Al+离子3s2 1S0→3s3p 3,1P1o跃迁同位素偏移的理论研究

张婷贤; 李冀光; 刘建鹏

doi:10.7498/aps.67.20172261

摘要

在多组态Dirac-Hartree-Fock方法对Al+离子3s2 1S0 → 3s3p 3，1P1o两个跃迁同位素偏移因子精细计算工作的基础上，细致研究了同位素偏移因子和能量本征值（或跃迁能）随着电子关联的收敛过程.研究发现：单个能级的同位素质量偏移因子随电子关联的收敛性与能量本征值随电子关联的收敛性之间有线性关系；对于跃迁而言，对电子关联的描述越充分，质量偏移因子和跃迁能随电子关联的收敛性之间的线性关系越明显.因此，在计算模型中包含大规模的电子关联的情况下，可以利用该线性关系根据跃迁能的误差评估同位素偏移因子的不确定度.

关键词:

Abstract

The accurate calculation of the isotope shift factors is helpful in extracting the mean-square charge radius of the nucleus,which is an important nuclear parameter to investigate the nuclear properties and improve nuclear structure theories.However,for atomic systems with many electrons the uncertainties of the calculated isotope shift factors are difficult to evaluate accurately,since high sensitivity of the isotope shift factor to the electron correlation and limitation of the computational resource.Based on the calculations of the isotope shift factors of the 3s2 1S0→ 3s3p 3,1P1o transitions in Al+by using the multi-configuration Dirac-Hartree-Fock method,the convergences of these physical quantities with the expansion of the configuration space are investigated in detail.In our calculation,the electron correlations are divided into the first-order correlation and the higher-order correlations according to the perturbation theory,and captured by using the active space approach.The effect of the first-order correlation are considered by including configuration state functions (CSFs) that are generated by the single and double substitutions from the occupied orbitals in the single reference configuration set.After the first-order correlation effect are taken into account adequately,the reference configuration sets are augumented by adding the dominant CSFs from the first-order correlation configuration space,in order to consider the higher-order correlation effect.We find that the convergence of the mass shift factors (including the normal shift factor and the specific mass shift factor) is linearly correlated with the convergence of the level energies in our computational model.For the transitions,the linear correlation of the convergence between the mass shift factors and the transition energies is not so good as that for the levels involved in the transitions due to the limited computational resource,but it can be improved with the expansion by including more higher-order correlation related 2s and 2p core electrons.Furthermore,we made use of the linear correlation to estimate the uncertainties of our isotope shift factors, and obtain the reasonable value of error.The authors hope that the linear correlation between the convergence of the mass shift factors and the level or transition energies can be proved and explained in more atomic systems,and the linear correlation can be used to evaluate accurately the uncertainties of the mass shift factors for the atoms and ions with many electrons in the near future.

Keywords:

multi-configuration Dirac-Hartree-Fock method /
electron correlation /
isotope shift /
Al+ ion

作者及机构信息

1.
北京应用物理与计算数学研究所, 北京 100088;

2.
西北师范大学物理与电子工程学院, 兰州 730070;

3.
国防科技大学文理学院, 长沙 410073

通信作者: 李冀光, li_jiguang@iapcm.ac.cn

基金项目: 国家科学自然基金（批准号：11404025，91536106）和中国博士后科学基金（批准号：2014M560061）资助的课题.

Authors and contacts

1.
Institute of Applied Physics and Computational Mathematics, Beijing 100088, China;

2.
College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070, China;

3.
College of Liberal Arts and Science, National University of Defense Technology, Changsha 410073, China

Corresponding author: Li Ji-Guang, li_jiguang@iapcm.ac.cn

Funds: Project supported by the National Natural Science Foundation of China (Grants Nos. 11404025, 91536106) and the China Postdoctoral Science Foundation (Grant No. 2014M560061).

参考文献

[1]	Campbell P, Moore I D, Pearson M R 2016 Prog. Part. Nucl. Phys. 86 127
[2]	Cheal B, Cocolios T E, Fritzsche S 2012 Phys. Rev. A 86 042501
[3]	Carette T, Godefroid M R 2011 Phys. Rev. A 83 062505
[4]	Carette T, Godefroid M R 2010 Phys. Rev. A 81 042522
[5]	Carette T, Godefroid M R 2013 J. Phys. B: At. Mol. Opt. Phys. 46 095003
[6]	Carette T, Godefroid M R 2016 arXiv: 1602.06574.
[7]	Liu J P, Li J G, Zou H X 2017 Chin. Phys. B 26 23104
[8]	Grant I P 2007 Relstivistic Quantum Theory of Atom and Molecules (New York: Spinger)
[9]	Li J G, Jönsson P, Godefroid M R, Dong C Z, Gaigalas G 2012 Phys. Rev. A 86 052523
[10]	Tupitsyn I I, Shabaev V M, Crespo López-Urrutia J R, Draganić I, Soria Orts R, Ullrich J 2003 Phys. Rev. A 68 022511
[11]	Filippin L, Beerwerth R, Ekman J, Fritzsche S, Godefroid M R, Jönsson P 2016 Phys. Rev. A 94 062508
[12]	Palmer C W P 1987 J. Phys. B: At. Mol. Opt. Phys. 20 5987
[13]	Torbohm G, Fricke B, Rosén A 1985 Phys. Rev. A 31 2038
[14]	Filippin L, Godefroid M R, Ekman J, Jönsson P 2016 Phys. Rev. A 93 062512
[15]	Filippin L, Bieroń J, Gaigalas G, Godefroid M R, Jönsson P 2017 Phys. Rev. A 96 042502
[16]	Gaidamauskas E, Nazé C, Rynkun P, Gaigalas G, Jönsson P, Gaigalas G 2011 J. Phys. B: At. Mol. Opt. Phys. 44 175003
[17]	Li J G, Godefroid M R, Wang J G 2016 J. Phys. B: At. Mol. Opt. Phys. 49 115002
[18]	Zhang T X, Xie L Y, Li J G, Lu Z H 2017 Phys. Rev. A 96 012514
[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]	Nazé C, Gaidamauskas E, Gaigalas G, Godefroid M R, Jönsson P 2013 Comput. Phys. Commun. 184 2187
[22]	Kramida A, Ralchenko Y, Reader J 2016 NIST Atomic Spectra Database (Version 5) https://www.nist.gov/pml/atomic-spectra-database
[23]	Godefroid M R, Fischer C F, Jönsson P 2001 J. Phys. B: At. Mol. Opt. Phys. 34 1079

施引文献

[1]	Campbell P, Moore I D, Pearson M R 2016 Prog. Part. Nucl. Phys. 86 127
[2]	Cheal B, Cocolios T E, Fritzsche S 2012 Phys. Rev. A 86 042501
[3]	Carette T, Godefroid M R 2011 Phys. Rev. A 83 062505
[4]	Carette T, Godefroid M R 2010 Phys. Rev. A 81 042522
[5]	Carette T, Godefroid M R 2013 J. Phys. B: At. Mol. Opt. Phys. 46 095003
[6]	Carette T, Godefroid M R 2016 arXiv: 1602.06574.
[7]	Liu J P, Li J G, Zou H X 2017 Chin. Phys. B 26 23104
[8]	Grant I P 2007 Relstivistic Quantum Theory of Atom and Molecules (New York: Spinger)
[9]	Li J G, Jönsson P, Godefroid M R, Dong C Z, Gaigalas G 2012 Phys. Rev. A 86 052523
[10]	Tupitsyn I I, Shabaev V M, Crespo López-Urrutia J R, Draganić I, Soria Orts R, Ullrich J 2003 Phys. Rev. A 68 022511
[11]	Filippin L, Beerwerth R, Ekman J, Fritzsche S, Godefroid M R, Jönsson P 2016 Phys. Rev. A 94 062508
[12]	Palmer C W P 1987 J. Phys. B: At. Mol. Opt. Phys. 20 5987
[13]	Torbohm G, Fricke B, Rosén A 1985 Phys. Rev. A 31 2038
[14]	Filippin L, Godefroid M R, Ekman J, Jönsson P 2016 Phys. Rev. A 93 062512
[15]	Filippin L, Bieroń J, Gaigalas G, Godefroid M R, Jönsson P 2017 Phys. Rev. A 96 042502
[16]	Gaidamauskas E, Nazé C, Rynkun P, Gaigalas G, Jönsson P, Gaigalas G 2011 J. Phys. B: At. Mol. Opt. Phys. 44 175003
[17]	Li J G, Godefroid M R, Wang J G 2016 J. Phys. B: At. Mol. Opt. Phys. 49 115002
[18]	Zhang T X, Xie L Y, Li J G, Lu Z H 2017 Phys. Rev. A 96 012514
[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]	Nazé C, Gaidamauskas E, Gaigalas G, Godefroid M R, Jönsson P 2013 Comput. Phys. Commun. 184 2187
[22]	Kramida A, Ralchenko Y, Reader J 2016 NIST Atomic Spectra Database (Version 5) https://www.nist.gov/pml/atomic-spectra-database
[23]	Godefroid M R, Fischer C F, Jönsson P 2001 J. Phys. B: At. Mol. Opt. Phys. 34 1079

[1]	赵国栋, 曹进, 梁婷, 冯敏, 卢本全, 常宏. 镱原子超精细诱导5d6s ³D_1,3→6s² ¹S₀ E2跃迁及超精细常数的精确计算. 物理学报, 2024, 73(9): 093101. doi: 10.7498/aps.73.20240028
[2]	邸淑红, 张阳, 杨会静, 崔乃忠, 李艳坤, 刘会媛, 李伶利, 石凤良, 贾玉璇. 铷簇同位素效应的量化研究. 物理学报, 2023, 72(18): 182101. doi: 10.7498/aps.72.20230778
[3]	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
[4]	张天成, 潘高远, 俞友军, 董晨钟, 丁晓彬. 超重元素Og(Z = 118)及其同主族元素的电离能和价电子轨道束缚能. 物理学报, 2022, 71(21): 213201. doi: 10.7498/aps.71.20220813
[5]	张祥, 卢本全, 李冀光, 邹宏新. Hg⁺离子5d¹⁰6s ²S_1/2→5d⁹6s^{2 2}D_5/2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
[6]	张斌, 赵健, 赵增秀. 基于多组态含时Hartree-Fock方法研究电子关联对于H2分子强场电离的影响. 物理学报, 2018, 67(10): 103301. doi: 10.7498/aps.67.20172701
[7]	余庚华, 颜辉, 高当丽, 赵朋义, 刘鸿, 朱晓玲, 杨维. 相对论多组态相互作用方法计算Mg+离子同位素位移. 物理学报, 2018, 67(1): 013101. doi: 10.7498/aps.67.20171817
[8]	徐海超, 牛晓海, 叶子荣, 封东来. 铁基超导体系基于电子关联强度的统一相图. 物理学报, 2018, 67(20): 207405. doi: 10.7498/aps.67.20181541
[9]	余庚华, 刘鸿, 赵朋义, 徐炳明, 高当丽, 朱晓玲, 杨维. 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. 物理学报, 2017, 66(11): 113101. doi: 10.7498/aps.66.113101
[10]	任桂明, 郑圆圆, 王丁, 王林, 谌晓洪, 王玲, 马敏, 刘华兵. 氢化氧化铝的同位素效应研究. 物理学报, 2014, 63(23): 233104. doi: 10.7498/aps.63.233104
[11]	王杰敏, 张蕾, 施德恒, 朱遵略, 孙金锋. AsO+同位素离子X2+和A2电子态的多参考组态相互作用方法研究. 物理学报, 2012, 61(15): 153105. doi: 10.7498/aps.61.153105
[12]	刘慧, 邢伟, 施德恒, 朱遵略, 孙金锋. 用MRCI方法研究CS+同位素离子X2Σ+和A2Π态的光谱常数与分子常数. 物理学报, 2011, 60(4): 043102. doi: 10.7498/aps.60.043102
[13]	胡峰, 杨家敏, 王传珂, 张继彦, 蒋刚, 朱正和. 电子关联效应对金离子的影响. 物理学报, 2011, 60(10): 103104. doi: 10.7498/aps.60.103104.1
[14]	张书锋, 邓景康, 黄艳茹, 刘昆, 宁传刚. N2价轨道的精细电子动量谱学研究. 物理学报, 2009, 58(4): 2382-2389. doi: 10.7498/aps.58.2382
[15]	刘延君, 董晨钟, 蒋军, 颉录有. 电子与类铍N3+和O4+离子碰撞激发截面的相对论扭曲波计算. 物理学报, 2009, 58(4): 2320-2327. doi: 10.7498/aps.58.2320
[16]	朱婧晶, 苟秉聪. 类氦离子高双激发态电子关联效应的研究. 物理学报, 2009, 58(8): 5285-5290. doi: 10.7498/aps.58.5285
[17]	刘建业, 郭文军, 左维, 李希国. 核子-核子碰撞截面对同位素标度参数α的同位旋效应. 物理学报, 2008, 57(9): 5458-5463. doi: 10.7498/aps.57.5458
[18]	张莉, 朱正和, 杨本福, 龙兴贵, 罗顺忠. 氢同位素化合物TiH2，TiD2和TiT2的电子振动近似理论方法. 物理学报, 2006, 55(10): 5418-5423. doi: 10.7498/aps.55.5418
[19]	苏国林, 任雪光, 张书锋, 宁传刚, 周晖, 李彬, 黄峰, 李桂琴, 邓景康. 环戊烯分子内价轨道1a′的电子动量谱学研究. 物理学报, 2005, 54(9): 4108-4112. doi: 10.7498/aps.54.4108
[20]	李文飞, 张丰收, 陈列文. 化学不稳定性和同位素分布的同位旋效应. 物理学报, 2001, 50(6): 1040-1045. doi: 10.7498/aps.50.1040

计量

文章访问数: 6005
PDF下载量: 170
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板