Calculationof isotope shift of Mg+ ion by using the relativistic multi-configuration interaction method

Yu Geng-Hua; Yan Hui; Gao Dang-Li; Zhao Peng-Yi; Liu Hong; Zhu Xiao-Ling; Yang Wei

doi:10.7498/aps.67.20171817

Abstract

The special mass shift coefficients and field shift factors for the atomic transitions 3s2S1/2-3s2P1/2 and 3s2S1/2-3s2S3/2 of Mg+ ion are calculated by the relativistic multi-configuration interaction method, and the isotope shifts are also obtained for the Mg+ isotopes with the neutron numbers 8 N 20. Our calculations are carried out by using the GRASP2 K package together with the relativistic isotope shift computation code package RIS3. In our calculations the nuclear charge distribution is described by the two-parameter Fermi model and the field shifts are calculated by the first-order perturbation. In order to generate the active configurations, a restricted double excitation mode is used here, the electron in the 3s shell (3s1) is chosen to be excited, another electron is excited from the 2s or 2p shells (2s22p6), and the two electrons in the inner 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 labeled by the principal quantum number n and contains the corresponding orbitals s, p, detc. The maximum principal quantum number n is 6 and the largest orbital quantum number lmax is g. According to our calculations, the normal mass shift coefficients are -586.99 GHzamu and -588.50 GHzamu, the special mass shift coefficients are -371.90 GHzamu and -371.95 GHzamu, the field shift factors are -117.10 MHzfm-2 and -117.18 MHzfm-2 for the 3s2S1/2-3s2P1/2 and the 3s2S1/2 -3s2S3/2 transitions of Mg+ ions, respectively. Then the isotope shifts for different Mg+ isotopes are obtained using the available data of the nuclear mass and the nuclear charge radii. Our results are coincident with other theoretical calculations and also with experimental results. The relative errors of our calculations are in a range from 0.13% to 0.28% compared with the latest measurements. Our calculations are the most consistent with the experimental measurements for the moment. The results provided here in this paper could be referred to for the experimental and theoretical study of Mg+ isotope shift, and they could be applied to the spectral measurement experiments of the short-lived Mg+ isotopes and also used for the research of the characteristics of exotic nuclei with Mg+ isotopes near the magic neutron numbers N=8 and N=20. The calculation method and the excitation mode used here could also be extended to other multi-electron systems with eleven orbital electrons, and the corresponding theoretical studies of the atomic spectral structures and isotope shifts could then be carried out.

Keywords:

Authors and contacts

1.
School of Information Science and Engineering, Chengdu University, Chengdu 610106, China;
2.
Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, South China Normal University, Guangzhou 510006, China;
3.
School of Science, Xi'an University of Architecture and Technology, Xi'an 710055, China;
4.
College of Physics and Electronic Science, Hubei Normal University, Huangshi 435002, China

Corresponding author: Yan Hui, yanhui@scnu.edu.cn

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, China (Grant No. 2015KJXX-33), the Fund of the Scientific Research Foundation of Sichuan Provincial Department of Education, China (Grant No. 14ZB0375) and the Open Fund of Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, China (Grant No. 00201607).

References

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[38]	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
[39]	Drullinger R, Wineland D, Bergquist J 1980 Appl. Phys. 22 365
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[41]	Yu G H, Liu H, Zhao P Y, Xu B M, Gao D L, Zhu X L, Yang W 2017 Acta Phys. Sin. 66 113101(in Chinese) [余庚华, 刘鸿, 赵朋义, 徐炳明, 高当丽, 朱晓玲, 杨维 2017 66 113101]
[42]	Shabaev V M 1985 Theor. Math. Phys. 63 588
[43]	Shabaev V M 1988 Sov. J. Nucl. Phys. 47 69
[44]	Zhang P P, Zhong Z X, Yan Z C, Shi T Y 2015 Chin. Phys.. 24 033101
[45]	Yan Z C, Drake G W F 2003 Phys. Rev. Lett. 91 113004
[46]	Tupitsyn I I, Kozlov M G, Safronova M S, Shabaev V M, Dzuba V A 2016 Phys. Rev. Lett. 117 253001

Cited By

[1]	Volotka A V, Glazov D A, Shabaev V M, Tupitsyn I I, Plunien G 2015 Phys. Rev. Lett. 112 253004
[2]	Yan Z C, Nörtershäuser W, Drake G W F 2008 Phys. Rev. Lett. 100 243002
[3]	Cheal B, Cocolios T E, Fritzsche S 2012 Phys. Rev.. 86 042501
[4]	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.. 72 044309
[5]	Neugart R, Balabanski D L, Blaum K, Borremans D, Himpe P, Kowalska M, Lievens P, Mallion S, Neyens G, Vermeulen N, Yordanov D T 2008 Phys. Rev. Lett. 101 132502
[6]	Nörtershäuser W, Sánchez R, Ewald G, Dax A, Behr J, Bricault P, Bushaw B A, Dilling J, Dombsky M, Drake G W F, Götte S, Kluge H J, Khl T, Lassen J, Levy C D P, Pachucki K, Pearson M, Puchalski M, Wojtaszek A, Yan Z C, Zimmermann C 2011 Phys. Rev.. 83 012516
[7]	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
[8]	Tang L Y, Yan Z C, Shi T Y, James F B 2009 Phys. Rev.. 79 062712
[9]	Duff M J, Okun L B, Veneziano G 2002 J. High Energy Phys. 2002 023
[10]	Webb J K, King J A, Murphy M T, Flambaum V V, Carswell R F, Bainbridge M B 2011 Phys. Rev. Lett. 107 191101
[11]	Hawking S W 1974 Nature 248 30
[12]	Drobyshevski E M, Drobyshevski M E, Izmodenova T Y, Telnov D S 2003 Astron. Astrophys. Trans. 22 263
[13]	Federman S R, Lambert D L, Cardelli J A, Sheffer Y 1996 Nature 381 764
[14]	Xu P, Yang J W, Liu M, He X D, Zeng Y, Wang K P, Wang J, Papoular D J, Shlyapnikov G V, Zhan M S 2015 Nat. Commun. 6 7803
[15]	Papp S B, Pino J M, Wieman C E 2008 Phys. Rev. Lett. 101 040402
[16]	Burke J P, Bohn J L, Esry B D, Greene C H 1998 Phys. Rev. Lett. 80 2097
[17]	Hamilton M S, Gorges A R, Roberts J 2012 J. Phys.. 45 095302
[18]	Filippin L, Godefroid M, Ekman J, Jönsson P 2016 Phys. Rev.. 93 062512
[19]	Korol V A, Kozlov M G 2007 Phys. Rev.. 76 022103
[20]	Yu G H, Zhao P Y, Xu B M, Zhu X L, Yang W 2017 Mod. Phy. Lett.. 31 1750003
[21]	Fenner Y, Murphy M T, Gibson B K 2005 Mon. Not. R. Astron. Soc. 358 468
[22]	Ashenfelter T P, Mathews G J, Olive K A 2004 Phys. Rev. Lett. 92 041102
[23]	Patra S K, Praharaj C R 1991 Phys. Lett.. 273 13
[24]	Shubhchintak N, Chatterjee R, Shyam R, Tsushima K 2015 Nucl. Phys. 939 101
[25]	Safronova M S, Johnson W R 2001 Phys. Rev.. 64 052501
[26]	Safronova M S, Tupitsyn I I 2015 Comput. Phys. Commun. 195 199
[27]	Dzuba V A, Johnson W R, Safronova M S 2005 Phys. Rev.. 72 022503
[28]	Sahoo B K 2010 J. Phys.. 43 231001
[29]	Kozhedub Y S, Volotka A V, Artemyev A N, Glazov D A, Plunien G, Shabaev V M, Tupitsyn I I, Stöhlker T 2010 Phys. Rev.. 81 042513
[30]	Yan Z C, Drake G W F 2002 Phys. Rev.. 66 042504
[31]	Nazé C, Gaidamauskas E, Gaigalas G, Godefroid M, Jönsson P 2013 Comput. Phys. Commun. 184 2187
[32]	Jönsson P, He X, Fischer C F, Grant I 2007 Comput. Phys. Commun. 177 597
[33]	Jönsson P, Gaigalas G, Bierón J, Fischer C F, Grant I 2013 Comput. Phys. Commun. 184 2197
[34]	Lunney D, Pearson J M, Thibault C 2003 Rev. Mod. Phys. 75 1021
[35]	Wang M, Audi G, Wapstra A H, Kondev F G, Maccormick M, Xu X, Pfeiffer B 2012 Chin. Phys.. 36 1603
[36]	Berengut J C, Dzuba V A, Flambaum V V 2003 Phys. Rev.. 68 022502
[37]	Tupitsyn I I, Shabaev V M, López-Urrutia J R C, Draganic I, Orts R S, Ullrich J 2003 Phys. Rev.. 68 022511
[38]	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
[39]	Drullinger R, Wineland D, Bergquist J 1980 Appl. Phys. 22 365
[40]	Batteiger V, Knnz S, Herrmann M, Saathoff G, Schssler H A, Bernhardt B, Wilken T, Holzwarth R, Hänsch T W, Udem T 2009 Phys. Rev.. 80 022503
[41]	Yu G H, Liu H, Zhao P Y, Xu B M, Gao D L, Zhu X L, Yang W 2017 Acta Phys. Sin. 66 113101(in Chinese) [余庚华, 刘鸿, 赵朋义, 徐炳明, 高当丽, 朱晓玲, 杨维 2017 66 113101]
[42]	Shabaev V M 1985 Theor. Math. Phys. 63 588
[43]	Shabaev V M 1988 Sov. J. Nucl. Phys. 47 69
[44]	Zhang P P, Zhong Z X, Yan Z C, Shi T Y 2015 Chin. Phys.. 24 033101
[45]	Yan Z C, Drake G W F 2003 Phys. Rev. Lett. 91 113004
[46]	Tupitsyn I I, Kozlov M G, Safronova M S, Shabaev V M, Dzuba V A 2016 Phys. Rev. Lett. 117 253001

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