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MBPT calculation for the fine-structure intervals of principal series np(n=39) for Na

Chen Sun Zhu Yun-Xia Ge Zi-Ming He Li-Ming

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MBPT calculation for the fine-structure intervals of principal series np(n=39) for Na

Chen Sun, Zhu Yun-Xia, Ge Zi-Ming, He Li-Ming
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  • 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.
    [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 物理学报 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 物理学报 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 原子与分子物理学报 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 物理学报 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 物理学报 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 物理学报 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

  • [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 物理学报 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 物理学报 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 原子与分子物理学报 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 物理学报 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 物理学报 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 物理学报 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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Publishing process
  • Received Date:  27 September 2011
  • Accepted Date:  11 December 2011
  • Published Online:  05 August 2012

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