搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

钫原子磁偶极超精细结构常数及其同位素的磁偶极矩的理论计算

娄冰琼 李芳 王沛妍 王黎明 唐永波

引用本文:
Citation:

钫原子磁偶极超精细结构常数及其同位素的磁偶极矩的理论计算

娄冰琼, 李芳, 王沛妍, 王黎明, 唐永波

Ab initio calculation of hyperfine-structure constant A of Fr and evaluation of magnetic dipole moments of Fr isotopes

Lou Bing-Qiong, Li Fang, Wang Pei-Yan, Wang Li-Ming, Tang Yong-Bo
PDF
HTML
导出引用
  • 应用基于B样条基组的相对论耦合簇理论方法, 计算了212Fr原子的nS (n = 7—12), nP (n = 7—12)和nD (n = 6—11)态的磁偶极超精细结构常数. 与精确实验值的比较说明这套理论方法能精确计算出磁偶极超精细结构常数, 其中7P态的磁偶极超精细常数的理论值与实验值之间的差异小于1%. 在忽略场移效应对Fr原子7P态超精细结构常数的影响下, 通过结合实验值进一步定出了207−213,220−228Fr核磁偶极矩$\mu $, 这些值与已有的测量值具有非常好的一致性. 本文报道了12S, nP (n = 9—12)和 nD (n = 10—11)态的磁偶极超精细结构常数.
    As the heaviest atom in alkali-metal elements, Fr atom has been regarded as a candidate for the search of the permanent electric dipole moment of the electron and of parity-nonconservation effects. Accurate knowledge of Fr atomic properties is of great interest. In this work, we use a relativistic coupled-cluster method to calculate the magnetic dipole hyperfine structure constants for nS (n = 7-12), nP (n = 7-12) and nD (n = 6-11) states of 212Fr. A finite B-spline basis set is used to expand the Dirac radial function, including completely the single and double excitation in correlation calculation. Our results are compared with available theoretical and experimental values. The comparison shows that our method can offer accurate calculation of magnetic dipole hyperfine structure constant. For 7P state the differences between our results and experimental values are within 1%. The magnetic dipole hyperfine structure constants for 12S, nP (n = 9-12) and nD (n = 10-11) states are reported for the first time, which are very useful as benchmarks for experimental measurements and calculations by other theoretical methods of these quantities. In the relativistic coupled-cluster theoretical framework, we study the electron correlation effect on hyperfine-structure constant A for the S, P, and D states of Fr. We observe that the electron correlation effect is very important for hyperfine-structure constant properties. The D state has a considerable correlation effect. At the same time, we also investigate contribution trends of individual electron correlation effects involving direct, core-polarization and pair-correlation ones in S, P, and D Rydberg series. It is found that the dominant contributions for the S1/2, P1/2,3/2 and nD3/2 (n = 7-11) states are to from the direct effect; however, the dominant contributions for the 6D3/2, and nD5/2 (n = 6-11) states are due to the pair-correlation and the core-polarization, respectively. For D5/2 states, there is very strong cancellation among these individual correlation effects. The knowledge of these correlation trends is useful for studying the permanent electric dipole moment and parity-nonconservation effect of Fr in future. Moreover, the magnetic dipole moment $ {\mu}$ for each of isotopes 207−213,220−228Fr is determined by combining with experimental values for magnetic dipole hyperfine structure constant of 7P state. For each of isotope 207−213Fr, our magnetic dipole moment $ {\mu}$ is perfectly consistent with the experimental value, and our uncertainties are twice smaller than those in the experiments . For each of isotope 220−228Fr, our magnetic dipole moment $ {\mu}$ has a larger uncertainty, but is still in agreement with the experimental magnetic dipole moment $ {\mu}$.
      通信作者: 唐永波, ybtang@whu.edu.cn
    • 基金项目: 国家自然科学基金(批准号: 1154094, 11774080)资助的课题.
      Corresponding author: Tang Yong-Bo, ybtang@whu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 1154094, 11774080).
    [1]

    Grant I P 2007 Relativistic Quantum Theory of Atoms and Molecules (New York: Springer) pp533−577

    [2]

    Fischer C F, Brage T, Jönsson P 1997 Computational Atomic Structure: An MCHF Approach (UK: Institute of Physics) pp1−67

    [3]

    Jönsson P, Gaigalas G, Bieroń J, Fishcher C F, Grant I 2013 Computer Physics Communications. 184 2197Google Scholar

    [4]

    Jönsson P, He X, Fishcher C F, Grant I 2007 Computer Physics Communications. 177 597Google Scholar

    [5]

    Dzuba V A, Flambaum V V, Kozlov M G 1996 Phys. Rev. A 54 3948Google Scholar

    [6]

    Dzuba V A, Johnson W R 1998 Phys. Rev. A 57 2459Google Scholar

    [7]

    Angstmann E J, Dzuba V A, Flambaum V V 2004 Phys. Rev. A 70 014102Google Scholar

    [8]

    Dinh T H, Dzuba V A, Flambaum V V, Ginges J S M 2008 Phys. Rev. A 78 054501Google Scholar

    [9]

    Kozlov M G, Porsev S G, Johnson W R 2001 Phys. Rev. A 64 052107Google Scholar

    [10]

    Pal R, Safronova M S, Johnson W R, Derevianko A, Porsev S G 2007 Phys. Rev. A 75 042515Google Scholar

    [11]

    Blundell S A, Johnson W R, Liu Z W, Sapirstein 1989 Phys. Rev. A 40 2233Google Scholar

    [12]

    Eliav E, Vikas M J, Ishikawa Y, Kaldor U 2005 Chem. Phys. 311 163Google Scholar

    [13]

    Mani B K, Angom D 2011 Phys. Rev. A 83 012501Google Scholar

    [14]

    Kallay M, Nataraj H S, Sahoo B K, Das B P, Visscher L 2011 Phys. Rev. A 83 030503Google Scholar

    [15]

    Nandy D K, Singh Y, Sahoo B K 2014 Phys. Rev. A 89 062509Google Scholar

    [16]

    Borschevsky A, Eliav E, Vilkas M J, Ishikawa Y, Kaldor U 2007 Phys. Rev. A 75 042514Google Scholar

    [17]

    Eliav E, Kaldor U, Ishikawa Y 1996 Phys. Rev. A 53 3050Google Scholar

    [18]

    Chaudhuri R K, Chattopadhyay S, Mahapatra U S 2013 J. Phys. Chem. A 117 12616Google Scholar

    [19]

    Tang Y B, Lou B Q, Shi T Y 2017 Phys. Rev. A 96 022513Google Scholar

    [20]

    Tang Y B, Gao N N, Lou B Q, Shi T Y 2018 Phys. Rev. A 98 062511Google Scholar

    [21]

    Byrnes T M R, Dzuba V A, Flambaum F F, Murray D W 1999 Phys. Rev. A 59 3082Google Scholar

    [22]

    Mukherjee D, Sahoo B K, Nataraj H S, Das B P 2009 J. Phys. Chem. A 113 12549Google Scholar

    [23]

    Sakemi Y, Harada K, Hayamizu T, Itoh M, Kawamura H, Liu S, Nataraj H S, Oikawa A, Saito M, Sato T 2011 J. Phys. Conf. Ser. 302 012051Google Scholar

    [24]

    Sahoo B K, Aoki T, Das B P, Sakemi Y 2016 Phys. Rev. A 93 032520Google Scholar

    [25]

    Atutov S N, Calabrese R, Corradi L, Dainelli A, Mauro C D, Khanbekyan A, Mariotti E, Minguzzi P, Moi L, Sanguinetti S, Stancari G, Tomassetti L 2008 Proc. SPIE 7027 70270C

    [26]

    Ekström C, Ingelman S, Wannberg G, Skarestad M 1978 Physica Scripta 18 51Google Scholar

    [27]

    Coc A, Thibault C, Touchard F, Duong H T, Juncar P, Liberman S, Pinard J, Lermé J, Vialle J L, Büttgenbach S, Mueller A C, Pesnelle A, the ISOLDE Collaboration 1985 Phys. Lett. B 163 66Google Scholar

    [28]

    Coc A, Thibault C, Touchard F, Duong H T, Juncar P, Liberman S, Pinard J, Carre M, Lermé J, Vialle J L, Büttgenbach S, Mueller A C, Pesnelle A, the ISOLDE Collaboration 1987 Nucl. Phys. A 468 1Google Scholar

    [29]

    Arnold E, Borchers W, Duong H T, Juncar P, Lermé J, Lievens P, Neu W, Neugart R, Pellerin M, Pinard J, Vialle J L, Wendt K, the ISOLDE Collaboration 1990 J. Phys. B 23 3511Google Scholar

    [30]

    Arnold E, Borchers W, Carré M, Duong H T, Juncar P, Lermé J, Liberman S, Neu W, Neugart R, Otten W, Pellerin M, Pinard J, Pesnelle A, Vialle J L, Wendt K, the ISOLDE Collaboration 1989 J. Phys. B 22 L391Google Scholar

    [31]

    Bauche J, Duong H T, Juncar P, Liberman S, Pinard J, Coc A, Thibault C, Touchard F, Lermé J, Vialle J L, Büttgenbach S, Mueller A C, Pesnelle A, the ISOLDE Collaboration 1986 J. Phys. B 19 L593Google Scholar

    [32]

    Grossman J S, Orozco L A, Simsarian J E, Sprouse G D, Zhao W Z 1999 Phys. Rev. Lett. 83 935Google Scholar

    [33]

    Sansonetti J E 2007 J. Phys. Chem. Ref. Data 36 497Google Scholar

    [34]

    Gomez E, Aubin S, Orozco L A, Sprouse G D, Iskrenova-Tchoukova E, Safronova M S 2008 Phys. Rev. Lett. 100 172502Google Scholar

    [35]

    Dzuba V A, Flambaum V V, Sushkov O P 1984 J. Phys. B: At. Mol. Phys. 17 1953Google Scholar

    [36]

    Owusu A, Dougherty R W, Gowri G, Das T P 1997 Phys. Rev. A 56 305Google Scholar

    [37]

    Safronova M S, Johnson W R, Derevianko A 1999 Phys. Rev. A 60 4476Google Scholar

    [38]

    Sahoo B K, Nandy D K, Das B P, Sakemi Y 2015 Phys. Rev. A 91 042507Google Scholar

    [39]

    Duong H T, Juncar P, Liberman S, Mueller A C, Neugart R, Otten E W, Peuse B, Pinard J, Stoke H H, Thibault C, Touchard F, Vialle J L, Wendt K, the ISOLDE Collaboration 1987 Europhys. Lett. 3 175Google Scholar

    [40]

    Barber Z W, Stalnaker J E, Lemke N D, Poli N, Oates C W, Fortier T M, Diddams S A, Hollberg L, Hoyt C W, Taichenachev A V, Yudin V I 2008 Phys. Rev. Lett. 100 103002Google Scholar

    [41]

    Kien F L, Balykin V I, Hakuta K 2005 J. Phys. Soc. Jpn. 74 910Google Scholar

    [42]

    Ingvar L 1978 Int. J. Quantum Chem. 12 33

    [43]

    Sinha D, Mukhopadhyay S, Mukherjee D 1986 Chem. Phys. Lett. 129 369Google Scholar

    [44]

    Blundell S A, Johnson W R, Sapiratein J 1991 Phys. Rev. A 43 3407Google Scholar

    [45]

    Porsev S G, Beloy K, Derevianko A 2010 Phys. Rev. D 82 036008Google Scholar

    [46]

    Sahoo B K, Sur C, Beier T, Das B P, Chaudhuri R K, Mukherjee D 2007 Phys. Rev. A 75 042504Google Scholar

    [47]

    Safronova M S, Safronova U I 2011 Phys. Rev. A 83 052508Google Scholar

  • 图 1  212Fr原子S1/2, P1/2, P3/2, D3/2和D5/2态磁偶极超精细结构常数中的电子关联效应

    Fig. 1.  Electron correlation effects in hyperfine-structure constant A for S1/2, P1/2, P3/2, D3/2 and D5/2 states of 212Fr.

    图 2  直接效应ADF、核极化效应ACP、对关联效应APC, 以及相对于CCSD的3种效应的总和AT = ADF + ACP + APC, 针对主量子数n的S, P和D态的结果A的比率 (a) ADF/A; (b) ACP/A; (c) APC/A; (d) AT/A

    Fig. 2.  Ratios of direct effect ADF, core polarization effect ACP, pair correlation effect APC, and the total of the three effects AT = ADF + APC + ACP to the CCSD, results A for S, P and D states against the principal quantum number n: (a) ADF/A; (b) ACP/A; (c) APC/A; (d) AT/A.

    表 1  212Fr原子S态的超精细结构常数A (单位: MHz)

    Table 1.  Hyperfine-structure constant A for the S states of 212Fr in MHz.

    能级${A_{{\rm{DF}}}}$${A_{{\rm{CCSD}}}}$$\varDelta /$%Ref.[38]实验值
    7S1/26001.769403.5630.939124(94)9064.2(2)[27]
    9064.4(1.5)[39]
    8S1/21538.032014.1017.371986(19)
    9S1/2631.98792.1913.66784(9)
    10S1/2321.24396.8611.95419(9)401(5)[29]
    11S1/2185.41225.7111.10212(9)225(3)[29]
    12S1/2116.42141.2510.80
    下载: 导出CSV

    表 2  212Fr原子P态的超精细结构常数A (单位: MHz)

    Table 2.  Hyperfine-structure constant A for the P states of 212Fr in MHz.

    能级${A_{{\rm{DF}}}}$${A_{{\rm{CCSD}}}}$$\varDelta /$%Ref.[38]实验值
    7P1/2642.481198.1041.961181(9)1189.1(4.6)[28]
    1187.1(6.8)[39]
    1192.0(2)[32]
    8P1/2228.04372.0433.66371(5)373.0(1)[39]
    9P1/2106.78167.2130.88
    10P1/258.3589.5329.46
    11P1/235.2653.3828.51
    12P1/222.8834.2427.68
    7P3/251.0597.8843.5596(3)97.2(1)[27]
    97.2(1)[39]
    8P3/218.6732.5137.8232(3)32.8(1)[39]
    9P3/28.8915.0035.83
    10P3/24.918.1534.75
    11P3/23.004.9234.01
    12P3/21.973.2033.33
    下载: 导出CSV

    表 3  212Fr原子D态的超精细结构常数A (单位: MHz)

    Table 3.  Hyperfine-structure constant A for the D states of 212Fr in MHz.

    能级${A_{{\rm{DF}}}}$${A_{{\rm{CCSD}}}}$$\varDelta / $%Ref.[38]实验值
    6D3/233.2592.9161.2779(5)
    7D3/216.8230.1739.6529(3)
    8D3/28.6513.8132.2013(1)13.0(6)[29]
    9D3/24.937.5028.757(1)7.1(7)[29]
    10D3/23.064.5226.64
    11D3/22.032.9324.97
    6D5/213.14–53.92126.38–54(5)
    7D5/26.32–13.64150.21–15(3)
    8D5/23.20–5.67161.12–6(1)–7.1(6)[29]
    9D5/21.81–2.96166.96–3.3(6)–3.6(4)[29]
    10D5/21.12–1.72170.59
    11D5/20.74–1.10173.16
    下载: 导出CSV

    表 4  Fr原子同位素的磁偶极矩$\mu$

    Table 4.  Magnetic dipole moment $\mu$ of Fr isotope.

    同位素核自旋7P1/27P3/2${\mu}$
    ${A_{{\rm{expt}}.}}$[33]${{\mu} _{1/2}}$${A_{{\rm{expt}}.}}$[33]${{\mu} _{3/2}}$${{\mu} _{{\rm{present}}}}$${{\mu} _{{\rm{expt}}{\rm{.}}}}$[33]
    207Fr9/290.7(6)3.85(3)3.85(3)3.89(9)
    208Fr7874.8(3)4.723(2)72.4(5)4.784(33)4.753(33)4.75(10)
    209Fr9/21127.9(2)3.914(1)93.3(5)3.963(21)3.939(22)3.95(8)
    210Fr6946.3(3)4.379(1)78.0(2)4.418(11)4.399(20)4.40(9)
    211Fr9/21142.1(2)3.964(1)94.9(3)4.031(13)3.998(34)4.00(8)
    212Fr51187(7)4.577(26)97.2(1)4.588(5)4.583(30)4.62(9)
    213Fr9/21150(8)3.991(28)95.3(3)4.047(13)4.019(30)4.02(8)
    220Fr1–73.2(5)–0.691(5)–0.691(5)–0.67(1)
    221Fr5/2808(12)1.558(23)65.5(6)1.545(14)1.552(25)1.58(3)
    222Fr233(1)0.623(19)0.623(19)0.63(1)
    223Fr3/283.3(9)1.179(13)1.179(13)1.17(2)
    224Fr142.1(7)0.397(7)0.397(7)0.40(1)
    225Fr3/277(3)1.090(42)1.090(42)1.07(2)
    226Fr17(1)0.066(9)0.066(9)0.071(2)
    227Fr1/2316(2)1.491(9)1.491(9)1.50(3)
    228Fr2–41(2)–0.77(4)–0.77(4)–0.76(2)
    下载: 导出CSV
  • [1]

    Grant I P 2007 Relativistic Quantum Theory of Atoms and Molecules (New York: Springer) pp533−577

    [2]

    Fischer C F, Brage T, Jönsson P 1997 Computational Atomic Structure: An MCHF Approach (UK: Institute of Physics) pp1−67

    [3]

    Jönsson P, Gaigalas G, Bieroń J, Fishcher C F, Grant I 2013 Computer Physics Communications. 184 2197Google Scholar

    [4]

    Jönsson P, He X, Fishcher C F, Grant I 2007 Computer Physics Communications. 177 597Google Scholar

    [5]

    Dzuba V A, Flambaum V V, Kozlov M G 1996 Phys. Rev. A 54 3948Google Scholar

    [6]

    Dzuba V A, Johnson W R 1998 Phys. Rev. A 57 2459Google Scholar

    [7]

    Angstmann E J, Dzuba V A, Flambaum V V 2004 Phys. Rev. A 70 014102Google Scholar

    [8]

    Dinh T H, Dzuba V A, Flambaum V V, Ginges J S M 2008 Phys. Rev. A 78 054501Google Scholar

    [9]

    Kozlov M G, Porsev S G, Johnson W R 2001 Phys. Rev. A 64 052107Google Scholar

    [10]

    Pal R, Safronova M S, Johnson W R, Derevianko A, Porsev S G 2007 Phys. Rev. A 75 042515Google Scholar

    [11]

    Blundell S A, Johnson W R, Liu Z W, Sapirstein 1989 Phys. Rev. A 40 2233Google Scholar

    [12]

    Eliav E, Vikas M J, Ishikawa Y, Kaldor U 2005 Chem. Phys. 311 163Google Scholar

    [13]

    Mani B K, Angom D 2011 Phys. Rev. A 83 012501Google Scholar

    [14]

    Kallay M, Nataraj H S, Sahoo B K, Das B P, Visscher L 2011 Phys. Rev. A 83 030503Google Scholar

    [15]

    Nandy D K, Singh Y, Sahoo B K 2014 Phys. Rev. A 89 062509Google Scholar

    [16]

    Borschevsky A, Eliav E, Vilkas M J, Ishikawa Y, Kaldor U 2007 Phys. Rev. A 75 042514Google Scholar

    [17]

    Eliav E, Kaldor U, Ishikawa Y 1996 Phys. Rev. A 53 3050Google Scholar

    [18]

    Chaudhuri R K, Chattopadhyay S, Mahapatra U S 2013 J. Phys. Chem. A 117 12616Google Scholar

    [19]

    Tang Y B, Lou B Q, Shi T Y 2017 Phys. Rev. A 96 022513Google Scholar

    [20]

    Tang Y B, Gao N N, Lou B Q, Shi T Y 2018 Phys. Rev. A 98 062511Google Scholar

    [21]

    Byrnes T M R, Dzuba V A, Flambaum F F, Murray D W 1999 Phys. Rev. A 59 3082Google Scholar

    [22]

    Mukherjee D, Sahoo B K, Nataraj H S, Das B P 2009 J. Phys. Chem. A 113 12549Google Scholar

    [23]

    Sakemi Y, Harada K, Hayamizu T, Itoh M, Kawamura H, Liu S, Nataraj H S, Oikawa A, Saito M, Sato T 2011 J. Phys. Conf. Ser. 302 012051Google Scholar

    [24]

    Sahoo B K, Aoki T, Das B P, Sakemi Y 2016 Phys. Rev. A 93 032520Google Scholar

    [25]

    Atutov S N, Calabrese R, Corradi L, Dainelli A, Mauro C D, Khanbekyan A, Mariotti E, Minguzzi P, Moi L, Sanguinetti S, Stancari G, Tomassetti L 2008 Proc. SPIE 7027 70270C

    [26]

    Ekström C, Ingelman S, Wannberg G, Skarestad M 1978 Physica Scripta 18 51Google Scholar

    [27]

    Coc A, Thibault C, Touchard F, Duong H T, Juncar P, Liberman S, Pinard J, Lermé J, Vialle J L, Büttgenbach S, Mueller A C, Pesnelle A, the ISOLDE Collaboration 1985 Phys. Lett. B 163 66Google Scholar

    [28]

    Coc A, Thibault C, Touchard F, Duong H T, Juncar P, Liberman S, Pinard J, Carre M, Lermé J, Vialle J L, Büttgenbach S, Mueller A C, Pesnelle A, the ISOLDE Collaboration 1987 Nucl. Phys. A 468 1Google Scholar

    [29]

    Arnold E, Borchers W, Duong H T, Juncar P, Lermé J, Lievens P, Neu W, Neugart R, Pellerin M, Pinard J, Vialle J L, Wendt K, the ISOLDE Collaboration 1990 J. Phys. B 23 3511Google Scholar

    [30]

    Arnold E, Borchers W, Carré M, Duong H T, Juncar P, Lermé J, Liberman S, Neu W, Neugart R, Otten W, Pellerin M, Pinard J, Pesnelle A, Vialle J L, Wendt K, the ISOLDE Collaboration 1989 J. Phys. B 22 L391Google Scholar

    [31]

    Bauche J, Duong H T, Juncar P, Liberman S, Pinard J, Coc A, Thibault C, Touchard F, Lermé J, Vialle J L, Büttgenbach S, Mueller A C, Pesnelle A, the ISOLDE Collaboration 1986 J. Phys. B 19 L593Google Scholar

    [32]

    Grossman J S, Orozco L A, Simsarian J E, Sprouse G D, Zhao W Z 1999 Phys. Rev. Lett. 83 935Google Scholar

    [33]

    Sansonetti J E 2007 J. Phys. Chem. Ref. Data 36 497Google Scholar

    [34]

    Gomez E, Aubin S, Orozco L A, Sprouse G D, Iskrenova-Tchoukova E, Safronova M S 2008 Phys. Rev. Lett. 100 172502Google Scholar

    [35]

    Dzuba V A, Flambaum V V, Sushkov O P 1984 J. Phys. B: At. Mol. Phys. 17 1953Google Scholar

    [36]

    Owusu A, Dougherty R W, Gowri G, Das T P 1997 Phys. Rev. A 56 305Google Scholar

    [37]

    Safronova M S, Johnson W R, Derevianko A 1999 Phys. Rev. A 60 4476Google Scholar

    [38]

    Sahoo B K, Nandy D K, Das B P, Sakemi Y 2015 Phys. Rev. A 91 042507Google Scholar

    [39]

    Duong H T, Juncar P, Liberman S, Mueller A C, Neugart R, Otten E W, Peuse B, Pinard J, Stoke H H, Thibault C, Touchard F, Vialle J L, Wendt K, the ISOLDE Collaboration 1987 Europhys. Lett. 3 175Google Scholar

    [40]

    Barber Z W, Stalnaker J E, Lemke N D, Poli N, Oates C W, Fortier T M, Diddams S A, Hollberg L, Hoyt C W, Taichenachev A V, Yudin V I 2008 Phys. Rev. Lett. 100 103002Google Scholar

    [41]

    Kien F L, Balykin V I, Hakuta K 2005 J. Phys. Soc. Jpn. 74 910Google Scholar

    [42]

    Ingvar L 1978 Int. J. Quantum Chem. 12 33

    [43]

    Sinha D, Mukhopadhyay S, Mukherjee D 1986 Chem. Phys. Lett. 129 369Google Scholar

    [44]

    Blundell S A, Johnson W R, Sapiratein J 1991 Phys. Rev. A 43 3407Google Scholar

    [45]

    Porsev S G, Beloy K, Derevianko A 2010 Phys. Rev. D 82 036008Google Scholar

    [46]

    Sahoo B K, Sur C, Beier T, Das B P, Chaudhuri R K, Mukherjee D 2007 Phys. Rev. A 75 042504Google Scholar

    [47]

    Safronova M S, Safronova U I 2011 Phys. Rev. A 83 052508Google Scholar

  • [1] 陈池婷, 吴磊, 王霞, 王婷, 刘延君, 蒋军, 董晨钟. B2+和B+离子的静态偶极极化率和超极化率的理论研究. 物理学报, 2023, 72(14): 143101. doi: 10.7498/aps.72.20221990
    [2] 王霞, 贾方石, 姚科, 颜君, 李冀光, 吴勇, 王建国. 类铝离子钟跃迁能级的超精细结构常数和朗德g因子. 物理学报, 2023, 72(22): 223101. doi: 10.7498/aps.72.20230940
    [3] 王昕, 康哲铭, 刘龙, 范贤光. 基于中值滤波和非均匀B样条的拉曼光谱基线校正算法. 物理学报, 2020, 69(20): 200701. doi: 10.7498/aps.69.20200552
    [4] 张祥, 卢本全, 李冀光, 邹宏新. Hg+离子5d106s 2S1/2→5d96s2 2D5/2钟跃迁同位素位移和超精细结构的理论研究. 物理学报, 2019, 68(4): 043101. doi: 10.7498/aps.68.20182136
    [5] 任雅娜, 杨保东, 王杰, 杨光, 王军民. 铯原子7S1/2态磁偶极超精细常数的测量. 物理学报, 2016, 65(7): 073103. doi: 10.7498/aps.65.073103
    [6] 张东玲, 汤清彬, 张金平, 施德恒, 余本海. 用耦合簇方法及相关一致基研究PH2(X2B1)自由基的解析势能函数. 物理学报, 2009, 58(8): 5323-5328. doi: 10.7498/aps.58.5323
    [7] 何永林, 周效信, 李小勇. 用B-样条函数研究静电场中锂原子里德伯态的性质. 物理学报, 2008, 57(1): 116-123. doi: 10.7498/aps.57.116
    [8] 孟慧艳, 康 帅, 史庭云, 詹明生. 平行电磁场中的Rydberg锂原子吸收谱的模型势计算. 物理学报, 2007, 56(6): 3198-3204. doi: 10.7498/aps.56.3198
    [9] 惠 萍. 用B样条技术研究半导体微晶中激子的量子受限效应. 物理学报, 2005, 54(9): 4324-4328. doi: 10.7498/aps.54.4324
    [10] 陈岁元, 刘常升, 李慧莉, 崔 彤. 非晶Fe73.5Cu1Nb3Si13.5B9合金激光纳米化的超精细结构研究. 物理学报, 2005, 54(9): 4157-4163. doi: 10.7498/aps.54.4157
    [11] 王晓峰, 乔豪学, 刘海林, 于国萍. 限制环境下类氢体系的共振增强现象. 物理学报, 2005, 54(8): 3530-3534. doi: 10.7498/aps.54.3530
    [12] 陈岁元, 刘常升, 傅贵勤, 王章涛, 才庆魁. 高硼钢中B与Fe作用的超精细结构研究. 物理学报, 2002, 51(8): 1711-1715. doi: 10.7498/aps.51.1711
    [13] 韩利红, 芶秉聪, 王菲. 类铍BⅡ离子激发态的相对论能量和精细结构. 物理学报, 2001, 50(9): 1681-1684. doi: 10.7498/aps.50.1681
    [14] 陈志骏, 马洪良, 陈淼华, 李茂生, 施 伟, 陆福全, 汤家镛. 单电荷态钡离子超精细结构光谱. 物理学报, 1999, 48(11): 2038-2041. doi: 10.7498/aps.48.2038
    [15] 姜泽辉, 赫晓东, 韩杰才, 杜善义. 均匀电场中颗粒簇偶极矩的确定. 物理学报, 1999, 48(6): 1037-1043. doi: 10.7498/aps.48.1037
    [16] 乔豪学, 饶建国, 李白文. 氦原子关联能的B样条计算. 物理学报, 1997, 46(11): 2104-2110. doi: 10.7498/aps.46.2104
    [17] 朱士尧, 徐纪华, 赵淑君, 李醒. B的KαX射线谱精细结构的研究. 物理学报, 1991, 40(9): 1411-1416. doi: 10.7498/aps.40.1411
    [18] 潘守甫, 张凤梧. Li原子的超精细结构计算. 物理学报, 1964, 20(8): 822-824. doi: 10.7498/aps.20.822
    [19] 余友文, 张宗烨. 关於镧La57的超精细结构. 物理学报, 1958, 14(6): 488-496. doi: 10.7498/aps.14.488
    [20] 赵广增, 郑志豪. 水银共振線超精细结构的强度分布. 物理学报, 1955, 11(4): 359-362. doi: 10.7498/aps.11.359
计量
  • 文章访问数:  8148
  • PDF下载量:  80
  • 被引次数: 0
出版历程
  • 收稿日期:  2019-01-21
  • 修回日期:  2019-03-09
  • 上网日期:  2019-05-01
  • 刊出日期:  2019-05-05

/

返回文章
返回