采用相对论多组态Dirac-Hartree-Fock方法对Mg原子同位素位移的理论研究

余庚华; 刘鸿; 赵朋义; 徐炳明; 高当丽; 朱晓玲; 杨维

doi:10.7498/aps.66.113101

摘要

利用相对论多组态Dirac-Hartree-Fock方法研究了Mg原子基态到低激发态1S0-1P1和1S0-3P1两条跃迁谱线的同位素位移参数，包括正常质量位移系数，特殊质量位移系数和场位移因子，并计算了24Mg，25Mg和26Mg三个稳定同位素的同位素位移.在计算中采用了一种受限制的双电子激发模式，并将同位素位移计算结果与已有的实验测量和理论计算结果进行了对比.结果表明，用本文的研究方法计算的Mg原子同位素位移与其他理论结果和实验测量值十分符合.本文的计算结果可以为20-40Mg同位素位移测量实验提供必要的参考，所用的计算方法也可以应用到其他类Mg体系（核外电子数等于12的离子）等多电子离子的光谱结构计算和同位素位移的研究中.

关键词:

Abstract

The isotope shift parameters for the atomic transitions 1S0-1P1 and 1S0-3P1 of Mg are calculated by the relativistic multiconfiguration Dirac-Hartree-Fock (MCDHF) method, including the normal mass shift (NMS) coefficients, the specific mass shift (SMS) coefficients and the field shift (FS) factors. The detailed calculations of the isotope shifts for the three stable isotopes 24Mg, 25Mg and 26Mg are also carried out, in which the GRASP2K package is used together with another modified relativistic isotope shift computation code package RIS3. The two-parameter Fermi model is used here to describe the nuclear charge distribution in order to calculate the field shift by the first-order perturbation. A restricted double excitation mode is used in our calculations, one electron is excited from the two electrons in the 3s shell (3s2), another electron is excited from the eight electrons in the 2s or 2p shells (2s22p6), and the two electrons in the 1s shell (1s2) are not excited. The active configurations are expanded from the occupied orbitals to some active sets layer by layer, each correlation layer is numbered by the principal quantum numbers n (n= 3, 4, 5, …) and contains the corresponding orbitals s, p, d, …. The active configurations with the mixing coefficients in the added layer can be optimized by the MCDHF calculations. In this work, the atomic state functions are optimized simultaneously by the self-consistent field method and the relativistic configuration interaction approach in which the Breit interaction is taken into account perturbatively as well. The maximum principal quantum number n equals 10 and the largest orbital quantum number lmax is g. In our calculations, the NMS coefficients are -576.8 and -359.9 GHz·u, the SMS coefficients are 133.9 and -479.6 GHz·u, and the FS factors are -62.7 and -78.0 MHz·fm-2 for the 1S0-1P1 and 1S0-3P1 transitions of Mg, respectively. The difference between our isotope shift calculations and the previous experimental measurements is in a range from 6 MHz to 20 MHz with the relative error range from 0.6% to 1.3%, which shows that our results are in good agreement with experimental values. Our calculations are also coincident with other theoretical results. The isotope shift parameters provided here can be applied to the quick calculations of isotope shifts for the short-lived Mg isotopes, including 20-23Mg and 27-40Mg, and can be referred to for the corresponding isotope shift experiments. The methods used here canbe applied to calculating the isotope shifts and the atomic spectroscopic structures for other Mg-like ions with twelve extranuclear electrons.

Keywords:

作者及机构信息

1.
成都大学信息科学与工程学院, 成都 610106;

2.
湖北师范大学物理与电子科学学院, 黄石 435002;

3.
中国海洋大学信息科学与工程学院, 青岛 266100;

4.
西安建筑科技大学理学院, 西安 710055

通信作者: 余庚华, genghuayu@aliyun.com

基金项目: 国家自然科学基金（批准号：11304093，11604253）、陕西省青年科技新星项目（批准号：2015KJXX-33）和四川省教育厅科研基金（批准号：14ZB0375）资助的课题.

Authors and contacts

1.
School of Information Science and Engineering, Chengdu University, Chengdu 610106, China;

2.
College of Physics and Electronic Science, Hubei Normal University, Huangshi 435002, China;

3.
School of Information Science and Engineering, Ocean University of China, Qingdao 266100, China;

4.
School of Science, Xi'an University of Architecture and Technology, Xi'an 710055, China

Corresponding author: Yu Geng-Hua, genghuayu@aliyun.com

Funds: Project supported by the National Natural Science Foundations of China (Grant Nos. 11304093, 11604253), the Plan Project of Youth Science and Technology New Star of Shaanxi Province (Grant No. 2015KJXX-33), and the Fund of the Scientific Research Foundation of Sichuan Provincial Department of Education (Grant No. 14ZB0375).

参考文献

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[2]	Nörtershäuser W, Neff T, Sanchez R, Sick I 2011 Phys. Rev. C 84 024307
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[8]	Drake G W F, Nörtershäuser W, Yan Z C 2005 Can. J. Phys. 83 311
[9]	Nörtershäuser W, Tiedemann D, Žáková M, Andjelkovic Z, Blaum K, Bissell M L, Cazan R, Drake G W F, Geppert C, Kowalska M, Krämer J, Krieger A, Neugart R, Sánchez R, Schmidt-Kaler F, Yan Z C, Yordanov D T, Zimmermann C 2009 Phys. Rev. Lett. 102 062503
[10]	Takamine A, Wada M, Okada K, Sonoda T, Schury P, Nakamura T, Kanai Y, Kubo T, Katayama I, Ohtani S, Wollnik H, Schuessler H A 2014 Phys. Rev. Lett. 112 162502
[11]	Paez E, Arnold K J, Hajiyev E, Porsev S G, Dzuba V A, Safronova U I, Safronova M S, Barrett M D 2016 Phys. Rev. A 93 042112
[12]	Safronova M S, Safronova U I, Clark C W 2015 Phys. Rev. A 91 022504
[13]	Sahoo B K 2010 J. Phys. B At. Mol. Opt. Phys. 43 231001
[14]	Berengut J C, Dzuba V A, Flambaum V V, Kozlov M G 2004 Phys. Rev. A 69 044102
[15]	Steenstrup M P, Brusch A, Jensen B B, Hald J, Thomsen J W 2010 Phys. Rev. A 82 054501
[16]	Nazé C, Gaidamauskas E, Gaigalas G, Godefroid M, Jönsson P 2013 Comput. Phys. Commun. 184 2187
[17]	Tupitsyn I I, Shabaev V M, López-Urrutia J R C, Draganic I, Orts R S, Ullrich J 2003 Phys. Rev. A 68 022511
[18]	Yu G H, Geng Y G, Zhou C, Duan C B, Li L, Chai R P, Yang Y M 2015 Chin. Phys. Lett. 32 073102
[19]	Jönsson P, He X, Fischer C F, Grant I 2007 Comput. Phys. Commun. 177 597
[20]	Jönsson P, Gaigalas G, Bierón J, Fischer C F, Grant I 2013 Comput. Phys. Commun. 184 2197
[21]	Radžiūtė L, Gaidamauskas E, Gaigalas G, Li J G, Dong C Z, Jönsson P 2015 Chin. Phys. B 24 043103
[22]	Parpia F A, Mohanty A K 1992 Phys. Rev. A 46 3735
[23]	Filippin L, Godefroid M, Ekman J, Jönsson P 2016 Phys. Rev. A 93 062512
[24]	Berengut J C, Flambaum V V, Kozlov M G 2005 Phys. Rev. A 72 044501
[25]	Konovalova E A, Kozlov M G 2015 Phys. Rev. A 92 042508
[26]	Korol V A, Kozlov M G 2007 Phys. Rev. A 76 022103
[27]	Yordanov D T, Bissell M L, Blaum K, de Rydt M, Geppert C, Kowalska M, Krämer J, Kreim K, Krieger A, Lievens P, Neff T, Neugart R, Neyens G, Nörtershäuser W, Sánchez R, Vingerhoets P 2012 Phys. Rev. Lett. 108 042504
[28]	Beverini N, Maccioni E, Pereira D, Strumia F, Vissani G, Wang Y Z 1990 Opt. Commun. 77 299
[29]	Sterr U, Sengstock K, Mller J H, Ertmer W 1993 Appl. Phys. B Photophys. Laser Chem. 56 62
[30]	Salumbides E J, Hannemann S, Eikema K S E, Ubachs W 2006 Mon. Not. R. Astron. Soc. 373 41
[31]	Hallstadius L 1979 Z. Phys. A 291 203
[32]	Boiteux S L, Klein A, Leite J R R, Ducloy M 1988 J. Phys. France 49 885
[33]	Huang K N, Aoyagi M, Chen M, Crasemann B 1976 At. Data Nucl. Data Tables 18 243
[34]	Lunney D, Pearson J M, Thibault C 2003 Rev. Mod. Phys. 75 1021
[35]	Liang Z Y, Liu J H, Liu M, Wang N 2011 Nucl. Phys. Rev. 28 257 (in Chinese) [梁祚盈, 刘俊华, 刘敏, 王宁 2011 原子核物理评论 28 257]
[36]	Wang N, Liang Z Y, Liu M, Wu X Z 2010 Phys. Rev. C 82 044304
[37]	Zhang P P, Zhong Z X, Yan Z C, Shi T Y 2015 Chin. Phys. B 24 033101
[38]	Yan Z C, Drake G W F 2003 Phys. Rev. Lett. 91 113004
[39]	Mohr P J, Plunien G, Soff G 1998 Physics Reports 293 227
[40]	Volotka A V, Glazov D A, Shabaev V M, Tupitsyn I I, Plunien G 2015 Phys. Rev. Lett. 112 253004
[41]	Yan Z C, Drake G W F 2002 Phys. Rev. A 66 042504
[42]	Yan Z C, Nörtershäuser W, Drake G W F 2008 Phys. Rev. Lett. 100 243002

施引文献

[1]	Anders M, Trezzi D, Menegazzo R, Aliotta M, Bellini A, Bemmerer D, Broggini C, Caciolli A, Corvisiero P, Costantini H, Davinson T, Elekes Z, Erhard M, Formicola A, Flöp Z, Gervino G, Guglielmetti A, Gustavino C, Gyrky G, Junker M, Lemut A, Marta M, Mazzocchi C, Prati P, Rossi-Alvarez C, Scott DA, Somorjai E, Straniero O, Szcs T 2014 Phys. Rev. Lett. 113 042501
[2]	Nörtershäuser W, Neff T, Sanchez R, Sick I 2011 Phys. Rev. C 84 024307
[3]	Kozhedub Y S, Andreev O V, Shabaev V M, Tupitsyn I I, Brandau C, Kozhuharov C, Plunien G, Stöhlker T 2008 Phys. Rev. A 77 032501
[4]	Hu M H, Wang Z W, Zeng F W, Wang T, Wang J 2011 Chin. Phys. B 20 083101
[5]	Pachucki K, Yerokhin V A 2015 J. Phys. Chem. Ref. Data 44 83
[6]	Xiong Z Y, Yao Z W, Wang L, Li R B, Wang J, Zhan M S 2011 Acta Phys. Sin. 60 113201 (in Chinese) [熊宗元, 姚战伟, 王玲, 李润兵, 王谨, 詹明生 2011 60 113201]
[7]	Borremans D, Balabanski D L, Blaum K, Geithner W, Gheysen S, Himpe P, Kowalska M, Lassen J, Lievens P, Mallion S, Neugart R, Neyens G, Vermeulen N, Yordanov D 2005 Phys. Rev. C 72 044309
[8]	Drake G W F, Nörtershäuser W, Yan Z C 2005 Can. J. Phys. 83 311
[9]	Nörtershäuser W, Tiedemann D, Žáková M, Andjelkovic Z, Blaum K, Bissell M L, Cazan R, Drake G W F, Geppert C, Kowalska M, Krämer J, Krieger A, Neugart R, Sánchez R, Schmidt-Kaler F, Yan Z C, Yordanov D T, Zimmermann C 2009 Phys. Rev. Lett. 102 062503
[10]	Takamine A, Wada M, Okada K, Sonoda T, Schury P, Nakamura T, Kanai Y, Kubo T, Katayama I, Ohtani S, Wollnik H, Schuessler H A 2014 Phys. Rev. Lett. 112 162502
[11]	Paez E, Arnold K J, Hajiyev E, Porsev S G, Dzuba V A, Safronova U I, Safronova M S, Barrett M D 2016 Phys. Rev. A 93 042112
[12]	Safronova M S, Safronova U I, Clark C W 2015 Phys. Rev. A 91 022504
[13]	Sahoo B K 2010 J. Phys. B At. Mol. Opt. Phys. 43 231001
[14]	Berengut J C, Dzuba V A, Flambaum V V, Kozlov M G 2004 Phys. Rev. A 69 044102
[15]	Steenstrup M P, Brusch A, Jensen B B, Hald J, Thomsen J W 2010 Phys. Rev. A 82 054501
[16]	Nazé C, Gaidamauskas E, Gaigalas G, Godefroid M, Jönsson P 2013 Comput. Phys. Commun. 184 2187
[17]	Tupitsyn I I, Shabaev V M, López-Urrutia J R C, Draganic I, Orts R S, Ullrich J 2003 Phys. Rev. A 68 022511
[18]	Yu G H, Geng Y G, Zhou C, Duan C B, Li L, Chai R P, Yang Y M 2015 Chin. Phys. Lett. 32 073102
[19]	Jönsson P, He X, Fischer C F, Grant I 2007 Comput. Phys. Commun. 177 597
[20]	Jönsson P, Gaigalas G, Bierón J, Fischer C F, Grant I 2013 Comput. Phys. Commun. 184 2197
[21]	Radžiūtė L, Gaidamauskas E, Gaigalas G, Li J G, Dong C Z, Jönsson P 2015 Chin. Phys. B 24 043103
[22]	Parpia F A, Mohanty A K 1992 Phys. Rev. A 46 3735
[23]	Filippin L, Godefroid M, Ekman J, Jönsson P 2016 Phys. Rev. A 93 062512
[24]	Berengut J C, Flambaum V V, Kozlov M G 2005 Phys. Rev. A 72 044501
[25]	Konovalova E A, Kozlov M G 2015 Phys. Rev. A 92 042508
[26]	Korol V A, Kozlov M G 2007 Phys. Rev. A 76 022103
[27]	Yordanov D T, Bissell M L, Blaum K, de Rydt M, Geppert C, Kowalska M, Krämer J, Kreim K, Krieger A, Lievens P, Neff T, Neugart R, Neyens G, Nörtershäuser W, Sánchez R, Vingerhoets P 2012 Phys. Rev. Lett. 108 042504
[28]	Beverini N, Maccioni E, Pereira D, Strumia F, Vissani G, Wang Y Z 1990 Opt. Commun. 77 299
[29]	Sterr U, Sengstock K, Mller J H, Ertmer W 1993 Appl. Phys. B Photophys. Laser Chem. 56 62
[30]	Salumbides E J, Hannemann S, Eikema K S E, Ubachs W 2006 Mon. Not. R. Astron. Soc. 373 41
[31]	Hallstadius L 1979 Z. Phys. A 291 203
[32]	Boiteux S L, Klein A, Leite J R R, Ducloy M 1988 J. Phys. France 49 885
[33]	Huang K N, Aoyagi M, Chen M, Crasemann B 1976 At. Data Nucl. Data Tables 18 243
[34]	Lunney D, Pearson J M, Thibault C 2003 Rev. Mod. Phys. 75 1021
[35]	Liang Z Y, Liu J H, Liu M, Wang N 2011 Nucl. Phys. Rev. 28 257 (in Chinese) [梁祚盈, 刘俊华, 刘敏, 王宁 2011 原子核物理评论 28 257]
[36]	Wang N, Liang Z Y, Liu M, Wu X Z 2010 Phys. Rev. C 82 044304
[37]	Zhang P P, Zhong Z X, Yan Z C, Shi T Y 2015 Chin. Phys. B 24 033101
[38]	Yan Z C, Drake G W F 2003 Phys. Rev. Lett. 91 113004
[39]	Mohr P J, Plunien G, Soff G 1998 Physics Reports 293 227
[40]	Volotka A V, Glazov D A, Shabaev V M, Tupitsyn I I, Plunien G 2015 Phys. Rev. Lett. 112 253004
[41]	Yan Z C, Drake G W F 2002 Phys. Rev. A 66 042504
[42]	Yan Z C, Nörtershäuser W, Drake G W F 2008 Phys. Rev. Lett. 100 243002

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