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The 5d96p-5d9(6d + 7s) transitions in the isoelectronic sequence Au II-Bi VI
J.-F. Wyart, A. Raassen, Y. Joshi, P. Uylings
To cite this version:
J.-F. Wyart, A. Raassen, Y. Joshi, P. Uylings. The 5d96p-5d9(6d + 7s) transitions in the iso- electronic sequence Au II-Bi VI. Journal de Physique II, EDP Sciences, 1992, 2 (4), pp.895-912.
�10.1051/jp2:1992174�. �jpa-00247680�
Classification Physics Abstracts
31.20P 32.20 32.70
The 5d~6p-5d~(6d + 7s) transitions in the isoelectronic sequence Au II-Bi VI
J.-F. Wyart II), A. J. J. Raassen (~), Y. N. Joshi (3) and P. H. M. Uylings (2) (~) Laboratoire Aim6 Cotton (*), Bit. 505, Centre universitaire, 91405 Orsay, France
(2) Van der Waals Zeeman Laboratorium, Valckenierstraat 65-67, 1018XE Amsterdam, the Netherlands
(3) St Francis Xavier University, Physics Department, Antigonish, B2G lC0 Canada (Received 3 October 1991, accepted 26 November 1991)
R4sum4. On a 4tudid systdmatiquement les transitions 5d~6d-5d~6p et sd~7s-5df6p dans les spectres de Hg III, Tl IV, Pb V et Bi VI avec l'aide de prdvisions th60riques par la m6thode de Slater-Condon. Les paramdtres de Slater et de spin-orbite pour 5d~6d + sd~7s ont 6t6 d6terminds
par la m6thode des moindres cart£s g6n6ralis6s h pant de 92 niveaux connus de la s6quence
Au II-Bi VI, parmi lesquels 59 niveaux nouveaux. Une bonne corrdlation entre les forces de raies calculdes et les intensitds observdes confirrne la classification de 95 raies de Hg III, 75 raies de Tl IV, 91 raies de Pb V et 90 raies de Bi VI. Le mdlange de 5d~6d et de 5d~7s n'est important que
dans le spectre de Tl IV. Los pr6cddentes valeurs des niveaux 5d~6p~Po de Tl IV, Pb V et Bi VI ont dtd corrig6es.
Abstrict. The transitions 5d~6d-5d~6p and 5d~7s-5df6p have been systematically investigated in the spectra of Hg III, Tl IV, Pb V and Bi VI with the support of Slater-Cond~n type calculations.
Energy parameters for 5d~6d + 5d~7s have been determined in
a generalized least squares fit from 92 known levels (including 59 new ones) of the Au II-Bi VI isoelectronic sequence. Line strength
calculations confirm the classification of 95 lines in Hg III, 75 lines in Tl IV, 91 lines in Pb V and 90 lines in Bi VI. The mixing of both even configurations is important in Tl IV only. The 5d~6p~Po levels reported earlier for Tl IV, Pb V and Bi VI have been revised.
1. Introduction.
The spectra of ions isoelectronic with Pt I had already been studied at the time of the critical
compilation of Atomic Energy Level tables [Ii. They have not been revised with the unique exception of improved wavelength measurements in Au II [2] and from Tl IV to Bi VI [3].
The 5d~°-5d~6p and 5d~6s-5df6p transitions are intense on the spectrograms used so far for
systematic investigations of 5d-6p transitions in Hg IV [4], Tl V, Pb VI and Bi VII [5], as well
as Au IV [6], Hg V [7], Pb VII and Bi VIII [8]. Recently, several strong broad features have been identified as 5d~°6s-sd~6snf transitions in Pb IV with the support of ab initio calculations
(*) Laboratoire associd h l'universit6 Paris-Sud.
of ionization widths [9]. These broad lines emitted by Au I-like ions may be considered as satellites of Pt I-like transitions 5d~°-sd~nf which
are unknown so far. We have undertaken a
systematic study of sd~nl-sd~n'l' transitions in Hg III, Tl IV, Pb V and Bi VI, starting from the energy level values of 5d~6p reported in [3] and dealing first with 6p-6d and 6p-7s
transitions. The status of the analysis for the even levels of these spectra varies substantially along the isoelectronic sequence. The four levels of 5d~7s
were known through Bi VI, except in Tl IV, and 5d~6d
was present in AFL tables [I] with only 8 levels of Au II. Mercury is
outstandlingly abundant in some chemically peculiar stars and spectroscopic data on Hg II and Hg III are needed for checking heavy element diffusion models in high atmospheric layers of these stars [10]. This was also an incentive for undertaking this work.
The spectra of mercury, thallium, lead and bismuth were photographed in the 600-2 000 I region on a 3m normal incidence spectrograph at Antigonish with a plate factor of
1.385 ilmm and
on a 6.65 m spectrograph in the region 600-1200i at the Amsterdam laboratory with a plate factor of 0.625 ilmm. The stigmatism of the spectrographs and the
intensity variations of the lines on exposures taken under different spark conditions enabled
us to discriminate among various ionization stages. Intemal standards were provided by O, C and Si ions for deriving wavelengths of studied elements with an estimated inaccuracy of
± 0.005 I. The intensities were measured on a scale 0-100 with a photomultiplier while
measuring the wavelengths on a semi-automatic comparator.
2. Theoretical interpretation.
The electrostatic and spin-orbit parameters which determine level energies of d~,
d~ 's and d~ ~~s~ configuration in the Slater-Condon approach are smoothly dependent on : la) the number N of d electrons at a constant ionization stage, and 16) the ionic charge at a constant N value. This is observed, for example, in 3d-elements II]. Empirical relationships
P
=
A + B x IN 5) + C x IN 5) ~ for the iso-ionic case la) and P
=
A + B x Z~ + C/(Z~ + D) where Z~ is the ionic charge plus one for isoelectronic case 16) can be
used as constraints in the determination of parameters by minimizing the root mean squares deviation on the energies (3(E~~~ E~ )~/N p )~/~ and for fitting A, B and C constants from the N levels E~~~ of various elements simultaneously. The first applications of these
generalized least-squares (GLS) fits are due to Shadmi et al. in iso-ionic studies of iron group elements [12]. Later advances in the classification of multicharged ion spectra allowed
isoelectronic GLS studies, for example on long isoelectronic sequences of 3d~ [13] and
3d~nl [14] configurations. This global parametric approach succeeded in rejecting erroneous
levels and stimulated the classification. This was true also for the 5d-group elements in which
a strong mixing of the low even configurations 5d~, 5d~ ~6s and 5d~ ~~6s~ misled the first investigators. The first [15] and second spectra [16] of these elements have already been surveyed by means of iso-ionic GLS studies. We have undertaken a similar interpretation of their multicharged ions in both iso-ionic and isoelectronic ways. A study of the latter kind is
briefly described in the next section.
2.I THE 5d~ CONFIGUILATION IN THE Pt II ISOELECTRONiC SEQUENCE. The lowest excited
configurations in the spectra isoelectronic with Pt I are built on the 5d~ core and therefore we studied the purity of its two levels within the mixed group 5d~ + 5d~6s + 5d?6si. The shifts
on
~D~~ and ~D~~ relevant to the 5d?6s~-5d~ and 5d~6s-5df interactions were deterrnined in a GLS fit from Pt II to Bi VII. In addition to the levels reported in the literature, 9 new levels of Pt II [17] and 15 levels of Bi VII [18] led to 120 experimental energies for fitting 35 free
parameters. The constraints in each ionization stage were :
the configuration interaction parameter R~(5d~, 6si) for 5d?6s~-5d~ and the exchange
Slater integral G~(5d, 6s) of 5d~6s
are equal ;
the values of the configuration interaction parameters (including the effective parame- ters a and p [12]) are the same in all 3 configurations 5d~, 5d~6s and 5d?6s~:
a (5d~6s)
= a (5d?6s~), p (5d~6s)
= p (5d?6s~), one single value for R~(5d~, 5d6s)
the spin-orbit parameters are constrained by f(5d?6si)-((5d~6s) =((5d~6s) flsd9).
The isoelectronic constraints were P ~
= A + BZ
~
+ D/ (Z~ + 2) for electrostatic parame- ters. A fourth order polynomial in Z~ should be assumed for spin-orbit parameters, but in weakly charged ions the terrns in Z/ and Z/ are relatively unimportant. These terrns stayed
undeterrnined in the least-squares fit and were discarded. Under these conditions, the root myan square deviation on the energies was 99.6 cni~ The coefficients of the interaction
parameters in intermediate coupling were used to evaluate the repulsions A~~~ and A~~~ on both levels of 5d~, as reported in table I. With the increase of the ionic charge, the energy ranges of the 3 configurations become well separated and these repulsions tend to be
equal. The comparison of the GLS fitted parameter (~~(5d~) and of the «empirical»
parameter (E(~D~~~) E(~D~~~)Y2.5 with the ab initio value determined from Hartree-Fock radial wavefunctions shows that the configuration interaction explains the breakdown of
smooth isoelectronic trends in the weakly charged ions. The conclusion of this preliminary study of the core of sd~nl configurations is that sd~6snl and 5d?6s~nl might be important perturbers at the beginning of the sequence and that parametric studies of the « isolated
group » 5d~6d
+ 5d~7s might lead to inaccurate predictions for the unknown upper levels in Au II.
Table I. Effect ofconfiguration interaction on the levels ~D~n and ~D
~nofsd~in the sequence Pt II-Bi VII. The experimental energies E, theoretical repulsions A and spin-orbit integrals (~~ are in cm~ The empirical (~~ is E(~D~n)/2.5.
~D5a ~D~n fsd
Spectrum E A ill E A ill H.F. GLS
Pt II 0 3 993 90.49 8 419.9 5 805 61.81 4 247 4 113.5 3 368.0
Au III 0 726 98.61 12 694.0 2 110 97.59 5 239 5 169.8 5 077.6
Hg IV 0 063 99.52 15 684.7 206 99.33 6 314 6
Tl V 0 761 99.78 18 823.6 836 99.71 7 474 7 545.7 7
Pb VI 0 593 99.87 22 191.9 639 99.85 8 726 8 8
Bi VII 0 481 99.92 25 820.0 5 II 99.91 10 073 10 329
2.2 THE 5d~6d+5d~7s
CONFIGURATIONS. The 22 levels of the mixed 5d~6d and
5d~7s configurations belong to 12LS-terms and may be described by 10 electrostatic parameters, if interaction with other configurations is neglected, and by 3 spin-orbit parameters. The « one hole-one electron » configurations have few matrix elements. In the
case of 5d~6d, the G$ G~ and G~ exchange Slater integrals only act on the respective terms
~S, ~D and ~G and the exchange integral R~(5d6d, 7s6d) only connects the ~D terms of both
configurations. In such cases, energy values of erroneous levels happen to be closely
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described by fitted parameters. Then, the smooth Z~-dependences of parameter values and of deviations AE
= E~~~ E~~j~ strengthen the reliability of the results. This is worthwhile when the levels are built from very few lines located in dense spectral regions.
in a first step, independent studies of the Au it, Hg iii and Pb V cases indicated that : the Z~-dependence of the parameters should be very regular ;
the spectrum of Tl IV should display more configuration mixing than the others.
The same isoelectronic constraints as for (5d + 6s)~ were used here.
in parallel, ab initio calculations of the transition arrays 5d~(6d+7s)-5d~6p were
perforrned in the framework of the Cowan's code [19]. The intensity predictions were
especially useful in eliminating a few spurious levels in Hg III and in deterrnining the Tl iV levels. By combining the accurate GLS energies derived from the Au II-Pb V sequence and these intensity predictions, the analysis of Bi VI concluded the present work quickly.
3. Results.
The 92 levels reported in table II have been used for fitting 34 generalized constants from which energy parameters might be derived for any ion of the Pti isoelectronic sequence.
Several constants had undeterrnined signs in first tries and were discarded from the last
Table iii. Coefficients ofthe energy parameters P
=
A + BZ~ + CZj + D/ (Z~ + 2) fitted by generalized least-squares in the sequence Au it-Bi Vi (Z~ = 2 through 6). Values and standard
errors are in cm~ Additive energies for all 5d~6d and 5d~7s configurations have not been
constrained.
Parameter A B C D
F(2)(5d, 6d) 0 3 131 (22) 0 9 040 c
F(4)(5d, 6d) 0 717 (31) 0 4 786 (290)
G(°)(5d, 6d) 0 610 (9) 0 2 231 (203)
G(2)(5d, 6d) 0 933 (26) 0 3 144 (619)
G(4)(5d, 6d) 0 779 (55) 0 2 lls (1 370)
G(2)(5d, 7s) 1488 (330) 431 (74) 0 500 f
R(2)(5d6d, 5d7s) 2 277 (126) 200 f 0 0
R(2)(5d6d, 7s5d) 362 (200) 160 f 0 0
X(1)(5d, 6d) 0 46 (14) 0 0
(5~ 3 076 (76) 912 (35) 47.6 (39) 0
(6d 193 (58) 146 (28) 30.1 (33) 0
A(5d96d) A(5d97s)
Au 11 122 477 (28) 115 275 (178)
Hg iii 191 175 (12) 187 225 (178)
Tl iV 263 319 (13) 265 953 (101)
Pb V 338 680 (12) 350 642 (108)
Bi VI 417 107 (13) 440 727 (152)
Notes : c, ratio with the next D-constant is fixed.
f, parameter is fixed.
optimization. Two generalized constants describing the Z~-linear dependence of the interac- tion parameters R~~~(5d6d, 5d7s) and R~~~(5d6d, 7s5d) have been fixed according to the
results of ab initio calculations by means of the HXR method [19], whereas the constant part of these parameters was free to vary. Under these conditions, GLS-fitted parameters and ab initio integrals are in a satisfactory agreement : I) the ratio of the GLS-fitted to ab initio
integral R~(5d6d, 5d7s) is nearly constant (0.88 ± 0.03) in the studied elements, and it) the small exchange integral R~(5d6d, 7s5d) changes its sign between Hg Ill and Pb V in both Slater-Condon and ab initio calculations. The Z~-expansion forrnulas collected in table III should be used with care. For Z~ = I (Pti), some Slater parameters of 5d~6d
are negative and, therefore, meaningless. The G~°~(5d, 6d) parameter which is derived from 5d~6d~Po only, determines the predicted energy of the highest level ~So. For this level, as well as for the
sub-configurations of Au it built on 5d~ ~D~~, neglected configuration interaction effects
might lead to uncertainties much larger than the r-m-s- deviation (42.3 cm~~) on the
interpreted energies.
Several levels 5d~6p~Po reported earlier in the literature were built from a single transition to 5d~6~D1. Except for Hg iii, they were not confirmed by transitions with 5d~6d
+ 5d~7s and
are now replaced by the following values : 183 087.5 cnl~ in Tl iV, 239 442.2 cnl~ in Pb V
and 299449.1cnl~ in Bi Vi. The corresponding transitions are given in table iX. The
parametric studies of 5d~6p [3] should be revised accordingly. This will be done in an isoelectronic survey of the 5d~6p + 5d~6s6p + 5d~7p + 5d~5f group which involves the same strong electrostatic interactions as those already studied in the neighbouring spectrum of Tl iii [20].
Table IV. Newly classified lines of Au iI with 5d~6d + sd~7s
as lower configuration of the transition. Wavelengths and Zeeman structures are from [22] and the g~ factors of the even levels are theoretical values from the present work.
A (A) zeeman structure Lower even level Upper odd level
Energy J~ g~ Energy Jo go
3 653.5 (0) 0.94 108 631 2 1.072 135 993 2 1.05
5 354.25 gi = 1.780 g2 = 1.256 116 049 1.782 134 722 2 1.25
5 380.70 gj =
1.782 gj = 1.325 116 049 1.782 134 629 1.32
5 409.35 (0) 1.07 117 5 II 3 1.181 135 993 2 1.05
5 661.87 (0. II) 1.29 117 065 2 1.308 134 722 2 1.25
5 691.71 (0) 1.32 117 065 2 1.308 134 629 1.32
5 737.29 gi
= 0.98 g2 = 1.264 117 296 0.956 134 722 2 1.25
5 759.38 (0) 1.08 117 511 3 1.181 134 870 4 1.14
5 898.97 (0) 0.84 116 945 4 1.032 133 893 3 1.1
5 919.66 (0) 1.18 117 982 3 1.102 134 870 4 1.14
5 988.75 (0.41) 1.05 II 8 028 2 1.066 134 722 2 1.25
6 022.55 (0) 1.58 II 8 028 2 1.066 134 629 1.32
6 102.62 (0) 1.14 117 5 II 3 1.181 133 893 3 1.1
6 301.66 (0) 1.09 II 8 028 2 1.066 133 893 3 1.1
6 589.76 gj = 0.494 g2 = 1.044 120 823 0.508 135 993 2 1.05
