全相对论多组态原子结构及物理量的精密计算——构建准完备基以及组态相互作用

青波; 程诚; 高翔; 张小乐; 李家明

doi:10.7498/aps.59.4547

摘要

从第一原理出发计算原子结构有多种理论方法,它们都是基于变分原理的,其关键是构建一组最适合描述真实物理体系的且适用于变分原理的准完备基.本文阐明了如何利用全相对论计算程序GRASPVU,通过单组态Dirac-Fock计算以及多组态Dirac-Fock自洽场计算建立准完备基.然后利用该准完备基进行组态相互作用计算以充分考虑关联作用;在此基础上,进一步考虑电磁相互作用的延迟效应和量子电动力学等修正.该准完备基对原子结构和电磁跃迁等物理量可进行精密的理论计算.最简单的He体系的能级和跃迁速率等物理量的计算值与目前

关键词:

Abstract

Based on the variation principle, many methods have been developed in atomic structure calculations. A high quality complete basis set is essential to the calculation of atomic structures. We present how to construct quasi-complete basis sets through Dirac-Fock calculations and multi-configuration Dirac-Fock self-consistent filed calculations by using the full-relativistic GRASPVU program package, which is based on the multi-configuration Dirac-Fock method. The relativistic configuration interaction calculations are carried out by using the quasi-complete basis sets to adequately consider correlations. The relativistic retardation effect of electromagnetic interactions and the quantum electron dynamic corrections are also taken into account. Our calculation results of He agree well with other theoretical results and experimental results, which validates the feasibility of our calculation scenario. Our calculations are full-relativistic, and can be extended to high Z helium-like ions in which the relativistic effect is important. Our scenario of constructing quasi-complete basis sets can be used in any many-electron atomic system. We calculated the energy levels of Mg and elucidated the mechanism of its interesting fine-structure splittings of 3 3D and 4 3D levels.

Keywords:

quasi-complete basis set /
multi-configuration Dirac-Fock self-consistent field method /
relativistic configuration interaction

作者及机构信息

(1)清华大学物理系,原子分子纳米科学教育部重点实验室,北京 100084; (2)清华大学物理系,原子分子纳米科学教育部重点实验室,北京 100084; 上海交通大学物理系,上海 200240; (3)上海交通大学物理系,上海 200240

基金项目: 国家自然科学基金(批准号:10734040)和国家863高技术专业委员会惯性约束核聚变主题和国家重点基础研究发展计划(批准号:2006CB921408)资助的课题.

Authors and contacts

(1)Department of Physics, Shanghai Jiao Tong University, Shanghai 200240, China; (2)Key Laboratory of Atomic and Molecular Nano Sciences of Ministry of Education, Department of Physics, Tsinghua University, Beijing 100084, China; (3)Key Laboratory of Atomic and Molecular Nano Sciences of Ministry of Education, Department of Physics, Tsinghua University, Beijing 100084, China; Department of Physics, Shanghai Jiao Tong University, Shanghai 200240, China

参考文献

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[2]	Dalgarno A 1979 Adv. At. Mol. Phys. 15 37
[3]	Kallman T R, Palmeri P 2007 Rev. Mod. Phys. 79 79
[4]	Clark R E H, Reiter D H 2005 Nuclear Fusion Research: Understanding Plasma-Surface Interactions(Berlin, Heidelberg:Springer-Verlag) Volume 78
[5]	Lindl J D, Amendt P, Berger R L, Glendinning S G, Glenzer S H, Haan S W,Kauffman R L, Landen O L, Suter L J 2004 Phys. Plasmas 11 339
[6]	Larsson M 1995 Rep. Prog. Phys. 58 1267
[7]	Xia J W, Zhan W L, Wei B W, Yuan Y J, Song M T, Zhang W Z, Yang X D, Yuan P,Gao D Q, Zhao H W, Yang X T, Xiao G Q, Man K T, Dang J R, Cai X H, Wang Y F,Tang J Y, Qiao W M, Rao Y N, He Y, Mao L Z, Zhou Z Z 2002 Nucl. Instrum. Meth. A 488 11
[8]	Augustin I 2007 Nucl. Instrum. Meth. B 261 1014
[9]	Drake G W F, Yan Z C 1992 Phys. Rev. A 46 2378
[10]	Mann J B, Johnson W R 1971 Phys. Rev. A 4 41
[11]	Grant I P, McKenzie B J 1980 J. Phys. B 13 2671
[12]	Grant I P 2006 Relativistic Quantum Theory of Atoms and Molecules (New York: Springer) pp222—228,562—568
[13]	Drake G W F 1988 Can. J. Phys. 66 586
[14]	Zhang T, Yan Z C, Drake G W F 1996 Phys. Rev. Lett. 77 1715
[15]	Drake G W F, Martin W C 1998 Can. J. Phys. 76 679
[16]	Fischer C F 1986 Comput. Phys. Rep. 3 273
[17]	Grant I P1970 Adv. Phys. 19 747
[18]	Brown G E, Ravenhall D G 1951 Proc. R. Soc. London Ser. A 208 552
[19]	Sucher J 1980 Phys. Rev. A 22 348
[20]	Parpia F A, Fischer C F, Grant I P 1996 Comput. Phys. Commun. 94 249
[21]	Peng Y L, Han X Y, Wang M S, Li J M 2005 J. Phys. B 38 3825
[22]	Qing B, Chen S H, Gao X, Li J M 2008 Chin. Phys. Lett. 25 2448
[23]	Parpia F A, Tong M, Fischer C F 1992 Phys. Rev. A 46 3717
[24]	Mohr P J, Plunien G, Soff G 1998 Phys. Rep. 293 227
[25]	Fullerton L W, Rinker Jr G A 1976 Phys. Rev. A 13 1283
[26]	Pastor P C, Giusfredi G, Natale P D, Hagel G, Mauro C D, Inguscio M 2004 Phys. Rev. Lett. 92 023001
[27]	Xie L Y, Dong C Z, Ma X W, Yuan P, Yan J, Qu Y Z 2002 Acta Phys. Sin. 51 1965(in Chinese)[颉录有、董晨钟、马新文、袁萍、颜君、曲一至 2002 物理学报 51 1965]
[28]	Dall R G, Baldwin K G H, Byron L J, Truscott A G 2008 Phys. Rev. Lett. 100 023001
[29]	Burger J M, Lurio A 1971 Phys. Rev. A 3 76
[30]	Drake G W F 1979 Phys. Rev. A 19 1387
[31]	ach G, Pachucki K 2001 Phys. Rev. A 64 042510
[32]	Schiff B, Pekeris C L 1964 Phys. Rev. 134 A638
[33]	Zhao P, Lawall J R, Pipkin F M 1991 Phys. Rev. Lett. 66 592
[34]	Drake G W F, Nōrtershāuser W, Yan Z C 2005 Can. J. Phys. 83 311
[35]	Wang X L, Liu L T, Gao X, Shen C, Li J M 2008 Chin. Phys. Lett. 25 4244
[36]	Isaksen S, Anderson A, Anderson T, Ramanujam P S 1979 J. Phys. B 12 893

施引文献

[1]	Eidelsberg M, Crifo-Magnant F, Zeippen C J 1981 Astron. Astrophys. Suppl. Ser. 43 455
[2]	Dalgarno A 1979 Adv. At. Mol. Phys. 15 37
[3]	Kallman T R, Palmeri P 2007 Rev. Mod. Phys. 79 79
[4]	Clark R E H, Reiter D H 2005 Nuclear Fusion Research: Understanding Plasma-Surface Interactions(Berlin, Heidelberg:Springer-Verlag) Volume 78
[5]	Lindl J D, Amendt P, Berger R L, Glendinning S G, Glenzer S H, Haan S W,Kauffman R L, Landen O L, Suter L J 2004 Phys. Plasmas 11 339
[6]	Larsson M 1995 Rep. Prog. Phys. 58 1267
[7]	Xia J W, Zhan W L, Wei B W, Yuan Y J, Song M T, Zhang W Z, Yang X D, Yuan P,Gao D Q, Zhao H W, Yang X T, Xiao G Q, Man K T, Dang J R, Cai X H, Wang Y F,Tang J Y, Qiao W M, Rao Y N, He Y, Mao L Z, Zhou Z Z 2002 Nucl. Instrum. Meth. A 488 11
[8]	Augustin I 2007 Nucl. Instrum. Meth. B 261 1014
[9]	Drake G W F, Yan Z C 1992 Phys. Rev. A 46 2378
[10]	Mann J B, Johnson W R 1971 Phys. Rev. A 4 41
[11]	Grant I P, McKenzie B J 1980 J. Phys. B 13 2671
[12]	Grant I P 2006 Relativistic Quantum Theory of Atoms and Molecules (New York: Springer) pp222—228,562—568
[13]	Drake G W F 1988 Can. J. Phys. 66 586
[14]	Zhang T, Yan Z C, Drake G W F 1996 Phys. Rev. Lett. 77 1715
[15]	Drake G W F, Martin W C 1998 Can. J. Phys. 76 679
[16]	Fischer C F 1986 Comput. Phys. Rep. 3 273
[17]	Grant I P1970 Adv. Phys. 19 747
[18]	Brown G E, Ravenhall D G 1951 Proc. R. Soc. London Ser. A 208 552
[19]	Sucher J 1980 Phys. Rev. A 22 348
[20]	Parpia F A, Fischer C F, Grant I P 1996 Comput. Phys. Commun. 94 249
[21]	Peng Y L, Han X Y, Wang M S, Li J M 2005 J. Phys. B 38 3825
[22]	Qing B, Chen S H, Gao X, Li J M 2008 Chin. Phys. Lett. 25 2448
[23]	Parpia F A, Tong M, Fischer C F 1992 Phys. Rev. A 46 3717
[24]	Mohr P J, Plunien G, Soff G 1998 Phys. Rep. 293 227
[25]	Fullerton L W, Rinker Jr G A 1976 Phys. Rev. A 13 1283
[26]	Pastor P C, Giusfredi G, Natale P D, Hagel G, Mauro C D, Inguscio M 2004 Phys. Rev. Lett. 92 023001
[27]	Xie L Y, Dong C Z, Ma X W, Yuan P, Yan J, Qu Y Z 2002 Acta Phys. Sin. 51 1965(in Chinese)[颉录有、董晨钟、马新文、袁萍、颜君、曲一至 2002 物理学报 51 1965]
[28]	Dall R G, Baldwin K G H, Byron L J, Truscott A G 2008 Phys. Rev. Lett. 100 023001
[29]	Burger J M, Lurio A 1971 Phys. Rev. A 3 76
[30]	Drake G W F 1979 Phys. Rev. A 19 1387
[31]	ach G, Pachucki K 2001 Phys. Rev. A 64 042510
[32]	Schiff B, Pekeris C L 1964 Phys. Rev. 134 A638
[33]	Zhao P, Lawall J R, Pipkin F M 1991 Phys. Rev. Lett. 66 592
[34]	Drake G W F, Nōrtershāuser W, Yan Z C 2005 Can. J. Phys. 83 311
[35]	Wang X L, Liu L T, Gao X, Shen C, Li J M 2008 Chin. Phys. Lett. 25 4244
[36]	Isaksen S, Anderson A, Anderson T, Ramanujam P S 1979 J. Phys. B 12 893

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