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Methods of calibrating kinetic energy release in dissociation process of molecular dications

Zhang Min Yan Shun-Cheng Gao Yong Zhang Shao-Feng Ma Xin-Wen

Zhang Min, Yan Shun-Cheng, Gao Yong, Zhang Shao-Feng, Ma Xin-Wen. Methods of calibrating kinetic energy release in dissociation process of molecular dications. Acta Phys. Sin., 2020, 69(20): 203401. doi: 10.7498/aps.69.20200901
Citation: Zhang Min, Yan Shun-Cheng, Gao Yong, Zhang Shao-Feng, Ma Xin-Wen. Methods of calibrating kinetic energy release in dissociation process of molecular dications. Acta Phys. Sin., 2020, 69(20): 203401. doi: 10.7498/aps.69.20200901

Methods of calibrating kinetic energy release in dissociation process of molecular dications

Zhang Min, Yan Shun-Cheng, Gao Yong, Zhang Shao-Feng, Ma Xin-Wen
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  • In the studies of fragmentation processes of molecules induced by extreme ultraviolet photons, intense laser fields, or charged particles, kinetic energy release (KER) is a key physical parameter. It can reveal the electronic states of the parent molecular ion, and provide an insight into the molecular structures and the dissociation dynamics. Therefore, it is essential to obtain the accurate KER spectrum for studying the fragmentation process of molecules. However, in the experiments using reaction microscope, experimental parameters such as the time-of-flight (TOF), the voltage of the TOF spectrometer and the detector image of the fragments have significant influence on the accuracy of KER determination. In this work, by taking the two-body fragmentation process of CO2+ → C+ + O+ induced by 108 keV/u Ne8+ impact on CO molecules as a prototype, we introduce two methods to accurately calibrate the reconstructed KER spectrum. The first method is to employ two-dimensional momentum spectra of C+ ions obtained by slicing the momentum sphere. The parameters are correctly calibrated when the circular distribution of the two-dimensional ion momentum image is restored. The second method is to use the correlation spectra of the KER as a function of the emission angle of the C+ ions to calibrate the experimental parameters, the calibration meets the required level only when the linear dependence of the emission angle on the KER is fulfilled. Then, calibrated KER spectrum is obtained for the dissociation process. By fitting the peak dissociated from the 3Σ+ state of CO2+ in the KER spectrum, the energy resolution is estimated at 0.24 eV under these experimental conditions. Although these two methods can be used to accurately calibrate the reconstructed KER spectrum, the second calibration method does not require particularly high data statistics, and is suitable for analyzing the processes with lower reaction cross section. Furthermore, this method is convenient for debugging the parameters. Both methods are reliable for parameter calibration and guarantee high accuracy KER for molecular fragmentation experiments in future.
      PACS:
      34.80.Ht(Dissociation and dissociative attachment)
      07.05.Kf(Data analysis: algorithms and implementation; data management)
      Corresponding author: Zhang Shao-Feng, zhangshf@impcas.ac.cn ; Ma Xin-Wen, x.ma@impcas.ac.cn
    • Funds: Project supported by the National Key R&D Program of China (Grant No. 2017YFA0402300) and the National Natural Science Foundation of China (Grant No. 11804347)

    中性气体分子在与高电荷态离子、电子和光子相互作用时会被电离而形成分子离子. 不稳定的分子离子在库仑排斥力的作用下会进一步碎裂成两个甚至多个离子碎片. 该过程广泛存在于彗星拖尾[1,2]、星际气体逃逸[3,4]、化学键的形成与断裂[5,6]、辐射损伤[7,8]等相关物理现象中. 不仅对物理、化学以及生物等科学领域具有重要的研究意义, 而且在人造等离子体环境[9], 以及聚变装置[10]等技术领域起着重要作用.

    在过去的几十年里, 随着多重符合离子动量成像技术[11-13]的不断发展与进步, 利用不同入射炮弹诱导的气体分子碎裂研究已被广泛报道[14-25]. 一般来说, 这些实验主要通过测量碎片离子的飞行时间和在探测器上的位置来获得分子离子在解离时碎片离子的动能以及离子碎片取向, 进而研究分子离子在碎裂时的以下现象: 1) 分子最外层电子轨道结构信息[20]; 2) 物质波干涉效应[21]; 3) 体系的势能函数和基态波函数模的平方[22]; 4) 解离机制[19,23,24]; 5) 重建解离前母体离子的构型[25].

    在这些实验当中, 涉及的最基本物理量就是分子离子在解离时的动能释放(KER). 在碰撞过程中, 完整的中性分子会在极短的时间内(10–17量级)被电离, 同时将剩余的分子离子制备到不同的离子态上, 而KER就是表征分子离子沿着势能曲线运动并将势能转化成动能的物理量. 通过重构碎片离子在碎裂时的KER就可以解读分子离子初始态的信息以及随后的碎裂动力学过程. 因此, 获得分子离子在解离时精确的KER分布对进一步深入研究分子碎裂物理过程至关重要.

    然而, 对于如何获得准确的KER分布却少有报道. 本文通过108 keV/u-Ne8+离子与CO气体的转移电离实验:

    Ne8++CONe7++C++O++e,
    (1)

    CO2+C++O+两体碎裂过程为例来讨论CO2+解离时KER的重构与校准, 并给出校准后的KER分布.

    本实验在中国科学院近代物理研究所320 kV高电荷态离子综合研究平台2号终端的反应显微成像谱仪(reaction microscopes)上完成. 反应显微成像谱仪的工作原理在文献[11-13]中有详细介绍, 在这里只做简要介绍. 首先, 由电子回旋共振离子源产生的离子束经过分析磁铁选择和静电加速管加速后得到实验所需要的电荷态以及能量(108 keV/u-Ne8+). 离子束再经过四极磁铁聚焦、狭缝准直后进入反应显微成像谱仪的反应腔室, 在飞行时间谱仪(time of flight spectrometer, TOF)的中心处与垂直向下的超音速CO气体冷靶交叉碰撞: 一方面, 反应后的反冲(碎片)离子在飞行时间谱仪的加速电场(约118 V/cm)作用下进入漂移区, 最后打在反冲离子探测器上, 并触发探测器获得对应的飞行时间信息和二维位置信息; 另一方面, 参与反应的散射离子经过静电偏转器后打在散射探测器上, 同时给出对应的时间信息和二维位置信息, 未参与反应的主束则被法拉第筒收集. 为了减少由于靶宽引起的飞行时间弥散, 提高TOF方向上反冲离子的动量分辨, 飞行时间谱仪在几何结构上满足一维时间聚焦条件[26], 即加速区和漂移区的长度比为1∶2. 实验中将散射离子和反冲离子的复合信号作为触发信号来触发数据获取系统, 时间信息和位置信息均由时间数字转换器(TDC)给出, 每道为25 ps. 在离线分析中, 根据测得的时间和位置信息, 就可以重构所有碎片离子的三维动量.

    为方便讨论, 定义: 束流沿着Z方向运动, 超音速气体冷靶的方向为Y方向, 则TOF的方向即为X轴.

    在实验中, 分子离子碎裂过程中的KER 是通过重构碎片离子的三维动量得到的, 因此想要获得准确的KER分布, 首先需要准确地刻度碎片离子的三维动量. 如图1所示, 在碰撞反应发生后, 产生的碎片离子在加速电场的约束下朝向探测器飞行, 在沿着TOF方向上为匀加速运动, 而在垂直于TOF的平面内为匀速运动.

    图 1 TOF结构装置示意图\r\nFig. 1. Schematic view of TOF
    图 1  TOF结构装置示意图
    Fig. 1.  Schematic view of TOF

    碎片离子从反应点被引至探测器表面的飞行时间t

    t=2a(1v+v2+2qUm+1v2+2qUm),
    (2)

    其中, a, U分别为加速区的长度和加载的电压; q, m, v分别为离子的电荷、质量、以及初速度. 考虑到在碰撞过程中, 离子在加速电场中获得的能量远大于碰撞过程中获得的能量, 即mv2/(2qU)0, 经过变换从(2)式可得碎片离子在TOF方向上的动量分量Px

    Px=qUa(t0t),
    (3)

    其中, t0为初速度为0的离子的飞行时间, 该值可从飞行时间谱特征峰的峰中心位置处得到.

    在垂直于TOF的平面内, 离子做匀速运动. 因此, 通过离子的飞行时间信息t和二维位置信息(y, z)便可重构其动量分量. 即

    {Py=myy0t,Pz=mzz0t,
    (4)

    其中, (y0, z0)为vy=0vz=0的离子打在探测器上的位置.

    通过以上的分析可以得到如下结论: 影响离子动量Px的主要参数为离子的飞行时间t和加速区电压U; 同时对Py, Pz有主要影响的参数为二维位置信息和飞行时间t. 在接下来的讨论中将详细介绍这些实验参数的获取与校准方法.

    3.1.1   飞行时间参数

    实验中, 由数据获取系统记录的飞行时间为碎片离子相对于炮弹的飞行时间, 同时这个测量的时间还受到信号在电子学电路中传播时间的影响, 因此, 在数据处理时需要先对飞行时间t进行修正以获得碎片离子的绝对飞行时间. 对于初速度为0的离子, 根据(2)式可知其绝对飞行时间t0

    t0=4a2Umq,
    (5)

    即初速度为0的离子的绝对飞行时间t0m/q为正比例函数关系. 而从数据获取得到的相对飞行时间函数关系为te0=km/q+b, 其截距b即为需要修正的由于炮弹飞行时间及电子学因素导致的相对偏移量参数(图2).

    图 2 相对飞行时间$ t_{0}^{\rm e} $与$\sqrt{{m}/{q}}$的关系图(每道为25 ps)\r\nFig. 2. Relationship between relative TOF $ t_{0}^{\rm e} $ and $\sqrt{{m}/{q}}$ (every channel is 25 ps)
    图 2  相对飞行时间te0m/q的关系图(每道为25 ps)
    Fig. 2.  Relationship between relative TOF te0 and m/q (every channel is 25 ps)

    通过该方法, 可以获得碎片离子的绝对飞行时间t. 图3为修正后的所有碎片离子的飞行时间谱, 从图中可以鉴别出各个离子的飞行时间, 原则上根据(3)式就可以计算TOF方向上的动量Px.

    图 3 Ne8+离子与CO作用后碎片离子的飞行时间谱\r\nFig. 3. TOF spectrum of fragment ions produced by Ne8+ interaction with CO
    图 3  Ne8+离子与CO作用后碎片离子的飞行时间谱
    Fig. 3.  TOF spectrum of fragment ions produced by Ne8+ interaction with CO

    但是在实际情况中, 不能精确确定加载在飞行时间谱仪上的电压, 同时TOF谱仪的长度精度也只能控制在毫米量级. 这两者都会在(3)式中引入很大的误差. 在这种情况下可以借助静电透镜分析设计软件来模拟并计算Px.

    首先, 将TOF的结构尺寸导入模拟软件, 模拟出不同TOF电压下初速度为0的所有碎片离子的飞行时间ts0. 当所有ts0t0都非常接近时, 说明模拟结果与实际离子的飞行情况相似, 以此获得的电压Us, 即为实际加载的TOF电压U.

    在此基础上, 进一步将Us代入该软件模拟出C+离子在不同初始动量Px下的飞行时间t(Px) (表1). 从中可以发现t(0)t(Px)与动量Px的关系(图4):

    表 1  C+在不同初始动量Px下的飞行时间t(Px)
    Table 1.  TOF of C+ under different initial momentum Px
    Px/arb. units t(Px)/ns t(0)t(Px)/ns
    0 3139.149 0
    1 3138.014 1.135
    2 3136.878 2.271
    3 3135.742 3.407
    4 3134.606 4.543
    5 3133.471 5.678
    10 3127.792 11.357
    20 3116.434 22.715
    30 3105.077 34.072
    40 3093.72 45.429
    50 3082.364 56.785
    100 3025.593 113.556
    下载: 导出CSV 
    | 显示表格
    图 4 $ t(P_{x}) $ – $ t(0) $与动量$ P_{x} $的关系图\r\nFig. 4. Relationship between $ t(P_{x}) $ – $ t(0) $ and $ P_{x} $.
    图 4  t(Px)t(0)与动量Px的关系图
    Fig. 4.  Relationship between t(Px)t(0) and Px.
    Px=[t(0)t(Px)]/K,K=1.136,
    (6)

    其斜率1/K是与电压和距离相关的参数. 通过(6)式便可得到沿TOF方向上碎片离子的动量Px.

    3.1.2   位置参数

    垂直于TOF平面的动量Py, Pz与离子打在探测器的二维位置及飞行时间相关. 飞行时间已通过3.1.1节介绍的方法获得, 现在只需要将离子的位置信息确定, 便可计算出动量Py, Pz. 在数据分析程序中, 位置信息是由数据系统测得的TDC信号及其相关的参数ScaleY, ScaleZ决定. 该参数的确定公式为

    {ScaleY=ϕChY1ChY2,ScaleZ=ϕChZ1ChZ2,
    (7)

    其中, ϕ为探测器有效探测面积的直径. ChY1 – ChY2为实验测得的反冲离子二维位置谱在Y轴上的投影. 同理, ChZ1 – ChZ2为Z轴上的投影(图5).

    图 5 Ne8+离子与CO作用后反冲离子的位置谱\r\nFig. 5. Position spectrum of recoil ions produced by Ne8+ interaction with CO.
    图 5  Ne8+离子与CO作用后反冲离子的位置谱
    Fig. 5.  Position spectrum of recoil ions produced by Ne8+ interaction with CO.

    尽管在上述的过程中, 可以初步得到计算碎片离子三维动量的参数: 飞行时间t, TOF电压U, 以及位置信息的参数ScaleY和ScaleZ, 但是未对这些参数进行刻度. 因此, 在后续的讨论中, 通过对离子三维动量的校准, 进一步精细刻度上述参数. 在校准碎片离子的三维动量Px, Py, Pz时不是独立进行的, 而是两两互相进行相对校准.

    考虑到分子离子在碎裂后, 碎片离子的动量在空间上为均匀分布的球壳, 而这个动量球壳的半径为分子离子碎裂时获得的动量P. 根据这一物理效应, 可通过切片的方式分别获得碎片离子的Py-Pz, Py-Px, Pz-Px二维动量分布, 并在数据分析程序中分别调试各个参数(飞行时间、电压参数、二维位置参数). 当每个参数校准准确时, 切片后碎片离子的二维动量分布应呈现出正圆形(图6(a)(c), 图中不同的圆环代表不同动量的碎片离子). 根据重构的碎片离子三维动量就能得到分子离子在碎裂时的KER, 对重构的KER还需要与已知的KER对进行进一步验证与校准.

    图 6 (a)−(c)切片后C+离子的二维动量分布(切片厚度为$ \pm $ 30 a.u.); (d)−(f) KER与$ \theta_{yz, yx, zx} $的二维关系图\r\nFig. 6. (a)–(c) Two-dimensional momentum distribution of C+ in yz, yx, zx plan after slicing (slice thickness is $ \pm $ 30 a.u.); (d)−(f) two-dimensional relationship between KER and $ \theta_{yz, yx, zx} $
    图 6  (a)−(c)切片后C+离子的二维动量分布(切片厚度为± 30 a.u.); (d)−(f) KER与θyz,yx,zx的二维关系图
    Fig. 6.  (a)–(c) Two-dimensional momentum distribution of C+ in yz, yx, zx plan after slicing (slice thickness is ± 30 a.u.); (d)−(f) two-dimensional relationship between KER and θyz,yx,zx

    除了上述传统方法外, 还可以考虑另一种校准方法[27]. 对于确定的解离过程, 动量球壳的半径不会随着空间位置而发生变化. 即碎裂过程的KER不会随着离子的动量与坐标轴的夹角发生变化. 因此, 可以通过KER与离子出射角θ的关系(KER-θyz,yx,zx二维关系)来校正KER (图6(d)图6(f), 不同的直线代表不同的KER峰值). 只有当KER-θyz,yx,zx的分布呈直线, 且得到的KER与参考KER结果符合很好时, 才能确定最终的碎片离子的三维动量, 并得到准确的KER分布.

    在根据图6校准的过程中, 选取了Lundqvist等[28]测量到的CO2+(3Σ+)振动态的KER=7.83 eV作为参考来校准重构的KER. 首先, 校准探测器平面内的动量PyPz. 校准过程中, 当Py > Pz (Py偏大)时, 在KER-θyz分布中(图6(d)), KER在θyz = 0°和 ±180°附近偏大. 当Pz > Py (Pz偏大)时, 在KER-θyz分布中, KER在θyz = ±90°附近偏大. 只有当Py = Pz时, KER才会呈直线分布. 此时, 影响动量Py, Pz的参数才校准准确. 接下来就可以校准TOF方向上的动量Px.

    Px>Pyz (Px偏大)时, 在KER-θyx,zx分布中(图6(e), 图6(f)), KER在θyx,zx=±90 附近偏大. 当Px<Py,z (Px偏小)时, 在KER-θyx,zx分布中, KER在θyx,zx = ±90附近偏小. 同理, 只有影响当动量Px的参数校准准确时, 在KER-θyx,zx分布中KER才会呈直线.

    图7为校准后的CO2+ C+ + O+碎裂过程的KER谱, 其峰值主要位于6.1, 7.8, 9.5 eV. 其中, 位于6.1 eV附近的峰来自于束缚态X3Π, 1Σ+1Π解离的贡献, 位于9.5 eV附近的峰来自于1Σ+(II)态解离的贡献, 而位于7.8 eV附近的峰主要来自于3Σ+振动态基态解离的贡献, 这与之前的实验结果[28-30]符合得很好. 对3Σ+振动态解离的峰进行高斯拟合(图7蓝色方框放大部分)得到的半高全宽(FWHM)为0.24 eV, 由此, 得到当前实验下KER的分辨为0.24 eV.

    图 7 CO2+ $ \rightarrow $ C+ + O+碎裂过程的KER\r\nFig. 7. KER spectrum of the fragmentation process of CO2+ $ \rightarrow $ C+ + O+
    图 7  CO2+ C+ + O+碎裂过程的KER
    Fig. 7.  KER spectrum of the fragmentation process of CO2+ C+ + O+

    以上两种校准方法在重构碎片离子的动量大小时均能使用, 但是切片校准方式只使用了部分数据, 因此要求数据的统计量要足够高. 而使用KER-θ方式校准参数时, 使用的是全部实验数据, 因而对数据的统计量要求不是特别高, 对分析反应截面较低的反应过程比较适用, 其次该方法在校准参数时更直观、方便.

    本文以108 keV/u-Ne8+离子与CO作用后, CO2+ C+ + O+碎裂过程为例分析了影响分子离子两体碎裂过程中动能释放(KER)重构的实验参数: 飞行时间参数、飞行时间谱仪电压参数、位置坐标参数. 通过切片方式和KER与离子出射角度的关系介绍了KER的校准过程, 并给出了校准后CO2+两体碎裂的KER, 通过拟合得到当前实验下的KER分辨为0.24 eV. 校准过程中, 只有当切片得到的碎片离子的二维动量分布呈圆形或者KER与碎片离子出射角的分布呈直线时, 影响KER重构的参数才符合校准标准. 尽管这两种方法都可以用来校准重构得到的KER, 但是使用KER-θ方式校准参数时对数据的统计量要求不是特别高, 且在调试参数时更直观、方便, 这为后续开展分子碎裂实验提供了很好的技术保障.

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    Falcinelli S, Pirani F, Alagia M, Schio L, Richter R, Stranges S, Balucani N, Vecchiocattivi F 2016 Atmosphere 7 112Google Scholar

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    Boudaïffa B, Cloutier P, Hunting D, Huels M A, Sanche L 2000 Science 287 1658Google Scholar

    [8]

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    [9]

    Märk T D, Dunn G H 1985 Electron-Impact Ionization (New York: Springer) pp320–374

    [10]

    Beiersdorfer P, Bitter M, Marion M, Olson R E 2005 Phys. Rev. A 72 032725Google Scholar

    [11]

    Ullrich J, Moshammer R, Dorn A, Dörner R, Schmidt L Ph H, Schmidt-Böcking H 2003 Rep. Prog. Phys. 66 1463Google Scholar

    [12]

    Ma X W, Zhang R T, Zhang S F, Zhu X L, Feng W T, Guo D L, Li B, Liu H P, Li C Y, Wang J G, Yan S C, Zhang P J, Wang Q 2011 Phys. Rev. A 83 052707Google Scholar

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    Guo D L, Ma X W, Feng W T, Zhang S F, Zhu X L 2011 Acta Phys. Sin. 60 113401Google Scholar

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    Martín F, Fernández J, Havermeier T, Foucar L, Weber Th, Kreidi K, Schöffler M, Schmidt L, Jahnke T, Jagutzki O, Czasch A, Benis E P, Osipov T, Landers A L, Belkacem A Prior M H, Schmidt-Böcking H, Cocke C L, Dörner R 2007 Science 315 629Google Scholar

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    Chen L, Shan X, Zhao X, Zhu X L, H u, X Q, Wu Y, Feng W T, Guo D L, Zhang R T, Gao Y, Huang Z K, Wang J G, Ma X W, Chen X J 2019 Phys. Rev. A 99 012710Google Scholar

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    Shen L L, Yan S C, Ma X W, Zhu X L, Zhang S F, Feng W T, Zhang P J, Guo D L, Gao Y, Hai B, Zhang M, Zhao D M 2018 Acta Phys. Sin. 67 043401Google Scholar

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    [27]

    Kim H K 2014 Ph. D. Dissertation (Frankfurt: Frankfurt University)

    [28]

    Lundqvist M, Baltzer P, Edvardsson D, Karlsson L, Wannberg B 1995 Phys. Rev. Lett. 75 1058Google Scholar

    [29]

    Pandey A, Bapat B, Shamasundar K R 2014 J. Chem. Phys. 140 034319Google Scholar

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    高永, 张少锋, 朱小龙, 闫顺成, 冯文天, 张瑞田, 郭大龙, 李斌, 汪寒冰, 黄忠魁, 海帮, 张敏, 马新文 2016 原子核物理评论 33 513Google Scholar

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    期刊类型引用(0)

    其他类型引用(1)

  • 图 1  TOF结构装置示意图

    Figure 1.  Schematic view of TOF

    图 2  相对飞行时间te0m/q的关系图(每道为25 ps)

    Figure 2.  Relationship between relative TOF te0 and m/q (every channel is 25 ps)

    图 3  Ne8+离子与CO作用后碎片离子的飞行时间谱

    Figure 3.  TOF spectrum of fragment ions produced by Ne8+ interaction with CO

    图 4  t(Px)t(0)与动量Px的关系图

    Figure 4.  Relationship between t(Px)t(0) and Px.

    图 5  Ne8+离子与CO作用后反冲离子的位置谱

    Figure 5.  Position spectrum of recoil ions produced by Ne8+ interaction with CO.

    图 6  (a)−(c)切片后C+离子的二维动量分布(切片厚度为± 30 a.u.); (d)−(f) KER与θyz,yx,zx的二维关系图

    Figure 6.  (a)–(c) Two-dimensional momentum distribution of C+ in yz, yx, zx plan after slicing (slice thickness is ± 30 a.u.); (d)−(f) two-dimensional relationship between KER and θyz,yx,zx

    图 7  CO2+ C+ + O+碎裂过程的KER

    Figure 7.  KER spectrum of the fragmentation process of CO2+ C+ + O+

    表 1  C+在不同初始动量Px下的飞行时间t(Px)

    Table 1.  TOF of C+ under different initial momentum Px

    Px/arb. units t(Px)/ns t(0)t(Px)/ns
    0 3139.149 0
    1 3138.014 1.135
    2 3136.878 2.271
    3 3135.742 3.407
    4 3134.606 4.543
    5 3133.471 5.678
    10 3127.792 11.357
    20 3116.434 22.715
    30 3105.077 34.072
    40 3093.72 45.429
    50 3082.364 56.785
    100 3025.593 113.556
    DownLoad: CSV
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    [4]

    Falcinelli S, Pirani F, Alagia M, Schio L, Richter R, Stranges S, Balucani N, Vecchiocattivi F 2016 Atmosphere 7 112Google Scholar

    [5]

    Zewail Ahmed H 2000 J. Phys. Chem. A 104 5660Google Scholar

    [6]

    Lin K, Hu X Q, Pan S Z, Chen F, Ji Q Y, Zhang W B, Li H X, Qiang J J, Sun F H, Gong X C, Li H, Lu P F, Wang J G, Wu Y, Wu J 2020 J. Phys. Chem. Lett 11 3129Google Scholar

    [7]

    Boudaïffa B, Cloutier P, Hunting D, Huels M A, Sanche L 2000 Science 287 1658Google Scholar

    [8]

    Kim H K, Titze J, Schöffler M, Trinter F, Waitz M, Voigtsberger J, Sann H, Meckel M, Stuck C, Lenz U, Odenweller M, Neumann N, Schössler S, Ullmann-Pfleger K, Ulrich B, Fraga R C, Petridis N, Metz D, Jung A, Grisenti R, Czasch A, Jagutzki O, Schmidt, L, Jahnke T, Schmidt-Böcking, H, Dörner R 2011 Proc. Natl. Acad. Sci. 108 11821Google Scholar

    [9]

    Märk T D, Dunn G H 1985 Electron-Impact Ionization (New York: Springer) pp320–374

    [10]

    Beiersdorfer P, Bitter M, Marion M, Olson R E 2005 Phys. Rev. A 72 032725Google Scholar

    [11]

    Ullrich J, Moshammer R, Dorn A, Dörner R, Schmidt L Ph H, Schmidt-Böcking H 2003 Rep. Prog. Phys. 66 1463Google Scholar

    [12]

    Ma X W, Zhang R T, Zhang S F, Zhu X L, Feng W T, Guo D L, Li B, Liu H P, Li C Y, Wang J G, Yan S C, Zhang P J, Wang Q 2011 Phys. Rev. A 83 052707Google Scholar

    [13]

    郭大龙, 马新文, 冯文天, 张少锋, 朱小龙 2011 物理学报 60 113401Google Scholar

    Guo D L, Ma X W, Feng W T, Zhang S F, Zhu X L 2011 Acta Phys. Sin. 60 113401Google Scholar

    [14]

    Martín F, Fernández J, Havermeier T, Foucar L, Weber Th, Kreidi K, Schöffler M, Schmidt L, Jahnke T, Jagutzki O, Czasch A, Benis E P, Osipov T, Landers A L, Belkacem A Prior M H, Schmidt-Böcking H, Cocke C L, Dörner R 2007 Science 315 629Google Scholar

    [15]

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    [17]

    Yan S, Zhang P, Stumpf V, Gokhberg K, Zhang X C, Xu S, Li B, Shen L L, Zhu X L, Feng W T, Zhang S F, Zhao D M, Ma X 2018 Phys. Rev. A 97 010701Google Scholar

    [18]

    Xu S Y, Zhao H Y, Zhu X L, Guo D L, Feng W T, Lau K C, Ma X W 2018 Phys. Chem. Chem. Phys. 20 27725Google Scholar

    [19]

    Chen L, Shan X, Zhao X, Zhu X L, H u, X Q, Wu Y, Feng W T, Guo D L, Zhang R T, Gao Y, Huang Z K, Wang J G, Ma X W, Chen X J 2019 Phys. Rev. A 99 012710Google Scholar

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    Alnaser A S, Voss S, Tong X M, Maharjan C M, Ranitovic P, Ulrich B, Osipov T, Shan B, Chang Z, Cocke C L 2004 Phys. Rev. Lett. 93 113003Google Scholar

    [21]

    Gao Y, Zhang S F, Zhu X L, Guo D L, Schulz M, Voitkiv A B, Zhao D M, Hai B, Zhang M, Zhang R T, Feng W T, Yan S, Wang H B, Huang Z K, Ma X 2018 Phys. Rev. A 97 020701Google Scholar

    [22]

    Zeller S, Kunitski M, Voigtsberger J, Waitz M, Trinter F, Eckart S, Kalinin A, Czasch A, Schmidt L Ph H, Weber T, Schöffler M, Jahnke T, Dörner R 2018 Phys. Rev. Lett. 121 083002Google Scholar

    [23]

    Chen L, Shan X, Wang E L, Ren X D, Zhao X, Huang W Z, Chen X G 2019 Phys. Rev. A 100 062707Google Scholar

    [24]

    申丽丽, 闫顺成, 马新文, 朱小龙, 张少锋, 冯文天, 张鹏举, 郭大龙, 高永, 海帮, 张敏, 赵冬梅 2018 物理学报 67 043401Google Scholar

    Shen L L, Yan S C, Ma X W, Zhu X L, Zhang S F, Feng W T, Zhang P J, Guo D L, Gao Y, Hai B, Zhang M, Zhao D M 2018 Acta Phys. Sin. 67 043401Google Scholar

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    Zhu X L, Yan S, Feng W T, Guo D L, Gao Y, Zhang R T, Zhang S F, Wang H B, Huang Z K, Zhang M, Hai B, Zhao D M, Wen W Q, Zhang P, Qian D B, Ma X 2017 Nucl. Instrum. Methods Phys. Res., Sect. B 408 42Google Scholar

    [26]

    Wiley W C, McLaren I H 1955 Rev. Sci. Instrum. 26 1150Google Scholar

    [27]

    Kim H K 2014 Ph. D. Dissertation (Frankfurt: Frankfurt University)

    [28]

    Lundqvist M, Baltzer P, Edvardsson D, Karlsson L, Wannberg B 1995 Phys. Rev. Lett. 75 1058Google Scholar

    [29]

    Pandey A, Bapat B, Shamasundar K R 2014 J. Chem. Phys. 140 034319Google Scholar

    [30]

    高永, 张少锋, 朱小龙, 闫顺成, 冯文天, 张瑞田, 郭大龙, 李斌, 汪寒冰, 黄忠魁, 海帮, 张敏, 马新文 2016 原子核物理评论 33 513Google Scholar

    Gao Y, Zhang S F, Zhu X L, Yan S C, Feng W T, Zhang R T, Guo D L, Li B, Wang H B, Huang Z K, Hai B, Zhang M, Ma X W 2016 Nucl. Phys. Rev. 33 513Google Scholar

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Publishing process
  • Received Date:  12 June 2020
  • Accepted Date:  03 July 2020
  • Available Online:  14 October 2020
  • Published Online:  20 October 2020

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