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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 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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[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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