Rh ⅩⅢ—Cd ⅩⅥ离子4s~24p~3—4s4p~4能级与跃迁的理论计算
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摘要
用HFR (Hartree-Fock with relativistic corrections)方法对Rb Ⅴ—Cd ⅩⅥ离子4s~24p~3和4s4p~4组态能级结构做了全面系统的理论计算研究.通过分析能级结构参数的HFR理论计算值与基于实验能级拟合得到的计算值之比值随着原子序数Z_c变化的规律,运用广义拟合外推方法预言了这些离子能级结构参数.由此进一步计算了Rh ⅩⅢ,Pd ⅩⅣ, Ag ⅩⅤ和Cd ⅩⅥ离子4s~24p~3 (~4S_(3/2),~2P_(1/2,3/2),~2D_(3/2,5/2))和4s4p~4 (~4P_(1/2,3/2,5/2),~2P_(1/2,3/2),~2D_(3/2,5/2),~2_(S_(1/2)))组态能级以及电偶极跃迁波长与振子强度.研究表明,对于4s~24p~3组态,单组态近似可以得到较满意的结果;而对于4s4p~4组态,只有在考虑了4s~24p~24d的组态相互作用效应时,计算结果的准确性才能明显得到提高.同时,本文还运用全相对论grasp2K-DEV程序包计算了Rh ⅩⅢ—Cd ⅩⅥ离子组态能级.对于Rh ⅩⅢ离子4s~24p~3 (~2P_(1/2)), Pd ⅩⅣ离子4S~24p~3(~4S_(3/2),~2P_(1/2,3/2),~2D_(3/2,5/2))和4s4p~4(~2P_(1/2,3/2),~2D_(3/2,5/2,)~2S_(1/2)),能级均无实验值;对于Ag ⅩⅤ和Cd ⅩⅥ离子,截至目前还没实验能级数据,没有实验能级值的所有数据均仅来自本文的计算数值.本文计算结果与已有实验值吻合得很好.
Ions from Rh ⅪⅢ to Cd ⅩⅥ belong to the arsenic isoelectronic sequence ions. Their ground configuration is 4 s~24 p~3, and the lower excited configurations are 4 s4 p~4, 4 s~24 p~24 d and 4 s~24 p~25 s etc. The present study aims to predict the energy levels and transition data unknown in experiment for configurations 4 s~24 p~3 and 4 s4 p~4 from Rh ⅩⅢ to Cd XVI ions, by analyzing the trend of the variation of Slater-Condon parameters along the As-like sequence based on the experimental energy levels available in the literature. So, the theoretical analyses of finestructure energy levels of these configurations are conducted for the sequence ions from Rb Ⅴ to Cd ⅩⅥ by Hartree-Fock with Relativistic correction(HFR) method in Cowan code. The Slater-Condon parameter values of energy levels are obtained by least-square-fit(LSF) technique for ions mentioned above with the available experimental data. For the unknown parameters, the generalized-least-square-fit(GLSF) technique is used together with the extra(or inter)-polation method. With these new parameter values, the energy levels of 4 s~24 p~3 and 4 s4 p~4, the wavelengths and oscillator strengths of the transition array 4 s~24 p~3-4 s4 p~4 are computed. This research shows that for 4 s~24 p~3, the single-configuration approximation of HFR calculation can present the satisfactory results, however, for 4 s4 p~4, the reasonable good results can be achieved only by multiconfiguration(4 s4 p~4 + 4 s~24 p~24 d) approximation, which can be verified by the obtained data. Comparing the absolute differences between observed and present LSF calculated levels' values(including multi-configuration interaction) for the 4 s4 p~4 configuration in ions from Rb V to Mo X with the results computed in a similar Hartree-Fock single-configuration approximate method by Person and Pettersson(Person W, Pettersson S G1984 Phys. Scr. 29 308), we can see that the present LSF energy levels are improved substantially. For example,the LSF minimum and maximum absolute deviation value at present are 1 cm 1 and 140 cm~(-1), respectively,much more accurate than the results presented by Person et al., which are 45 cm~(-1) and 382 cm~(-1). The predicted data are in good agreement with the experimental results. For obtaining more information, the energy levels of4 s~24 p~3 and 4 s4 p~4 configurations are computed by grasp2 K-DEV package in valence-valence correlation scheme,which is based on the fully relativistic multi-configuration Dirac-Hartree-Fock(MCDHF) theory. The overall MCDHF energy levels are generally in accordance with the experimental results. The data obtained in this research are expected to be used in the future relevant theoretical and experimental investigations.
Ions from Rh ⅪⅢ to Cd ⅩⅥ belong to the arsenic isoelectronic sequence ions. Their ground configuration is 4 s~24 p~3, and the lower excited configurations are 4 s4 p~4, 4 s~24 p~24 d and 4 s~24 p~25 s etc. The present study aims to predict the energy levels and transition data unknown in experiment for configurations 4 s~24 p~3 and 4 s4 p~4 from Rh ⅩⅢ to Cd XVI ions, by analyzing the trend of the variation of Slater-Condon parameters along the As-like sequence based on the experimental energy levels available in the literature. So, the theoretical analyses of finestructure energy levels of these configurations are conducted for the sequence ions from Rb Ⅴ to Cd ⅩⅥ by Hartree-Fock with Relativistic correction(HFR) method in Cowan code. The Slater-Condon parameter values of energy levels are obtained by least-square-fit(LSF) technique for ions mentioned above with the available experimental data. For the unknown parameters, the generalized-least-square-fit(GLSF) technique is used together with the extra(or inter)-polation method. With these new parameter values, the energy levels of 4 s~24 p~3 and 4 s4 p~4, the wavelengths and oscillator strengths of the transition array 4 s~24 p~3-4 s4 p~4 are computed. This research shows that for 4 s~24 p~3, the single-configuration approximation of HFR calculation can present the satisfactory results, however, for 4 s4 p~4, the reasonable good results can be achieved only by multiconfiguration(4 s4 p~4 + 4 s~24 p~24 d) approximation, which can be verified by the obtained data. Comparing the absolute differences between observed and present LSF calculated levels' values(including multi-configuration interaction) for the 4 s4 p~4 configuration in ions from Rb V to Mo X with the results computed in a similar Hartree-Fock single-configuration approximate method by Person and Pettersson(Person W, Pettersson S G1984 Phys. Scr. 29 308), we can see that the present LSF energy levels are improved substantially. For example,the LSF minimum and maximum absolute deviation value at present are 1 cm 1 and 140 cm~(-1), respectively,much more accurate than the results presented by Person et al., which are 45 cm~(-1) and 382 cm~(-1). The predicted data are in good agreement with the experimental results. For obtaining more information, the energy levels of4 s~24 p~3 and 4 s4 p~4 configurations are computed by grasp2 K-DEV package in valence-valence correlation scheme,which is based on the fully relativistic multi-configuration Dirac-Hartree-Fock(MCDHF) theory. The overall MCDHF energy levels are generally in accordance with the experimental results. The data obtained in this research are expected to be used in the future relevant theoretical and experimental investigations.
引文
[1] Moore C E 1952 Atomic Energy Levels(Vol.Ⅱ)(Washington:Nat. Bur. Stand. Circ.)p467
[2] Rao Y B 1956 Ind. J. Phys. 30 371
[3] Rahimullah K, Chaghtai M S Z, Khatoon S 1976 Phys. Scr.14 221
[4] Reader J, Acquista N 1981 J. Opt. Soc. Am. 71 434
[5] Person W, Pettersson S G 1984 Phys. Scr. 29 308
[6] Biemont E, Hansen J E 1986 Phys. Scr. 33 117
[7] Sullivan G O, Kane M 1989 Phys. Scr. 39 317
[8] Sullivan G O, Dunne P, Costello J T 1990 J. Phys. B:At.Mol. Opt. Phys. 23 575
[9] Grant I P, McKenzie B J, Noyyington P H, Mayers D F,Pyper N C 1980 Comput. Phys. Commun. 21 233
[10] Mu Z D, Wei Q Y, Chen D Y 2006 Acta Phys. Sin. 55 4070(in Chinese)[牟致栋,魏琦瑛,陈涤缨2006物理学报55 4070]
[11] Cowan R D 1981 Theory of Atomic Structure and Spectra(Berkeley:University of California Press)p197
[12] Mu Z D, Wei Q Y 2005 Acta Phys. Sin. 54 2614(in Chinese)[牟致栋,魏琦瑛2005物理学报54 2614]
[13] Mu Z D, Wei Q Y 2013 Acta Phys. Sin. 62 103101(in Chinese)[牟致栋,魏琦瑛2013物理学报62 103101]
[14] Mu Z D, Wei Q Y 2014 Acta Phys. Sin. 63 083402(in Chinese)[牟致栋,魏琦瑛2014物理学报63 083402]
[15] Grant I P 2007 Relativistic Quantum Theory of Atoms and Molecules(New York:Springer)
[16] Jonsson P, Bieron J, Brage T,Ekman J,Fischer C F,Gaigalas G, Godefroid M, Grant I P, Grumer J 2015 The Computational Atomic Structure Group, see http://ddwap.mah.se/tsj oek/compas/[2018-11-5]
[17] Jonsson P, Gaigalas G, Bieron J C, Fischer C F, Grant I P2013 Comput. Phys. Commun. 184 2197
[18] Jonsson P, He X, Fischer C F, Grant I P 2007 Comput. Phys.Commun. 177 597
[19] Mohr P J, Plunien G, Soff G 1998 Phys. Rep. 293 227
[20] Drake G W 2006 Springer Handbook of Atomic, Molecular and Optical Physics(New York:Springer)p173
[21] Fischer C F, Brage T, Jonsson P 1997 Computational Atomic Structure(An MCHF Approach)(Bristol:Institute of Physics Publishing)
[22] Fischer C F 1977 The Hartree-Fock Method for Atoms(A Numerical Approach)(New York:John Wiley and Sons)
[2] Rao Y B 1956 Ind. J. Phys. 30 371
[3] Rahimullah K, Chaghtai M S Z, Khatoon S 1976 Phys. Scr.14 221
[4] Reader J, Acquista N 1981 J. Opt. Soc. Am. 71 434
[5] Person W, Pettersson S G 1984 Phys. Scr. 29 308
[6] Biemont E, Hansen J E 1986 Phys. Scr. 33 117
[7] Sullivan G O, Kane M 1989 Phys. Scr. 39 317
[8] Sullivan G O, Dunne P, Costello J T 1990 J. Phys. B:At.Mol. Opt. Phys. 23 575
[9] Grant I P, McKenzie B J, Noyyington P H, Mayers D F,Pyper N C 1980 Comput. Phys. Commun. 21 233
[10] Mu Z D, Wei Q Y, Chen D Y 2006 Acta Phys. Sin. 55 4070(in Chinese)[牟致栋,魏琦瑛,陈涤缨2006物理学报55 4070]
[11] Cowan R D 1981 Theory of Atomic Structure and Spectra(Berkeley:University of California Press)p197
[12] Mu Z D, Wei Q Y 2005 Acta Phys. Sin. 54 2614(in Chinese)[牟致栋,魏琦瑛2005物理学报54 2614]
[13] Mu Z D, Wei Q Y 2013 Acta Phys. Sin. 62 103101(in Chinese)[牟致栋,魏琦瑛2013物理学报62 103101]
[14] Mu Z D, Wei Q Y 2014 Acta Phys. Sin. 63 083402(in Chinese)[牟致栋,魏琦瑛2014物理学报63 083402]
[15] Grant I P 2007 Relativistic Quantum Theory of Atoms and Molecules(New York:Springer)
[16] Jonsson P, Bieron J, Brage T,Ekman J,Fischer C F,Gaigalas G, Godefroid M, Grant I P, Grumer J 2015 The Computational Atomic Structure Group, see http://ddwap.mah.se/tsj oek/compas/[2018-11-5]
[17] Jonsson P, Gaigalas G, Bieron J C, Fischer C F, Grant I P2013 Comput. Phys. Commun. 184 2197
[18] Jonsson P, He X, Fischer C F, Grant I P 2007 Comput. Phys.Commun. 177 597
[19] Mohr P J, Plunien G, Soff G 1998 Phys. Rep. 293 227
[20] Drake G W 2006 Springer Handbook of Atomic, Molecular and Optical Physics(New York:Springer)p173
[21] Fischer C F, Brage T, Jonsson P 1997 Computational Atomic Structure(An MCHF Approach)(Bristol:Institute of Physics Publishing)
[22] Fischer C F 1977 The Hartree-Fock Method for Atoms(A Numerical Approach)(New York:John Wiley and Sons)