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Fully relativistic distorted-wave method of studying electron-atom collision excitation process

LI Wenbo ,  LI Bingbing ,  CHEN Hao ,  XIE Luyou ,  WU Zhongwen ,  DING Xiaobin ,  ZHANG Denghong ,  JIANG Jun ,  DONG Chenzhong

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Fully relativistic distorted-wave method of studying electron-atom collision excitation process

LI Wenbo, LI Bingbing, CHEN Hao, XIE Luyou, WU Zhongwen, DING Xiaobin, ZHANG Denghong, JIANG Jun, DONG Chenzhong
Acta Phys. Sin.,
doi: 10.7498/aps.74.20241467
cstr: 32037.14.aps.74.20241467
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  • Abstract

    The electron-atom (ion) collision excitation process is one of the most common inelastic scattering processes. It is of great significance in the fields of astrophysics and laboratory plasma. The relativistic distorted-wave method is a widely used theoretical tool for studying electron-atom (ion) collisions, with the aim of obtaining scattering parameters, such as impact cross sections and rate coefficients.In recent years, we have developed a set of fully relativistic distorted-wave methods and programs of studying the electron-atom collision excitation processes. This method is based on the multi-configuration Dirac-Hartree-Fock (MCDHF) method, together with the corresponding packages GRASP 92/2K/2018 and RATIP. In the present work, continuum state wave functions, total and differential cross sections, state multipoles, integral and differential Stokes parameters of the radiation photon after the impact excitation processes of polarized electrons and atoms are calculated. The influences of electron correlation effects, Breit interaction, and plasma screening effects on the excitation cross sections are discussed. The present methods and programs possess several advantages below.1) In the calculations of the continuum electron wave functions, the direct interaction and exchange interaction between the bound electron and the continuum electron are both included. Then, the anti-symmetrized coupling wave function, which is composed of the continuum electron wave function and the continuum ion wave function, is utilized as the wave function of the system. This method is employed to study the low-energy electron scattering process and medium energy electron scattering process.2) In this method, the target state wave function is obtained form the MCDHF theory and the corresponding GRASP packages. The MCDHF method has the advantage of being able to consider the electron correlation effects, including valence-valence, core-valence, and core-core correlations, as well as the influence of Breit interaction and quantum electrodynamics (QED) effect on the target state wave function. Furthermore, the calculation of the collision excitation matrix elements also includes the contribution of the Breit interaction. Consequently, the present method integrates the advantages of both the MCDHF method and distorted-wave method, thus is made suitable for studying the scattering processes of highly charged ions. In addition, it facilitates the study of the influence of higher-order effects on the collision dynamics, thereby obtaining high-precision theoretical data.3) The current method and program can also be utilized to study the scattering cross section of electron-atom collision excitation processes, as well as the influence of plasma screening effects on collision excitation. Furthermore, the state multipoles, differential Stokes parameters, integral Stokes parameters, and orientation parameters of electron-complex atom collision excitation can be studied in detail by using the present method and program.

  • 图 1  极化电子与光子Stokes参数测量示意图

    Figure 1.  Schematic diagram of polarized electron and photon Stokes parameter measurement.

    DownLoad: Full-Size Img PowerPoint

    图 2  Xe原子的激发截面随入射电子能量的变化, 方形为模型A的结果, 三角形为模型B的结果, 带误差条的圆形为Jung 等[115]的实验(数据图片来自于文献[116])

    Figure 2.  Excitation cross section of Xe atom varies with the energy of incident electron. The square is the result of model A, the triangle is the result of model B, and the circle with error bars is the experiment of Jung et al[115]. From Ref. [116].

    DownLoad: Full-Size Img PowerPoint

    图 3  入射电子能量为8 eV时, 不同计算模型下Hg原子1S0 - 3P1电子碰撞激发微分截面, 其中SC为模型I单组态近似的计算结果, 6l为模型II的计算结果, 7l为模型III的计算结果, Experiment为Goeke等[117]的实验结果

    Figure 3.  Differential cross sections of electron collision excitation of Hg atom 1 S0-3P1 under different calculation models, when the incident electron energy is 8 eV. The SC is the calculation result of single configuration approximation of model I, 6l is the calculation result of model II, 7l is the calculation result of model III, Experiment is the result of Goeke et al[117].

    DownLoad: Full-Size Img PowerPoint

    图 4  从基态2p6 J = 0到2p53s J = 2的磁能级之间的激发截面(数据图片来自于文献[108])

    Figure 4.  Excitation cross sections from ground state 2p6 J = 0 to 2p53s J= 2 magnetic energy levels. From Ref. [108].

    DownLoad: Full-Size Img PowerPoint

    图 5  入射电子能量为45 eV时, 电子与Ca原子从基态到1P1的碰撞激发微分Stokes参数P1, P2和-P3, 其中$ \kappa $为最大分波量子数, Experiment为Dyl等[120]的实验结果

    Figure 5.  Collision excitation differential Stokes parameters P1, P2 and -P3 of electron and Ca atom from ground state to 1 P1, when the incident electron energy is 45 eV. $ \kappa $ is the maximum partial wave quantum number, and Experiment is the result of Dyl et al[120].

    DownLoad: Full-Size Img PowerPoint

    图 6  入射电子能量为8 eV时, 不同关联模型下计算的Hg原子1S0-3P1归一化的态多极, 其中SC为利用单组态计算的结果, MC 6l为考虑了6l关联轨道的计算结果, MC 7l为考虑了7l关联轨道的计算结果, Experiment为Sohn等[122]的实验结果

    Figure 6.  Normalized state multipoles of Hg atom 1S0-3P1 calculated under different correlation models, when the incident electron energy is 8 eV. The SC is the calculation result using a single configuration, MC 6l is the calculation result considering the 6l correlation orbit, MC 7l is the calculation result considering the 7l correlation orbit, and Experiment refers to the results of Sohn et al[122]

    DownLoad: Full-Size Img PowerPoint

    图 7  入射电子能量为15 eV时, 不同关联模型下计算的Hg原子1S0-3P1归一化的态多极, 其中SC为利用单组态计算的结果, MC 6l为考虑了6l关联轨道的计算结果, MC 7l为考虑了7l关联轨道的计算结果, RDW R 为Srivastava等[121]的理论结果, Experiment为Sohn等[122]的实验结果

    Figure 7.  Normalized state multipoles of Hg atom 1S0-3P1 calculated under different correlation models, when the incident electron energy is 15 eV. The SC is the calculation result using a single configuration, MC 6l is the calculation result considering the 6l correlation orbit, MC 7l is the calculation result considering the 7l correlation orbit, RDW R is the theoretical result of Srivastava et al[121], and Experiment refers to the results of Sohn et al[122].

    DownLoad: Full-Size Img PowerPoint

    图 8  从基态1s2 1S0 到 1s2p 1P1和3P1的激发截面随屏蔽长度的变化(数据图片来自于文献[128])

    Figure 8.  Excitation cross sections from ground state 1s2 1S0 to 1s2p 1P1 and 3P1 vary with shielding length. From Ref. [128].

    DownLoad: Full-Size Img PowerPoint
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Publishing process
  • Received Date:  20 October 2024
  • Accepted Date:  02 December 2024
  • Available Online:  25 December 2024

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