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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
$^{3}\Sigma^{+}$ 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.[1] Feldman P D, Brune W H 1976 Astrophys. J. 209 L45
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[2] Cravens T E 2002 Science 296 1042
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[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
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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 032725
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[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
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[13] 郭大龙, 马新文, 冯文天, 张少锋, 朱小龙 2011 物理学报 60 113401
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Guo D L, Ma X W, Feng W T, Zhang S F, Zhu X L 2011 Acta Phys. Sin. 60 113401
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[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
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[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
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[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
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[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
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[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
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[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
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[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
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[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
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[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
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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 043401
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[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
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[26] Wiley W C, McLaren I H 1955 Rev. Sci. Instrum. 26 1150
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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 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
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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
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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)Fig. 2. Relationship between relative TOF
$ t_{0}^{\rm e} $ and$\sqrt{{m}/{q}}$ (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
Fig. 3. TOF spectrum of fragment ions produced by Ne8+ interaction with CO
图 4
$ t(P_{x}) $ –$ t(0) $ 与动量$ P_{x} $ 的关系图Fig. 4. Relationship between
$ t(P_{x}) $ –$ t(0) $ and$ P_{x} $ .
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.
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Fig. 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 7 CO2+
$ \rightarrow $ C+ + O+碎裂过程的KERFig. 7. KER spectrum of the fragmentation process of CO2+
$ \rightarrow $ C+ + O+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 
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[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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