Theoretical calculations on isotope shifts of Mg I by using relativistic multiconfiguration Dirac-Hartree-Fock method

Yu Geng-Hua; Liu Hong; Zhao Peng-Yi; Xu Bing-Ming; Gao Dang-Li; Zhu Xiao-Ling; Yang Wei

doi:10.7498/aps.66.113101

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:

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).

References

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[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
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[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
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[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

Cited By

[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 物理学报 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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