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

doi:10.7498/aps.69.20200901

Abstract

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 $^{3}\Sigma^{+}$ 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.

Keywords:

Authors and contacts

1.
Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China
2.
University of Chinese Academy of Sciences, Beijing 100049, China

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)

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References

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Cited By

图 1 TOF结构装置示意图

Figure 1. Schematic view of TOF

DownLoad: Full-Size Img PowerPoint

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)

Figure 2. Relationship between relative TOF $ t_{0}^{\rm e} $ and $\sqrt{{m}/{q}}$ (every channel is 25 ps)

DownLoad: Full-Size Img PowerPoint

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

DownLoad: Full-Size Img PowerPoint

图 4 $ t(P_{x}) $ – $ t(0) $与动量$ P_{x} $的关系图

Figure 4. Relationship between $ t(P_{x}) $ – $ t(0) $ and $ P_{x} $.

DownLoad: Full-Size Img PowerPoint

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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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} $

DownLoad: Full-Size Img PowerPoint

图 7 CO²⁺ $ \rightarrow $ C⁺ + O⁺碎裂过程的KER

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

DownLoad: Full-Size Img PowerPoint

表 1 C⁺在不同初始动量$ P_{x} $下的飞行时间$ t(P_{x}) $

Table 1. TOF of C⁺ under different initial momentum $ P_{x} $

$P_{x}$/arb. units	$t(P_{x})$/ns	$t(0)$ – $t(P_{x})$/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

[1]	Feldman P D, Brune W H 1976 Astrophys. J. 209 L45 Google Scholar
[2]	Cravens T E 2002 Science 296 1042 Google Scholar
[3]	Falcinelli S, Rosi M, Candori P, Vecchiocattivi F, Farrar J M, Pirani F, Balucani N, Alagia M, Richter R, Stranges S 2014 Planet Space Sci. 99 149 Google Scholar
[4]	Falcinelli S, Pirani F, Alagia M, Schio L, Richter R, Stranges S, Balucani N, Vecchiocattivi F 2016 Atmosphere 7 112 Google Scholar
[5]	Zewail Ahmed H 2000 J. Phys. Chem. A 104 5660 Google 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 3129 Google Scholar
[7]	Boudaïffa B, Cloutier P, Hunting D, Huels M A, Sanche L 2000 Science 287 1658 Google 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 11821 Google 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 032725 Google Scholar
[11]	Ullrich J, Moshammer R, Dorn A, Dörner R, Schmidt L Ph H, Schmidt-Böcking H 2003 Rep. Prog. Phys. 66 1463 Google 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 052707 Google Scholar
[13]	郭大龙, 马新文, 冯文天, 张少锋, 朱小龙 2011 物理学报 60 113401 Google Scholar Guo D L, Ma X W, Feng W T, Zhang S F, Zhu X L 2011 Acta Phys. Sin. 60 113401 Google 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 315 629 Google Scholar
[15]	Yan S, Zhu X L, Zhang P, Ma X, Feng W T, Gao Y, Xu S, Zhao Q S, Zhang S F, Guo D L, Zhao D M, Zhang R T, Huang Z K, Wang H B, Zhang X J 2016 Phys. Rev. A 94 032708 Google Scholar
[16]	Zhang W B, Li Z C, Lu P F, Gong X C, Song Q Y, Ji Q Y, Lin K, Ma J Y, He F, Zeng H P, Wu J 2016 Phys. Rev. Lett. 117 103002 Google Scholar
[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 010701 Google 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 27725 Google 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 012710 Google Scholar
[20]	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 113003 Google 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 020701 Google 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 083002 Google 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 062707 Google 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 043401 Google 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 043401 Google Scholar
[25]	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 42 Google Scholar
[26]	Wiley W C, McLaren I H 1955 Rev. Sci. Instrum. 26 1150 Google 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 1058 Google Scholar
[29]	Pandey A, Bapat B, Shamasundar K R 2014 J. Chem. Phys. 140 034319 Google 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 33 513 Google 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. 33 513 Google Scholar

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