硼原（离）子内壳激发高自旋态能级和辐射跃迁

钱新宇; 孙言; 刘冬冬; 胡峰; 樊秋波; 苟秉聪

doi:10.7498/aps.66.123101

摘要

采用Rayleigh-Ritz变分方法计算了B原子（离子）内壳层激发高自旋态（4，5，6L，L=S，P）里德伯系列的能量和精细结构劈裂，利用截断变分方法改进非相对论能量，并利用一阶微扰理论计算了相对论能量修正和质量极化效应修正，利用屏蔽的类氢公式计算了量子电动力学效应和高阶相对论效应，从而得到了高精度的组态能量.利用精确计算的波函数，计算了这些高自旋态的电偶极辐射跃迁波长、振子强度和辐射跃迁概率.通过长度规范和速度规范计算的振子强度的一致性证明了本文计算的波函数是精确的.相比其他理论计算结果，本文计算的高自旋态的能级及跃迁波长数据与实验数据符合得更好.对于一些高位的内壳层激发高自旋态，相关的能级和跃迁数据为首次报道，本文的计算结果对相关实验光谱谱线标定具有重要意义.

关键词:

Abstract

Energy levels of the core-excited high-spin Rydberg states (4,5,6L, L = S, P) in boron atom (ion) are calculated by the Rayleigh-Ritz variation method with using large-scale multi-configuration wave functions. The important orbital-spin angular momentum partial waves are selected based on the rule of configuration interaction. The computational convergence is discussed by the example of the contribution from each partial wave in the non-relativistic energy calculations of the high-spin state 1s2s2p2 5Pe in B+ ion. To saturate the wave functional space and improve the non-relativistic energy, the restricted variational method is used to calculate the restricted variational energy. Furthermore, the mass polarization effect and relativistic energy correction are included by using a first-order perturbation theory. The quantum electrodynamic effects and higher-order relativistic contributions to the energy levels are also calculated by the screened hydrogenic formula. Then, the accurate relativistic energy levels of these high-spin states of B atom (ion) are obtained by adding the non-relativistic energy and all corrections. The fine structure splitting of these high-spin states is also calculated by the Breit-Pauli operators in the first-order perturbation theory. Compared with other theoretical results, our calculation results are in good accordance with the experimental data. The absorption oscillator strengths, emission oscillator strengths, absorption rates, emission rates, and transition wavelengths of the electric-dipole transitions between these high-spin states of B atom (ions) are systematically calculated by using the optimized wave functions. The oscillator strengths and transition rates are obtained in both the length and velocity gauges. By comparing the two gauge results of oscillator strength, we find that there is a good consistency between them when fl 0.3, and a reasonable consistency is obtained when fl 0.3. The accordance between the length and the velocity gauge results reflects that the calculated wave functions in this work are reasonably accurate. The calculated transition data are also compared with the corresponding experimental and other theoretical data. Good agreement is obtained except the wavelengths for two transitions: 1s2p4p 4Se1s2p3d 4P and 1s2p4d 4P1s2p3p 4Pe. The relative differences between our theoretical results and experimental data are 0.7% and 0.3%, respectively. They need to be verified by further theoretical and experimental studies. For some core-excited high-spin states, the related energy levels and transition data are reported for the first time. Our calculation results will provide valuable data for calculating the spectral lines in the relevant experiments.

Keywords:

作者及机构信息

1.
徐州工程学院数学与物理科学学院, 徐州 221018;

2.
北京理工大学物理学院, 北京 100081

通信作者: 孙言, suenyangu@163.com

基金项目: 国家自然科学青年基金（批准号：11604284）和国家自然科学基金（批准号：11474020）资助的课题.

Authors and contacts

1.
School of Mathematic and Physical Science, Xuzhou University of Technology, Xuzhou 221018, China;

2.
School of Physics, Beijing Institute of Technology, Beijing 100081, China

Corresponding author: Sun Yan, suenyangu@163.com

Funds: Project supported by the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 11604284) and the National Natural Science Foundation of China (Grant No. 11474020).

参考文献

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[3]	Gu M F, Beiersdorfer P, Lepson J K 2011 Astrophys. J. 732 91
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[6]	Agentoft M, Andersen T, Chung K T, Davis B F 1985 Phys. Scr. 31 74
[7]	Chung K T, Bruch R, Trbert E, Heckmann P H 1984 Phys. Scr. 29 108
[8]	Baudinet-Robinet Y, Garnir H P, Dumont P D 1986 Phys. Rev. A 34 4722
[9]	Baudinet-Robinet Y, Dumont P D, Garnir H P, Trbert E, Heckmann P 1987 Z. Phys. D: Atoms, Molecules and Clusters 7 47
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[12]	Jannitti E, Nicolosi P, Tondello G 1984 Physica C 124 139
[13]	Lynam W G, Carroll P K, Costello J T, Evans D, O'Sullivant G 1992 J. Phys. B: At. Mol. Opt. Phys. 25 3963
[14]	Ryabtsev A N, Kink I, Awaya Y, Ekberg J O, Mannervik S, lme A, Martinson I 2005 Phys. Scr. 71 489
[15]	Kramida A E, Ryabtsev A N 2007 Phys. Scr. 76 544
[16]	Kramida A E, Ryabtsev A N, Ekberg J O, Kink I, Mannervik S, Martinson I 2008 Phys. Scr. 78 025301
[17]	Fuhr J R, Wiese W L 2010 J. Phys. Chem. Ref. Data 39 013101
[18]	Mller A, Schippers S, Phaneuf R A, Scully S W J, Aguilar A, Cisneros C, Gharaibeh M F, Schlachter A S, McLaughlin B M 2014 J. Phys. B: At. Mol. Opt. Phys. 47 135201
[19]	Beck D R, Nicolaides C A 1977 Phys. Lett. A 61 227
[20]	Gou B C, Deng W S 2000 Phys. Rev. A 62 032705
[21]	Yang H Y, Chung K T 1995 Phys. Rev. A 51 3621
[22]	Gou B C, Wang F 2004 Phys. Rev. A 69 042513
[23]	Qu L H, Wang Z W, Li B W 1998 J. Phys. B: At. Mol. Opt. Phys. 31 2469
[24]	Qu L H, Wang Z W, Li B W 1998 Chin. Phys. Lett. 15 329
[25]	Sun Y, Liu D D, Mei M F, Zhang C M, Han C, Hu F, Gou B C 2015 J. Quant. Spectrosc. Radiat. Transfer 167 145
[26]	Brooks R L, Hardis J E, Berry H G, Curtis L J, Cheng K T, Ray W 1980 Phys. Rev. Lett. 45 1318
[27]	Larsson S, Crossley R 1982 Int. J. Quantum Chem. 22 837
[28]	Ritz W, Reine J 1908 Agnew. Math. 35 1
[29]	Chung K T 1979 Phys. Rev. A 20 1743
[30]	Davis B F, Chung K T 1984 Phys. Rev. A 29 1878
[31]	Drake G W F 1982 Adv. Mol. Phys. 18 399
[32]	Lin B, Berry H G, Shibata T, Livingston A E, Garnir H P, Bastin T, Dsequelles J, Savukov I 2003 Phys. Rev. A 67 062507
[33]	Sun Y, Gou B C, Zhu J J 2010 Acta Phys. Sin. 59 3878 (in Chinese) [孙言, 苟秉聪, 朱婧晶 2010 59 3878]
[34]	Chung K T, Bruch R 1983 Phys. Rev. A 28 1418

施引文献

[1]	Johansson S G, Litzn U, Kasten J, Kock M 1993 Astrophys. J. 403 L25
[2]	Lin B, Berry H G, Shibata T, Livingston A E, Garnir H, Bastin T, Dsesquelles J 2004 J. Phys. B: At. Mol. Opt. Phys. 37 2797
[3]	Gu M F, Beiersdorfer P, Lepson J K 2011 Astrophys. J. 732 91
[4]	Martinson I, Bickel W S, Olrne A 1970 J. Opt. Soc. Am. 60 1213
[5]	Agentoft M, Andersen T, Chung K T 1984 J. Phys. B: At. Mol. Opt. Phys. 17 L433
[6]	Agentoft M, Andersen T, Chung K T, Davis B F 1985 Phys. Scr. 31 74
[7]	Chung K T, Bruch R, Trbert E, Heckmann P H 1984 Phys. Scr. 29 108
[8]	Baudinet-Robinet Y, Garnir H P, Dumont P D 1986 Phys. Rev. A 34 4722
[9]	Baudinet-Robinet Y, Dumont P D, Garnir H P, Trbert E, Heckmann P 1987 Z. Phys. D: Atoms, Molecules and Clusters 7 47
[10]	Mannervik S, Cederquist H, Martinson I 1986 Phys. Rev. A 34 231
[11]	Mannervik S, Cederquist H, Martinson I, Brage T, Fischer C F 1987 Phys. Rev. A 35 3136
[12]	Jannitti E, Nicolosi P, Tondello G 1984 Physica C 124 139
[13]	Lynam W G, Carroll P K, Costello J T, Evans D, O'Sullivant G 1992 J. Phys. B: At. Mol. Opt. Phys. 25 3963
[14]	Ryabtsev A N, Kink I, Awaya Y, Ekberg J O, Mannervik S, lme A, Martinson I 2005 Phys. Scr. 71 489
[15]	Kramida A E, Ryabtsev A N 2007 Phys. Scr. 76 544
[16]	Kramida A E, Ryabtsev A N, Ekberg J O, Kink I, Mannervik S, Martinson I 2008 Phys. Scr. 78 025301
[17]	Fuhr J R, Wiese W L 2010 J. Phys. Chem. Ref. Data 39 013101
[18]	Mller A, Schippers S, Phaneuf R A, Scully S W J, Aguilar A, Cisneros C, Gharaibeh M F, Schlachter A S, McLaughlin B M 2014 J. Phys. B: At. Mol. Opt. Phys. 47 135201
[19]	Beck D R, Nicolaides C A 1977 Phys. Lett. A 61 227
[20]	Gou B C, Deng W S 2000 Phys. Rev. A 62 032705
[21]	Yang H Y, Chung K T 1995 Phys. Rev. A 51 3621
[22]	Gou B C, Wang F 2004 Phys. Rev. A 69 042513
[23]	Qu L H, Wang Z W, Li B W 1998 J. Phys. B: At. Mol. Opt. Phys. 31 2469
[24]	Qu L H, Wang Z W, Li B W 1998 Chin. Phys. Lett. 15 329
[25]	Sun Y, Liu D D, Mei M F, Zhang C M, Han C, Hu F, Gou B C 2015 J. Quant. Spectrosc. Radiat. Transfer 167 145
[26]	Brooks R L, Hardis J E, Berry H G, Curtis L J, Cheng K T, Ray W 1980 Phys. Rev. Lett. 45 1318
[27]	Larsson S, Crossley R 1982 Int. J. Quantum Chem. 22 837
[28]	Ritz W, Reine J 1908 Agnew. Math. 35 1
[29]	Chung K T 1979 Phys. Rev. A 20 1743
[30]	Davis B F, Chung K T 1984 Phys. Rev. A 29 1878
[31]	Drake G W F 1982 Adv. Mol. Phys. 18 399
[32]	Lin B, Berry H G, Shibata T, Livingston A E, Garnir H P, Bastin T, Dsequelles J, Savukov I 2003 Phys. Rev. A 67 062507
[33]	Sun Y, Gou B C, Zhu J J 2010 Acta Phys. Sin. 59 3878 (in Chinese) [孙言, 苟秉聪, 朱婧晶 2010 59 3878]
[34]	Chung K T, Bruch R 1983 Phys. Rev. A 28 1418

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