.     

原子核高自旋态的半径典研究

用推广的汤马斯-费米近似和Skyrme势研究了原子核的高自旋态,应用推转模型给出了含转动的能量密度公式,并计算了¹¹⁶Sn,¹⁵⁸Yb和²⁴⁰Pu这三个典型核在不同角动量下的核形变与转动能.计算结果定性地与液滴模型相似,在数值上则有一定差别.计算结果表明,对转动能的量子修正,即使不考虑壳修正,也不能忽略.     

μ－在原子核上的俘获

利用多体场论方法,本文对μ^－在原子核上的俘获作了系统研究.在没有任何可调参数的情况下,对于从轻核到重核各种原子核上的μ^－俘获率作了计算.发现,自旋-同位旋相关的强作用的重整化效应及μ^－在原子核上的束缚能效应是透彻理解这种弱作用过程的关键.     

相对论类壳模型方法对轻核中的α集团现象的研究

利用相对论类壳模型方法(RMF+SLAP), 研究了包含对关联情况下, 轻核⁸Be, ¹²C, ¹⁶O, ²⁰Ne中的可能出现的α集团效应. 结果很好地再现了轻核的α集团结构. 与没有考虑对关联的情形相比, 对关联可以使原子核基态性质发生改变, 导致不同的α集团结构.     

A≈80区奇–奇核80,82Rb的晕带能谱计算

在A≈80区奇-奇核旋称反转问题上已提出几种机制,但没有一种理论推断是结论性的.在本工作中将角动量投影壳模型应用到^80,82Rb核,对组态为πg_9/2⊙νg_9/2的正宇称晕带和组态为π(p_1/2,p_3/2,f_5/2)⊙νg_9/2 的负宇称晕带理论计算和实验结果进行了比较,特别是对正宇称晕带中的signature反转机制进行了探讨.角动量投影壳模型计算显示正宇称晕带中的signature反转是原子核随自旋增加形状发生变化的信号,其间原子核从低自旋的长椭球变到高自旋的扁椭球.此外,还确定了此两带的原子核形状     

Relativistic calculation of spectra of 2-2 transitions in O- and F-like atomic ions

We have studied theoretically the structure of 1s²2s^n₁2p^n₂ levels in O- and F-like ions with z = 25 ÷ 40. Relativistic perturbation theory is used for the total interelectronic interaction. Allowance is made for Coulomb and relativistic interelectronic interactions. The first order perturbation theory for retardation of the interaction has been calculated fully. The complete calculation has also been made for the nonrelativistic correction in the second order and the Hartree-Fock part of the nonrelativistic correction in the third order. The Hartree-Fock relativistic correction in the second order has been taken into account fully for F-like ions and partially for O-like ions. Corrections to higher orders for z ? 28 have been found empirically and extrapolated to the region z = 29 ÷ 40. For energies of 2-2 transitions, calculation errors for z ? 28 do not exceed 900 cm^-1 and do not increase with z. Typical errors obtained with conventional, more cumbersome calculations are 5000 cm^-1 at z = 30.     

On the calculation of densities of light nuclei

For certain classes of wave functions one can calculate the exact expressions of the charge distribution and similar densities. One has to make use of the asymptotic behaviour of these wave functions (whose radial parts have to be of the form \(r^{2k} e^{ - \beta r^2 } \) , in order to obtain a closed form forp(r); the problem is then reduced to the computation of moments, which can be evaluated by a generating function technique. No complications due to a spurious center-of-mass motion do appear. The method is most appropriate for the calculation of densities of refined cluster model functions or translationally invariant shell model functions (both for a nucleon or an alpha-particle shell model) including short-range correlation factors that take care of a soft core in nuclear potentials.     

Electro-optic response of metal halide $$\hbox {CsPbI}_3$$: A first-principles study

In this work, we have obtained energy levels and charge radius for the β-stability line nucleus, in relativistic shell model. In this model, we considered a close shell for each nucleus containing double magic number and a single nucleon energy level. Here we have taken ⁴¹Ca with a single neutron in the ⁴⁰Ca core as an illustrative example. Then we have selected the Eckart plus Hulthen potentials for interaction between the core and the single nucleon. By using parametric Nikiforov–Uvarov (PNU) method, we have calculated the energy values and wave function. Finally, we have calculated the charge radius for ¹⁷O, ⁴¹Ca, ⁴⁹Ca and ⁵⁷Ni. Our results are in agreement with experimental values and hence this model can be applied for similar nuclei.     

Test of new shell model wave functions by means of 166 MeV alpha particle inelastic scattering

The nuclear wave functions for the first 2⁺ levels of ²⁴Mg, ²⁸Si and ⁵⁸Ni obtained by diagonalizing an effective Hamiltonian in a large shell model basis are used to calculate 166 MeV α-particle inelastic scattering cross sections. The results are compared with experimental measurements. Good agreement is found for ²⁴Mg and ²⁸Si but the model wave function seems to be inadequate for describing ⁵⁸Ni.     

Analysis of fission excitation functions and the determination of shell effects at the saddle point

A method is proposed to deduce the shell correction energy corresponding to the fission transition state shape of nuclei in the mass region around 200, from an analysis of the first chance fission values of the ratio of fission to neutron widths, (Γ _f /Γ _n )₁. The method is applied to the typical case of the fissioning nucleus²¹²Po, formed by alpha bombardment of²⁰⁸Pb. For the calculation of the neutron width, the level densities of the daughter nucleus after neutron emission were obtained from a numerical calculation starting from shell model single particle energy level scheme. It is shown that with the use of standard Fermi gas expression for the level densities of the fission transition state nucleus in the calculation of the fission width, an apparent energy dependence of the fission barrier height is required to fit the experimental data. This energy dependence, which arises from the excitation energy dependence of shell effects on level densities, can be used to deduce the shell correction energy at the fission transition state point. It is found that in the case of²¹²Po, the energy of the actual transition state point is higher than the energy of the liquid drop model (LDM) saddle point by (3 ± 1) MeV, implying significant positive shell correction energy at the fission transition state. Further, the liquid drop model value of level density parametera is found to be a few per cent smaller for the saddle point shape as compared to its spherical shape.     

THE ENERGY SPECTRUM AND WAVEFUNCTION OF NUCLEUS 31Si——A TEST ON THE COMPOSITE PARTICLE REPRESENTATION THEORY

The nuclecus ³¹Si₁₇ is studied by the composite particle representation theory and compared with the shell model calculations. It is shown that the entire energy spectrum agrees with the shell model results very well, and the wave function is equivalent to the shell model wavefunction exactly. Therefore it strongly supports the composite particle representation theory.     

Binding corrections for reactions on the deuteron in the 3-3 resonance region

Binding corrections evaluated to all orders in a phenomenological nucleon-nucleon potential are compared with the leading term and with a double scattering correction in the Watson expansion for breakup and for coherent reactions on the deuteron at intermediate pion or photon energies. As principal result, we establish that for charged pion photoproduction, and for certain pion induced “spectator” reactions, the binding correction remains sufficiently small that truncation of the Watson expansion at terms of second order in the projectile-nucleon amplitudes is justifiable, but sufficiently large that it cannot be neglected in comparison with multiple scattering corrections. For the reactions π⁺d → π⁺p + spectator neutron and π^?d → π^?n + spectator proton, our theory predicts deviations from the simplest impulse approximation which become very large in well-defined kinematical regions, and should be easily accessible to experimental investigation.     

Mixing of the giant magnetic dipole state with the 1+ state in 88Sr at 3.49 MeV

The ground state magnetic dipole transition width from the 1⁺ state in ⁸⁸Sr at 3.49 MeV is calculated using a reasonable wave function for the ground state and a wave function for the 1⁺ state calculated by diagonalizing one particle-one hole shell model 1⁺ states starting with a basis of reasonable dimensions. The calculated value of the width is 0.17 eV. The measured value is 0.15 ± 0.024 eV.     

On maximum-overlap orbitals in nuclei

A formulation of the maximum overlap requirement is given which brings the scheme conceptually closer to the Hartree-Fock method. A procedure of solving the necessary condition for the maximum overlap is suggested and the stability conditions for the solutions as well as some symmetry aspects to the method are discussed.Using the suggested procedure the hyperspherical wave function of⁴He as well as the shell model wave function of¹⁸F are analyzed.     

Recent progress in simulation of the ground state of many Boson systems

We present two recent advances in the simulation of ⁴He in the condensed phase at zero temperature. Within the variational theory of strongly interacting bosons we have studied a cluster of ⁴He atoms with one alkali ion K⁺. For the wave function we have used a new shadow wave function (SWF) in which the coupling between one ⁴He atom and its shadow variable depends on its distance from the ion. This substantially improves the energy. The first shell around the ion contains 14 atoms which are spatially ordered. However the atoms of the first shell are not completely localized and frequent exchanges with atoms which are further from the ion take place. This also suggests that at least for the ion K⁺ the atoms of the first shell participate in the superfluidity. We have also introduced a new extension of the path integral ground state (PIGS) method which is able to compute exact ground state expectation values without extrapolations and with a SWF as the trial variational wave function to project on the ground state. This is an important extension which opens up the possibility of studying disorder phenomena in the solid phase by an exact method at zero temperature. We have applied this technique to compute the energy of formation of a vacancy at different densities in the solid phase of ⁴He. This computation confirms the variational result that a vacancy is a delocalized defect in the low density helium solid.