钠原子主线系精细结构的多体微扰计算

陈笋; 朱云霞; 葛自明; 贺黎明

doi:10.7498/aps.61.153104

摘要

在相对论的框架下采用多体微扰理论(MBPT)方法计算了纳原子 np(n=39)态的能级精细结构分裂值. 为避免多体微扰计算中需要计算大量连续态的困扰, 通过引入外势的方法可以构建离散、有限和近似完备的数值基函数. 经求解相对论Hartree-Fock (RHF)方程及外势作用下的RHF方程可获得零级近似波函数和能级值. 为了使微扰展开能够收敛, 计算中用到了轨道角量子数l 6的在一定能量分布范围内的中间态, 其中以在外势作用下的收缩态为主. 依此方法计算了纳原子主线系系列能级二阶微扰修正值, 同时还考虑了Breit效应的一级微扰修正对精细结构的影响. 通过与其他理论计算结果比较可看出, 本文计算结果在较大程度上更接近于实验值.

关键词:

Abstract

The fine-structure intervals of Na principal series np(n=39) are calculated by the many-body perturbation theory (MBPT) within the framework of relativity. To deal with the problem that a large set of continuum states is required in the MBPT calculation, an exponential potential is employed to generate a discrete, finite and nearly complete set of numerical basis functions. The zeroth-order wavefunctions and eignvalues are obtained by solving the relativistic Hartree-Fock (RHF) equation and the RHF equation with the action of a potential barrier. The basis set used in this work contains intermediate orbitals with the angular momentum l 6 and in an appropriate energy range, and most of them are the so called contracted orbitals. Encouraging results are obtained using this technique to calculate the second-order correlation corrections, combining the Breit effects in a first-order perturbation approach. Compared with other theoretical calculations, the present results are much close to the experimental results.

Keywords:

作者及机构信息

1.
华东理工大学物理系, 上海 200237

Authors and contacts

1.
Department of Physics, East China University of Science and Technology, Shanghai 200237, China

参考文献

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[18]	Kang S, Liu Q, Zhang Z X, Zhang X Z, Shi T Y 2006 Acta Phys. Sin. 55 3380 (in Chinese) [康帅, 刘强, 钟振祥, 张现周, 史庭云 2006 55 3380]
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[20]	Younger S M 1980 Phys. Rev. A: At. Mol. Opt. Phys. 21 1364
[21]	Kim Y K 1967 Phys. Rev. 154 17
[22]	Froese Fischer C 1977 The Hartree-Fock Method for Atoms: a numerical approach (New York: A Wiley-Interscience Publication) p221-273
[23]	Lindgren I, Morrison J 1982 Atomic Many-Body Theory (Berlin: Springer-Verlag)p236
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[25]	Grant I P, Pyper N C 1976 J. Phys. B: At. Mol. Phys. 9 761
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施引文献

[1]	Banerjee A, Natarajan V 2004 Phys. Rev. A: At. Mol. Opt. Phys. 70 052505
[2]	Liu L, Li J M 1988 Acta Phys. Sin. 37 2053 (in Chinese) [刘磊, 李家明 1988 37 2053]
[3]	Yan J, Zhang P H, Tong X M, Li J M 1996 Acta Phys. Sin. 45 1978 (in Chinese) [颜君, 张培鸿, 仝晓明, 李家明 1996 45 1978]
[4]	Xia D, Li J M 2001 Chin. Phys. Lett. 18 1334
[5]	Gupta G P, Msezane A Z 2011 Phys. Scr. 83 055301
[6]	Gupta G P, Msezane A Z 2010 Phys. Scr. 81 045302
[7]	Zatsarinny O, Froese Fischer C 2009 Comput. Phys. Commun. 180 2041
[8]	Godefroid M R, Van Meulebeke G, Jönsson P, Froese Fischer C 1997 Z. Phys. D 42 193
[9]	Wang X L, Liu L T, Gao X, Shen C, Li J M 2008 Chin. Phys. Lett. 25 4244
[10]	Li P C, Dong C Z, Zhou X X, Jie L Y, Ding X B 2003 J. Al. Mol. Phys. 20 467 (in Chinese) [李鹏程, 董晨钟, 周效信, 颉录有, 丁晓彬 2003 原子与分子 20 467]
[11]	Sternheimer R M, Rodgers J E, Lee T, Das T P 1976 Phys. Rev. A: At. Mol. Opt. Phys. 14 1595
[12]	Holmgren L, Lindgren I, Morrison J, Martensson A M 1976 Z. Physik. A 276 179
[13]	Chen C, Han X Y, Li J M 2005 Phys. Rev. A: At. Mol. Opt. Phys. 71 042503
[14]	He L M, Zhu Y X, Zhang M, Tu Y Q 2011 J. Phys. B: At. Mol. Opt. Phys. 44 225007
[15]	Dzuba V A, Flambaum V V, Sushkov O P 1983 J. Phys. B: At. Mol. Phys. 16 715
[16]	Johnson W R 2007 Atomic Structrue Theory (Berlin: Springer-Verlag) p203-209, p197-198
[17]	He Y L, Zhou X X, Li X Y 2008 Acta Phys. Sin. 57 116 (in Chinese) [何永林, 周效信, 李小勇 2008 57 116]
[18]	Kang S, Liu Q, Zhang Z X, Zhang X Z, Shi T Y 2006 Acta Phys. Sin. 55 3380 (in Chinese) [康帅, 刘强, 钟振祥, 张现周, 史庭云 2006 55 3380]
[19]	He L M, Cao W, Chen X Q, Zhu Y X 2005 Acta Phys. Sin. 54 5077 (in Chinese) [贺黎明, 曹伟, 陈学谦, 朱云霞 2005 54 5077]
[20]	Younger S M 1980 Phys. Rev. A: At. Mol. Opt. Phys. 21 1364
[21]	Kim Y K 1967 Phys. Rev. 154 17
[22]	Froese Fischer C 1977 The Hartree-Fock Method for Atoms: a numerical approach (New York: A Wiley-Interscience Publication) p221-273
[23]	Lindgren I, Morrison J 1982 Atomic Many-Body Theory (Berlin: Springer-Verlag)p236
[24]	Johnson W R, Idrees M, Sapirstein J 1987 Phys. Rev. A: At. Mol. Opt. Phys. 35 3218
[25]	Grant I P, Pyper N C 1976 J. Phys. B: At. Mol. Phys. 9 761
[26]	Moore C E 1949 Atomic Energy Levels (Vol. I) Natl. Bur. Stds. Circ. No. 467 (Washington, D. C.: U.S. GPO) p89-90
[27]	Martin W C, Zalubas R 1981 J. Phys. Chem. Ref. Data 10 153
[28]	Froese Fischer C 1972 Comput. Phys. Commun. 4 107
[29]	Sternheimer R M, Peierls R F 1971 Phys. Rev. A: At. Mol. Opt. Phys. 3 837

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