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129Xeq+ induced near-infrared light and X-ray emission at Cu surface

Zhang Xiao-An Mei Ce-Xiang Zhang Ying Liang Chang-Hui Zhou Xian-Ming Zeng Li-Xia Li Yao-Zong Liu Yu Xiang Qian-Lan Meng Hui Wang Yi-Jun

Citation:

129Xeq+ induced near-infrared light and X-ray emission at Cu surface

Zhang Xiao-An, Mei Ce-Xiang, Zhang Ying, Liang Chang-Hui, Zhou Xian-Ming, Zeng Li-Xia, Li Yao-Zong, Liu Yu, Xiang Qian-Lan, Meng Hui, Wang Yi-Jun
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  • During the interaction of highly charged ions with solid target in the energy region near the Bohr velocity, the potential energy of the projectiles will be deposited on a nanometer-scale target surface within the time on the order of femtoseconds. That will lead the target atoms to be ionized into ions and the ions to be excited, resulting in the multiple ionization states and the complex configuration of energy levels. The de-excitation radiations of these levels cover the radiations from near-infrared spectral line to X-ray. Investigation of these spectral lines is significant for investigating the mechanism of such an interaction, diagnosing plasma and studying astrophysics. The experimental results show that the near-infrared spectral lines and X-ray spectra are produced by the 129Xeq+ (q = 21, 23, 25, 27) with kinetic energy of 1360 keV and 129Xe20+ with kinetic energy of 4 MeV impacting on the Cu surface, separately. The experiment is carried out in the National Laboratory of Heavy Ion Research Facility in Lanzhou, HIRFL. The beam intensity is on the order of nA. The highly charged ions capture the electrons of the Cu target and thus being neutralized in a femtosecond time. The energy of the highly charged ions is deposited on the target surface, and the target atoms are excited or ionized, resulting in the transition between complex configurations, such as the dipole forbidden transition (magnetic dipole and quadrupole transition) and magnetic dipole transition of the Cu22+. The infrared spectral lines of the atoms and ions from deexcitation radiation are measured. With the 4 MeV 129Xe20+ ions impacting on solid Cu surfsce, the X-rays are measured, such as, the magnetic dipole deexcitation radiation transition of Cu22+, the X-rays of the L1 edge transition and Lβ3 of the Cu I, Lη and Lβ3 X-rays of the Xe ions. The results show that during the neutrilization of highly charged Xe ions with lower energy above the Cu surface, the infrared lines are mainly from the deexcitation of the incident ions and the ionized or excited target atoms. The increasing trend of the the single ion fluorescence yield of the infrared spectral line is the same as that of the potential energy of the projectile. The characteristic L X-rays of the Xe atom are emitted by the second generation of hollow atoms formed below the surface.
      Corresponding author: Zhang Xiao-An, zhangxiaoan2000@126.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11605147, 11075135) and the Natural Science Basic Research Plan in Shaanxi Province, China (Grant No. 2020JM-624)
    [1]

    Lemell C, Stöck J, Burgdörfer J, Betz G, Winter H P, Aumayr F 1998 Phys. Rev. Lett. 81 1965Google Scholar

    [2]

    Woolsey N C, Hammel B A, Keane C J, Back C A, Moreno J C, Nash J K, Calisti A, Mosse C, R. Stamm, Talin B, Asfaw A, Klein L S, Lee R W 1998 Phys. Rev. E 57 4650Google Scholar

    [3]

    Kim K Y, Taylor A J, Glownia J H, Rodriguez G 2008 Nat. Photonics 2 605Google Scholar

    [4]

    Krasheninnikov A V, Nordlund K 2010 J. Appl. Phys. 107 071301Google Scholar

    [5]

    Lake R E, Pomeroy J M, Grube H, Sosolik C E 2011 Phys. Rev. Lett. 107 063202Google Scholar

    [6]

    段斌, 吴泽清, 王建国 2009 中国科学 G 39 43Google Scholar

    Duan B, Wu Z Q, Wang J G 2009 Sci. China G 39 43Google Scholar

    [7]

    段斌, 吴泽清, 王建国 2009 中国科学 G 39 241Google Scholar

    Duan B, Wu Z Q, Wang J G 2009 Sci. China G 39 241Google Scholar

    [8]

    Gruber E, Wilhelm R A, Pétuya R, Smejkal V, Kozubek R, Hierzenberger A, Bayer B C, Aldazabal I, Kazansky A K, Libisch F, Krasheninnikov A V, Schleberger M, Facsko S, Borisov A G, Arnau A, Aumayr F 2016 Nat. Commun. 7 13948Google Scholar

    [9]

    Ferguson B, Zhang X C 2002 Nat. Mater. 1 26Google Scholar

    [10]

    Hagstrum H D 1954 Phys. Rev. 96 336Google Scholar

    [11]

    Datz S 1983 Phys. Scr. T 3 79Google Scholar

    [12]

    Briand J P, de Billy L, Charles P, Essabaa S, Briand P, Desclaux J P, Geller R, Bliman S, Ristori C 1990 Phys. Rev. Lett. 65 1259Google Scholar

    [13]

    Burgdörfer J, Lerner P, Meyer F W 1991 Phys. Rev. A 44 5674Google Scholar

    [14]

    Köhrbrück R, Sommer K, Biersack J P, Neuhaus B J, Schippers S, Roncin P, Lecler D, Fremont F, Stolterfoht N 1992 Phys. Rev. A 45 4653Google Scholar

    [15]

    Beiersdorfer P, Olson R E, Brown G V, Chen H, Harris C L, Neill P A, Schweikhard L, Utter S B, Widmann K 2000 Phys. Rev. Lett. 85 5090Google Scholar

    [16]

    Morishita Y, Hutton R, Torii H A, Komaki K, Brage T, Ando K, Ishii K, Kanai Y, Masuda H, Sekiguchi M, Rosmej F B, Yamazaki Y 2004 Phys. Rev. A 70 012902Google Scholar

    [17]

    赵永涛, 张小安, 李福利, 肖国青, 詹文龙, 杨治虎 2003 物理学报 52 2768Google Scholar

    Zhao Y T, Zhang X A, Li F L, Xiao G Q, Zhan WL, Yang Z H 2003 Acta Phys. Sin. 52 2768Google Scholar

    [18]

    Sporn M, Libiseller G, Neidhart T, Schmid M, Aumayr F, Winter H P, Varga P, 1997 Phys. Rev. Lett. 79 945Google Scholar

    [19]

    张小安, 杨治虎, 王党朝, 梅策香, 牛超英, 王伟, 戴斌, 肖国青 2009 物理学报 58 6920Google Scholar

    Zhang X A, Yang Z H, Wang D C, Mei C X, Niu C Y, Wang W, Dai B, Xiao G Q 2009 Acta Phys. Sin. 58 6920Google Scholar

    [20]

    Wilhelm R A, Gruber E, Schwestka J, Kozubek Roland, Madeira T I, Marques J P, Kobus J, Krasheninnikov AV, Schleberger M, Aumayr F 2017 Phys. Rev. Lett. 119 103401Google Scholar

    [21]

    Hurricane O A, Callahan D A, Casey D T, Celliers P M, Cerjan C, Dewald E L, Dittrich T R, Döppner T, Hinkel D E, Berzak Hopkins L F, Kline J L, Le Pape S, Ma 1T, MacPhee A G, Milovich J L, Pak A, Park H S, Patel P K, Remington B A, Salmonson J D, Springer P T, Tommasini R 2014 Nature 506 343Google Scholar

    [22]

    Hollmann E M, Parks P B, Shiraki D, Alexander N, Eidietis N W, Lasnier C J, Moyer R A 2019 Phys. Rev. Lett. 122 065001Google Scholar

    [23]

    Dasgupta A, Clark R W, Ouart N D, Giuliani J L 2014 Phys. Scr. 89 14008Google Scholar

    [24]

    Träbert E, Grieser M, Hoffmann J, Krantz C, Repnow R, Wolf A 2012 Phys. Rev. A 85 042508Google Scholar

    [25]

    Dasgupta A, Clark R W, Ouart N D, Giuliani J L, Thornhill W, Davis J, Jones B, Ampleford D J, Hansen S B, Coverdale CA 2012 High Energy Density Phys. 8 284Google Scholar

    [26]

    Kawaguchi K, Sanechika N, Nishimura Y, Fujimori R, Oka T N, Hirahara Y, Jaman A I, Civiš S 2008 Chem. Phys. Lett. 463 38Google Scholar

    [27]

    Hinnov E, Suckewer S, Cohen S, Sato K 1982 Phys. Rev. A 25 2293Google Scholar

    [28]

    李家明, 赵中新 1981 物理学报 30 105Google Scholar

    Li J M, Zhao Z X 1981 Acta Phys. Sin. 30 105Google Scholar

    [29]

    Han X Y, Gao X, Zeng D L, Jin R, Yan J, Li J M 2014 Phys. Rev. A 89 042514Google Scholar

    [30]

    Wu Z W, Dong C Z, Jiang J 2012 Phys. Rev. A 86 022712Google Scholar

    [31]

    腾华国, 王永昌 1988 西北师范大学学报 4 45Google Scholar

    Teng H G, Wang Y C 1988 J. Northwest Nor. Univ. 4 45Google Scholar

    [32]

    Wang K, Guo X L, Liu H T, Li D F, Long F Y, Han X Y, Duan B, Li J G, Huang M, Wang Y S 2015 Astrophys. J. Suppl. 218 16Google Scholar

    [33]

    Wang W J 1993 Nucl. Instrum. Methods B 73 159Google Scholar

    [34]

    Bastiaansen J, Philipsen V, Vervaecke F, Vandeweert E, Lievens P, Silverans R E 2003 Phys. Rev. B 68 073409Google Scholar

    [35]

    Kramida A, Ralchenko Yu, Reader J, NIST ASD Team https://www.nist.gov/pml/atomic-spectra-database [2019-02-19]

    [36]

    Atomic and Molecular Datebase http://www.camdb.ac.cn/ nsdc/ [2019-03-19]

    [37]

    Deslattes R D, Kessler Jr E G, Indelicato P, de Billy L, Lindroth E, Anton J 2003 Rev. Mod. Phys. 75 35Google Scholar

    [38]

    徐克尊 2000 高等原子分子物理 (北京: 科学出版社) 第117−119页

    Xu K Z 2000 Advanced Atomic Molecular Physics (Beijing: Science Press) pp117−119 (in Chinese)

    [39]

    曾谨言 2000 量子力学(卷Ⅱ)第三版 (北京: 科学出版社) 第660−661页

    Zeng J Y 2000 Quantum Mechanics (Vol.Ⅱ 3th Ed) (Beijing: Science Press) pp660−661 (in Chinese)

    [40]

    Nordlander P, Tully J C 1990 Phys. Rev. B 42 5564Google Scholar

    [41]

    Briand J P, Giardino G, Borsoni G, Froment M, Eddrief M, Sébenne C, Bardin S, Schneider D, Jin J, Khemliche H, Xie Z, Prior M 1996 Phys. Rev. A 54 4136Google Scholar

    [42]

    Clark M W, Schneider D, Dewitt D, McDonald J W, Bruch R, Safronova U I, Tolstikhina I Y, Schuch R 1993 Phys. Rev. A 47 3983Google Scholar

    [43]

    Zhou X M, Zhao Y T, Xiao G Q, Cheng R, Wang Y Y, Wang X, Sun Y B 2013 Nucl. Instrum. Methods B 299 61Google Scholar

    [44]

    Ren J R, Zhao Y T, Zhou X M, Wang X, Lei Y, Xu G, Cheng R, Wang Y Y, Liu S D, Sun Y B, Xiao G Q 2015 Phys. Rev. A 92 062710Google Scholar

  • 图 1  兰州重离子加速器国家实验室ECR离子源原子物理实验平台

    Figure 1.  Schematic experimental setup for atomic physics platform on ECRIS in HIRFL.

    图 2  Si漂移探测器探测效率随X射线能量变化的关系图(在能量0.6−1.8 keV之间用5次多项式拟合, 能量1.8−4.0 keV用4次多项式拟合, 4.0−10 keV用3次多项式拟合)

    Figure 2.  Efficiency values of the Silicon Drift Detector. The curve is a fifth polynomial in the 0.6−1.8 keV energy interval, a fourth polynomial in the 1.8−4.0 keV energy interval and a third polynomial in the 4.0–10 keV energy interval.

    图 3  动能一定(1360 keV)的129Xeq+离子入射Cu靶表面激发的近红外光谱线 (a) 129Xe21+; (b) 129Xe27+

    Figure 3.  Measured near-infrared spectral lines induced by 129Xeq+ ions with 1360 keV kinetic energy impacting on Cu surface: (a) 129Xe21+; (b) 129Xe27+

    图 4  动能为4 MeV的129Xe20+离子入射Cu靶表面辐射的X射线谱

    Figure 4.  X-ray spectra induced by 129Xe20+ ions with 4 MeV kinetic energy impacting on Cu surface.

    图 5  (a) 129Xeq+离子携带势能随电荷态q增加的趋势; (b)近红外光谱线的单粒子产额随电荷态q增加的趋势

    Figure 5.  (a) Potential energy of the 129Xeq+ ion vs. the charge q; (b) single ion fluorescence yield of the near-infrared spectral lines as a function of the projectile charge q where the near-infrared spectral lines are induced by 1360 keV 129Xeq+ (q = 21—27) ion impacting on a Cu surface.

    表 1  129Xeq+入射Cu靶激发的红外光谱线

    Table 1.  Measured near-infrared spectral lines induced by 129Xeq+ ions on Cu surface

    IonObserved
    wavelength/nm
    Reference
    wavelength/nm
    Upper levelLower levelTransition
    type
    ConfigurationTermJConfigurationTermJ
    Xe I949.99 ± 0.05949.71[35]$5{\rm{p}}^5(2{\rm{P}}^\circ_{3/2})4{\rm{f}}$2[3/2]2$5{\rm{p} }^5(2{\rm{P} }^\circ_{3/2})5{\rm{d} }$2[3/2]°2E1
    Xe I1240.91 ± 0.011240.91[35]$5{\rm{p}}^5(2{\rm{P}}^\circ_{1/2})6{\rm{p}}$2[3/2]1$5{\rm{p} }^5(2{\rm{P} }^\circ_{3/2})5{\rm{d} }$2[3/2]°2E1
    Xe I1435.46 ± 0.011435.46[35]$5{\rm{p}}^5(2{\rm{P}}^\circ_{3/2})8{\rm{p}}$2[1/2]1$5{\rm{p} }^5(2{\rm{P} }^\circ_{3/2})7{\rm{s} } $ 2[3/2]°2E1
    Cu I1665.00 ± 0.021664.99[35]3d105d2D3/23d105p21/2E1
    Cu II829.78 ± 0.03829.85[35]3d9(2D5/2)7d2[2/5]23d8(3F)4s4p(1P°)3Fo2E1
    Cu II900.14 ± 0.02900.14[35]3d9(2D3/2)8s2[3/2]23d9(2D3/2)6p2[3/2]°1E1
    Cu II1079.74 ± 0.051079.79[35]3d9(2D5/2)5f 2[7/2]°43d9(2D5/2)5d 2[9/2]4E1
    Cu XXIII1140.06 ± 0.011140.0[36]2s22p2(3P)4p2Po3/22s22p2(3P)4p4So3/2M1, E2
    Cu XXIII1216.44 ± 0.041216.5[36]2p4(3P)3d4D5/22p4(1D)3p2Fo5/2E1
    Cu XXIII1345.36 ± 0.061345.5[36]2s22p2(3P)4f2Fo5/22s22p2(1D)4p2Fo5/2M1, E2
    Cu XXIII1374.79 ± 0.071374.0[36]2s2p3(1P)3d2Do5/22p4(3P)3s4P5/2E1
    Cu XXIII1420.31 ± 0.061420.1[36]2s22p2(3P)4f4Do1/22s22p2(1D)4p2Do1/2M1, E2
    DownLoad: CSV
  • [1]

    Lemell C, Stöck J, Burgdörfer J, Betz G, Winter H P, Aumayr F 1998 Phys. Rev. Lett. 81 1965Google Scholar

    [2]

    Woolsey N C, Hammel B A, Keane C J, Back C A, Moreno J C, Nash J K, Calisti A, Mosse C, R. Stamm, Talin B, Asfaw A, Klein L S, Lee R W 1998 Phys. Rev. E 57 4650Google Scholar

    [3]

    Kim K Y, Taylor A J, Glownia J H, Rodriguez G 2008 Nat. Photonics 2 605Google Scholar

    [4]

    Krasheninnikov A V, Nordlund K 2010 J. Appl. Phys. 107 071301Google Scholar

    [5]

    Lake R E, Pomeroy J M, Grube H, Sosolik C E 2011 Phys. Rev. Lett. 107 063202Google Scholar

    [6]

    段斌, 吴泽清, 王建国 2009 中国科学 G 39 43Google Scholar

    Duan B, Wu Z Q, Wang J G 2009 Sci. China G 39 43Google Scholar

    [7]

    段斌, 吴泽清, 王建国 2009 中国科学 G 39 241Google Scholar

    Duan B, Wu Z Q, Wang J G 2009 Sci. China G 39 241Google Scholar

    [8]

    Gruber E, Wilhelm R A, Pétuya R, Smejkal V, Kozubek R, Hierzenberger A, Bayer B C, Aldazabal I, Kazansky A K, Libisch F, Krasheninnikov A V, Schleberger M, Facsko S, Borisov A G, Arnau A, Aumayr F 2016 Nat. Commun. 7 13948Google Scholar

    [9]

    Ferguson B, Zhang X C 2002 Nat. Mater. 1 26Google Scholar

    [10]

    Hagstrum H D 1954 Phys. Rev. 96 336Google Scholar

    [11]

    Datz S 1983 Phys. Scr. T 3 79Google Scholar

    [12]

    Briand J P, de Billy L, Charles P, Essabaa S, Briand P, Desclaux J P, Geller R, Bliman S, Ristori C 1990 Phys. Rev. Lett. 65 1259Google Scholar

    [13]

    Burgdörfer J, Lerner P, Meyer F W 1991 Phys. Rev. A 44 5674Google Scholar

    [14]

    Köhrbrück R, Sommer K, Biersack J P, Neuhaus B J, Schippers S, Roncin P, Lecler D, Fremont F, Stolterfoht N 1992 Phys. Rev. A 45 4653Google Scholar

    [15]

    Beiersdorfer P, Olson R E, Brown G V, Chen H, Harris C L, Neill P A, Schweikhard L, Utter S B, Widmann K 2000 Phys. Rev. Lett. 85 5090Google Scholar

    [16]

    Morishita Y, Hutton R, Torii H A, Komaki K, Brage T, Ando K, Ishii K, Kanai Y, Masuda H, Sekiguchi M, Rosmej F B, Yamazaki Y 2004 Phys. Rev. A 70 012902Google Scholar

    [17]

    赵永涛, 张小安, 李福利, 肖国青, 詹文龙, 杨治虎 2003 物理学报 52 2768Google Scholar

    Zhao Y T, Zhang X A, Li F L, Xiao G Q, Zhan WL, Yang Z H 2003 Acta Phys. Sin. 52 2768Google Scholar

    [18]

    Sporn M, Libiseller G, Neidhart T, Schmid M, Aumayr F, Winter H P, Varga P, 1997 Phys. Rev. Lett. 79 945Google Scholar

    [19]

    张小安, 杨治虎, 王党朝, 梅策香, 牛超英, 王伟, 戴斌, 肖国青 2009 物理学报 58 6920Google Scholar

    Zhang X A, Yang Z H, Wang D C, Mei C X, Niu C Y, Wang W, Dai B, Xiao G Q 2009 Acta Phys. Sin. 58 6920Google Scholar

    [20]

    Wilhelm R A, Gruber E, Schwestka J, Kozubek Roland, Madeira T I, Marques J P, Kobus J, Krasheninnikov AV, Schleberger M, Aumayr F 2017 Phys. Rev. Lett. 119 103401Google Scholar

    [21]

    Hurricane O A, Callahan D A, Casey D T, Celliers P M, Cerjan C, Dewald E L, Dittrich T R, Döppner T, Hinkel D E, Berzak Hopkins L F, Kline J L, Le Pape S, Ma 1T, MacPhee A G, Milovich J L, Pak A, Park H S, Patel P K, Remington B A, Salmonson J D, Springer P T, Tommasini R 2014 Nature 506 343Google Scholar

    [22]

    Hollmann E M, Parks P B, Shiraki D, Alexander N, Eidietis N W, Lasnier C J, Moyer R A 2019 Phys. Rev. Lett. 122 065001Google Scholar

    [23]

    Dasgupta A, Clark R W, Ouart N D, Giuliani J L 2014 Phys. Scr. 89 14008Google Scholar

    [24]

    Träbert E, Grieser M, Hoffmann J, Krantz C, Repnow R, Wolf A 2012 Phys. Rev. A 85 042508Google Scholar

    [25]

    Dasgupta A, Clark R W, Ouart N D, Giuliani J L, Thornhill W, Davis J, Jones B, Ampleford D J, Hansen S B, Coverdale CA 2012 High Energy Density Phys. 8 284Google Scholar

    [26]

    Kawaguchi K, Sanechika N, Nishimura Y, Fujimori R, Oka T N, Hirahara Y, Jaman A I, Civiš S 2008 Chem. Phys. Lett. 463 38Google Scholar

    [27]

    Hinnov E, Suckewer S, Cohen S, Sato K 1982 Phys. Rev. A 25 2293Google Scholar

    [28]

    李家明, 赵中新 1981 物理学报 30 105Google Scholar

    Li J M, Zhao Z X 1981 Acta Phys. Sin. 30 105Google Scholar

    [29]

    Han X Y, Gao X, Zeng D L, Jin R, Yan J, Li J M 2014 Phys. Rev. A 89 042514Google Scholar

    [30]

    Wu Z W, Dong C Z, Jiang J 2012 Phys. Rev. A 86 022712Google Scholar

    [31]

    腾华国, 王永昌 1988 西北师范大学学报 4 45Google Scholar

    Teng H G, Wang Y C 1988 J. Northwest Nor. Univ. 4 45Google Scholar

    [32]

    Wang K, Guo X L, Liu H T, Li D F, Long F Y, Han X Y, Duan B, Li J G, Huang M, Wang Y S 2015 Astrophys. J. Suppl. 218 16Google Scholar

    [33]

    Wang W J 1993 Nucl. Instrum. Methods B 73 159Google Scholar

    [34]

    Bastiaansen J, Philipsen V, Vervaecke F, Vandeweert E, Lievens P, Silverans R E 2003 Phys. Rev. B 68 073409Google Scholar

    [35]

    Kramida A, Ralchenko Yu, Reader J, NIST ASD Team https://www.nist.gov/pml/atomic-spectra-database [2019-02-19]

    [36]

    Atomic and Molecular Datebase http://www.camdb.ac.cn/ nsdc/ [2019-03-19]

    [37]

    Deslattes R D, Kessler Jr E G, Indelicato P, de Billy L, Lindroth E, Anton J 2003 Rev. Mod. Phys. 75 35Google Scholar

    [38]

    徐克尊 2000 高等原子分子物理 (北京: 科学出版社) 第117−119页

    Xu K Z 2000 Advanced Atomic Molecular Physics (Beijing: Science Press) pp117−119 (in Chinese)

    [39]

    曾谨言 2000 量子力学(卷Ⅱ)第三版 (北京: 科学出版社) 第660−661页

    Zeng J Y 2000 Quantum Mechanics (Vol.Ⅱ 3th Ed) (Beijing: Science Press) pp660−661 (in Chinese)

    [40]

    Nordlander P, Tully J C 1990 Phys. Rev. B 42 5564Google Scholar

    [41]

    Briand J P, Giardino G, Borsoni G, Froment M, Eddrief M, Sébenne C, Bardin S, Schneider D, Jin J, Khemliche H, Xie Z, Prior M 1996 Phys. Rev. A 54 4136Google Scholar

    [42]

    Clark M W, Schneider D, Dewitt D, McDonald J W, Bruch R, Safronova U I, Tolstikhina I Y, Schuch R 1993 Phys. Rev. A 47 3983Google Scholar

    [43]

    Zhou X M, Zhao Y T, Xiao G Q, Cheng R, Wang Y Y, Wang X, Sun Y B 2013 Nucl. Instrum. Methods B 299 61Google Scholar

    [44]

    Ren J R, Zhao Y T, Zhou X M, Wang X, Lei Y, Xu G, Cheng R, Wang Y Y, Liu S D, Sun Y B, Xiao G Q 2015 Phys. Rev. A 92 062710Google Scholar

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Metrics
  • Abstract views:  10259
  • PDF Downloads:  71
  • Cited By: 0
Publishing process
  • Received Date:  06 April 2020
  • Accepted Date:  02 July 2020
  • Available Online:  22 October 2020
  • Published Online:  05 November 2020

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