Abstract
Owing to the development of XUV and X ray of the free-electron lasers, the photoelectron angular distribution in the sequential two-photon double ionization has received increasing attention of theorists and experimentalists, because it provides the valuable information about the electronic structure of atom or molecule systems and allows the obtaining of additional information about mechanisms and pathways of the two-photon double ionization. In this paper, the expression of the sequential two-photon double ionization process of the photoelectron angular distributions, including the non-dipole effects, is obtained based on the multi-configuration Dirac-Fock method and the density matrix theory, and the corresponding calculation code is also developed. Based on the code, the sequential two-photon double ionization process of the 3p and 2p shells of Ar atom and K<sup>+</sup> ion are studied, in which, the dipole and the non-dipole parameters of photoelectron angular distribution are investigated systematically. It is found that the angular distributions of the first- and second-step electrons in sequential two-photon double ionization are similar and the two photoionization processes affect each other. Near the ionization threshold, the photoionization cross-sections and anisotropy parameters for the 3p shell and the 2p shell show a large difference. While away from the threshold, the cross-section and angular anisotropy parameters of the 3p and 2p shells show similar behaviors. At the position of Cooper minimum of the photoionization cross section, the contribution of the electric dipole is suppressed, and the non-dipole effect is obvious. The non-dipole effect leads to a forward-backward asymmetric distribution of photoelectrons relative to the direction of incident light. The results of this paper will be helpful in studying the nonlinear processes of photon and matter interaction in the XUV range.
Highlights
In this paper, the expression of the sequential two-photon double ionization process of the photoelectron angular distributions, including the nondipole effects, have been presented based on the multi-configuration Dirac-Fock method and the density matrix theory, and we also developed the corresponding calculating code
图 8 K+离子 3p3/2 壳层 2PDI 过程第一个光电子角分布 Fig. 8 The first photoelectron angular distribution in 2PDI of the K+ ion 3p3/2 shell
Summary
序列双光双电离(2PDI)是指原子在辐射场的作用下,吸收一个光子后电离一 个束缚态电子,紧接着再次吸收一个光子并电离另一个束缚态电子的双电子电离 过程。2PDI 是 XUV 波段最简单的非线性原子过程,它广泛地存在星际介质[1]和 太阳系行星电离层外部介质[2]中。2PDI 产生光电子的角分布和角向关联包含了 量子体系的电子结构以及光与物理相互作用动力学过程的重要信息。对其研究为 揭示光与物质相互作用的非线性物理机制、建立非线性原子碰撞理论模型具有重 近年,由于 XUV 和 X 射线自由电子激光光源技术的进步,极大地推动了人 们对原子光电离过程的实验和理论研究的开展。对 2PDI 光电子能谱和角分布谱 的研究是自由电子激光主要的实验任务之一。2007 年,M. 对光电离的实验与理论工作的开展相互促进。最初,理论计算主要是基于电 偶极(E1)近似[15,16,17]展开的。在光子能量不是很高时,电偶极近似的理论计算结果 可以很好解释实验测量结果。然而,近年的实验发现在几百电子伏特甚至更低的 入射光子能量时,电偶极近似已经不再适用,需要考虑 E1 与电四极(E2)和磁偶 极(M1)之间的干涉[18,19,20,21,22]。由于 2PDI 过程在 XUV 及更短的波段上发生,因此该 过程中的非偶极效应更加值得关注。2012 年,Grum-Grzhimailo 等人[23]利用密度 矩阵理论给出了包含所有电多极和磁多极辐射场下 2PDI 光电子角分布的一般性 表达式。作为应用,他们计算了一级非偶极修正下 Ne 原子 2p 壳层 2PDI 的光电 子角分布,并讨论了非偶极效应导致光电子角向散射的不对称分布现象。2013 年, Gryzlova 等人[24]在此基础上进一步计算了 Ar 原子 3p 壳层的 2PDI 光电子角分 布,并与 Ne 原子 2p 壳层的结果进行了比较。Ar 原子 3p 壳层光电离截面存在 Cooper 极小,Ne 原子 2p 壳层的光电离不存在这一现象。在 Cooper 极小能量附
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