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