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用HFR (Hartree-Fock with relativistic corrections)方法对Rb V—Cd XVI离子4s24p3和4s4p4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Zc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4s24p3 (4S3/2, 2P1/2, 3/2, 2D3/2, 5/2)和4s4p4 (4P1/2, 3/2, 5/2, 2P1/2, 3/2, 2D3/2, 5/2, 2S1/2)组态能级以及电偶极跃迁波长与振子强度. 研究表明, 对于4s24p3组态, 单组态近似可以得到较满意的结果; 而对于4s4p4组态, 只有在考虑了4s24p24d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4s24p3 (2P1/2), Pd XIV离子4s24p3 (4S3/2, 2P1/2, 3/2, 2D3/2, 5/2)和4s4p4 (2P1/2, 3/2, 2D3/2, 5/2, 2S1/2), 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.
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关键词:
- Rh XIII—Cd XVI离子 /
- 能级 /
- 跃迁波长 /
- 振子强度
Ions from Rh XIII to Cd XVI belong to the arsenic isoelectronic sequence ions. Their ground configuration is 4s24p3, and the lower excited configurations are 4s4p4, 4s24p24d and 4s24p25s etc. The present study aims to predict the energy levels and transition data unknown in experiment for configurations 4s24p3 and 4s4p4 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 fine-structure 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 4s24p3 and 4s4p4, the wavelengths and oscillator strengths of the transition array 4s24p3−4s4p4 are computed. This research shows that for 4s24p3, the single-configuration approximation of HFR calculation can present the satisfactory results, however, for 4s4p4, the reasonable good results can be achieved only by multi-configuration(4s4p4 + 4s24p24d) 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 4s4p4 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 G 1984 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 of 4s24p3 and 4s4p4 configurations are computed by grasp2K-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.-
Keywords:
- ions Rh XIII−Cd XVI /
- energy levels /
- wavelengths /
- oscillator strengths
[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
Google Scholar
[4] Reader J, Acquista N 1981 J. Opt. Soc. Am. 71 434
Google Scholar
[5] Person W, Pettersson S G 1984 Phys. Scr. 29 308
Google Scholar
[6] Biemont E, Hansen J E 1986 Phys. Scr. 33 117
Google Scholar
[7] Sullivan G O, Kane M 1989 Phys. Scr. 39 317
Google Scholar
[8] Sullivan G O, Dunne P, Costello J T 1990 J. Phys. B: At. Mol. Opt. Phys. 23 575
Google Scholar
[9] Grant I P, McKenzie B J, Noyyington P H, Mayers D F, Pyper N C 1980 Comput. Phys. Commun. 21 233
Google Scholar
[10] 牟致栋, 魏琦瑛, 陈涤缨 2006 55 4070
Google Scholar
Mu Z D, Wei Q Y, Chen D Y 2006 Acta Phys. Sin. 55 4070
Google Scholar
[11] Cowan R D 1981 Theory of Atomic Structure and Spectra (Berkeley: University of California Press) p197
[12] 牟致栋, 魏琦瑛 2005 54 2614
Google Scholar
Mu Z D, Wei Q Y 2005 Acta Phys. Sin. 54 2614
Google Scholar
[13] 牟致栋, 魏琦瑛 2013 62 103101
Google Scholar
Mu Z D, Wei Q Y 2013 Acta Phys. Sin. 62 103101
Google Scholar
[14] 牟致栋, 魏琦瑛 2014 63 083402
Google Scholar
Mu Z D, Wei Q Y 2014 Acta Phys. Sin. 63 083402
Google Scholar
[15] Grant I P 2007 Relativistic Quantum Theory of Atoms and Molecules (New York: Springer)
[16] Jönsson P, Bieroń 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/tsjoek/compas/ [2018-11-5]
[17] Jönsson P, Gaigalas G, Bieroń J C, Fischer C F, Grant I P 2013 Comput. Phys. Commun. 184 2197
Google Scholar
[18] Jönsson P, He X, Fischer C F, Grant I P 2007 Comput. Phys. Commun. 177 597
Google Scholar
[19] Mohr P J, Plunien G, Soff G 1998 Phys. Rep. 293 227
Google Scholar
[20] Drake G W 2006 Springer Handbook of Atomic, Molecular and Optical Physics (New York: Springer) p173
[21] Fischer C F, Brage T, Jönsson 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)
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图 1 4p3, 4s4p4和4p24d组态GLSF平均能Eav随Zc的变化
Fig. 1. Variations of GLSF average energy of 4p3, 4s4p4 and 4p24d configurations with Zc.
图 2 4p3组态GLSF参数随Zc的变化
Fig. 2. Variations of 4p3 configuration GLSF parameters with Zc.
表 1 Rb V—Mo X离子4s4p4组态能级实验值与理论计算值之差(单位cm–1)的比较
Table 1. Comparasion of differences between observed and calculated levels values for the 4s4p4 configuration in Rb V−Mo X
离子能级 Rb V Sr VI Y VII Zr VIII Nb IX Mo X ${\varDelta _{\rm{s}}}$ ${\varDelta _{\rm{m}}}$ ${\varDelta _{\rm{s}}}$ ${\varDelta _{\rm{m}}}$ ${\varDelta _{\rm{s}}}$ ${\varDelta _{\rm{m}}}$ ${\varDelta _{\rm{s}}}$ ${\varDelta _{\rm{m}}}$ ${\varDelta _{\rm{s}}}$ ${\varDelta _{\rm{m}}}$ ${\varDelta _{\rm{s}}}$ ${\varDelta _{\rm{m}}}$ 2D5/2 218 7 260 –14 293 3 332 –5 373 –15 435 –29 4P5/2 –327 –8 –359 –50 –329 –33 –316 –7 –320 18 –334 36 2P3/2 –214 4 –25 –15 60 –7 100 –2 126 –1 151 –8 2D3/2 –212 12 –258 –71 –294 –47 –336 5 –382 66 –452 122 4P3/2 121 4 150 36 163 39 183 43 215 53 259 64 2S1/2 –259 8 –275 –25 –265 69 –271 1 –289 –75 –319 –140 2P1/2 468 17 300 102 210 –12 181 1 180 17 196 32 4P1/2 45 9 206 –4 162 –21 127 –36 97 –50 66 –59 
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表 3 Rh XIII—Cd XVI离子4s24p3, 4s4p4组态能级和本征矢纯度
Table 3. Energy levels and percentage compositions of the 4s24p3 and 4s4p4 configurations for ions from Rh XIII to Cd XVI.
离子 能级 Eexp/cm–1 ELSF/cm–1 EGLSF/cm–1 EMCDHF/cm–1 本征矢纯度 Rh XIII 4s24p3 4S3/2 0 0 0 0 71% + 21%2P3/2 + 9%2D3/2 2D3/2 35762 35820(58) 35863(101) 35992(230) 66% + 22%4S3/2 + 12%2P3/2 2D5/2 49151 49072(–79) 49110(–41) 49284(133) 100% 2P1/2 72267p 72237(–30)p 72279(12)p 72915(648) 100% 2P3/2 100673 100642(–31) 100722(49) 100668(–5) 68% + 25%2D3/2 + 7%4S3/2 4s4p4 4P5/2 284236 284230(–6) 284111(–125) 283365(–871) 87% + 6%2D5/2 + 5%4s24p24d 4P5/2 4P3/2 308739 308504(–235) 308770(31) 307548(–1191) 86% + 6%4s24p24d 4P3/2 + 5%2D3/2 4P1/2 313989 314205(36) 314507(518) 313218(–771) 82% + 11%2S1/2 + 6%4s24p24d 4P1/2 2D3/2 349977 350012(35) 349934(–43) 352413(2436) 69% + 14%4s24p24d 2D3/2 + 7%4P3/2 2D5/2 359733 359722(–11) 359614(–119) 361457(1724) 76% + 15%4s24p24d 2D5/2 + 7%4P5/2 2S1/2 395765 395592(–173) 395707(–58) 399771(4006) 47% + 26%2P1/2 + 9%4s24p24d 2S1/2 2P3/2 401975 401960(–15) 401883(–92) 408136(6161) 55% + 28%4s24p24d 2P3/2 + 8%2D3/2 2P1/2 439005 439001(–4) 439405(400) 444364(5359) 33% + 25%2S1/2 + 23%4s24p24d 2P1/2 Pd XIV 4s24p3 4S3/2 0 0 0 0 66% + 23%2P3/2 + 10%2D3/2 2D3/2 40021p 40092(71)p 40175(154)p 40147(126) 64% + 26%4S3/2 + 11%2P3/2 2D5/2 54958p 54852(–106)p 54935(–23)p 54996(38) 100% 2P1/2 79147p 79112(–35)p 79189(42)p 79766(619) 100% 2P3/2 113280p 113224(–56)p 113295(15)p 113113(–167) 66% + 26%2D3/2 + 8%4S3/2 4s4p4 4P5/2 305545 305506(–39) 305289(–256) 304542(–1003) 87% + 7%2D5/2 + 5%4s24p24d 4P5/2 4P3/2 333774 333809(35) 333389(–385) 332461(–1313) 86% + 6%2D3/2 + 6%4s24p24d 4P3/2 4P1/2 339032 339356(324) 339321(289) 338267(–765) 80% + 13%2S1/2 + 6%4s24p24d 4P1/2 2D3/2 376537p 377555(1019)p 376256(–281)p 378921(2384) 67% + 13%4s24p24d 2D3/2 + 9%4P3/2 2D5/2 388385p 387860(–525)p 387887(–498)p 389905(1520) 76% + 14%4s24p24d 2D5/2 + 8%4P5/2 2S1/2 425277p 424079(–1189)p 424752(–525)p 429012(3735) 45% + 28%2P1/2 + 9%4P1/2 2P3/2 432003p 431953(–50)p 431264(–739)p 438183(6180) 53% + 27%4s24p24d 2P3/2 + 10%2D3/2 2P1/2 468322p 468558(236)p 474603(6281)p 480060(11738) 30% + 25%2S1/2 + 21%4p24d 2P1/2 Ag XV 4s24p3 4S3/2 0 0 62% + 26%2P3/2 + 12%2D3/2 2D3/2 45260 45098 62% + 29%4S3/2 + 9%2P3/2 2D5/2 61485 61457 100% 2P1/2 86808 87360 100% 2P3/2 127267 127015 65% + 26%2D3/2 + 9%4S3/2 4s4p4 4P5/2 327358 326566 86% + 8%2D5/2 + 5%4s24p24d 4P5/2 4P3/2 358887 358483 81% + 8%4s24p24d 4P3/2 + 6%2D3/2 4P1/2 364986 364313 78% + 15%2S1/2 + 6%4s24p24d 4P1/2 2D3/2 403533 406661 64% + 12%4p24d 2D3/2 + 12%4P3/2 2D5/2 417320 419813 76% + 14%4s24p24d 2D5/2 + 9%4P5/2 2S1/2 454883 459653 43% + 29%2P1/2 + 10%4s24p24d 2S1/2 2P3/2 461039 469489 47% + 26%4s24p24d 2P3/2 + 12%2D3/2 2P1/2 510793 517520 26% + 24%2S1/2 + 20%4s24p24d 2P1/2 Cd XVI 4s24p3 4S3/2 0 0 58% + 28%2P3/2 + 14%2D3/2 2D3/2 51168 50914 59% + 33%4S3/2 + 8%2P3/2 2D5/2 68806 68729 100% 2P1/2 95174 95759 100% 2P3/2 142703 142486 64% + 27%2D3/2 + 9%4S3/2 4s4p4 4P5/2 350419 349499 85% + 7%2D5/2 + 5%4s24p24d 4P5/2 4P3/2 385245 385637 78% + 9%4s24p24d 4P3/2 + 5%2D3/2 4P1/2 391550 391382 76% + 17%2S1/2 + 5%4s24p24d 4P1/2 2D3/2 431691 435771 60% + 15%4s24p24d 2D3/2 + 10%4P3/2 2D5/2 447887 451301 76% + 13%4s24p24d 2D5/2 + 9%4P5/2 2S1/2 486090 491836 41% + 30%2P1/2 + 12%4s24p24d 2S1/2 2P3/2 489808 502144 33% + 23%4s24p24d 2P3/2 + 15%2D3/2 2P1/2 547585 556756 21% + 29%2S1/2 + 23%4s24p24d 2P1/2
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表 2 Rh XIII—Cd XVI离子4s24p3, 4s4p4和4s24p44d组态能级结构参数(单位: cm–1)
Table 2. Energy parameters of configurations 4s24p3, 4s4p4 and 4s24p44d for ions from Rh XIII to Cd XVI.
离子参数 Rh XIII Pd XIV Ag XV Cd XVI HFR LSF GLSF HFR LSF GLSF HFR GLSF HFR GLSF Eav(4s24p3) 84293 49254 49278 93187 55055 54835 103082 61632 114034 67464 F2(4p, 4p) 135018 95436 95372 139395 99964 100188 143769 104494 148147 109733 $\alpha $(4p, 4p) 50 –65 –70 50 –67 –90 50 –61 50 –127 ${\zeta _{4{\rm{p}}}}$ 52094 28120 28143 58686 32620 32403 65899 37541 73770 42137 Eav(4s4p4) 465733 373048 373412 494416 399046 401829 524621 428489 556932 460700 F2(4p, 4p) 134929 108077 108197 139305 112434 113134 143679 117141 148056 122299 $\alpha $(4p, 4p) 50 25 27 50 68 28 50 34 50 32 ${\zeta _{4{\rm{p}}}}$ 52046 28688 28919 58636 43974 34588 65846 37300 73714 47415 G1(4s, 4p) 157248 125955 126094 162275 130973 131787 167303 136397 172339 142349 Eav(4s24p44d) 607730 512551 511233 639800 1064552 547714 673345 589678 708331 624580 F2(4p, 4p) 134980 113841 113545 139352 231866 119342 143723 125896 148098 130840 $\alpha $(4p, 4p) 50 –8170 –8516 50 –31872 –12109 50 –9682 50 –19122 ${\zeta _{4{\rm{p}}}}$ 52183 26219 28282 58781 37685 32566 66000 44423 73875 44653 ${\zeta _{4{\rm{d}}}}$ 6735 7573 6146 7648 361714 9397 8649 7711 9744 17964 F2(4p, 4d) 118694 100105 99845 122677 204120 105062 126654 110945 130628 115408 G1(4p, 4d) 146907 123899 123578 151575 252202 129812 156229 136856 160878 142141 G3(4p, 4d) 94580 79768 79561 97657 162489 83636 100724 88236 103787 91702 R(4p4p, 4s4d) 151283 121177 121309 156089 125980 126756 160886 131151 165684 136827
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表 4 Rh XIII—Cd XVI离子4s24p3—4s24p4跃迁波长和振子强度(gf × 10)
Table 4. Wavelengths and oscillator strengths of transitions 4s24p3−4s24p4 for ions from Rh XIII to Cd XVI.
离子跃迁 $\lambda $/nm ${\lambda _{\exp }}$/nm ${\Delta _\lambda }$/nm gf × 10 Rh XIII 2P3/2—2D3/2 40.126 40.079b –0.047 0.01 4S3/2—4P5/2 35.197 35.186 –0.011 2.58 —4P3/2 32.386 32.394 0.008 2.42 2D5/2—2D5/2 32.205 32.197 –0.008 3.77 4S3/2—4P1/2 31.795 31.852 0.057 1.17 2D3/2—2D3/2 31.839 31.829 –0.01 3.74 2P1/2—2S1/2 30.918 1.87 2P3/2—2P1/2 29.526 29.56 0.034 3 4S3/2—2D3/2 28.576 0.27 2D5/2—2P3/2 28.346 28.345 –0.001 6.79 2D3/2—2S1/2 27.789 27.781 –0.008 2.08 —2P3/2 27.32 27.31 –0.01 0.59 —2P1/2 24.78 24.802 0.022 0.37 4S3/2—2P3/2 24.882 24.88 –0.002 0.34 —2P1/2 22.758 0.01 Pd XIV 2P3/2—2D3/2 38.008 0.01 4S3/2—4P5/2 32.749 32.732 –0.017 2.55 —4P3/2 29.92 29.964 0.044 2.59 2D5/2—2D5/2 29.993 29.974 –0.019 3.48 4S3/2—4P1/2 29.411 29.499b 0.088 1.2 2D3/2—2D3/2 29.766 3.6 2P1/2—2S1/2 28.908 1.84 2P3/2—2P1/2 27.534 2.54 4S3/2—2D3/2 26.603 0.23 2D5/2—2P3/2 26.499 26.525 0.026 6.36 2D3/2—2S1/2 25.973 2.02 —2P3/2 25.507 25.513 0.006 0.62 —2P1/2 17.106 0.82 4S3/2—2P3/2 23.148 0.37 —2P1/2 21.009 0.01 Ag XV 2P3/2—2D3/2 36.196 0.01 4S3/2—4P5/2 30.547 2.38 —4P3/2 27.863 2.73 2D5/2—2D5/2 28.102 3.96 4S3/2—4P1/2 27.398 1.27 2D3/2—2D3/2 27.911 3.94 2P1/2—2S1/2 27.168 1.94 2P3/2—2P1/2 26.739 0.01 4S3/2—2D3/2 24.781 0.36 2D5/2—2P3/2 25.027 6.14 2D3/2—2S1/2 24.412 2.27 —2P3/2 24.051 0.21 —2P1/2 21.93 0.07 4S3/2—2P3/2 21.69 0.19 —2P1/2 19.95 0.77 Cd XVI 2P3/2—2D3/2 34.603 0.01 4S3/2—4P5/2 28.537 2.26 —4P3/2 25.957 2.87 2D5/2—2D5/2 26.379 4.05 4S3/2—4P1/2 25.539 1.32 2D3/2—2D3/2 26.279 3.97 2P1/2—2S1/2 25.58 1.96 2P3/2—2P1/2 26.066 0.01 4S3/2—2D3/2 23.164 0.35 2D5/2—2P3/2 23.752 4.35 2D3/2—2S1/2 22.992 2.37 —2P3/2 22.797 0.01 —2P1/2 21.045 0.03 4S3/2—2P3/2 20.416 0.01 —2P1/2 18.999 1.54 注: ${\lambda _{\exp }}$表示实验值取自文献[8], b表示该谱线为混合谱线
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[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
Google Scholar
[4] Reader J, Acquista N 1981 J. Opt. Soc. Am. 71 434
Google Scholar
[5] Person W, Pettersson S G 1984 Phys. Scr. 29 308
Google Scholar
[6] Biemont E, Hansen J E 1986 Phys. Scr. 33 117
Google Scholar
[7] Sullivan G O, Kane M 1989 Phys. Scr. 39 317
Google Scholar
[8] Sullivan G O, Dunne P, Costello J T 1990 J. Phys. B: At. Mol. Opt. Phys. 23 575
Google Scholar
[9] Grant I P, McKenzie B J, Noyyington P H, Mayers D F, Pyper N C 1980 Comput. Phys. Commun. 21 233
Google Scholar
[10] 牟致栋, 魏琦瑛, 陈涤缨 2006 55 4070
Google Scholar
Mu Z D, Wei Q Y, Chen D Y 2006 Acta Phys. Sin. 55 4070
Google Scholar
[11] Cowan R D 1981 Theory of Atomic Structure and Spectra (Berkeley: University of California Press) p197
[12] 牟致栋, 魏琦瑛 2005 54 2614
Google Scholar
Mu Z D, Wei Q Y 2005 Acta Phys. Sin. 54 2614
Google Scholar
[13] 牟致栋, 魏琦瑛 2013 62 103101
Google Scholar
Mu Z D, Wei Q Y 2013 Acta Phys. Sin. 62 103101
Google Scholar
[14] 牟致栋, 魏琦瑛 2014 63 083402
Google Scholar
Mu Z D, Wei Q Y 2014 Acta Phys. Sin. 63 083402
Google Scholar
[15] Grant I P 2007 Relativistic Quantum Theory of Atoms and Molecules (New York: Springer)
[16] Jönsson P, Bieroń 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/tsjoek/compas/ [2018-11-5]
[17] Jönsson P, Gaigalas G, Bieroń J C, Fischer C F, Grant I P 2013 Comput. Phys. Commun. 184 2197
Google Scholar
[18] Jönsson P, He X, Fischer C F, Grant I P 2007 Comput. Phys. Commun. 177 597
Google Scholar
[19] Mohr P J, Plunien G, Soff G 1998 Phys. Rep. 293 227
Google Scholar
[20] Drake G W 2006 Springer Handbook of Atomic, Molecular and Optical Physics (New York: Springer) p173
[21] Fischer C F, Brage T, Jönsson 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)
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