Entrance Channel Mass Asymmetry Effects in Sub-Barrier Fusion Dynamics by Using Energy Dependent Woods–Saxon Potential

The present article highlights the inconsistency of static Woods Saxon potential and the applicability of energy dependent Woods Saxon potential to explore the fusion dynamics of ~(48)_(22)Ti+~(58,60,64)_(28)Ni,~(46)_(22)Ti+~(64)_(28)Ti+~(50)_(22)Ti+~(60)_(28)Ni,and~(19)_9F+~(93)_(41)Nb reactions leading to formation of different Sn-isotopes via different entrance channels.Theoretical calculations based upon one-dimensional Wong formula obtained by using static Woods Saxon potential unable to provide proper explanation for sub-barrier fusion enhancement of these projectile-target combinations.However,the predictions of onedimensional Wong formula based upon energy dependent Woods Saxon potential model(EDWSP model) accurately describe the observed fusion dynamics of these systems wherein the significantly larger value of diffuseness parameter ranging from a = 0.85 fm to a = 0.97 fm is required to address the experimental data in whole range of energy.Therefore,the energy dependence in nucleus-nucleus potential simulates the influence of the nuclear structure degrees of freedom of the colliding pairs.     

Sub-barrier fusion excitation function data and energy dependent Woods–Saxon potential

This paper analyzed the role of intrinsic degrees of freedom of colliding nuclei in the enhancement of sub-barrier fusion cross-section data of various heavy ion fusion reactions. The influences of inelastic surface vibrations of colliding pairs are found to be dominant and their couplings result in the significantly larger fusion enhancement over the predictions of the one dimensional barrier penetration model at sub-barrier energies. The theoretical calculations are performed by using energy dependent Woods–Saxon potential model (EDWSP model) in conjunction with the one dimensional Wong formula. The effects of dominant intrinsic channels are entertained within framework of the coupled channel calculations obtained by using the code CCFULL. It is quite interesting to note that the energy dependence in Woods–Saxon potential simulates the effects of inelastic surface vibrational states of reactants wherein significantly larger value of diffuseness parameter ranging from a = 0.85fm to a = 0.95fm is required to address the observed fusion excitation function data of the various heavy ion fusion reactions.     

Zur Theorie der Coulombenergiedifferenzen isobarer Analogzustände

The splitting of isobaric multiplets caused by the differences in kinetic energies and magnetic moments is estimated. The differences in Coulomb energies are calculated, assuming the radial charge distribution to be given by a Fermi function as deduced from electron scattering. As a result, the diffuseness is more important than antisymmetrization and much more important than the deformation. The decrease of the charge radius with increasing neutron excess found from muonic X rays, has to be taken into account for heavy nuclei. Approximating this effect by a two parameter formula and using the radius parameter and diffuseness derived from electron scattering and muon atoms, good overall-agreement with experimental data is achieved.     

Potential of interaction between nuclei and nucleon-density distribution in nuclei

Nuclear-interaction potentials that are calculated by using Skyrme forces within the extended Thomas-Fermi approximation and Hartree-Fock-Bardeen-Cooper-Schrieffer theory are studied in detail. It is shown that the nuclear component of the potential simulating the interaction between nuclei grows with increasing number of neutrons in colliding isotopes and with increasing diffuseness parameter of the density distribution in interacting nuclei. An increase in the diffuseness parameter of the density distribution in interacting nuclei leads to a decrease in the height of the barrier between the nuclei and to an increase in the depth of the capture well and in the fusion cross section. It is shown that the diffuseness parameter calculated for the nuclear component of the potential at large distance between interacting nuclei by using Skyrme forces exceeds the diffuseness parameter of the nucleon-density distribution in these nuclei by a factor of about 1.5. Realistic values of the diffuseness parameter of nuclear interaction between medium-mass and heavy nuclei fall within the range a ≈ 0.75–0.90 fm.     

Woods-Saxon势下的赝自旋对称性

通过求解具有Woods-Saxon径向标量势与矢量势的Dirac方程, 分别分析了原子核中赝自旋双重态能级劈裂和波函数下分量劈裂随着Woods-Saxon势参数的变化关系, 其中Wood-Saxon势中的参数a以及R对于赝自旋能级劈裂和波函数劈裂的影响最大, 而势阱深度V₀只产生微小的影响. 随着平均场的变化, 赝自旋双重态会出现能级反转现象. 具有较大n或l的赝自旋双重态能级劈裂对于参数的变化更敏感. 赝自旋波函数下分量劈裂随着参数a和R的增大向核表面扩散, 并且在核表面附近达到最大. 赝自旋波函数劈裂随着参数a的增大而增大, 但是随着参数R或V₀的增大它却在减小的. 由于在特定的同位素链中, 参数R和V₀都与核子数有关系, 而参数a又是描述核的表面性质的, 所以以这些参数为变量对于赝自旋劈裂的研究是有意义的, 研究的结果至少在定性上可以应用到大部分原子核中.     

Resonant peak splitting in graphene superlattices with one-dimensional periodic potentials

We have investigated theoretically the resonant tunneling phenomenon of Dirac electrons through graphene superlattices with periodic potentials of square barriers. It is found that there are two resonance conditions for the graphene superlattices. Some of the resonance transmission peaks present N – 1-fold resonance splitting for $ N{\text{-barriers}} $ , which is the analogy of the resonance splitting in semiconductor superlattices. The resonance splitting effect depends on the incidence angle rather than the height and width of the potential. However, there is no explicit splitting rule for the conductance and shot noise, which is different from the magnetic case. Furthermore, the resonant splitting rule of the transmission is not sensitive to the shape of the potential barrier. These properties in graphene superlattices may lead to potential applications in graphene-based electron devices.     

The role of spin-orbit potential in nuclear prolate-shape dominance

It is confirmed, in terms of the Woods-Saxon-Strutinsky method, that the spin-orbit potential plays a decisive role in the predominance of prolate deformation, which has been a long standing problem in nuclear physics. It is originated from the combined effects of the spin-orbit coupling and the diffused surface of the potential, in agreement with the previous work based on a more schematic Nilsson-Strutinsky method. The degree of prolate-shape dominance exhibits an oscillatory behavior with respect to the strength of spin-orbit potential and, the prolate-shape dominance is realized at the proper strength of the spin-orbit potential together with the standard surface diffuseness; this oscillatory behavior disappears in case of small diffuseness corresponding to ellipsoidal cavity. The calculated energy differences between oblate and prolate minima in this Letter are consistent with those of our extensive self-consistent calculations of the Hartree-Fock + BCS method with the Skyrme interaction.     

Polaron in a superlattice with δ-like potentials

The problem of the polaron spectrum is studied in a superlattice having narrow quantum wells and relatively wide potential barriers. A δ-like superlattice potential is chosen to solve the problem. This model is adequate, if the penetration depth of the electron wave function into the barrier region is much greater than the width of the quantum well. A weak-coupling polaron at low temperature is studied. Only volume phonons are considered. Expressions are obtained for the polaron mass and the shift of the polaron energy under these assumptions. To test the model, numerical calculations were performed for an InAs-GaSb superlattice, whose quantum wells are quite deep (the energy offset of the conduction bands in InAs and GaSb equals 830 meV), narrow (the width of a quantum well corresponds to the width of an InAs monolayer 6 Å), and the barrier width corresponding to the thickness of the GaSb layers equals 150 Å. The assumption that the penetration depth of the wave function is much greater than the barrier width holds well.     

太赫兹偶数分束器设计与公差分析

本文运用二元光学矢量理论设计了一种硅基太赫兹偶数分束器, 实现高衍射效率、高均匀性、有效抑制零级的偶数分束, 突破传统标量方法设计局限性, 给出了分束器脊宽、槽宽、槽深、占空比、基底厚度等结构参数的最优设计值, 并进行了公差分析, 得到分束器各结构参数的加工允许偏差范围, 对器件的设计和制作具有指导意义.     

α-Decay calculations of medium mass nuclei within generalized density-dependent cluster model

The α-decay half-lives of even–even medium mass nuclei have been systematically investigated using a radial wave function within the generalized density-dependent cluster model. The α-decay width is calculated using the overlap integral of the quasi-bound initial state wave function, the scattering final state wave function, and the difference of potentials. The effective α–nucleus potential is constructed using the double-folded integral of realistic nucleon–nucleon interactions with the mass density distributions of α particles and daughter nuclei. For comparison calculations are also carried out for the Woods–Saxon shape potential. The present study is restricted to even–even nuclei with 82<N126, where the shell effect on the α-preformation factor has been taken into account for even–even N=126 isotones. The obtained α-decay half-lives are found to agree with the experimental data with a mean factor of less than 2 for both the double-folded potential and the Woods–Saxon shape potential.     

Effect of nuclear-surface diffuseness on the energy and width of the giant dipole resonance

The effect of nuclear-surface diffuseness on the energy and width of the giant dipole resonance is studied, and approximating formulas are obtained for these quantities. These formulas make it possible to describe experimental data in the mass range 16<A<240.     

Nd: YAG激光烧蚀裂解加工技术模拟分析与实验研究

激光裂解技术能够极大改善发动机缸体主轴承座的加工质量并显著提高加工效率. 为探寻Nd:YAG激光烧蚀球墨铸铁材料裂解槽的裂解性能, 本文基于有限元法成功构建了发动机缸体主轴承座激光裂解加工过程仿真模型, 针对QT500-7球墨铸铁主轴承座的裂解参数进行了仿真分析. 研究结果表明: 在影响裂解质量的三个裂解槽几何参数中, 槽深较张角及曲率半径对裂解载荷的影响效应更为明显; 裂解载荷随槽深的增加而迅速降低, 随槽张角和曲率半径的增加而升高; QT500-7球墨铸铁发动机缸体主轴承座激光裂解加工优化参数应为裂解槽深选为0.5 mm, 裂解槽张角选为60^o, 裂解槽半径选为0.2 mm. 有限元模拟分析结果得到了单向拉伸实验结果的验证. 本工作通过ABAQUS仿真模拟及大量裂解载荷试验确立了裂解槽几何形状的优化参数, 为显著降低裂解载荷和优化裂解工艺提供了数值参考, 有利于实现发动机缸体加工的快速发展, 从而促进汽车工业实现绿色制造.     

Nonlinear optical properties of a Woods–Saxon quantum dot under an electric field

A theoretical study of the effect of the confining potential on the nonlinear optical properties of two dimensional quantum dots is performed. A three-parameter Woods–Saxon potential is used within the density matrix formalism. The control of confinement by three parameters and an applied electric field gives one quite an advantage in studying their effects on the nonlinear properties. The coefficients investigated include the optical rectification, second and third-harmonic generation and the change in the refractive index. Their dependence on the electric field values, dot size and the energy of the incoming photons is studied extensively.It is shown that the Woods–Saxon potential can be used to model the confinement in quantum dots with considerable success.     

Nuclear shapes and interaction potentials of two colliding208Pb nuclei at finite temperature

The effect of nuclear and Coulomb interactions on the shapes of two colliding²⁰⁸Pb nuclei at finite temperature is investigated. The complex potential energy density derived by Faessler and collaborators and the kinetic energy density and entropy density for two Fermi spheres at finite temperature are used to calculate the free energy of the²⁰⁸Pb +²⁰⁸Pb system in the energy density formalism. Shell corrections are added to the free energy in the framework of the Strutinsky method. The total free energy is minimized with respect to the quadrupole deformation and the diffuseness to determine the density distribution of²⁰⁸Pb nucleus at certain distanceR and temperatureT assuming the deformed Woods-Saxon shape for each nucleus. It is found that the nucleus acquires larger deformation and diffuseness as the temperature increases. The interaction potential between two²⁰⁸Pb nuclei is calculated from the minimized free energy. The total (nuclear + Coulomb) potential is found to decrease with increasing temperature, whereas the real part of the nuclear potential becomes more repulsive as the temperature increases.     

Approximate penetration factor and reduced width for a diffuse edge well

The so-called anticlassical approximation for solutions of the radial Schrödinger equation with rapidly varying potentialsU(r) for which ¦(kU)^–1 dU/dr¦ 1 is worked out. With the diffuseness as a small parameter and using the method of matched asymptotic expansions the regular and irregular wave functions for the Woods-Saxon potential well with Coulomb and centrifugal barrier are obtained. The penetration factor and the reduced width are also deduced and used to express the resonance width.Communicated by X. Campi     

Double folding analysis of ~(3)He elastic and inelastic scattering to low lying states on ~(90)Zr,~(116)Sn and ~(208)Pb at 270 MeV

The experimental data on elastic and inelastic scattering of 270 MeV~3 He particles to several low lying states in~(90)Zr,~(116)Sn and~(208)Pb are analyzed within the double folding model(DFM). Fermi density distribution(FDD) of target nuclei is used to obtain real potentials with different powers. DF results are introduced into a modified DWUCK4 code to calculate the elastic and inelastic scattering cross sections. Two choices of potentials form factors are used; Woods Saxon(WS) and Woods Saxon Squared(WS~2) for real potential, while the imaginary part is taken as phenomenological Woods Saxon(PWS) and phenomenological Woods Saxon Squared(PWS~2). This comparison provides information about the similarities and differences of the models used in calculations.     

Spin-Orbit Splitting in Semiconductor Quantum Dots with a Two-Dimensional Ring Model

We present a theoretical study of the energy levels with two-dimensional ring confining potential in the presence of the Rashba spin-orbit interaction. The features of some low-lying states in various strengths of the Rashba spin-orbit interaction are investigated. The Rashba spin-orbit splitting can a/so be influenced by the width of the potential barrier. The computed results show that the spin-polarized electronic states can be more easily achieved in a weakly confined dot when the confinement strength for the Rashba spin-orbit interaction is larger than a critical value.     

软X射线Mo/Si多层膜反射率拟合分析

由于多层膜的表界面粗糙度和材料之间的相互扩散等因素，导致多层膜的实际反射率小于理论计算的反射率，因此，多层膜结构参量的确定对镀膜工艺参量的标定具有重要意义。由于描述单个非理想粗糙界面散射的Stearns法适用于软X射线短波段区域，采用它的数学模型来描述软X射线多层膜的粗糙度，利用最小二乘法曲线拟合法对同步辐射测得的Mo／Si多层膜的反射率曲线进行拟合，得到了非常好的拟合结果，从而确定了多层膜结构参量，同时分析了多层膜周期厚度，厚度比率，界面宽度以及仪器光谱分辨率对多层膜反射特性的影响，这些工作都为镀膜工艺改进提供了一定的理论依据。     

Any J-State Solution of the Duffin–Kemmer–Petiau Equation for a Vector Deformed Woods–Saxon Potential

By using the Pekeris approximation, the Duffin–Kemmer–Petiau (DKP) equation is investigated for a vector deformed Woods–Saxon (dWS) potential. The parametric Nikiforov–Uvarov (NU) method is used in calculations. The approximate energy eigenvalue equation and the corresponding wave function spinor components are calculated for any total angular momentum J in closed form. The exact energy equation and wave function spinor components are also given for the J?=?0 case. We use a set of parameter values to obtain the numerical values for the energy states with various values of quantum levels (n, J) and potential’s deformation constant q and width R.