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量子计算正三角形腔内的氢负离子光剥离截面

刘志刚 刘伟龙 赵海军

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量子计算正三角形腔内的氢负离子光剥离截面

刘志刚, 刘伟龙, 赵海军

Quantum calculations for photodetachment cross sections of H- in an equilateral triangle cavity

Liu Zhi-Gang, Liu Wei-Long, Zhao Hai-Jun
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  • 用传统量子力学方法研究了横截面为正三角形的腔内氢负离子光剥离, 得到了光剥离截面随能量变化的解析表达公式. 该公式还给出了剥离截面的阈值行为. 进一步研究发现, 当氢负离子处于正三角形一角附近时, 用量子力学方法得到的结果与氢负离子处于60°角域内时使用闭合轨道理论得到的结果一致.
    In this paper, the photodetachment cross section of negative hydrogen ion inside a tube cavity with an equilateral triangle cross section is investigated by the traditional quantum approach. Then the analytic formulas each as a function of photon energy having been derived, some interesting oscillations in the photodetachment cross section are shown from the numerical illustrations. The formulas indicate that the oscillations are related to the positions of the ion and the photon polarization. The polarization of photons being perpendicular to the normal direction of the triangle, the cross sections apparently display large amplitude sawtooth-shaped oscillations, while being parallel to the normal direction of the triangle, oscillations are still present and observable from the quantum calculations, although the amplitudes of the oscillations are rather small. The subtle effect is also observed in the quantum theory for photodetachment in an electric field. The formulas also reveal threshold behaviors in the photodetachment cross sections. The threshold is expressed as Eth=(8π2/9l2)(m2+n2-mn), where l is the length of the triangle side, n and m are for all integers with m≥2n. When the polarization of photons is perpendicular to the normal direction of the triangle and the energy of the detached electron is above each threshold, the threshold behavior is Δσ∝(E-Eth)-1/2. When the polarization of photons is parallel to the normal direction of the triangle and the energy of the detached electron is above each threshold, the threshold behavior is Δσ∝(E-Eth)1/2. Furtherly, if the negative hydrogen ion is placed near one corner of the equilateral triangle, the quantum results show agreement with those from the closed-orbit theory when the negative hydrogen ion is in a wedge with an opening angle of 60 degrees. If that occurs, the five sinusoidal oscillations, each of which will correspond to one closed orbit, can be extracted from the photodetachment cross sections. These five closed orbits are definitely the orbits when the negative hydrogen ion is in a wedge with an opening angle of 60 degrees.
    • 基金项目: 国家自然科学基金(批准号:10804066)、山西省自然科学基金(批准号: 2009011004)和山西省高等学校优秀青年学术带头人支持计划资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 10804066), the Natural Science Foundation of Shanxi Province of China (Grant No. 2009011004), and the Shanxi Provincial Foundation for Leaders of Disciplines in Science, China.
    [1]

    Bryant H C, Mohagheghi A, Stewart J E, Donahue J B, Quick C R, Reeder R A, Yuan V V, Hummer C R, Smith W W, Cohen S, Reinhardt W P, Overman L 1987 Phys. Rev. Lett. 58 2412

    [2]

    Du M L, Delos J B 1988 Phys. Rev. A 38 5609

    [3]

    Rau A, Wong H 1988 Phys. Rev. A 37 632

    [4]

    Du M L 2004 Phys. Rev. A 70 055402

    [5]

    Peters A D, Delos J B 1993 Phys. Rev. A 47 3036

    [6]

    Du M L 1989 Phys. Rev. A 40 1330

    [7]

    Du M L 2006 Eur. Phys. J. D 38 533

    [8]

    Yang G C, Mao J M, Du M L 1999 Phys. Rev. A 59 2053

    [9]

    Rous P J 1999 Phys. Rev. Lett. 83 5086

    [10]

    Yang G C, Zheng Y Z, Chi X X 2006 Phys. Rev. A 73 043413

    [11]

    Zhao H J, Du M L 2009 Phys. Rev. A 79 023408

    [12]

    Wang D H, Yu Y J, Wang H R 2009 Chin. Opt. Lett. 7 176

    [13]

    Yang G C, Zheng Y Z, Chi X X 2006 J. Phys. B: At. Mol. Opt. Phys. 39 1855

    [14]

    Afaq A, Du M L 2007 J. Phys. B: At. Mol. Opt. Phys. 40 1309

    [15]

    Yang G C, Rui K K, Zheng Y Z 2009 Physica B 404 1576

    [16]

    Wang D H, Ma X G, Wang M S, Yang C L 2007 Chin. Phys. 16 1307

    [17]

    Li S S, Wang D H 2014 Chin. Phys. B 23 023402

    [18]

    Zhao H J, Du M L 2011 Phys. Rev. E 84 016217

    [19]

    Wang D H, Li S S, Wang Y H, Mu H F 2012 J. Phys. Soc. Jpn. 81 114301

    [20]

    Wang D H, Liu S, Li S S, Wang Y H 2013 Chin. Phys. B 22 073401

    [21]

    Richens P J, Berry M V 1981 Physica D 2 495

    [22]

    Li W K, Blinder S M 1987 J. Chem. Educ. 64 130

    [23]

    Li W K, Blinder S M 1985 J. Math. Phys. 26 2784

    [24]

    Lin S L, Gao F, Hong Z P, Du M L 2005 Chin. Phys. Lett. 22 9

  • [1]

    Bryant H C, Mohagheghi A, Stewart J E, Donahue J B, Quick C R, Reeder R A, Yuan V V, Hummer C R, Smith W W, Cohen S, Reinhardt W P, Overman L 1987 Phys. Rev. Lett. 58 2412

    [2]

    Du M L, Delos J B 1988 Phys. Rev. A 38 5609

    [3]

    Rau A, Wong H 1988 Phys. Rev. A 37 632

    [4]

    Du M L 2004 Phys. Rev. A 70 055402

    [5]

    Peters A D, Delos J B 1993 Phys. Rev. A 47 3036

    [6]

    Du M L 1989 Phys. Rev. A 40 1330

    [7]

    Du M L 2006 Eur. Phys. J. D 38 533

    [8]

    Yang G C, Mao J M, Du M L 1999 Phys. Rev. A 59 2053

    [9]

    Rous P J 1999 Phys. Rev. Lett. 83 5086

    [10]

    Yang G C, Zheng Y Z, Chi X X 2006 Phys. Rev. A 73 043413

    [11]

    Zhao H J, Du M L 2009 Phys. Rev. A 79 023408

    [12]

    Wang D H, Yu Y J, Wang H R 2009 Chin. Opt. Lett. 7 176

    [13]

    Yang G C, Zheng Y Z, Chi X X 2006 J. Phys. B: At. Mol. Opt. Phys. 39 1855

    [14]

    Afaq A, Du M L 2007 J. Phys. B: At. Mol. Opt. Phys. 40 1309

    [15]

    Yang G C, Rui K K, Zheng Y Z 2009 Physica B 404 1576

    [16]

    Wang D H, Ma X G, Wang M S, Yang C L 2007 Chin. Phys. 16 1307

    [17]

    Li S S, Wang D H 2014 Chin. Phys. B 23 023402

    [18]

    Zhao H J, Du M L 2011 Phys. Rev. E 84 016217

    [19]

    Wang D H, Li S S, Wang Y H, Mu H F 2012 J. Phys. Soc. Jpn. 81 114301

    [20]

    Wang D H, Liu S, Li S S, Wang Y H 2013 Chin. Phys. B 22 073401

    [21]

    Richens P J, Berry M V 1981 Physica D 2 495

    [22]

    Li W K, Blinder S M 1987 J. Chem. Educ. 64 130

    [23]

    Li W K, Blinder S M 1985 J. Math. Phys. 26 2784

    [24]

    Lin S L, Gao F, Hong Z P, Du M L 2005 Chin. Phys. Lett. 22 9

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  • 文章访问数:  1767
  • PDF下载量:  143
  • 被引次数: 0
出版历程
  • 收稿日期:  2015-03-12
  • 修回日期:  2015-04-20
  • 刊出日期:  2015-08-05

量子计算正三角形腔内的氢负离子光剥离截面

  • 1. 山西师范大学物理与信息工程学院, 大分子研究中心, 临汾 041000
    基金项目: 

    国家自然科学基金(批准号:10804066)、山西省自然科学基金(批准号: 2009011004)和山西省高等学校优秀青年学术带头人支持计划资助的课题.

摘要: 用传统量子力学方法研究了横截面为正三角形的腔内氢负离子光剥离, 得到了光剥离截面随能量变化的解析表达公式. 该公式还给出了剥离截面的阈值行为. 进一步研究发现, 当氢负离子处于正三角形一角附近时, 用量子力学方法得到的结果与氢负离子处于60°角域内时使用闭合轨道理论得到的结果一致.

English Abstract

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