Triple differential cross section in (e, 2e) collisions for sodium in a coplanar symmetric geometry

The triple differential cross sections for (e, 2e) ionization of sodium in a coplanar symmetric geometry have been studied in distorted wave Born approximation with the modified semiclassical exchange potential. The present calculations improve the agreement between the theoretical and experimental results. The post-collision interaction and target polarization effects have also been studied. In addition, the variation trends of the shape and ratio for the forward and backward scattering peaks have been discussed. Besides, the small bump observed between these two peaks has been analyzed by the interaction between active electron and passive electrons.     

Xe(4d~(10))(e,2e)反应三重微分截面的理论研究

采用修正后的扭曲波玻恩近似理论,计算了共面不对称几何条件下Xe(4d~(10))(e,2e)反应的三重微分截面.散射电子能量为1000 eV,敲出电子能量为20 eV,散射电子角度分别固定在2°,4°和7.5°.理论计算与Avaldi等人的实验结果和扭曲波玻恩近似理论计算进行了比较,发现出射电子之间的后碰撞相互作用较弱,极化效应在反应过程中起着重要作用.     

On the observation of the fine structure effect in non-relativistic (e, 2e) processes

The spin asymmetry arising in an (e,2e) process using spin-polarized incoming electrons with non-relativistic energies is shown to be dominated by the fine structure effect if a suitable kinematical regime is chosen. Calculations in the distorted wave Born approximation (DWBA) for both the triple differential cross-section and the spin asymmetry are presented for the inner shell ionization of argon. This process would provide an accessible target for existing experimental set-ups.     

Relativistic effects in low energy electron scattering from atoms

Recent relativistic calculations on low energy elastic scattering of electrons from atoms are reviewed. Two aspects are emphasized : mathematical transformations and numerical methods used in the solution of the Dirac equation and the summation of the partial wave series ; and the results of relativistic calculations, in particular the behaviour of the cross sections and spin polarizations for different atoms, different energies of the incident electron, and in different approximations. The effects of the screening of the nucleus by the atomic electrons, electron exchange (including the use of approximate exchange potentials) and the distortion of the atom by the incident electron are discussed. Detailed results for cross sections and spin polarizations are given for mercury and the inert gases. The differences arising from use of the Dirac equation instead of the Schrödinger equation are considered.     

低能电子碰撞He+(e,2e)反应绝对三重微分截面的理论研究

利用Berakdar和Briggs对BBK波函数Sommerfeld参数的修正结果，即考虑第三个粒子存在对两个粒子间相互作用的影响，考虑了入射道的库仑相互作用及出射粒子的交换对称性，计算了在共面等能分配几何情况下低能电子碰撞He⁺(e,2e)反应绝对三重微分截面.结果表明，入射道库仑场对较低的入射能量及小的碰撞参数的三重微分截面影响较大. 关键词：     

Quasi-binary incident electron—centre of mass collision in (e, 3e) process on He and He-like ions

We present in this communication the results of our first Born calculation in the three-Coulomb (3C) wave approach for the (e, 3e) process on He and He-like ions at an incident electron energy 5599 eV in the coplanar constant θ12 as well as out-of-plane constant φ12 modes. These two geometrical modes are such that the quasi-binary collision between the incident electron and centre of mass of the ejected electrons is in the scattering plane. The theoretical formalism has been developed using plane waves, Le Sech wave function and approximated BBK-type wave function respectively for the incident and scattered, bound and ejected electrons to calculate five-fold differential crosssection (FDCS) of the (e, 3e) process. We emphasize on the similarities and dissimilarities (asymmetries) in the angular profile of the FDCS in two modes as well as the effects of post-collision interaction (between the ejected electrons) and nuclear chargeZ on the angular profile of the FDCS. We observe that with the increment of nuclear charge the two quasi-binary collisions approach towards identical behaviour at larger mutual angles and thus bringing less asymmetry in FDCS for higherZ target.     

Ne原子(e,2e)反应中反冲离子动量分析

利用冷靶反冲离子动量谱仪,对电子轰击Ne原子的单电离反应(e,2e)进行了研究,实验测量了70—3300eV入射能量情况下,反应过程中产生的一价反冲离子的动量分布,并对反冲离子的总动量进行了还原。介绍了一个简单的碰撞机制,据此着重分析了反冲离子纵向动量和横向动量二维谱形成的原因,该碰撞机制能够较好地解释较高能量入射时的实验结果。最后根据反冲离子的动量,估算了出射电子的能量范围,为下一步进行电子、离子的符合测量奠定了基础。     

Li+低能(e,2e)反应角分布

利用修正的BBK理论，考虑入射道的库仑相互作用及出射电子的交换对称性，在共面-等能分享-垂直角度碰撞几何中，分别计算了能量为79.6，105.6，227.6和375.6eV的入射电子碰撞Li⁺(1s²)(e，2ｅ)反应三重微分截面(TDCS).结果表明：在接近阈能的碰撞中，两出射电子连线平行于入射电子方向时，TDCS最大；两出射电子连线垂直于入射电子方向时，TDCS最小；入射电子能量达5倍的电离阈能时，主要为单次双体碰撞，而且入射道库仑场对决定低能碰撞的TDCS起着重要作用. 关键词：     

(e, 3e) test on e-e correlations in helium

The angular variations of the five-fold differential cross section obtained by using different wave functions of helium are compared with experimental data. It is found that in the coplanar geometry two kinematical arrangements, (i) equal energy sharing between the two ejected electrons with one of them ejected along the momentum transfer direction and the other along varying direction and (ii) the Bethe ridge condition with fixed sum of ejected electron energies and varying angle between them, are very sensitive to e-e correlations contained in the target wave function. This comparison has been used to show that open-shell class of wave functions better incorporate e-e correlations than the closed-shell class.     

Possibility of new effects in quantum wells coupled by Coulomb interaction

The hamiltonian for two 2-dimensional layers of electrons (neglecting spin), is similar to that of a free electron gas with the role of spin-up and spin-down electrons being played by electrons in two layers. An anomalous ground state analogous to the spiral spin density wave (SSDW) state presents intriguing possibilities.     

(e,2e)反应中冲量近似的理论研究

利用冲量近似理论和玻恩近似方法, 以氢原子(1s)为例, 在共面不对称几何条件下用多种模型分别计算了若干入射能、 散射角情形下电子碰撞电离(e, 2e) 反应的三重微分散射截面. 与其他的理论方法和实验数据进行了比较, 分析了曲线结构差异及原因, 对其适用范围进行了研究, 并探讨了交换效应的贡献, 验证了早期的研究. 关键词： 扭曲波冲量近似 平面波冲量近似 三重微分截面     

Theoretical calculation of the triple differential cross sections of the 2p orbital of argon in a coplanar highly asymmetric（e,2e） reaction

The triple differential cross sections of the 2p electron of argon in a coplanar highly asymmetric geometry have been calculated with the modified distorted wave Born approximation (DWBA) and the target Hartree－Fock approximation methods. The damping polarization of the semi-classical short-range potentials and the M_ee factor are included in the distorting potentials of the modified DWBA. Theoretical results are compared with a recent experiment. The dynamic mechanism of inner shell ionization in a coplanar highly asymmetric geometry (e, 2e) reaction are also discussed.     

Spin eigen-states of Dirac equation for quasi-two-dimensional electrons

Dirac equation for electrons in a potential created by quantum well is solved and the three sets of the eigen-functions are obtained. In each set the wavefunction is at the same time the eigen-function of one of the three spin operators, which do not commute with each other, but do commute with the Dirac Hamiltonian. This means that the eigen-functions of Dirac equation describe three independent spin eigen-states. The energy spectrum of electrons confined by the rectangular quantum well is calculated for each of these spin states at the values of energies relevant for solid state physics. It is shown that the standard Rashba spin splitting takes place in one of such states only. In another one, 2D electron subbands remain spin degenerate, and for the third one the spin splitting is anisotropic for different directions of 2D wave vector.     

Quasi-elastic electron scattering (e,e′p) and (e,e′d) from 6Li in a coincidence experiment

Coincidence cross sections for the reactions ⁶Li(e, e′p) and ⁶Li(e, e′d) have been measured in the region of quasi-elastic scattering. Using incident electrons of 2.5 and 2.7 GeV, the four-momentum transfers to the proton were 6.6 fm^?2, 10.0 fm^?2 and 11.6 fm^?2. The proton coincidence data agree with shell-model distributions assuming a Woods-Saxon potential and including short-range nucleon-nucleon correlations. The best fit to the deuteron coincidence data is obtained with a cluster wave function for the p-nucleons and a harmonic oscillator wave function for the s-nucleons taking into account the deuteron yield from the s-shell. The ratio of the deuteron cross section from ⁶Li divided by the elastic e-d scattering cross section depends only slightly on the four-momentum transfer and has a value of ≈ 2.     

Calculations of total ionization cross sections of Ne,Ar, Kr,and Xe atoms in the born approximation allowing for electron perturbations in the continuous spectrum

Electron impact ionization cross sections of Ne, Ar, Kr, and Xe atoms are numerically calculated. The electron perturbation in the continuous spectrum in the target field is taken into account. The matrix elements are calculated in many-electron, nonrelativistic approximation with allowance for the superposition of configurations and relaxation effect. The radial part of the electron wave function in the continuum is calculated by solving the single-configuration Hartree-Fock equation. The wave functions of electrons in the continuum are orthogonalized with respect to the core orbital functions. The calculated cross sections are compared to the experimental data and calculations made using the plane-wave Born approximation and that involving generalized oscillator strengths.     

Electron dichroism effects in the relativistic (e, 2e) process for K-shell ionization of atoms

In this communication we present theoretical demonstration of electron dichroism in the relativistic (e, 2e) process for K-shell ionization of atoms in non-coplanar asymmetric geometry. The theoretical formalism has been developed in plane wave Born approximation and in this approximation the triple differential cross-section (TDCS) has been expressed as a product of kinematical factors and atomic structure functions. The longitudinal spin asymmetry in the relativistic (e, 2e) process on K-shell of atoms has been shown to depend on the interference between the transition charge and component of the transition current in the direction perpendicular to the scattering plane. Further, the longitudinal spin asymmetry has been shown to depend on incident electron energy, atomic number of the target, azimuthal angle of the ejected electron and scattered electron angle.     

自旋相关的电子隧穿和自旋极化

研究了电子的自旋相关的隧穿和极化。在外加磁场的作用下，自旋向上的电子与自旋向下的电子具有不同的隧穿系数。当电子的自旋方向与磁场方向相反时，其隧穿概率受到磁场的抑制而变小；反之，当两平行时，电子的了隧穿系数增大。这种差异可以用本中定义的自旋极化率来表示。本对不同磁场下的自旋极化率进行了计算，结果也表明当电子的动能较小，这种自旋极化的效应越显。     

He原子电子动量谱学实验结果的理论分析

对作者所在实验室最近完成的Ｈｅ原子电子动量谱学实验结果进行了详细的理论分析。在平面波冲量近似和扭曲波冲量近似下，利用三类典型的Ｈｅ原子基态波函数，对Ｗｅｉｇｏｌｄ几何条件下的（ｅ，２ｅ）反应的三重微分截面进行了计算，并与实验结果作了详细的比较，结果表明Ｌ（１）电子动量谱学是直接获取电子波函数信息的有用方法；（２）平面波冲量近全民族 扭曲波冲量近似得到的电子动量谱形状的差别并不大。     

Experiment and theory for the 2H(e,p)e′n reaction

Differential cross sections and angular distributions of protons from the ²H(e, p)e′n reaction have been measured at four incident electron energies. The proton angular distributions were measured with the neutron-proton relative energy approximately constant, and an 85° differential cross section was measured as a function of the incident electron energy. The electrodisintegration cross section was calculated using the Hulthén wave function for the ground state with a plane wave for the final state. Reasonable agreement between experiment and theory is found.