A compendium and critical review of neutral atom resonance line oscillator strengths for atomic absorption analysis

~

Spectrochimica Acta, Vol. 50B, No. 3, pp. 21)9-263, 1995 Printed in Great Britain. 058,1-8547/95 $26.00 + .00

)Pergamon 0584-8547(94)01199-4

REVIEW

A compendium and critical review of neutral atom resonance line oscillator strengths for atomic absorption analysis P. S. DOIDGE Varian Optical Spectroscopy Instruments, Box 222, Rosebank MDC, Clayton, Victoria 3169, Australia

(Received 29 April 1994; accepted 5 August 1994)

Abstraet--A summary of literature data for oscillator strengths of some neutral atomic resonance lines of 65 elements is given, with special emphasis on values obtained from radiative lifetime and branching ratio measurements. Lifetimes, transition probabilities and oscillator strengths from the literature are compared critically, with the aim of presenting a consistent and accurate set of values for elements determined by electrothermal atomic absorption spectrometry. For several resonance lines of interest for atomic absorption analysis, f-value data newly derived from relative line intensities and previously measured lifetimes are presented. Some implications for absolute atomic absorption analysis are discussed.

1. INTRODUCTION 1.1. Preliminary THE IDEA of absolute analysis can be dated to the early years of the atomic absorption (AA) method, having been suggested by WALSH in his early paper [1] and later treated by L'Vov [2]. The notion of complete atomisation in electrothermal atomisers is implicit in the measurements by L'Vov [3] of oscillator strengths, but practical attempts to measure A A atomisation efficiencies were first made with flames [4-7]. It was subsequently argued [8] that uncertainties in the degree of uniformity of free atom distribution in flames, as well as problems in determining efficiencies of nebulisation and vaporisation, make flames unsuited for implementation of the absolute A A methods; it was further argued [9] that electrothermal atomisation ( E T A ) is a more suitable method. Attempts to establish absolute analysis by E T A have been investigated by L'Vov and others [10-17] using a model [10] for diffusion-limited characteristic mass to determine the atomisation efficiency in pulse-heated furnaces, usually equipped with a platform [10, 11] to provide constant temperature conditions for atomisation; it was reported [10-12] that atomisation efficiencies of many elements approach 100% when the model of diffusion-limited analyte loss and atomisation is used. Recent developments in the technique of absolute analysis by AAS include refinement of the values of physical constants used in the equation [11], use of a computer program to calculate characteristic mass for any set of conditions [15], the determination of Er [16], Cd [17], and more rigorous characterisation of the spectral properties of hollow cathode lamps [18]. Since determination of N, the atomic number density, depends on knowledge of f, the oscillator strength, it is clear that accuracy in results for N depends directly on the accuracy of f. WILLIS [7] suggested that uncertainty in f-values represented the main barrier to determination of flame A A absolute efficiencies. (This remark was one point of departure for the present survey.) There were then relatively few data for f-values of many lines and values for some lines varied widely, there being no easy way to evaluate them critically; theoretical values were also few. It is recognised 209

210

P.S. DOIDGE

that many atomic f-values derived from older measurements have poor accuracy. For example, in one tabulation [19], many values for A, the transition probability, might be in error by up to 50% (the letter "D", attached to a large proportion of the A values, indicates up to +-50% uncertainty). The gf data in the otherwise valuable treatise by MAVRODINEANU and BoIa~F.ux [20] are almost useless. It was noted as recently as 1980 [21] that A-values for Ni I reported in the previous few years differed up to four fold; this kind of variation in values from the primary literature is common. In recent years, many transition probability data have been produced for theorists and for astronomers; accurate f-value data are needed to derive solar and stellar elemental abundances, etc. [22]. It is now considered that many transition probabilities have been measured with good accuracy [23]. For example, lifetimes of the zSF~5state and f-values of the 371.99 nm resonance line of Fe have been tabulated by WIESE [24]; recent values agree to within a few per cent. Although tabulations for neutral atom lines [25] and atom and ion lines [19, 26] have been published in the last ten years, incorporating much newer data, some data remains in the primary literature and there is still a need for the newer data to be collected so that they can be used critically by spectrochemists. In the "Results" section, lifetimes and f-values have been drawn from the primary literature. Data sheets compiled for 33 elements by SALOMAN[27--30], the "Fundamental Reference Data" columns of this Journal, and Chemical Abstracts have all been used as starting points for literature searches. Resonance lines of some 67 elements have been surveyed, and attempts at a critical evaluation of data have been made, although for some elements there is only one f- or lifetime value that is likely to be reliable. The survey has been deliberately restricted to the most sensitive neutral atom lines of elements determinable in electrothermal atomisers.

1.2. Measurement of oscillator strengths There are many experimental methods for measuring oscillator strengths; they have been reviewed by HUBER and SANDEMAN [31]. It is not the purpose here to give a summary of the principles of the various methods used to measure f-values: the interested reader is directed to their comprehensive review. As they emphasise, some "classical" methods yield only a product Nil, and uncertainty in either N (number density) or 1 (path length) means a corresponding uncertainty in f. In these methods, knowledge of the line shape is needed for equivalent width measurement by absorption, or of the saturated vapour pressure over a metal (in the "hook" method), or about the closeness to Boltzmann equilibrium in a high temperature atomiser (in comparing relative absorption or emission from levels of different energies). Number densities are measured with some difficulty and many errors in published f- and A- values may be traced to errors in the determination of N. There is thus an obvious advantage in using techniques that are independent of N. As noted by Huber and Sandeman, the methods for oscillator strength measurement based on the "classical" methods of emission, absorption, or dispersion of radiation are well suited to the measurement of complex spectra having large numbers of lines of widely differing intensities and much recent work has been done in this way for elements of astrophysical importance. It is necessary to use only a single lifetime measurement to put a large number of relative f- or A- values on an absolute scale. It is, moreover, possible to extend measurements on a single level to connected levels in a way that does not depend on assumptions about closeness to thermodynamic equilibrium, the so-called 'Ladenburg method' [31]. Lifetime measurements have the great advantage of being independent of the atom density, but usually need to be combined with the measurements of relative A-values (either from emission branching ratios or absorption or "hook" f-values) to yield absolute f-values. It is obvious that when an atomic state decays to only a single lower state (i.e. when there is no branching), a lifetime measurement will yield the A- or fvalue directly, according to the familiar relations (see below). If there is branching, one must measure the ratios of intensities in the branches. According to the methods

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used and the line studied, the limiting accuracy may be either in the lifetime or the branching ratio measurement. Since the lifetime/branching ratio method encompasses an ever-increasing number of modern f-value measurements and underpins nearly all the values listed here, a brief discussion of the methods of lifetime and branching ratio measurement is appropriate. (This emphasis on lifetime measurement is not meant to imply that fvalues from lifetimes are necessarily any more accurate than those by absorption, emission, or dispersion methods; accurate f-values have moreover been measured by methods that, while not lifetime methods, nonetheless are independent of N, e.g., magnetorotation in the wings of absorption lines [21, 31].) Some elementary formulae are first restated. From the absolute lifetime "r of an (excited) atomic state k, the total transition probability for all decays from upper (k) states to lower (i) states is simply 1/'rk = ]~Aki.

(1)

i

The branching fraction R defines the proportion of all decays from an upper state k, going to a particular lower state j: Rki = Aki(XAki) -1-

(2)

i

(It is worth preserving the valuable distinction between branching ratio and fraction noted by HtmER and SANDEMAN[31]: a branching fraction (BF) is defined for the case ]~i Rki ---- 1, while a branching ratio may be stated even when this normalisation has not been carried out, i.e. if all branches have not been measured.) The Aki for a particular transition is related to the absorption f-value through the formula: J~k = 1.50(gk/gi)Aki xz. 10 -8,

(3)

where A has units of 108s-1 and h is in/~ngstr6ms; the constant (= mc/8,tree2, with e in e.s.u.) can be evaluated to the desired accuracy from the individual constants. Branching ratios are usually determined from emission or absorption ratios, so that combination of a measured (or calculated) lifetime with an R value yields the f-value directly from these three equations. (In some cases, such as the first principal series (resonance) line of the alkalis, there is no branching ratio to be measured, since the ground state is the only state below the resonance level; lifetime measurements then give f directly and exactly.) 1.3. Measurement of radiative lifetimes [32-49] A brief survey of often-used methods for radiative lifetime determination is now given. Since lifetime measurements have been discussed comprehensively by IMrIOF and READ [32] and by CORNEY [33--35], the discussion here is necessarily brief; apportioning of space reflects, in part, the author's opinion as to the merits and accuracies of the respective techniques. Hanle (zero-field level-crossing) effect and double resonance [32, 35-40]. The depolarisation of resonant fluorescence radiation in external magnetic fields is the Hanle effect. When atoms excited by polarised light are subjected to a magnetic field, polarisation of the scattered light is a maximum (or minimum) at zero field (depending on geometry and quantum numbers Jf----~ J2"'~ J3) and decreases (or increases) thereafter. With a suitable geometry (e.g. orthogonality between the incident light, field and fluorescing light directions), the depolarisation vs field strength plot is an inverted Lorentzian, the width of which is inversely related to the excited state lifetime athrough the Land6 g-factor, gj, AB = h/2"n'(Ixagj'r)-~,

(4)

212

P.S. DO1DGE

where h and ~a have their usual meanings. Thus, it suffices to measure AB, the FWHM, to determine -r, if gj is known. The crossings of the Zeeman levels that occur at finite (nonzero) fields can be used, as well as the zero-field crossings. To measure gj to high accuracy (1 part in 104 or better), the optical double resonance (ODR) effect can be used. Changes in the polarisation of light fluorescing from atoms in a homogeneous but time-varying radiofrequency (RF) field correspond to induced magnetic dipole transitions between Zeeman sublevels [39, 40]. The dependence of the resonance width on the RF field strength in measurement by double resonance means that "r can be found by extrapolating to zero field strength. The Hanle effect can be applied to determination of lifetimes of states with integral or half-integral J values, although the polarisation of the incident light and its orientation with respect to the field must be chosen accordingly [37]. When the observed sample has atoms with some nonzero spin nuclei, so that hyperfine structure (hfs) is present, the observed signal is a superposition of different resonances from the different hyperfine levels. This can pose problems in some cases, because of the finite width of the field crossings. The natural lifetime is found by extrapolating to zero atom density, as narrowing of the signal through coherent radiation trapping is often observed at quite low atomic densities. The shorter the radiative lifetime, the wider is the Hanle signal, with the consequence that the Hanle effect is well suited to measuring short lifetimes. Beam-foil and related methods [34, 41, 42]. A beam of fast ions from an accelerator can be passed through a thin carbon foil. The excitation that follows is intense, and because of the velocity of the atoms (~10 6 m/s), the distance travelled during a typical lifetime can be of the order of cm. This emission is observed in a spatially resolved measurement and converted to an absolute time scale through the known velocity of the atoms. The method can be applied to highly excited and ionised atoms. An extension of this method was introduced during the 1970s, and entails replacing the nonselective foil excitation by selective laser excitation. A major problem with nonselective foil methods, that of "cascading" from levels higher than the sought one is thus avoided, and this fast beam-laser (FBL) method yields the most accurate radiative lifetimes yet reported [23], but has been applied only to relatively few elements. Since spatial measurements of intensity can be made with a resolution much better than 1 mm, fast-beam methods are well suited to measurement of short ~-. Phase-shift method [32, 33]. The intensity modulation of exciting radiation causes a phase shift in the emitted or fluorescent radiation which is related both to the lifetime of the excited state and to the angular frequency. This method, developed in the 1960s, is capable of lifetime measurement to -10% accuracy but is now seldom used. Phase-shift lifetimes are sometimes overestimated because of unrecognised contributions from radiation trapping or multiple scattering or cascading [32]. Delayed coincidence method (DCM) [32-34, 43]. In this method, pulsed excitation of an atomic state either by a beam from an electron gun crossing an atomic beam or by a light source provides the input to one side of a coincidence circuit. The fluorescent photons produce pulses at the detector that are fed into the other side of the circuit, and variable delays introduced by a delay cable establish a time base. Plots of coincidence rate vs delay length yield the lifetimes directly. Multichannel variants of the method are discussed by CORNEV [33, 34]: pulses from the electron gun or light source trigger the start for charging of a time-to-amplitude converter (TAC), the pulses emitted giving the stop. The pulse height vs time yields an exponential decay curve, and thus "r. Lifetimes of a few ns can be measured with accuracy of a few per cent, although accuracies of about 10% seemed more typical, until quite recently. Newer techniques [43] have led to further improvements in the accuracy of the method. An argon CW laser has been used to pump a mode-locked dye laser which, with pulse lengths as short as 6 ps (at very high repetition rates), provides an excitation pulse sufficiently short that deconvolution of exciting and fluorescent pulses does not have to be made; single-photon counting techniques are then used, with the exciting

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laser pulse used as stop, rather than start, for the TAC. The measured lifetime for the first 2p state of Na, with an estimated error within 0.5%, is among the most accurately measured of all atomic lifetimes [43]. Delayed coincidence and phase-shift methods are essentially variants of a class of methods that monitor the response of a state to pulsed or modulated excitation. A third variant has been developed since the early 1980s, based on the use of pulsed lasers to excite sputtered vapours. Laser-induced fluorescence (Lib-) on sputtered metal vapours [44-49]. The atomic vapour produced, for example, by cathodic sputtering [44] is especially suited for lifetime measurements on atoms of all the solid elements. Time-resolved measurement of the exponential decay of a state excited by a pulsed laser in a low-pressure discharge has been turned into a powerful method for the measurement of lifetimes [44-49]. The advantage of using a low-pressure discharge is that lifetimes can then be measured for elements of low volatility which would be vaporised only with difficulty in thermal sources. In one embodiment [45] the atoms are produced in a cathodic sputtering cell and excited by a pulsed dye laser, itself pumped by a nitrogen laser; the decay is captured by a fast photomultiplier and digitiser and processed. In another version of the method [47], the atoms form an uncollimated beam by effusing past a nozzle, shaped as a flared 1 mm diameter hole at one end of a hollow cathode; a low background pressure minimises collisional depopulation, which otherwise can be a problem. Fluorescence signals are processed by boxcar integrator or transient digitiser [48]. In these methods, measured lifetimes must be corrected for any distorting effects of radiation trapping and of quantum beats, or time-of-flight effects in the beam method [49]. As HANNAFORDand Low~ [46] note, radiation trapping is minimised by operating at suitably low atom density, while depopulating collisions are studied by operating at varying fill gas pressures. Effects of fine- and hyperfine quantum beats can also be taken into account [46]. As LAWLER[48] notes, LIF methods make possible fast and routine determination of lifetimes as short as 2 ns, often with 2 - 5 % accuracy. Newer techniques [49] have allowed extension of lifetime measurement by LIF into the vacuum ultraviolet. Branching ratios. LAWLER[48] has discussed problems in measuring branching ratios, giving a comparison of the relative merits of the CORLISS/BOZMANtables [50] (obtained from arcs by photographic recording), photoelectric recording of hollow cathode spectra, and Fourier Transform Spectrometry (FTS). Branching ratios can now be measured to accuracies of a few per cent by FTS techniques [48]. NBS Monograph 53 [50] has shortcomings that have been treated in the literature. (See, for example, Refs [51, 52].) It did, however, serve for many years as the only source of A-values for many elements, such as those of the 4d and 5d series. Branching through infrared channels can usually be ignored when there are strong ultraviolet branches, since the Einstein coefficients vary as the cube of transition frequencies, but there are cases (e.g. in the 4d and 5d series) where infrared paths can contribute appreciably to the decays from a particular level (for references to discussion of such effects, see the element data for Hf, §2.1.10). In relating branching ratios to intensities and transition probabilities, or in interconverting branching ratios and intensities, the relationship between the two must be considered:

I -- 4 ~ A N I .

(5)

In the CORLISS/BOZMANtables [50], for example, photographic intensities are tabulated and converted (Eqn (5)), the spectra sensitivity of the detector system also contributes a wavelength-dependent factor.

P. S. DOIDGE

214

Table 1. Lithium radiative lifetimes State

• (ns)

2paP" (J = 1/2,3/2) 27.2 + 0.4 26.2 -+ 1.0 26.4 -+ 0.8 27.29 +- 0.04 27.0 +-1.0 27.24 27.11 27.09 27.07 27.00

Method

Year

Hanle effect beam-foil Hanle effect beam-laser LIF Coulomb approx. ab initio calc. ab initio calc.

1967 1969 1978 1982 1983 1984 1989 1990

ab initio (MCHFL)* ab initio (MCHFV)t

1992 1992

Authors, reference Broget al. [61] Andersenet al. [62] Nagourneyet al. [63] Gaupp et al. [60] Hansen[64] Theodosiou [56] Blundellet al. [57] M~rtensson-Pendrill, Ynnerman [58] Weiss[59] Weiss[59]

* MCHFL = Multi-configuration Hartree-Fock, length form of operator. t MCHFV = Multi-configurationHartree-Fock, velocity form of operator.

1.4. Presentation o f the s u m m a r y Candidate lines were selected from AAS listings [53, 54]. In comparing and evaluating the results, certain guiding principles were adopted. G o o d agreement among different experimental results, especially those obtained using different techniques, was the primary criterion. It will be shown in the summary that some methods give more accurate and consistent results than other methods. Reliance is naturally on experimental values, although in some cases (e.g. Se), there is apparently only one measured lifetime, and it differs from theoretical values. Some calculated f-values are listed in the summary. Whilst alkali atom f-values can now be calculated to high accuracy (see below), calculation of f-values for atoms other than one-electron ones remains difficult. Quantities like f-values are of little use unless the associated errors are known and these are included, wherever possible, mainly from the original papers. Recently, MORTON [55] has given an extensive summary of A values and wavelengths of lines from low-lying (<0.275 eV) levels of elements H through Ge. His emphasis is somewhat different from that of this summary, being mainly on data for far- and vacuum-UV lines, and for nonmetals (C, N, C1, O . . .). Nevertheless, there is some overlap of his survey with the material of the present summary.

2. RESULTS AND DISCUSSION 2.1.

T h e oscillator strengths

The arrangement is by periodic groups for elements in Groups l a - 6 a , and rows for 3d, 4d, 5d and lanthanide elements, except that Group lb and 2b elements are discussed after their analogues (the alkalis and alkaline earths, respectively). 2.1.1. A l k a l i metals [43, 45, 56-97]

As emphasised by WIESE [23], advances in measurement accuracy of some alkali resonance line f-values have given further impetus to the calculation of f-values for one-electron atoms. In general, the spin-orbit interaction causes not only increasing splitting of the J = 1/2 and J = 3/2 states but also an increasing difference between the lifetimes of these states as atomic number increases. The difference, while definite for the theoretical lifetimes (see, e.g., Refs [56, 72]), is hardly apparent in experimental values until K, Rb and Cs are reached. The f-values listed here are from lifetimes listed in Tables 1 - 5 , excepting magneto-rotation results [75] and "other values" [94-97], listed in Table 6 for comparison. For the lifetimes, only literature values with estimated errors <+-5% have been used.

REVIEW Table 2. Sodium radiative lifetimes State

-r (ns)

3p2p ° (J = 1/2, 3/2) 16.1" 16.2 - 0.3 16.30 (J = 1/2)

(J = 3/2)

16.4 16.40 16.38 16.11 16.40 16.1

- 0.6 ± 0.03 ± 0.08

16.12 16.0 16.0 16.1 16.36 16.06 16.35

- 0.22 -+ 0.5 ± 0.2 - 0.2 +- 0.10

± 0.2

Method

Year

Authors, reference

various phase-shift semiempirical (model potential) calc. LIF beam-laser DCM ab initio calc. Coulomb approx. level-crossingt

1969 1967 1992

B~istlein et al. [65] Cunningham, Link [66] Laughlin [74]

1972 1982 1988 1987 1988 1968

level-crossing level-crossing Hanle effect LIF DCM a b initio calc. Coulomb approx.

1970 1970 1977 1981 1988 1987 1988

E r d m a n n et al. [67] Gaupp et al. [60] Carlsson [43] Johnson et al. [73] Theodosiou, Curtis [72] Sch6nberner, Z i m m e r m a n n [681 Mashinskii, Chaika [69] Schmieder et al. [70] Burgmans [71] Hannaford, Lowe [45] Carlsson [43] Johnson et al. [73] Theodosiou, Curtis [72]

* Mean of nine lifetimes tabulated by B~istlein et al. [65]. t "Level-crossing" in this and other Tables denotes "high-field" (nonzero-field), as distinct from zerofield (Hanle effect) crossings (see text). Table 3. Potassium radiative lifetimes State

"r (ns)

4pEp ° (J = 1/2, 3/2) 27.1 - 0.9 27.8 +-- 0.5 26.75

Method

(J = 1/2)

27.8 -+ 0.8 27.3 - 0.3 26.67 --- 0.07 27.51

magnetorotation phase-shift semiempirical calculation DCM Hanle effect beam-laser Coulomb approx.

(J = 3/2)

26.0 27.6 28 26.52 27.16

level-crossing DCM LIF beam-laser Coulomb approx.

+-- 0.5 --- 0.8 ± 1 ± 0.05

Year

Authors, reference

1951 1966 1992

Stephenson [75] Link [77] Laughlin [74]

1969 1975 1990 1984

Copley, Krause [78] Zimmerman [79] Roth et al. [80] Theodosiou [56]

1968 1969 1986 1990 1984

Schmieder et al. [81] Copley, Krause [78] Hart and Atkinson [82] Roth et al. [80] Theodosiou [56]

Lithium [56-64]. Lifetimes [60-64] for the (unresolved) 22P state are given in Table 1. The value "r(22p) = 27.29 - 0.04 ns reported by GAUPP et al. [60] (FBL method) agrees very well with calculated values (for both J = 1/2, 3/2 states) from theoretical papers [56-59]. The f-values (Table 6) derived from this experimental lifetime, as given in Table 1 are, together with those of Na (see below), the most accurately known f-values in existence [23]. Calculated (ab initio) f-values and reduced transition matrix elements a for the 22S-22P lines of Li are listed, respectively, by WmSE [23] and by MARTENSSOr~-PEr~D~LL and YNNE~AN [58]. As several authors [23, 58, 59] emphasise, ab initio transition probabilities [57-59], proportional to the square of the matrix elements, agree to better than 0.2°/'0, but differ systematically from the beamlaser value [60] of 0.15% (one-sigma) estimated error: the difference amounts to - 1 % . This remains an unsolved problem in atomic physics. Such discrepancies, while a See Appendix for conversion of matrix elements to f-values and lifetimes.

216

P. S. DOIDGE Table 4. Rubidium radiative lifetimes

State

~ (ns)

Method

Year

Authors, reference

5p2p° (J = 1/2) 28.5 28.1 28.5 29.4 28.6 27.04 28.30

-+ 0.5 - 0.5 -+ 1.1 ± 0.7

27.8 28.2 27.9 27.0 27.1 25.5 25.8 27.0 26.8 25.69 26.88

-+ 0.9 ± 0.9 - 1.3 ± 0.5 ± 1.4 ± 0.5 ± 0.8 ± 0,5 ± 0.9

magnetorotation phase-shift Hanle effect Hanle effect weighted mean* (n = 4) Coulomb approx. ab initio calc.

1951 1966 1970 1974

Stephenson [75] Link [77] Altman, Kazantsev [84] Gallagher, Lewis [85]

1984 1987

Theodosiou [56] Johnson et al. [731

1951 1965 1965 1966 1967 1970 1971 1974

Stephenson [75] Schfissler [86] Violino [87] Link [77] Feichtner et al. [88] Schmieder et al. [70] Belin, Svanberg [89] Gallagher, Lewis [85]

1984 1987

Theodosiou [56] Johnson et al. [73]

5p2P° (J = 3/2) magnetorotation double resonance level-crossing phase-shift Hanle effect level-crossing level-crossing Hanle effect weighted mean * (n = 7) Coulomb approx. ab initio calc.

* Weighted means have been calculated by weighting each lifetime in inverse proportion to the absolute magnitude of the quoted experimental error. Table 5. Caesium radiative lifetimes State

r (ns)

Method

Year

Authors, reference

6p2p° (J = 1/2) 34.0 -+ 0.6 35.2 -+ 1.5 33.66 36.62

phase-shift phase-shift Coulomb approx. ab initio calc.

1966 1969 1984 1987

Link [77] Doddet al. [90] Theodosiou [56] Johnson et al. [73]

30.5 30.8 32.7 29.9 29.48 30.13

phase-shift phase-shift level-crossing level-crossing Coulomb approx. ab initio calc.

1966 1969 1970 1972 1984 1987

Link [77] Doddet al. [90] Schmieder et al. [70] Rydberg, Svanberg [91] Theodosiou [56] Johnson et al. [73]

6pzP° (J = 3/2) ± 0.6 -+ 1.5 -+ 1.5 -+ 0.2

o f g r e a t i n t e r e s t to physicists, a r e h a r d l y a c o n c e r n in s p e c t r o c h e m i c a l analysis. It is a p p a r e n t t h a t e x p e r i m e n t a l lifetimes for Li a r e n o w a l m o s t g o o d e n o u g h to a f f o r d a critical test o f t h e w a v e f u n c t i o n s u s e d in calculations. Sodium [43, 45, 56, 60, 65L77]. L i f e t i m e s r e p o r t e d to 1969 w e r e s u m m a r i s e d by B.~STLEIN e t al. [65], a n d GAUPP e t al. [60] h a v e listed s u b s e q u e n t values. THEODOSIOU a n d CURTIS [56, 72] a n d LAUGHLIN [74] listed c a l c u l a t e d ,r o r f - v a l u e s o f 32p states (J = 1/2 a n d 3/2) ( b y C o u l o m b a p p r o x , a n d m o d e l p o t e n t i a l m e t h o d s ) ; Ref.[73] gives a b i n i t i o values. A s m e n t i o n e d a b o v e for Li, t h e F B L m e a s u r e m e n t s by GAUPP e t al. [60], w h o also m e a s u r e d t h e 3p2p (J = 1/2) state o f N a , a r e the m o s t a c c u r a t e a v a i l a b l e , b u t d i s a g r e e with the m o s t a c c u r a t e a b i n i t i o v a l u e s (e.g. Ref.[73]) by s e v e r a l s t a n d a r d d e v i a t i o n s . A s to t h e f - v a l u e s o f t h e D lines, t h e r e r e m a i n s u n c e r t a i n t y a b o u t r e l a t i v e e x p e r i m e n t a l f - v a l u e s , which d i s a g r e e slightly with lifetimes [43]. A c c u r a t e lifetime m e a s u r e m e n t s i n d i c a t e a r a t i o "r(J = 3/2)/'r(J = 1/2) -- 0.999 [43], a n d calculations [56, 73] i n d i c a t e 0.997, w h e r e a s a p r e c i s i o n m e a s u r e m e n t [76] o f f ( D 2 ) / f ( D 1 ) ( = 1.985 -+ 0.004) b y t h e r e s o n a n t F a r a d a y effect gave a r a t i o o f 1.006. Thus, the f -

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Table 6. f-Values, Grp la (ns 2S~/~-np2p~u2.3/2 lines) Element, h (nm)

n

Li 670.791 Li 670.776

2 1/2 3/2

29.27 -+ 0.04 29.27 -+ 0.04

Na 589.592 Na 588.995

3 1/2 3/2

16.40 -+ 0.03 (16.40- 0.03)

K 769.898 K 766.491

4 1/2 3/2

26.67 -+ 0.07 26.52 --- 0.05

Rb 794.760 Rb 780.023

5 1/2 3/2

28.6 26.8 -+ 0.9

Cs 894.350 Cs 852.110

6 1/2 3/2

34.0 29.8

Jk

Experimental r (ns)

f-values Experimental*

Theoreticalt

0.2472 -+ 0.0004 0.4944 - 0.0008 sum = 0.7415 - 0.0009~ 0.3179 --- 0.0006 0.6343 + 0.0012 sum = 0.9522 --- 0.0013:~ 0.3332 -+ 0.0009 0.6642 --+0.0012 sum = 0.9974 _+ 0.0015:~ 0.331 0.681 -+ 0.023 sum = 1.012 0.347 --- 0.017 0.721 -+ 0.021 sum = 1.068

--0.7478-0.7498 --0.9584 0.323 0.649 0.972 0.350 0.710 0.960 0.356 0.738 1.094

Other values (experimental)

-0.32a 0.64a 1.15 -+ 0.03b 1.032 --- 0.03c -1.20d 0.98d

* Experimental f-values from Refs [60], [60], [80], & [92] for Li, Na, K, and Cs, respectively and from Table 4 weighted mean lifetime for Rb. t Theoretical values from Ref.[59] for Li, Ref.[74] for Na, and calculated from Ref.[73] (for K, Rb, and Cs). Errors for sums of f from quadratically added individual values. a Ref.[94]; b Ref.[95]; c Ref.[96]; d Ref.[97]. values (Table 6) are limited in accuracy by this ratio, t h o u g h accuracy of < 1 % can still be claimed. Potassium [56, 70, 7 3 - 7 5 , 7 7 - 8 3 ] . Lifetimes are set out in Table 3. In the 42p (J -- 3/2) state, the m a g n i t u d e s of radiative width and magnetic dipole (A) constant are about the same, with the c o n s e q u e n c e that in H a n l e effect m e a s u r e m e n t s , the n o n z e r o field level crossings overlap strongly with the zero-field crossings [79]; m e a s u r e m e n t s are then m a d e with s o m e difficulty on this 42p resonant state (J = 3/2). Phase-shift [77], delayed coincidence [78], and beam-laser [80] m e a s u r e m e n t s do not suffer this drawback. T h e most accurate values for the lifetimes are again beam-laser results [80], for which accuracy at the 0 . 2 - 0 . 3 % level was r e p o r t e d (Table 3), and lifetimes of the J = 1/2 and J -- 3/2 c o m p o n e n t s o f the 4p2p resonant level of K are just resolved at the one-sigma level in the beam-laser results (Table 3). Table 6 gives f-values derived from these lifetimes [80]; Ref.[83] lists o t h e r principal series f-values. Rubidium [56, 70, 73, 75, 77, 84-89]. A lifetime difference for the J = 1/2 and J = 3/2 terms of the 5zP state of R b is readily a p p a r e n t f r o m the m e a s u r e d lifetimes listed in Table 4. E x p e r i m e n t a l results are not, however, as consistent as they are for Na: although the values all have estimated (one-sigma) errors of 5% or less, the m a x i m u m variation in the "r values a m o u n t s to - 1 1 % , and it follows that 52S-52p fvalues based on a m e a n c a n n o t be considered as accurately defined as for Li, Na, and K, either in terms of consistency of the experimental results, or in terms of a g r e e m e n t with theory. Caesium [56, 70, 73, 77, 87, 9 0 - 9 3 ] . F o r 62p, distinctly different lifetimes for J = 1/ 2 and 3/2 levels are again a p p a r e n t (Table 5). T h e Table 6 f-values are f r o m SHABANOVA et al. [92] w h o used the m e a n of m e a s u r e d lifetimes [70, 77, 87, 90, 91] to get an absolute scale for their h o o k data and derive an f-value for the 6 z S - 6 2 p (J = 3/2) line. T h e f - s u m rule is not strictly o b e y e d for Cs ( ~ f - l . 0 7 ) , because of appreciable core polarisation [77]. 2.1.2. Group lb (Cu, Ag, Au) [46, 66, 9 8 - 1 2 6 ] Lifetimes and f-values have b e e n r e p o r t e d for the 2p resonance states of these three elements by HAm~AFORD and LOWE [46, 98, 125], by L I F , and lifetimes (by D C M ) have also been r e p o r t e d for 2p states by BEZUCLOV et al. [99]. T h e lifetimes and f-

P. S. DOIDGE

218

Table 7. Copper radiative lifetimes State

r (ns)

Method

Year

Authors, reference

4poP ° (J = 1/2, 3/2)

7.2 ± 0.3 7.5 ± 0.8* 7.6 - 0.7

phase-shift beam-foil beam-foil

1967 1971 1976

Cunningham, Link [66] Andersen et al. [105] Curtis et al. [106]

7.1 ± 0.6

electron-excitation optical chronography electron-excitation DCM electron-excitation DCM LIF DCM

1978

Malakhov [111]

1982 1982 1983 1989

Bezuglov et al. [99] Verolainen et al. [112] Hannaford, Lowe [46, 98] Carlsson et al. [100]

1966 1966 1966 1975 1978

Bucka et al. [107] Levin, Budick [108] Ney [109] Krellmann et al. [110] Malakhov [111]

1982 1982 1983 1989

Bezuglov et al. [99] Verolainen et al. [112] Hannaford, Lowe [46, 98] Carlsson et al. [100]

4p2p~l/2

7.0 7.0 7.4 7.27

± 0.9 +- 0.9 ± 0.2 +- 0.06

7.0 7.2 7.0 7.24 7.2

± ± ± ±

0.7 0.2 0.15 1.0

7.0 7.0 7.1 7.17

± ± ± ±

0.9 0.9 0.2 0.06

4p2p~/2 level-crossing Hanle effect level-crossing Hanle effect electron-excitation optical chronography electron-excitation DCM electron-excitation DCM LIF DCM

* Not stated in Ref.[105]; inferred from graphically presented results.

v a l u e s g i v e n h e r e f o r C u a n d A g ( T a b l e 10) a r e f r o m CARLSSON e t al. [100, 124], whose lifetimes for these two elements are now the most accurate available. Tables 7 - 9 list all k n o w n l i f e t i m e s f o r t h e first 2p s t a t e s o f C u , A g , a n d A u . C o p p e r [46, 66, 9 8 - 1 1 4 ] . E a r l y r e s u l t s , a n d e r r o r s in t h e m , w e r e s t u d i e d b y BELL a n d T t J a a s [101] w h o c o n s i d e r e d s o u r c e s o f e r r o r in e a r l i e r a t o m i c b e a m m e a s u r e m e n t s Table 8. Silver radiative lifetimes State

"r (ns)

5p2p° (J = 1/2, 3/2) 8.7 + 0.4*

Method

Year

Authors, reference

beam-foil

1971

Andersen et al. [105]

phase-shift electron-excitation DCM LIF Hanle effect photon-photon DCM

1967 1982 1983 1983 1990

Cunningham, Link [66] Bezuglov et al. [99] Hannaford, Lowe [46, 98] Soltanolkotabi, Gupta [118] Carlsson et al. [124]

level-crossing Hanle effect phase-shift level-crossing level-crossing electron-excitation DCM LIF electron-excitation DCM LIF Hanle effect photon-photon DCM

1966 1966 1967 1971 1972 1975

Bucka et al. [107] Levin, Budick [108] Cunningham, Link [65] Bucka et al. [119] Moe, McDermott [120] Klose [121]

1978 1982

Selter, Kunze [122] Bezuglov et al. [99]

1983 1984 1990

Hannaford, Lowe [46, 98] Soltanolkotabi, Gupta [123] Carlsson et al. [124]

5p21~.2 7.5 7.5 6.8 7.56 7.41

± 0.4 ± 0.7 ± 0.3 -+ 0.22 -+ 0.04

6.7 7.4 6.7 6.3 6.5 6.5

± 0.7 ± 0.4 ± 0.6 ± 0.6 -+ 0.6

5p2P~3/2

7.3 + 0.4 7.5 --- 0.7 6.3 ± 0.2 6.35 --- 0.17 6.79 ± 0.03

* Not stated in Ref.[105]; inferred from graphically presented results.

REVIEW

219

Table 9. Gold radiative lifetimes State

r (ns)

Method

Year

Authors, reference

6p2p~'/2 6.0 -+ 0.1 7.4 +- 0.7

LIF electron-excitationDCM

1981 1982

Hannafordet al. [125] Bezuglovet al. [99]

5.3 _+ 1.0 4.6 4.6 --- 0.2 5.6 --- 0.8 4.8

Hanle effect level-crossing LIF electron-excitationDCM weighted mean (n = 4)

1966 1966 1981 1982

Levin,Budick [108] Bucka,Ney [126] Hannafordet al. [125] Bezuglovet al. [99]

6p2~,2

and established f(324.7 nm) at 0.43. A- and f-values of Cu lines were surveyed by BmLSKI [102] and by HANNAFORD and McDorqALI9 [103]. The "best" values listed by BIELSKI for the 42S-42p resonance doublet are very close to those from lifetime results of HArqNAFORD and LOWE [46], and of CARLSSON et al. [100]. From the latter's -c values and branching fractions reported by KocI~ and RICHTER [104], which are nearly unity, the Table 10 f-values follow; f(324.7 nm) = 0.434 - 0.004 is one of the most accurately measured f-values. Silver [46, 66, 98, 99, 105, 107, 111-124]. For Ag, solar abundances have been mainly derived from measurements of the 52S-52p resonance lines [22]. Table 8 lists -r measurements on the 2p states. Laser-excited DCM measurements of the 5pZP states by CARLSSON et al. [124] indicate that Ag f-values are now known to better than 1%, since the branching fractions for both transitions can be taken as unity [124]. Agreement with theoretical f-values [114], as for Au, is no better than - 1 0 - 1 5 % . G o l d [46, 98, 99, 108, 114, 116, 117, 125, 126]a. Branching ratios of Au lines (242.8, 267.6 nm) were remeasured by HANNAFORO et al. [125], since earlier values were appreciably in error. Furthermore, literature f-values of the 242.8 nm line varied by more than an order of magnitude! HANNAFORD et al. were able to give, for the first time, a lifetime for the 62p (J = 3/2) state and to confirm an earlier lifetime of 4.6 ns for the 62p (J = 1/2) state of BUCr,A and NEY [126] by the level-crossing method. The f-values (Table 10) of the 242.8 and 267.6 nm lines appear then well founded. (The weighted mean -r of 4.8 ns for the J = 3/2 state is consistent with all four experimental values.) Table 10 shows f-value comparisons with theoretical [113, 114] and other values [115-117]. 2.1.3. A l k a l i n e earths, G r o u p 2a (Be, M g , Ca, Sr, Ba) [127-163] Lifetimes of 1p states and f-values of 1S-Ip resonance lines of Mg, Ca, Sr and Ba have been summarised by KELLY and MATHUR [127]. For Ca, Sr, and Ba, for which PARgIrqSON et al. listed f-values [128], branching to metastable levels n s ( n - 1 ) d 1.3D, just below the 1p states and giving far infrared lines, must be considered. Calculations of alkaline earth f-values were made by HUrqTER and BERRY [129], and values by various theoretical methods were compared with the experimental results. Beryllium [130-134]. Oscillator strengths of Be lines were calculated by CHANG [130] and compared with experimental values. A range of theoretical f-values, from -1.35 to 1.44, was reported for the 234.8 nm line. Transition probabilities for Be I have also been calculated by MOCCIAand SPizzo [131], and compared with experimental results. Experimental results were reviewed by MARTIrqSONet al. [132], who compared their beam-foil lifetime (Table 11) with earlier results. They concluded that lifetimes measured prior to those of HOYTZEAS et al. [133] were probably erroneous, because of cascade effects. Lifetimes of 1.80 +-0.15 ns and 1.85---0.07ns from these later references [132, 133] correspond, respectively, to f-values of 1.34-4--0.05 and ° See also recent lifetime results of GAARDEet al. [434].

220

P.S.

DOIDGE

i

+1 +1

+1 +1 +1

+1

+1

+1

¢q +1 +1 +1

+1

¢ q .~- ¢,q

0

8

09

0

o

.r~

t~

o

+1

~8 +1

+1

¢q

¢q

~6

¢¢

e~ ..s

¢q

"a ,.~ e~

k~

c9

,-~L9 ~. rZ. ~. cq u3,,~

<

<

¢q

REVIEW

221

Table 11. Berylliumradiative lifetimes State

x (ns)

Method

Year

AuthoL Reference

2plP~l 1.80 -+ 0.15 1.85 -+ 0.07

beam-foil beam-foil

1972 1974

Hontzeaset al. [133] Martinsonet al. [132]

1.38 --- 0.10, in good agreement with theoretical values, which range from -1.33 to -1.41 [130, 131, 134]. Thus, f(h234.8 nm) seems established within about 5%. M a g n e s i u m [135-144] MoccIA and Salzzo [135] listed both experimental and calculated f-values. Calculations were also made by MENDOZA and ZEIPPEN [136]; their f-values (from close-coupling methods) for the 285.2 nm line were compared with previous values and indicate f(h285.2 nm) = 1.76-1.78, several per cent lower than the best experimental value (Table 16). The Table 12 lifetimes of the 3p~P~ state are from six experimental results [137-142]; two further results listed by MOCOA and SvIzzo [135], older measurements by the beam-foil method, are discarded as probably being in appreciable error. The mean lifetime of all six measurements of 2.02 - 0.04 ns is in excellent agreement with the most accurate, which are the three Hanle effect results. The most accurate of these, by KELLYand MATHUR [142], is clearly consistent with the mean and indicates accuracy at the 2% level. Thus, A- and f-values of the 285.2 nm line of Mg seem well established at, respectively, 4.95 × 10Ss-~ and 1.83, with a 2% level of accuracy. The agreement between calculated [135, 136] and experimental results is not particularly good (cf. Li and Na above) but suffices to show that the theoretical values [135, 136] are well founded. It remains only to suggest reasons for the large discrepancy between the lifetime results and some older values, such as one obtained from some hook/absorption experiments [97, 143] (f = 1.2 - 0.3; cf. Table 16). MITCHELL[144] used the hook method to measure relative f-values of the 285 nm resonance line and other Mg I lines and pointed to serious errors introduced to the resonance line result through strong, asymmetrical line broadening, attributed to molecular Mg (Mg2). This broadening contributed to uncertainty in the hook separation, and the effect on Nfl (directly proportional to the square of the hook separation) was considered to be -30%. C a l c i u m [45, 137, 138, 145-152]. The f-value of the 422.7 nm line is established at 1.77. This was derived from the mean of ten experimental lifetimes [45, 137, 138, 145-151] shown in Table 13, by phase-shift, Hanle effect, beam-foil, and LIF methods. KELLY and MATHUR [151] noted that some beam-foil, magnetic rotation, absorption and hook values showed inconsistencies and fluctuations; Hanle effect measurements again gave excellent agreement with each other and generally with theoretical results. Clearly, there is very good agreement among the results for Ca shown in Table 13; a weighted mean "r has a standard deviation of only 2%. Branching to 4s3dlD2 (5547.1 nm) was studied by PECKand HUNTER[152] who reported an upper limit to the 4s3dtDE-4s4p~P~ f-value of 6.5 × 10-4 (corresponding to the negligible branching fraction of 10-5). S t r o n t i u m [145-147, 153-156]. Recently, WEedJ et al. [153] reported calculated fvalues in Sr I, with fair to good agreement with experimental values. Lifetime measurements [145-147, 155, 156] of the 5pIp ° resonance state of Sr, and a summary by KELLY and MATHUR [127], form the basis for the f-value listed here (Table 16) of 1.94 - 0.06, corresponding to that reported by the latter authors, who argued that branching to the metastable 5s4dlD state (6460nm) should be small (<5%). Measurements by HUNTER et al. [154], the first on this weak branch in the spectrum, confirmed that branching through the 10 2 channel is indeed negligible for Sr: only ca 2 × 10 -5 of decays occur through this channel. Agreement among lifetimes (Table 14) is only fair and the f-value (Table 16) cannot be considered quite as well defined as for Mg, Ca or Ba.

P. S. DOIDGE

222

Table 12. Magnesium radiative lifetimes State

• (ns)

Method

Year

Author, reference

3plP~ 1.99 2.03 1.90 2.09 2.03 2.00 2.02

-+ 0.08 -+ 0.06 +- 0.3 -+ 0.10 --- 0.15 -+ 0.04 -+ 0.04

Hanle effect Hanle effect phase-shift beam-foil phase-shift Hanle effect weighted mean (n = 6)

1964 1966 1971 1973 1973 1978

Lurio [137] Smith, Gailagher [138] Smith, Liszt [139] Lundin et al. [140] Marek, Richter [141] Kelly, Mathur [142]

Table 13. Calcium radiative lifetimes State 4p~P'~

-r (ns) 4.67 4.48 4.62 4.6 4.6 4.6 4.45 4.7 4.49 4.6 4.55

-+ 0.11 - 0.15 -+ 0.15 - 0.6 -+ 0.2 -+ 0.6 -+ 0.07 -+ 0.5 -+ 0.07 -+ 0.2 -* 0.09

Method phase-shift Hanle effect Hanle effect phase-shift Hanle effect beam-foil Hanle effect LIF Hanle effect LIF weighted mean (n = 10)

Year

Author, reference

1964 1964 1966 1971 1974 1975 1976 1977 1980 1981

Hulpke et al. [145] Lurio et al. [146] Smith, Gallagher [138] Smith, Liszt [139] Kluge, Sauter [147] Emmoth et al. [148] Gibbs, Hannaford [149] Havey et al. [150] Kelly, Mathur [151] Hannaford, Lowe [45]

Table 14. Strontium radiative lifetimes State

r (ns)

Method

Year

Author, reference

5plP~ 4.56 4.97 4.8 4.68 5.4 4.80

- 0.21 -+ 0.15 - 0.2 -+ 0.10 +- 0.5 -+ 0.22

phase-shift Hanle effect Hanle effect Hanle effect electron-excitation DCM weighted mean (n = 5)

1964 1964 1974 1974 1976

Hulpke et al. [145] Lurio et al. [146] Kluge, Sauter [147] Kelly et al. [155] Erdevdi, Shimon [156]

Table 15. Barium radiative lifetimes State

r (ns)

Method

Year

Author, reference

6p'P~ 8.36 8.37 8.3 8.2 8.45 8.37

-+ 0.25 +- 0.20 +-- 0.5 -+ 0.2 -+ 0.6 -+ 0.08

phase-shift Hanle effect LIF Hanle effect electron-excitation DCM Hanle effect

1964 1968 1973 1974 1976 1977

Hulpke et al. [145] Swagel, Lurio [160] Schenk et al. [161] Kluge, Sauter [147] Erdevdi, Shimon [156] Kelly, Mathur [162]

REVIEW

223

Table 16. f-values, Orp IIa (ns 2 1So-nsnp 1p$~) transitions Element, n

h (nm)

Be 2 Mg 3 Ca 4 Sr 5 Ba 6

234.861 285.213 422.673 460.733 553.548

x (nsnp lp), ns (weighted mean) 1.85 2.02 4.55 4.80 8.34

± 0.07 --- 0.04 ± 0.09 ± 0.22 ± 0.07

f-Value from mean "r 1.34 1.83 1.77 1.94 1.64

- 0.05 ± 0.04 ± 0.035 -+ 0.06 -+ 0.016

Other experimental f-values -1.2 1.49 1.54 1.40

± 0.3 a ± 0.04 b --+ 0.05 b ± 0.05 b

a Ref.[143]; b Ref.[163]. Table 17. Zinc radiative lifetimes State

r (ns)

Method

Year

Author, reference

4s4plP$ 1.38 1.41 1.75 1.45 1.41 1.33 1.40

- 0.05 + 0.04 ± 0.2 _+ 0.15 - 0.04 + 0.07 ± 0.03

Hanle effect Hanle effect phase-shift beam-foil Hanle effect beam-foil weighted mean (n = 5)

1964 1964 1970 1973 1976 1979

Landman, Novick [164] Lurio et al. [146] Baumann, Smith [165] Andersen, S0rensen [166] Kowalski, Tr~iger [167] Martinson et al. [168]

double resonance

1964

Byron et al. [174]

4s4p3p~ 2000 _+ 200

Barium [145, 147, 156-163]. JAHREISS and HUBER [157] recommended a change of ca +3% to the literature [19] A-value of 1.15 × 108s-1 (f = 1.59) for the 553 nm resonance line; their new value was f = 1.64. The correction was introduced to account for a discrepancy in the apparent number densities measured before and after excitation and ionisation when dense Ba vapour was excited and ionised by a pulsed laser; their new value for A(553.5 nm) = 1.19 x 108s-1 amounts to identification of mki with the inverse lifetime, the latter reported for 6p 1p$ from reliable measurements [145, 147, 156, 160-162] as 8.37 ns (Table 15). Later measurements of branching ratios [159] confirmed their findings and gave a correction to results [158] suggesting a somewhat higher aggregate rate for decays to 6s5d(~D,3D) metastable states; thus, R(h553 nm) = 0.9966. Considering the Group 2a elements as a whole, the lifetime measurements give appreciably higher f-values than results of PEr~KIN et al. [97, 143, 163] from hook/ absorption results (cf. Table 16). This is discussed further below (§2.2.1). 2.1.4. Group 2b (Zn, Cd, Hg) For the nlS-nlP and nlS-n3p (n = 4, 5, 6) lines from the ground state, lifetimes give the f-values directly, there being no branching to consider. Zinc [164-171]. The f-value of the 213.8 nm line is well established at 1.47, from both lifetimes [164-168] (Table 17) and an absolute absorption measurement [169]. Table 18. Cadmium radiative lifetimes State

T (ns)

Method

Year

Author, reference

5s5pq~l 1.66 - 0.05 2.1 ± 0.3 1.9 ± 0.15

Hanle effect phase-shift beam-foil

1964 1970 1973

Lurio, Novick [172] Baumann, Smith [165] Andersen, SOrensen [166]

2390 --+ 40

double resonance

1964

Byron et al. [175]

5s5p3p~l

P. S. DotagE

224

Table 19. Mercury radiative lifetimes State

r (ns)

Method

Year

Authors, reference

1959 1967 1970

Barrat [177] N u s s b a u m , Pipkin [178] Dodd et al. [179]

1970 1971 1971 1974 1975 1982 1983 1985 1989

P o p p e t al. [180] Deech, Baylis [181] A n d e r s e n et al. [105] King, Adams [182] Osherovich et al. [183] Halstead, Reeves [184] M o h a m e d [185] van de Weijer, Cremers [186] Benck et al. [187]

1965 1967 1973

Lurio [191] Jean et al. [192] A n d e r s e n , S0rensen [166]

6s6p3p~l 118 ± 2 114 +- 14 117.4 -+ 1.0 120 117 127 120.0 115 122 116 120 125 119

± 2 -+ 1 ± 10 -+ 0.7 -+ 5 ± 2 ± 5 -+ 2 - 6 -+ 2

double resonance DCM D C M following magnetic field pulse DCM DCM beam-foil electron-excitation D C M electron-excitation D C M DCM electron-excitation D C M LIF LIF weighted m e a n (n = 10)*

1.31 1.36 1.27 1.33

± 0.08 -+ 0.05 ± 0.10 ± 0.05

Hanle effect Hanle effect beam-foil weighted m e a n (n = 3)

6s6p~

* Weighted m e a n calculated on the "best" ten results (see text).

Table 20. f-Values of some G r o u p 2b resonance lines Element, k (nm) Zn

f-value T e r m combination

from lifetimes*

213.856

4~So-4~P~1

1.47 - 0.03

307.590 228.802 326.106 Hg 184.950

41So-43P~1

1.9 1.42 2.0 1.16

Cd

253.652

51So-51P~1 51So-53p~1 6~So-611~1

61So-63p~

× 10 -4 -+ 0.04 × 10 -3 ± 0.04

0.0243 -+ 0.0004

Other f-values 1.45 ± 0.15 a 1.49 b 1.47 ¢

1.19 1.08 1.15 0.0255

-+ 0.02 d ± 0.05 ~ -+ 0.11 f --- 0.00058

* Lifetimes are weighted m e a n s from Tables 1 7 - 1 9 , except for Cd, for which x from Ref.[172] is used. a Atomic b e a m absorption [169]; b N R M C H F ( = nonrelativistic multiconfiguration Hartree-Fock) [170]; c Coulomb approximation [171]; a hook m e t h o d [190]; ~ resonance broadening [193]; f atomic b e a m absorption [194]; g hook m e t h o d [189].

An experimental -r for the 4 p i p ° state of 1.75 ns by the phase-shift method [165] is somewhat higher than the other lifetimes and has been disregarded in calculating an f-value. Theoretical values can also be cited: a Hartree-Fock result [170], and a semiempirical one [171]. Results are summarised in Tables 17 and 20. Cadmium [165, 166, 172-176]. Reported lifetimes of the 5s5plp~ state of Cd vary widely. The average of the three Table 18 lifetimes leads to "r = 1.9 ns and A -- 5.3 x 108s -1, as given in an NBS listing [19], while a value (f = 1.42) listed by SALOraAN [27] comes from Hanle effect studies of LtJeao and NovicK [172]; their result is almost certainly the most accurate, though it is disturbing that these three values vary so widely. LURIO and NoxqcK [172] noted that earlier experimental lifetimes were - 2 0 % longer than their own, although their result agreed well with the theoretical (Coulomb approx.) value of BAXES and DAMGAARD [173]. As noted above for Zn, a phase-shift value [165] is somewhat longer than the others and is probably subject to error. Lifetimes of longlived 43P and 53p states of Zn and Cd (Tables 17 and 18),

REVIEW

225

Table 21. Boron radiative lifetimes State 3s'

• (ns)

Method

Year

Author, reference

251/2 5.7 3.8 2.5 4.0

-+ 0.2 -+ 0.2 -+ 0.5 _+ 0.2

beam-foil beam-foil phase shift LIF

1969 1969 1971 1992

Bergstr6m et al. [198] Andersen et al. [199] Smith, Liszt [139] O'Brian, Lawler [195]

23.0 23.1 18.4 26.4 23.1

+ 2.0 -+ 2.5 -+ 0.8 -+ 1.0 -+ 1.2

phase-shift Hanle effect beam-foil beam-foil LIF

1966 1968 1969 1969 1992

Lawrence, Savage [196] Hese, Weise [197] Bergstr6m et al. [198] Andersen et aL [199] O'Brian, Lawler [195]

2p 2 2D3a

from double resonance measurements [174, 175], lead to ratios f ( 1 S - l p ) / f ( I S - 3 p ) determined from these lifetimes for Cd and Zn close to hook ratios reported by FILIPPOV [176]. Mercury [105, 177-194]. Lifetimes of the excited states 63p and 61p, giving rise to the 253.7 nm and 184.95 nm lines (to the ground state (61So)) are accurately known. The former line is one of the most often measured of all spectral lines; Table 19 summarises thirty years of lifetime measurements on 63p. As follows from Table 19, the lifetime of 63p is 119 ns. For the Table 19 mean -r, two values [105, 178] with much larger errors were neglected. Likewise, a value reported by BROSSELand Bn'rER [188] and overestimated [35] is ignored. The weighted mean lifetime (Table 19) is within the range of values allowed by the errors of essentially all the individual values. The 185 nm resonance line has an f-value nearly 50 times that of the intercombination line; its f-value is well established from a variety of "r and f measurements (Table 20). As implied by the data in Table 20, the ratio of f(1S-3p) to f(1S-1P) increases in the sequence Zn to Hg, as the j - j coupling increases. 2.1.5. Group 3a (B, Al, Ga, In, Tl) Resonance lines of Group 3a elements arise from transitions between the np2p ground state and the (n + 1)s2S and nd2D states. With increasing atomic number, the lines from the 2D states become stronger than those from the 2S states. For AI, the 308/309 nm lines are comparable in gf-value to the 394/396 nm lines, but with Ga, In, and TI, the lines from 2D absorb more strongly in flames and furnaces. Unfortunately for AAS, most lifetime measurements concern the 2S state (except for B- see below); f-values of resonance lines of Ga, In and TI between ground 2p and excited 2D states are defined with less accuracy than are those from the 2S states, because of uncertainties in both the lifetime and the branching fractions. Boron [195-200]. A recent paper by O'BRIAN and LAWLER[195] summarises results for B I from the LIF-hollow cathode beam method, and gives comparisons with earlier literature data. In their experiments, frequency-doubled pulses from the dye laser were Raman scattered, producing several anti-Stokes-shifted orders, each several thousand wavenumbers higher in frequency than the preceding one; this enabled lines in the far and vacuum u.v. to be excited, and levels up to -60,000 cm -~ were studied. Resolved level lifetimes (Table 21) were reported; comparison of these results for different fine structure terms within the same multiplet indicated that lifetimes were identical for J = 3/2 and J = 5/2 components of 2D multiplets, within the experimental error (reported as 5% or less). They pointed to wide variation among lifetimes measured previously by the beam-foil method [198, 199], while results by phase-shift [196] and Hanle effect [197] methods for the levels in common showed less scatter from their own. Their LIF results agreed well with the means from six earlier sets of results. Their f-values for B resonance lines of interest, from the lifetimes and the assumption that relative strengths within a multiplet are given by the LS coupling

P. S. DOIDGE

226

Table 22. Aluminium radiative lifetimes State

T (ns)

Method

Year

Author, reference

4s2Sz/2 7.05 6.3 6.9 6.94 6.8 6.78 6.6 6.71 6.92 6.80

-- 0.30 -+ 0.4 -+ 0.7 +- 0.35 -+ 0.3 +- 0.06 +- 0.3 -+ 0.14 +- 0.07 +- 0.15

phase-shift beam-foil phase-shift phase-shift LIF DCM LIF LIF LIF weighted mean (n = 9)

1968 1969 1971 1973 1977 1979 1981 1982 1986

Cunningham [205] Andersen et al. [206] Smith, Liszt [139] Marek, Richter [141] Havey et al. [207] Klose [208] Hannaford, Lowe [44] Duquette, Lawler [209] Buurman et al. [202]

13.6 +- 1.4

level crossing

1966

Budick [204]

13.7 13.4 13.1 13.6 12.3 13.1 16 14.0 13.4

phase-shift beam-foil phase-shift phase-shift LIF LIF LIF LIF weighted mean (n = 8)

1968 1969 1971 1973 1978 1981 1983 1990

Cunningham [205] Andersen et al. [206] Smith, Liszt [139] Marek, Richter [141] Selter, Kunze [122] Hannaford, Lowe [44] JSnsson, Lundberg (201] Davidson et al. [203]

3d2D (J = 5/2) (J = 3/2, 5/2) +- 0.40 -+ 0.3 -+ 2.0 -+ 0.8 +- 0.5 - 0.2 -+ 3 -+ 0.2

formulae (see also Grp 3a elements A1 through TI below) are reproduced in Table 27. Aluminium [45, 66, 122, 139, 141,201-209]. A number of lifetime measurements have been made for the 4s2S and 3d2D states. No less than nine lifetimes can be cited for the former, with very good agreement (the mean falls in the error range of nearly all these measurements). The 3d2D state is actually of more interest for atomic absorption analysis, since it gives rise to the strongest resonance lines (308.22; 309.27/ Table 23. Gallium radiative lifetimes State

r (ns)

Method

Year

Authors, reference

5S2Sv2 7.6 6.8 6.9 6.8 7.0 6.2 7.6 7.1 4d2D (J = 3/2, 5/2) 7.7 6.4 7.4 6.8 4dZD3/2 6.6 4.7 6.8 4d2I)5/2 6.9 5.8

-+ 0.4 -+ 0.3 -+ 0.5 + 0.5 +- 0.4 - 0.3 +- 0.8 - 0.3

phase-shift Hanle effect beam-foil electron-excitation DCM LIF laser photoionisation electron-excitation DCM weighted mean (n = 5)

1967 1971 1972 1976 1977 1984 1989

Cunningham, Link [66] Norton, Gallagher [211] Andersen, S0rensen [212] Erdevdi, Shimon [215] Havey et al. [207] Tursunov, Eshkobilov [216] Verolainen et al. [213]

-+ 0.3 +- 0.5 -+ 0.3 - 0.6

phase-shift beam-foil DCM electron-excitation DCM

1967 1972 1986 1989

Cunningham, Link [66] Andersen, S0rensen [212] Carlsson et al. [217] Verolainen et al. [213]

-+ 0.5 -+ 0.5 - 0.4

electron-excitation DCM laser photoionisation electron-excitation DCM

1976 1984 1989

Erdevdi, Shimon [215] Tursunov, Eshkobilov [216] Verolainen et al. [213]

+- 0.5 --- 0.3

electron excitation DCM laser photoionisation

1976 1984

Erdevdi, Shimon [215] Tursunov, Eshkobiiov [216]

REVIEW

227

Table 24. Indium radiative lifetimes State

r (ns)

Method

Year

Authors, reference

6s2S1/2 7.5 7.0 7.5 7.2 7.4 6.9 7.2 7.0

± 0.3 - 0.3 ± 0.7 ± 0.5 ± 0.3 - 0.3 -+ 0.2

phase-shift Hanle effect beam-foil electron-excitation DCM LIF electron-excitation DCM weighted mean (n = 6) semiemp, calc.

1967 1971 1972 1976 1977 1985

Cunningham, Link [66] Norton, Gallagher [211] Andersen, S0rensen [212] Erdevdi, Shimon [156] Havey et al. [207] Blagoev et al. [221]

1978

Gruzdev, Afanaseva [214]

5d2D3/2 7.9 ± 7.0 + 6.3 ± 6.9 ± 7.6 ± 7.1

0.5 0.4 0.5 0.5 0.6

phase-shift level crossing beam-foil electron-excitation DCM electron-excitation DCM weighted mean (n = 5)

1967 1969 1972 1976 1985

Cunningham, Link [66] Brieger et al. [220] Andersen, S0rensen [212] Erdevdi, Shimon [156] Blagoev et al. [221]

7.9 7.1 7.6 7.8 7.8 6.4

0.5 0.6 0.5 0.5 0.6

phase-shift Hanle effect beam-foil electron-excitation DCM electron-excitation DCM semiemp, calculation

1967 1969 1972 1976 1985 1978

Cunningham, Link [66] Zimmermann [219] Andersen, S0rensen [212] Shimon, Erdevdi [156] Blagoev et al. [221] Gruzdev, Afanaseva [214]

5d2Ds/2 ± ± ± ±

Table 25. Thallium radiative lifetimes State

"r (ns)

Method

Year

Authors, reference

7S251/2 8.7 7.4 7.6 7.65 7.45 7.55 7.7 7.61 7.8 7.4 7.57 7.4

± 0.3 ± 0.3 ± 0.2 -+ 0.2 + 0.2 ± 0.08 ± 0.5 --- 0.16 ± 0.3 ± 0.5 -+ 0.11

phase-shift double resonance Hanle effect phase-shift Hanle effect Hanle effect beam-foil Hanle effect LIF electron-excitation DCM weighted mean (n = 9) semiempirical calc.

1962 1964 1964 1967 1971 1972 1972 1973 1977 1977

DemtrOder [210] Gallagher, Lurio [222] Gallagher, Lurio [222] Cunningham, Link [66] Norton, Gallagher [211] Hsieh, Baird [224] Andersen, Sorensen [212] Rebolledo et al. [225] Havey et al. [207] Shimon, Erdevdi [226]

1978

Gruzdev, Afanaseva [214]

6.2 5.2 6.9 6.8 6.9 6.9 6.9

--- 1 ± 0.8 --- 0.4 -+ 0.5 -+ 0.5

level crossing Hanle effect phase-shift beam-foil electron-excitation DCM semiempir, calc. mean value (n = 4)

1964 1965 1967 1972 1977 1978

Gallagher, Lurio [222] Gough, Series [223] Cunningham, Link [66] Andersen, S0rensen [212] Shimon, Erdevdi [226] Gruzdev, Afanaseva [214]

7.6 ± 0.5 7.2 -+ 0.6

beam-foil electron-excitation DCM

1972 1977

Andersen, Sorensen [212] Shimon, Erdevdi [226]

6d2D3/2

6d2Ds/2

309.28 n m ) . A m e a n l i f e t i m e f r o m 7 e x p e r i m e n t a l r e s u l t s w e i g h t e d a c c o r d i n g to t h e e r r o r s ( T a b l e 2 2 - - m e a n = 13.5 ns) c o r r e s p o n d s t o f - v a l u e s as s h o w n ( T a b l e 27); t h e r e s u l t o f JONSSON a n d LUNDBERG [201] w a s d i s r e g a r d e d f o r this c a l c u l a t i o n , s i n c e it has a s o m e w h a t g r e a t e r s t a t e d e r r o r t h a n t h e o t h e r s . T h e 42S s t a t e , w i t h a m e a n l i f e t i m e o f 6.76 ns f r o m t h e r e s u l t s in T a b l e 22, g i v e s l i n e s w i t h f - v a l u e s as i n d i c a t e d

228

P . S . DOIDGE

Table 26. Measured branching fractions* in the first member (J = 1 / 2 - - J = 1/2) of the first line of the principal series np2P°--(n + 1)2S (Grp III elements)

Element

h (nm)

Quantum No. (n)

AI Ga

394.4 403.3

3 4

In

410.2

5

TI

377.6

6

Branching fraction, % 33 34_+2 34 36_+ 2 40 47.5 _+ 0.5 46_+2 43.5 _+ 1.5 43

Method, Reference anomalous dispersion ~ anomalous dispersion a atomic beam absorption h anomalous dispersion ~ atomic beam absorption b anomalous dispersion c relative emissiond relative emission and fluorescence ~ radiation trapping in level-crossingf

* LS-coupling value = 0.333. " Ref.[218]; b Ref.[ll7]; ~ Ref.[228]; o Ref.[222]; e Ref.[229]; ' Ref.[224].

(Table 27). As in the case of B, the corresponding f-values were calculated from the lifetimes assuming pure L S coupling. The accuracy of these f-values must be considered very good ( - 2 % ) , since the "r values are well defined and A1 is very close to pure LS in its coupling. More recent results by BUURMAN et al. [202] by LIF are only just within the range of a- values allowed for the 4s2S~ state from other LIF measurements by DUQUETTE and LAWLER [209] and HANNAFORD and LOWE [45], but other results [203] from the same laboratory for the 3d eD (J = 3/2, 5/2) states are discrepant with the HANNAFORD/ LOWE value (Table 22). Because there is no easy way of resolving the discrepancy, a weighted mean has been used to obtain the lifetimes listed after the experimental lifetimes for each state. The error, in any case, is not likely to be large. For the same reason, the f-values listed in these later papers [202, 203], based on their lifetimes, have not been used, and the values here (Table 27) are from a weighted mean "r and the relative intensities for pure LS coupling. The remaining elements of the group show increasing departures from LS coupling. Gallium [66, 117, 210-218]. For the last three elements of this group, reference is made to the generalised partial term diagram of Figure 1. The levels A, B, C, and D form a "bowtie" in the sense described by HUBER and SANDEMAN [31]. It is obvious that if, say, fax is known, from "r and branching ratio measurements on level X, as well as the ratio of the values fax and fay (or the Axa/Aya ratio)--this ratio can be measured accurately by hook methods, for example--then the value fay can easily be deduced. With the group IIIa elements, the transition from eD5/2 to eP~/2 indexed as h~z is the only one from z and measurement of the lifetime of 2D~/e therefore gives fb~ directly; relative f-values of lines from level B can be used to calculate f- or Avalues from the opposite side of the " b o w t i e ' , providing a consistency check. The available lifetime data for the 52S and 42D states are set out in Table 23. With the exception of -r values of TURSUNOV and ESHKOBILOV[216], the data are consistent. For 5zs, a weighted mean lifetime is calculated for all the -r values whereas for the 42D (J = 3/2) state, the CUNNINGHAM/LINK result [66] has been left out, because of comment by ANDERSON and SgDRENSEN [212], who considered that cascade processes might have led to overestimation of the phase-shift result. For the eD states, most measurements of ~" do not distinguish between J = 3/2 and J = 5/2 levels; only Refs [215] and [216] do so. Branching ratios for the 287.4 nm and 294.4 nm lines can be deduced from relative f-values reported by PENKIN and SHABANOVA [218], whose hook values are very good in relative terms, but about 10% in error in absolute terms. This can be seen by comparing f-values derived from the hook values (Table 27) for the 403.3 nm and 417.2 nm lines. The relative hook f-values correspond to branching fractions of 34% and 66%, respectively, very close to the LS values. From "r(2S) = 7.1 ns, and the hook ratio f( 403.3 )/f( 287. 4 ) = 2.46, the value f (287.4) = 0.285

REVIEW

229

c5

_=

c5 t~

÷1 ÷1 ÷1 ÷1 ÷1 ÷1 ÷1

÷1 ÷1 ÷1 ÷1 ÷1 ÷1 ÷i ÷1

÷J ÷1

+~

,~

d

E .o

O

8

i

,5

t~

¢,

r~ ¢q

¢.)

co .O

[-

H

~d

230

P.S. DOIDGE

(n+l)Zs

/

//

/

/

n2/D3z,

/ >'by'

//

nZD5/2

/ xbz

~bx

3/2

n2 p It 2

Fig. 1. Generalised schematic diagram of lowest 2p, 2S, and 2D levels of the Group 3a elements. follows. This is 10% lower than the Ref.[218] hook value (Table 27), which has a 10% estimated absolute uncertainty. Indium [66, 117, 145, 156, 212, 218-221]. For In, the f-values have again been calculated by combining a lifetime derived from the Table 24 data with relative hook f-values [218]. For the 6s 2S state, the lifetimes (Table 24) lead to a mean "r = 7.2 ns; a phaseshift lifetime of 8.53 - 0.09 ns reported by HULPKE et al. [145] is discrepant for an unknown reason. The least certain of the listed values, a beam-foil result [212], hardly affects the mean. According to CUNNINrHAra and LINK [66], lifetimes of the 2D state for J = 3/2 and 5/2 are the same, although the magnitude of the spin-orbit splitting should lead to different lifetimes; ANDERSEN and SORENSEN [212] reported that the lifetimes were appreciably different. Inclusion of the beam-foil result [212] for 52D (J = 3/2) affects the mean result by - 5 % (7.1 vs 7.4 ns). The absolute f-values (Table 27) follow from these lifetimes and relative hook f-values [218]; the latter were estimated as accurate to 2 - 3 % . The branching fractions from 62S now correspond to 36% and 64%, and from the mean "r(2S) -- 7.2 ns, and the ratio f(303.9 nm)/ f(410.2 nm) -- 2.50, the value f(303.9) = 0.313 follows. This is almost identical to the value (0.305) derived using the value for "r(52D, J = 5/2) = 7.6 ns and the ratio of fvalues of the 325.61 and 325.86 nm lines, together with r(52D, J = 3/2) = 7.4 ns; measured lifetimes for 62S and 52D then support one another. Thallium [66, 210, 222-229]. GALLAGHER and LURIO [222] gave a comprehensive discussion of the f-values of Tl lines and pointed to errors in earlier works; their results form the basis of some NBS listings (e.g. Ref.[19]). In particular, they pointed to hook measurements that were in error because of erroneous vapour pressure data. They used a mean value (-r = 7.5 ns) of the lifetimes of the 7s25 state from Hanle effect and double resonance measurements (Table 25), together with relative f-values for lines from 72S and 62D states to establish a set of A- and f-values for 25 lines; absolute accuracies for strong lines were estimated at - 5 % . As can be seen from Table 25, their lifetimes for 7s25 are in excellent agreement with more recent data: seven of these lifetimes have stated errors better than 5%, and a weighted mean of

REVIEW

231

Table 28. Silicon f-values f-Values X (nm)

Terms

Ji

Jk

Ref.[230]

Ref.[231]

Other values [232]

250.6897 251.6112 251.9202 252.8509

3p_3po 3p 3po 3p 3po 3p 3po

1 2 1 2

2 2 1 1

0.086 _+ 0.004 0.159 _+ 0.008 0.055 _+ 0.003 0.052 _+ 0.003

0.061 _+ 0.009 0.112 _+ 0.019 0.040 _+ 0.007 0.040 _+ 0.007

0.073 _+0.007 0.115 _+ 0.012 0.043 ___0.004 0.039 _+ 0.004

all (except [210]) agrees with the most accurate, that of Ref.[224]. The discrepant value of DEMTR6DER [210] was noted as being in error by CUNNINGHAM and LINK [66] and was discarded in calculating the weighted mean lifetime (Table 25); it was suggested by GALLAGNERand LURIO [222] that multiple scattering might cause an error in the phase shift and r. Branching fractions from the 72S state come from four experiments [222, 224, 228, 229] summarised in Table 26. Relative A-values for the transition to the ground state (h = 377.6 nm) correspond to branching fractions varying between 43% and 47.5%. Since the range amounts to some 10%, it may be supposed that the limiting accuracy of f- or A-values of the 377.6 and 535.0 nm lines (Table 27) is set by the accuracy of the branching measurements. When one turns to lifetime results for 6d 2D (Table 25), the situation is less satisfactory. There are now no results with better than 5% accuracy, and the levelcrossing results [222, 223] have p o o r quoted accuracies and disagree with three other results [66, 212, 226] having better quoted accuracies, and with a calculated lifetime [214]. Although accuracy of the f-value corresponding to the resonance line from 62D (J = 3/2) (h = 276.8 nm) assessed in this way seems to be no better than - 10%, there are reasons (from considerations of consistency between values derived by combining lifetimes and hook relative f-values) for believing that the value f(276.8 nm) = 0.29 is reliable; this problem is treated further in §2.2.2. 2.1.6. Group I V (Si, Ge, Sn, Pb) [66, 230-252] Tables 2 8 - 3 4 show lifetimes and r e c o m m e n d e d f-values for Si, Ge, Sn, and Pb. Silicon [230-232]. A study by O'BI~AN and LAWLER [230] has been used for the Si f-values listed here (Table 28). They combined branching ratios previously reported by SMITH et al. [231] with L I F lifetimes (cf. Ref.[195]) to give absolute A-values for 36 lines. Results of these authors [230] suggest revisions to the earlier f-values [231] on at least two grounds. First, the lifetimes used by SMITH et al. to establish their absolute scale show a greater scatter than do the L I F ones: in spite of good agreement of the average of all these lifetimes (by beam-foil, phase-shift, and LIF) with the newer values, individual lifetimes differed somewhat, as can be seen by comparison of lifetimes for the 4s3P~1 state (the 251.61 and 250.69 nm lines)---'r is some 30% higher in the beam-foil results used by SMITH et al. to establish their scale. (Table 28 lists fvalues of lines from 4s3p ° (J = 2, 1, 0).) Second, the SMITH et al. branching ratios Table 29. Germanium f-values* f-Values from various authors h (nm)

Terms

Ji

Jk

[19]

[237]

[238]

[240]

265.118 265.158 303.906 270.963

3p_ 3po 3p_3po ~D-1P ° 3p_3po

2 0 2 1

2 1 1 0

0.21 0.27 0.23 0.10

0.176 0.26 0.204 0.10

0.200 0.234 0.208 0.084

0.13 0.16 0.14 0.068

* Absolute values; Ref.[229] values scaled to a lifetime [232] for 3P~o.

[2331 0.218 + 0.273 + 0.237 + 0.102 +

0.033 0.040 0.036 0.011

P. S. DOIDGE

232

Table 30. Germanium radiative lifetimes State

r (ns)

Method

Year

Authors, reference

4p5s3p~z 6.0 ± 0.9 4.0 - 0.4 7.4 ± 0.6

phase-shift beam-foil electron excitation DCM

1967 1975 1989

Lawrence [234] Andersen et al. [236] Komarovskii, Verolainen [240]

3.7 ± 0.5 6.8 ± 0.7

beam-foil electron-excitation DCM

1975 1989

Andersen et al. [236] Komarovskii, Verolainen [240]

3.6 -+ 0.4 6.0 ± 0.5

beam-foil electron-excitation DCM

1975 1989

Andersen et al. [236] Komarovskii, Verolainen [240]

4.4 ± 0.7 3.9 ± 0.5 6.2 ± 0.6

phase-shift beam-foil electron-excitation DCM

1967 1975 1989

Lawrence [234] Andersen et al. [236] Komarovskii, Verolainen [240]

4p5s3p'~l

4p5s3p~

4p5slP~

Table 31. Tin f-values

h (nm)

Terms

J~

Jk

Branching fractions (BF) and f-values BF f-values [247] [241] [247] [241]

286.332 283.999 235.484

3p 3po 3p_3po 3p-3D°

0 2 1

1 2 2

0.27 0.22 --

0.25 0.29 --

0.209 ± 0.021" 0.230 ± 0.005 0.19 ± 0.02* 0.22 ± 0.02 0.25 ± 0.0251

* Value from Ref.[241] adjusted by - 2 % to mean lifetime of 3p~ (Table 32). t Value for h = 235.5 nm derived from f(286.3) = 0.209 and ratio f(235.5)/f(286.3) from Penkin and Slavenas [247].

Table 32. Tin radiative lifetimes State

r (ns)

Method

Year

Authors, reference

5p6s~ 6.0 4.5 4.84 4.75 4.2 5.0 4.8

--- 0.9 - 0.7 ± 0.26 ± 0.18 - 0.4 +- 0.5

phase-shift level-crossing Hanle effect Hanle effect beam-foil electron-excitation DCM weighted mean (n = 4)

1967 1967 1968 1972 1973 1985

Lawrence [234] Brieger, Zimmermann [243] deZafra, Marshall [242] Holmgren, Svanberg [244] Andersen [245] Gorshkov, Verolainen [246]

4.7 4.25 4.3 4.6 4.3

+ 0.7 ± 0.23 -+ 0.5 - 0.5

phase-shift Hanle effect beam-foil electron-excitation DCM weighted mean (n = 3)

1967 1972 1973 1985

Lawrence [234] Holmgren, Svanberg [244] Andersen [245] Gorshkov, Verolainen [246]

Hanle effect electron-excitation DCM

1972 1985

Holmgren, Svanberg [244] Gorshkov, Verolainen [246]

6s3p~

5d3D~ 5.5 ± 0.4 6.8 +- 0.7

REVIEW

233

Table 33. Lead radiative lifetimes State

T (ns)

Method

Year

Authors, reference

7saP'~ 5.75 ± 0.20 6.05 - 0.3 5.58 -+ 0 . 7 2 5.59 -+ 0.23 5.6 -+ 0.3 6.1 ± 0.5 5.75 --- 0.2

Hanle effect; levelcrossing phase-shift Hanle effect Hanle effect beam-foil electron-excitation DCM weighted mean (n = 6)

1966

Saloman, Happer [250]

1967 1968 1971 1973 1985

Cunningham, Link [66] DeZafra, Marshall [242] Garpman et al. [251] Andersen [245] Gorshkov, Verolainen [252]

6.08 --- 0.26 5.9 - 0.5 6.2 -+ 0.6

Hanle effect beam-foil electron-excitation DCM

1971 1973 1985

Garpman et al. [251] Andersen [245] Gorshkov, Verolainen [252]

7.3 ± 0.7

electron-excitation DCM

1985

Gorshkov, Verolainen [252]

Hanle effect electron-photon DCM

1971 1985

Garpman et al. [251] Gorshkov, Verolainen [2521

6d~

7s3p~ 7s3D~ 3.74 --+ 0 . 2 8 5.2 - 0.5

Table 34. Lead f-values f-Values h (nm)

Terms

Ji

Jk

Recommended

Other literature 0.39 --- 0.02° 0.212 - 0.003°; 0.197 --- 0.030~ 0.116 ± 0.003°

216.999 283.306

3p-3D° 3p_3po

0 0

1 1

0.35a 0.19 ± 0.02

368.347

3p_3po

1

0

0.093 --- 0.009

O.19d

Value derived fromf(h283.3) = 0.19 and the ratiof(h217.0)/f(283.3) = 1.84 [247]; b Ref.[247]; c Ref.[ll7]; d Ref.[3]; ~ Ref.[242]. a

(from c o m b i n e d emission and h o o k results, with the "bowties" m e t h o d providing links between i n t e r c o n n e c t e d sets of levels) were considered reliable sources of branching fractions for transitions f r o m levels below 3dlP~ (53,387 c m - 1 ) , but less reliable for lines from higher levels. G e r m a n i u m [233-240]. A - or f-values of the 265.118/265.158 n m line pair have been given in various papers [ 2 3 3 - 2 3 5 , 2 3 7 - 2 4 0 ] , with a wide range (about two-fold) in the values (Table 29). LOTRIAN et al. [237] m e a s u r e d relative intensities in a hollow cathode and an arc which, w h e n c o m b i n e d with the lifetimes (Table 30) m e a s u r e d by ANDERSEN et al. [236] (beam-foil m e t h o d ) , gave absolute f-values. As they noted, their gf-values are in g o o d a g r e e m e n t with relative h o o k values f r o m SLAVENAS [233], if the latter are put on an absolute scale using the lifetime for the ( u n b r a n c h e d ) 3p~ state (270.96 n m line). This p r o c e d u r e was also followed by POKRZYWKA et al. [238], who m e a s u r e d relative A-values in a wall-stabilised arc and put their value for the 303.91 n m line on an absolute scale by least-squares fitting to the ANDERSEN et al. lifetime for the ~P~ state. T h e LOTRIAN et al. values contain errors, e.g., for the branching fraction o f the 3p1-3P ~ transition (259.25 n m ) and gA(468.58 nm). SLAVENAS' f-values [233] were also used m o r e recently by KOMAROVSKn and VEROLAINEN [240], with the absolute scale set using D C M lifetimes for the 3p~ state. U n f o r t u n a t e l y , the beam-foil lifetimes used by LOTmAN et al. and those r e p o r t e d in Ref.[240] are almost two-fold different for the 4p5s3p states of interest (Table 30). F u r t h e r m o r e , there is no w a y of deciding b e t w e e n the "r values f r o m theoretical fvalues: although intermediate coupling calculations [234, 239] agree better with the Ref.[240] values, ab initio calculations [235] give values that are close to these in the dipole velocity a p p r o x i m a t i o n and close to the beam-foil lifetimes in the dipole length

234

P.S. DOID~E

approximation. Whether the lifetimes of 3po (j = 0, 1, 2) are about 7 ns or 4 ns is thus an unresolved problem, and the f-values are likely to remain uncertain until more lifetime data are at hand. Tin [234, 241-248]. Three studies [241,242, 247] have been used for f-values in Table 31. In Refs [241,242], lifetimes were used to scale relative values, in Ref.[242] only for lines from the first (5p6s)3p~ state, from their own Hanle effect value, and in Ref.[241] for u.v. lines from several levels, with an absolute scale from a mean of Hanle effect lifetimes [242-244]. It was noted [242] that relative A- and f-values from emission and hook measurements differed somewhat, although two sets of hook values [247, 248] agreed well, especially for the three strongest lines to 3p~, with the hook results of Ref.[247] used to give branching ratios. LOTRIAN et al. listed some of these lines and noted, especially for three common lines (286.3,300.9, 317.5 nm), that hook relative f-values [247] were higher than theirs. This does not, however, imply a higher branching ratio for the 286 line. As noted by LOTRIAN et al. [24], beam-foil [245] and phase-shift [234] lifetimes of 3p~ appear erroneous, whereas the Hanle values are more accurate and consistent, and confirmed by more recent DCM lifetimes [246] (Table 32). Table 31 lists values from Ref. [241], adjusted slightly ( - - 2 % ) to a weighted mean of four "r values [242-244, 246]. Lead [66, 242, 245, 247,249-252]. Lifetimes of the 6p7s3p~ state were listed by LOTRIAN et al. [249]. They combined average literature lifetimes with their own branching ratios, determined experimentally in a hollow cathode discharge run at low current; their results are used in recent NBS tabulations [19]. As in their study of Ge (see above) their branching ratios from the 6p7s3p~ state do not add up exactly to unity; it is not clear whether one or all of the values are erroneous. To -r values summarised by them are added other lifetimes [245,252] (Table 33) of the 3p~ and 3F~ states not used by, or not available to, them [249]. These extra data hardly affect the mean ,r. Apparently, "r(6p7s 3p~) is known with better accuracy than the branching fraction to the ground state [242]; Hanle effect lifetimes (Table 33) have stated accuracies of better than 5%, and agree well, but reported branching ratios for h = 283.3 nm vary from 27(+_3)% [250] to 32.4(+_2.6)% [249]. The dominant branching channels are to the 3p (j = 2, 1, 0) states and account for >99.5% of the transitions [249]. A ratio of 27% reported by SALOMAN and HAPPER [250] is from a fit of level-crossing data to coherence-narrowing theory and may be slightly underestimated. As deZAFRA and MARSHALL indicate [242], the implication is that the lifetime measurements yield no more accurate a result for the 283 nm line than the hook values of PENKIN and SLAVENAS [247] and they considered the latters' results to be " . . . p r o b a b l y . . . t h e most accurate experimental values listed." If the weighted mean lifetime from Table 33 is used with R = 30%, from Ref.[247], then f = 0.19 results, in good agreement with PENKIN and SLAVENAS' own f = 0.21, and L'Vov's f = 0.19 [3] (Table 34). The letter "D" listed beside NBS/NIST values [19] seems too conservative, and the uncertainty in the value f(283 nm) is probably less than +_ 10%. The lifetime of the 6d3D ° state (giving the 217 nm transition) is much less reliably established, with two reported lifetimes differing by - 3 0 % (Table 33). Strong coherence-narrowing noted by GARPMANet al. [251] in their level-crossing experiments may have reduced the accuracy of r measurements on this state. 2.1.7. Group V (P, As, Sb, Bi) Short wavelengths of the resonance lines and short lifetimes of the excited states limit the range of methods for lifetime measurement that can be used for these elements. Indeed, in considering the data for the Group V and VI elements, the striking fact is that for certain of them (e.g. As, Se) there is only one ~" value that allows determination of absolute f-values. In estimating errors of the listed (Table 35) f-values of Group V and VI resonance lines, sums of estimated relative errors from the branching and the lifetime measurements have been taken. Phosphorus [234, 253-256]. LAWRENCE[234] calculated A-values of the far UV lines of P at 213.5 nm; his tabulation is the basis for NBS listings (e.g. Ref.[19]). An

REVIEW

235

Table 35. Grp V f-values

h (nm)

Transition

Ji

Jk

f-Values R e c o m m e n d e d ref,

Other values

P P

213.547 213.620

3p 2 D ° - 4 s 2p 3/2 3p 2 D ° - 4 s 2p 5/2

3/2 3/2

0.014 -+ 0.002 0.129 -+ 0.016

[234] [234]

---

As As

193.696 197.197

4p 4 S ° - 5 s 4p 4p 4 S ° - 5 s 4p

3/2 3/2

3/2 1/2

0.139 -+ 0.025 0.073 -+ 0.014

[257] [257]

- - -

Sb Sb

217.581 231.147

5p 4 S ° - 6 s 4p 5p 4 S ° - 6 s 4p

3/2 3/2

3/2 1/2

0.124 -+ 0.016 0.068 + 0.013

[259] [259]

- --

Bi Bi

223.061 306.772

6p 4 S ° - 6 d 2D 3/2 6p 4 S ° - 7 s 4p 3/2

5/2 1/2

0.291 --- 0.047 0.118 - 0.012"

[262] [43,262]

- 0.146 - 0.018 [262] f +0.061

0.131~

~01039

[266]

* From lifetime [43] and branching ratio [262].

absolute scale for the intermediate coupling values was derived from measured phaseshift lifetimes [253]. Although radiative lifetimes of P have also been measured by CURTIS et al. [254] (beam-foil method) and by LIVINGSTOn et al. [255], (also beam-foil method), values were measured only for the 4s4P and 4s2D states. Their values agree well with LAWRENCE'Sfor these states, suggesting his value "r(4s2p) is reliable. The fvalues for lines from the 3p4S3/2 ground state were calculated by GANAS [256] by a semi-empirical (model potential) method and fair agreement with experiment reported. A r s e n i c [257, 258]. LOTRIANet al. [257] reported A- and f-values for ultraviolet lines of As, drawing on their own emission branching ratio measurements and a single absolute lifetime result (by beam-foil method [258]) of each state. They further checked for self-absorption in the source; this was reported to be negligible in the range of currents 5-11 mA. The f-values thus derived (Table 35) are somewhat higher than earlier values; e.g., for the 193.7 nm line, a value of A k i = 2.48 × 108s-1 (f = 0.139) was measured, compared to 2.0 x 10Ss-1 listed by WIESE and MARTIN [19]. The main limitation in the accuracy of values of LOTRIAN et al. seems to lie with the lifetimes, reportedly accurate to no better than - 10% in the beam-foil study [258]. A n t i m o n y [258-261]. GUERN and LOTRIAN [259] tabulated A- and f-values for a number of lines of Sb, using branching ratios measured in a hollow cathode discharge and mean values from absolute lifetimes measured by ANDERSEN et al. [258] (beamfoil), BELIN et al. [260] (Hanle effect), and by OSHEROVICHand TEZlKOV [261] (DCM). These lifetimes, and those from the first two groups in particular, agree well (within 10%) for the 6s4p3/2 state (for the 217.6 nm line), but the beam-foil and DCM results for the 6s4Pl/2 state (the 231.1 nm line) barely agree: the ranges of values allowed by the quoted errors of the methods just overlap. The corresponding f-values are shown in Table 35. As for As, the f-values are higher than earlier atomic absorption values; e.g.L'Vov [3] reported a value of 0.042 for the 231.1 nm line, while LOTRIAN et al. suggested that the discrepancy was caused by Sb2 formation in the furnace. (See, however, discussion in Section 2.2.1 following.) B i s m u t h [43, 66, 262-266]. GUERN et aL [262] have listed A-values for Bi, again by combining branching ratios and lifetimes [66, 263-265]. They used hollow cathode lamps, filled either with Ne or Ar and run at 3-5 mA to obtain branching fractions. The f-values they obtained are incorporated in more recent NBS compilations (e.g. Ref.[19]). Their value for the 306.7 nm line is almost double a previous value (f = 0.077) obtained in a graphite cuvette by L'Vov [3] by the absorption method. They attributed the difference to Bi2 formation in graphite furnaces. [But see §2.2.1.] The value f(306.7 nm) calculated by GUERN et al. from the mean of lifetimes listed by them is in any case a slight miscalculation (they used a nonexistent ~!). More recently, the lifetime of the 6 p 2 7 s 4 p 1 / 2 s t a t e was reported by CARLSSON [43], whose value (by laser/DCM) is apparently the most accurate of the various experimental T values. This value also a~rees well with the phase-shift result of CUNNINGHAMand

P. S. DOIDGE

236

Table 36. Group VI f-values f-Values

Se Se Te Te

h (nm)

Transition

J~

Jk

196.026 203.985 214.275 225.904

4paP-5s3S° 4p3p- 5s3S° 5p3p-6s3S ° 5p3p-6sSS °

2 1 2 2

1 1 1 2

Recommended 0A26 0.104 0.128 0.0098

- 0.018 _+ 0.016 +- 0.005 + 0.0003

ref.

Other values

[270] [270] ]273] [273]

---0.0018 [3]

LINK [66], whose work is among the most careful and thorough with this method, but is somewhat different from other results [264, 265]. The f-value for h = 306.77 nm that results from CARLSSON'Slifetime (,r = 5.66 +- 0.03 ns) and the branching fraction of 94.6% reported by GOERN et al. [262] is 0.118. Since the branching fraction obviously cannot be greater than 100%, the f-value is probably reliable to better than the +-_ 10% indicated in Table 35. This new value for f(306.7 nm) is close to that reported by RICE and RAGONE [266], by atomic beam absorption, but differs more from that of GUERN et al., because of the lifetime difference. Unfortunately, "r(6p26d 2D5/2) has not yet been measured with the accuracy of Carlsson's result for 7s 4P1/2. Hence f(223.06 nm) is less well defined. 2.1.8. Group VI (S, Se, Te) [267-273] Relative transition probabilities for the 38-3p lines of Se and Te have been given by (JBELIS and B~RZINSn [268], measured using emission methods, and compared with both theory and other experimental results. The departures from the predictions of LS coupling are particularly striking in the case of Te. Sulfur [55,267]. Experimental f-values of far UV lines of S near 180 nm were listed by MORTON [55] and A-values were calculated by AYMAR [267]; they are not listed here, since S is seldom measured by AAS. Selenium [268-272]. For Se there is apparently only one lifetime measurement [269] on which absolute f-values can be based. Absolute transition probabilities for Se have been reported by I~JBELIS and BERZINSH [270] from combined emission branching ratios and lifetimes, the latter given by DYNEFORS [269] who used the beam-foil method. The value reported for the 196.1 nm line is about twice as high as intermediate coupling results [271]. It is interesting that the f-value of 0.125 for this line is similar to the value that follows from the CORLISS/ BOZMAN listing [50] (f = 0.12). Accuracy of the results (Table 36) was reported [270] as being about -+ 12%. Agreement with other (ab initio) calculated values [272] is not especially good either. Tellurium [269,273,274]. Absolute A values were reported for Te by I~JBELIS and BgRZlNSH [273] by the same method as for Se. They used combined absorption and emission values, which were placed on an absolute scale using a lifetime for the 5p6sSS~ state measured by GARPMAN et al. [274] ('r = 71.8 +-- 2.2 ns), by O D R and level-crossing methods. This lifetime was considered more accurate than the beam-foil one reported by DYNEFORS [269] ('r = 60 --+ 18 ns). As a check on the consistency of the values, they calculated the lifetime for the state 5p6s 3S~ that corresponds to their relative values, from the lifetime for 5p6s 5S~, and the value thus obtained ('r = 2.31 -+ 0.08 ns) agrees very well with the beam-foil result (a- = 2.35 -+ 0.4 ns). The f-values (Table 36) derived from their results are also markedly higher than earlier experimental values, most notably for the 225.9 nm line, for which an atomic absorption f-value (f = 0.0018) [3] was just one fifth as large. 2.1.9. First (3d) transition series (Sc, Ti, V, Cr, Mn, Fe, Co, Ni) A- and f-values for the 3d row, Sc through Ni, have been listed by WIESE et al. [275-277]. Some of these data are, however, supplanted by later listings, as will be

REVIEW

237

Table 37. f-Values of some 3d Transition metal lines

h (nm) Sc 391.181 390.749 402.369 Ti 363.5462 364.2675 365.3497 Fe 248.3271 248.8143 252.2850 371.9935 Co 240.7249 242.4932 Ni 232.0026 232.5794 228.9982 341.4765 352.4541

Transition upper lower 4s a2Ds~2-4p y2F~/2 4s a2Da/2-4p y2F'js// 4s a2Ds/2-4p y2D~/2 4s a3F2-4p y3G~ 4s a3F3-4p y3G~ 4s a3F4-4p y3G~ 4s aSD4-4p xSF'J5 4s aSD3-4p xSF~4 4s aSD4-4p x~D~ 4s aSD4-4p zSF-~5 4s a4Fg/2-4p x4G~t/2 4s a4Fg/2-4p x4F~9/2 4s 3F4-4p 3G~ 4s 3F3-4p 3G~ 4s 3F4-4 p 3D~ 4s a3D3-4p z3P~4 4s a3D3-4p zaP~2

f-Values Recommended 0.547 - 0.028a 0.343 -+ 0.017a 0.400 -+ 0.020a 0.243 -+ 0.006* 0.219 -+ 0.005* 0.210 -+ 0.005* 0.543 -+ 0.054d 0.501 - 0.050d 0.203 -+ 0.018d 0.0412 -+ 0.0003f 0.38 - 0.08h 0.28 -+ 0.05h 0.69 --+ 0.076 i 0.37 -+ 0.037i 0.128 --- 0.013~ 0.124 -+-0.012~ 0.133 -+ 0.013~

Other results 0.48 -+ 0.03b 0.55 -+ 0.03b 0.36 -+ 0.02b 0.251 -+ 0.010t 0.227 -+ 0.009t 0.211 -+ 0.008t 0.56e

0.66c 0.70¢ 0.56c 0.20~ 0.16~ 0.14c

0.043g

--

--0.134 - 0.009J 0.141 -+ 0.010J

* Values from mean level -r [289] and branching ratios [291] of individual lines. t Values from Ref.[284], adjusted to log[f(h394.87 rim)] = -0.409 [289]. a Ref.[280]; bRef.[281]; c Ref.[275]; d Ref.[314]; e Ref.[277]; f Ref.[24]; g Ref.[315]; h Ref.[316]; i Ref.[317]; J Ref.[320]. shown in the following discussion for V I, and in the following, the WIESE et al. data are s u p p l e m e n t e d by, and c o m p a r e d with, n e w e r f-value m e a s u r e m e n t s . M e a s u r e d 3delement f-values up to 1977 were s u m m a r i s e d by HUBER [278]. S c a n d i u m [ 2 7 5 , 2 7 9 - 2 8 2 ] . A b s o l u t e transition probabilities have b e e n r e p o r t e d by LAWLER and DAKIN [280] and w e r e based on lifetime m e a s u r e m e n t s (by L I F ) [279]; they established their absolute lifetime scale to about 5% accuracy and indicated earlier h o o k m e a s u r e m e n t s by PARKINSON et al. [281] as likely to be of high reliability. Also to be considered are results by PENKIN et al. [282]: their lifetimes agree well (within a few per cent) for the longest-lived levels m e a s u r e d in both studies, but for the shorter lifetimes ( < 1 0 ns), there is a large and systematic disagreement: the PENKIN et al. values are f r o m 15% to 40% longer, the latter difference in the case of the shortest-lived levels. A l t h o u g h the LAWLER et al. values [279, 280] have b e e n accepted here, it would be desirable to k n o w the reason for the difference (e.g., w h e t h e r caused by unrecognised cascading in the D C M m e a s u r e m e n t s [282]). Titanium [ 2 7 5 , 2 8 3 - 2 9 1 ] . T h e critical compilation by WIESE and FUHR [275] was based on several data sources; later atomic absorption results [283,284] s u p p o r t e d their relative values. L a t e r lifetime data [285] suggested, h o w e v e r , a revision to the absolute scale. D C M lifetimes of several states of Ti (below - 2 8 , 0 0 0 cm -1) were reported by RUDOLPH and HELBIG [285]. T h e y r e c o m m e n d e d a scale change to the WIESE/FUHR values [275] by a factor of 0.90 (with respect to lifetime); renormalised values are n o w used in the m o r e recent N B S listings (e.g.[26]). M o r e recently, GREVESSE et al. [286] used the Ref.[285] lifetimes to set an absolute scale for the O x f o r d relative f-values [284]. E v e n m o r e recently, the RUDOLPH/HELBIG lifetimes have b e e n confirmed by SALIH and LAWLER [287, 288] and LOWE and HANNAFORD [289], by sputtering cell/LIF experiments; these later m e a s u r e m e n t s gave slightly i m p r o v e d accuracy and discrepancies in lifetimes for some longer-lived levels have now b e e n settled [288, 289]. It was shown [289] that the n e w e r lifetime data [287-289] allowed the uncertainty in renormalisation of the O x f o r d relative f-values to be r e d u c e d from 4% to 2.5%. For three lines of interest in A A spectrochemical analysis, f-values are listed in Table 37; two sets o f f - v a l u e s , derived by combining m e a n "r values [289] with branching ratios of WHALING et al. [290, 291] for individual lines, and f r o m the O x f o r d [284]

238

P.S. DOIDGE

values, renormalised to log(g/(394.87 nm)) -- -0.409 [289], are given. They compare very well, showing the high consistency of the various data [284, 286, 289-291]. The Table 37 f-values for these three lines amount to an increase of some 25% over the WIESE and FUHR [275] values. The branching ratio measurements [290, 291] seem to be of impressive accuracy: e.g. for h = 364.27 nm, a branching fraction of 84 -+ 1% was reported, while CORLISS and BOZMAN [50] indicate 80% for this line. V a n a d i u m [276, 285,292-299]. There are several strong lines of V I near 318.4 nm, all involving levels of the multiplet a4F (J = 3/2-9/2), the upper levels belonging to xaG°(J = 5/2-11/2); in flame or furnace AAS with low resolution monochromators, at least four of these lines can contribute to the absorption measured at 318 nm [292]. Wavelengths of these lines from the NBS (and other) tables are slightly different from values measured more recently [292, 293]; the Ref.[293] values are used here. Lifetimes and branching ratios reported by WHALING et al. [294] lead to f-values, tabulated previously [292], of these lines that are about twice as high as earlier results compiled by YOUNGER et al. [276], as shown in Table 38. Also included are results for two of these lines reported by DOERR et al. [295], from combined relative hook and emission measurements, the absolute scale provided by their own lifetime measurements (by LIF) of low-lying y6F° and y4D° states. DOERR et al. [295] did not list lifetimes for the x4G° states of the lines near 318 nm and the WHALINGet al. values, with --15% accuracy levels set by the short lifetimes measured (3.6 ± 0.5 ns) are the only reliable lifetimes on which to base absolute fvalues. DOERR et al. noted that there was a large scatter, as well as a systematic difference, of -0.14, on logarithmic ("dex") scale, between their log(gD results and the YOUNGER et al. ones. The latter values are derived mainly from relative f-values measured by KING [296] (atomic absorption) and OSTROVSKn and PENKIN [297] (hook method) with the absolute scale provided by curve-of-growth atomic absorption measurements [298] on five lines from low-lying (<26,500 cm -1) levels. As can be seen from Table 38, branching fractions inferred from MIE and RICHTER'Sresults [298] agree very well with those from WHALINGet al. There is a clear difference between the LIF lifetimes and earlier beam-foil results [299] for levels measured by both methods, the beam-foil values being generally somewhat longer. Since the LIF lifetimes [285,294, 295] agree well for levels in common, the WHALINGet al. values, given in a recent listing [26], are adopted here. C h r o m i u m [45, 141,276, 300-308]. YOUNGER et al. [276] averaged f-values of lines between y7po and z7P° states and the ground (a7S) state from several listings, with an absolute scale from lifetimes (mainly from Refs [141,302]). The lifetimes used for their absolute scale have been substantially confirmed by more recently published data [45, 303-305]. For y/z7P~, there are no other levels of appropriate parity and J for branching to occur, whereas for the other y/z7P states (J = 2, 3), there are very weak decays by spin change through other channels (a5S2 and aSD4). This means that lifetimes for z7P~ and y7p~ can be converted to exact f-values, while lifetimes for the other levels of these states can likewise be converted with minimal error, since the branching fractions exceed 99%. The more recent Oxford f-values [307] were scaled to the z7P~ level, using -r = 31.3 ns; this lifetime agrees almost exactly with the mean of the three most accurate of Table 39 (from Refs [45,302, 303]). Other Cr f-values listed by Tozzi et al. [308] do not include any of the Table 40 lines. The lifetimes for the three y7po levels deduced from the Oxford data [307] suggest that these lifetimes are essentially the same, in contrast to slight differences ( - 1 0 % ) implied by the Table 39 data. This similarity in "r(7p) is also apparent from LIF data of MEASURES et al. [303] for the three z7P° levels, for which a maximum variation in "r of only 3% was reported. The high relative accuracy of the Oxford data ( " . . . b e t t e r than 1%" [307]) and of the absolute "r(zTP~) implies accuracies better than 1.5% for f(425.435 rim), and better than 2.5% for other Table 40 lines. M a n g a n e s e [97, 141,276, 301,309-313]. For Mn, f-values of the resonance lines with y6p and z6P upper terms are essentially as given by YOUNGER et al. [276], who tabulated f-values for these two multiplets using values of OSTROVSKII and PENraN

REVIEW

239

C)

I

H

o.0 e~ ,-.i O

I +1 +1 ÷1 +~ I ¢q

oo ¢'4

II

_z t~

+1 ÷l ÷1 +1

O

t~

O

.=_

+1÷1+1÷1

,.d

.o rn [-.,

+~

P. S. DOIDGE

240

Table 39, Chromium radiative lifetimes State

r (ns)

Method

Year

Author, Reference

4p yTp~4 6.51 6.22 6.94 7.0 6.79

+- 0.9 --- 0.8 -+ 0.2 _+ 0.9

Hanle effect phase-shift Hanle effect DCM weighted mean (n = 4)

1966 1973 1977 1985

Bucka et al. [300] Marek, Richter [141] Becker et al. [302] Plekhotkin, Verolainen [305]

6.27 -+ 0.9 7.12 -+ 0.2 6.8 -+ 0.8 6.94

phase-shift Hanle effect DCM weighted mean (n = 3)

1973 1977 1985

Marek, Richter [141] Becker et al. [302] Plekhotkin, Verolainen [305]

6.00 _+ 0.6 6.34 -+ 0.2 6.5 -+ 0.8 6.29

phase-shift Hanle effect DCM weighted mean (n = 3)

1973 1977 1985

Marek, Richter [141] Becker et al. [302] Plekhotkin, Verolainen [305]

33.4 31.4 31.8 31.4 31.2 31.6 31.9 31.4

Hanle effect phase-shift DCM Hanle effect LIF LIF DCM mean (n = 3, from Refs.[45,302,

1966 1973 1975 1977 1977 1981 1985 303])

Bucka et al. [300] Marek, Richter [141] Marek [301] Becker et al. [302] Measures et al. [303] Hannaford, Lowe [45] Plekhotkin, Verolainen [305]

4p y7p~

4p y71~z

4p z7P] +- 5.0 -+ 2.9 -+ 2.5 -+ 0.8 _+ 1 +- 0.5 - 3.2

Table 40. Chromium f-values f-Values h (nm)

Terms

357.869 359.349 360.533 425.435

a7S3-y7P~4 a753-y7P~3 a7S3-y7p~ a7S3-z7P~

[307]* 0.366 0.286 0.205 0.111

-+ 0.008 -+ 0.007 -+-0.005 -+ 0.002

[306] 0.34 0.28 0.21 0.106

Other values [117] 0.30 - 0.03 0.24 - 0.024 0.18 -+ 0.018

[97] 0.34 0.27 0.19 0.10

* Recommended. [309] for the triplet ("multiplet 4") f r o m y6p, from BELL e t al. [310] for h = 403.076 nm, and from BLACKWELL and COLLINS [311] (for o t h e r lines of "multiplet 2 " - - a 6 S - z 6 P ° ) . O t h e r tabulated values were c h e c k e d f r o m lifetime data. HUBER [278] pointed to a rather wide difference b e t w e e n lifetimes f r o m laser m e t h o d s and those f r o m beamfoil measurements. T h e f-values m e a s u r e d with the O x f o r d long tube furnace were later reexamined by BOOTH et al. [312]. T h e y reevaluated the scale for normalising their relative f-values, using phase-shift [141] and laser/DCM [301] values. N o n e of the papers just listed, except the Ref.[309] used for the YOUNGER et al. listing, give values for multiplet 4, which includes the 279.48 n m line used in A A S . The Ref.[309] values for multiplets 2 and 4 were later listed by PENKIN [97]. Their value for h279.5 n m agrees well with that o b t a i n e d f r o m a beam-foil lifetime [313], if it be assumed that branching t h r o u g h X540.743 n m can be neglected; this assumption is justified by the low f-value ( = 0.0022) of this line [312]. T h e Ref.[309] f-values for h403.08 n m agree well with o t h e r values (Table 41), generally being within a b o u t 10%, so the Ref.[309] value for h279.5 n m is a d o p t e d here. I r o n [24, 277, 314, 315]. I r o n is o f particular importance for astrophysical studies and m u c h w o r k has b e e n d o n e on it; a s u m m a r y by FUHR e t al. [277] e m b o d i e s a

REVIEW

241

Table 41. Manganesef-values k (nm)

Terms

Ji

Jk

a

279.482 279.827 280.108 403.076

a6S-y6p °

5/2 5/2 5/2 5/2

7/2 5/2 3/2 7/2

0.57 0.42 0.29 0.056

a6S- yrP °

arS- yrP° a6S- z6P°

b 0.58 0.42 0.29 0.056

f-Values d

e

f

--. . . . . . 0 . 0 5 7 0.061

-. . 0.059

0.56 ± 0.02

c

--

References: (a) Ostrovskii and Penkin [309]; (b) Penkin [97]; (c) Booth et al. [312]; (d) Bell et al. [310]; (e) Marek [301]; (f) Pinnington, Lutz [313].

critical evaluation of a very large body of work. Their values are based mainly on emission results from wall-stabilised arcs, which were placed on absolute scales using lifetimes. FUHR et al. established their absolute scale using the lifetime for zSF~ which has been established to ca 1% accuracy from at least six independent measurements. (For a summary of these, see WIESE [24].) In evaluating f-values for the resonance lines 248.3 and 248.8 nm (see Table 37), a further comprehensive study by O'BRIAN et al. [314] has been consulted. These authors used combined lifetime results (by LIF) and branching ratios (from Fourier-transformed spectra of a hollow cathode or an inductively coupled argon plasma); lifetimes as short as 2 ns were measured with good ( - 5 % ) accuracy. For the 248.3 and 248.8 nm lines, values listed by FUIJR et al. and by O'BRIAN et al. are very similar (Table 37) and a mean of the two values has therefore been chosen. The likely error seems to be <-+ 10%. It is noteworthy that an early value [315] for k372 nm agrees well with values from lifetimes (Table 37). C o b a l t [277, 316]. Extensive f-values for Co lines from low-lying levels have been listed by CARDON et al. [316]. This study, like that on Si (cf. above), combined relative hook and emission ratios and lifetimes with the "bowtie" technique [287], giving large sets of consistent absolute f-values. This method, also discussed by Sram-I et al. [231] and HUBER and SANDEMAN [31], permits the indirect measurement of lines joined by common upper or lower levels. These results were already used by FUHR et al. for their critical compilation [277] and f-values for two resonance lines are listed in Table 37. Nothing on Co appears to have been published since. N i c k e l [277, 317-321]. The listing of Ni f-values by FUHR et al. [277] is based in large part on a comprehensive study by HUBER and SANDEMAN [317], by combined hook and furnace absorption measurements, with an absolute scale from lifetimes and branching ratios. Subsequently, BECKER et al. [318] checked the absolute scale from DCM lifetimes, reporting consistently good agreement with Ref.[317] values; they stated that " . . . t h e gf-values of HUBER and SANDEMAN. . . . . should be regarded as the most reliable data available for transition probabilities in neutral Ni at this time." Ni f-values were also measured by DOERR and KocK [319] who combined hook and emission measurements in a graphite furnace on lines from 280 to 620 nm (upper levels <36,000 cm-1), lifetimes [318] giving an absolute scale. They reported that no systematic errors were apparent in comparing groups of lines with common lower levels. Because of the good agreement of the various results, the HUBEP,/SANDEMAN data are used for the Table 37 values. The Oxford group [320] also scaled their absorption/-values to D C M lifetimes [318] and argued for a relative accuracy of 0.7% in their results. More recently still, BERrESON and LAWLER [321] extended LIF measurements to 57,000 cm -1 and recommended a small change (3.5%) to the scale of Ref.[320]. The average Ref.[321] lifetimes differ by < 1 % from those of Ref.[318] (individually to <5%), and remove much uncertainty (0.09 on log (dex) scale) in the absolute scale of Ref.[317]; the residual (2cr) uncertainties in log g f-values 0.05-0.1 (on log scale) reflect mainly relative uncertainties, and f s (Table 37) are of modest accuracy.

242

P.S. DOIDGE

2.1.10. Second and third Transition Series (Y through Pt) [50,322-353] Many of these elements are refractory and therefore not often determined by AAS (none of the 5d period has yet been determined by absolute AAS methods), and this involatility long made f-value measurement difficult; it is by no means coincidental that good f-values for solar abundance determinations have been lacking until quite recently. Indeed, accurate r values were not measured for many 4d and 5d elements until the 1980s. For a bibliography of lifetime papers, see Ref.[48]. Yttrium [322-325]. Lifetimes of Y levels have been reported by GORSHKOV and KOMAROVSKn [322], by RUDOLPH and HELBIG [323], and by HANNAFORDet al. [324]. These papers list T values that agree very well for listed levels in common, but disagree with earlier results for some levels by the beam-foil and Hanle methods. HANNAFORD et al. [324] also listed large numbers of values of gf, using their branching ratios. A more recent paper [325] lists even more extensive sets of values of gf for lines in the 340-620 nm region, from relative f-values derived from shock tube spectra. The absolute scale was provided by the HANNAFORD et al. lifetimes. The f-values for sensitive AA analysis lines, from Ref.[324], are given in Table 42; the 412 and 414 nm lines have much less uncertain f-values than the 410 and 407 nm lines, on account of greater uncertainties in branching ratio for the latter lines. Zirconium [46, 326-328]. BI~MONT et al. [326] noted that their newly measured fvalues were often somewhat different from the Ref. [50] values, leading to a considerably revised solar abundance; their data are used for an f-value given here (Table 42). RUDOLPH and HELBIG [327] and DUQUEa'rE et al. [328] also measured (by LIF) levels up to 29,002 cm -~. The RUDOLPH/HELBIGdata tend to be in good agreement with the BII~MONT et al. and DUQUETrEet al. values, except for a few levels; the disagreement (up to 30%) was discussed by HANNAFORDand LOWE [46]. For the 360.1 nm line, an f-value is derived here from the slightly revised lifetime (= 6.9 -+ 0.3 ns) of the latter authors [46] for the 29,002 cm -1 level and a branching ratio (92%) derived from Ref.[3261. N i o b i u m [209,329-331]. Lifetimes in Nb were reported by KWIATKOWSKI et al. [329], from LIF data, and g(-values were deduced from branching ratios inferred from Ref.[50]. A single line of interest for AA analysis was studied by them (Table 42); the Table 42 gf-value is derived from the value r(25200 cm -1) = 8.1 ns [329, 330]. Other strong AA lines were not reported, but their f-values could be derived from lifetimes given by DUQUETrE and LAWLER [209], from the Ref.[50] data. The lifetimes of Ref.[209] agree very well with those of KWIATKOWSKIet al. and of RUDOLPh and HELmG [331]. M o l y b d e n u m [332]. An extensive compilation of Mo A-values by WHALING and BRAULT [332] fills a gap in the literature [19]. Their results, from LIF lifetimes and branching ratios measured on a FTS instrument using both hollow cathode and ICP sources, were, at the time of publication (1988), the most comprehensive set of A values for any element. The listed f-values (Table 42) are derived directly from Ref.[332]. R u t h e n i u m [50, 333, 334]. SALm and LAWLER [333] list Ru lifetimes (by LIF) that are the basis for an f-value given here (Table 42). Neither they nor BII~MONTet al. [334], however, listed branching ratios or f-values for the sensitive AA lines (349.9, 392.6 nm). NBS Monograph 53 [50] is therefore used to derive here a branching ratio for the 392.6 nm line (Table 42), but Ref.[50] does not list all branches from zSG~ (for the 349.9 nm line). Lifetimes reported in Refs [333,334] agree well, as expected. R h o d i u m [329,335, 336]. Studies by KWIATKOWSKIet al. [329] and LAWLER et al. [335, 336] furnish the f-values given here (Table 42). The method in these studies was again LIF for the lifetimes, while branching ratios are from Ref.[50] in Ref.[329] or are new data in Ref.[336]. DUQUErrE and LAWLER[336] noted that their own branching ratios were generally in agreement with those deduced from Ref.[50], except for lines prone to radiation trapping. Lifetimes from the two groups [329, 335] agree very well (<5%) but only KwImKOWSm et al. give data for the sensitive 343.5 nm line; the branching fraction (from Ref.[50]) is almost 100% and probably quite accurate.

REVIEW

243

o

+1

©

O O O

e. ,-.i t~

O tL e~

oooo

o

~

~. ~. ~.

+1 ÷1 +1 +1

+1

+1 +1

+1 +1 ÷1

O

8 ~2

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

,a, 'O 'O

8 O

r-i

:-2

e~

[.,

[-., t¢3 ~

W3 ~ t'q~

e~

. . . .

"2.

• e-]. ~.

u,?. ~. ~ . , q .

~.

m.

P. S. DOIDGE

244

Table 43. Palladium radiative lifetimes State

-r (ns)

Method

Authors, reference

5p lp,~, 4.99 +-- 0.35 4.8 -+ 0.3

Hanle effect LIF

Baumann, Liening [338] Bi6mont et al. [339]

8.7 - 0.9 7.46 -+ 0.32 7.7 --+ 0.4

Hanle effect Hanle effect LIF

Budick [337] Baumann, Liening [338] Bi6mont et al. [339]

4.89 -+ 0.40

Hanle effect

Baumann, Liening [338]

5p ~P'i'

5p 3D~

Palladium [50, 337-340]. Lifetimes of levels of the 4d95p configuration in Pd have been measured by the Hanle effect [337, 338] and by LIF [339]; values of "r for the ~P~ and 3p~ states agree well (Table 43). BII~MONTet al. [339] used branching ratios from Ref.[50] and lifetimes to obtain f-values. If, however, Ref.[50] data are used to derive a branching ratio for the 244.7 nm resonance line, a very low value (5%) for branching to the ground state results; Ref.[50] indicates stronger branching through the 325.16 nm and 343.345 nm channels. The value f(244.7 n m ) = 0.029 resulting from R = 5% seems far too low. Similarly for the 247.6 nm line used for absolute AAS [11], the BF from 3D~ implied by the Ref.[50] data is - 1 2 % ; correspondingly, f(247.6) -- 0.052 (f = 0.10 from Ref.[50]). In fact, recent measurements by LARKINS [340] suggest that branching through the 244.7 nm channel is about five times as strong as indicated by Ref.[50]; the latter results were apparently distorted by radiation trapping and the corresponding value is then f --- 0.15. Similarly for the 276 nm line, f = 0.057 (from r [339] and Ref.[50] intensities) differs from an absorption value (f = 0.036 [117]). Until more measurements are made, these remain open questions. Hafnium [330, 341]. The source for the f-values listed here is a paper by DUQUE'ITE et al. [330]. Unfortunately, their studies [330, 341] report lifetimes only for levels up to 31,611 cm -t, thus excluding the most sensitive lines for AA: sensitivities of the two lines in Table 44 are a factor of 5-10 worse than for preferred lines [53, 54]. They indicated [330] the importance of "missing" infrared branches (especially for decays from zSF levels), not listed in Ref.[50], which extends only up to -900 nm. Tantalum and Tungsten [305,335, 342-345]. Absolute A-values for both these elements have been listed by DEN HARTOG et al. [342]. Again, the method was LIF on a hollow cathode beam, with branching ratios from Fourier transform spectrometry on the hollow cathode spectra and with checks for "missing" infrared branches. Earlier "r results for W are listed in Ref.[343]. For Ta, the lifetime measurements [335,342] do not go sufficiently high in energy to furnish gf data for sensitive AA lines [53, 54]: for Ta, the important lines for astronomy do not coincide with the AA resonance lines. Apparently, Ref.[50] remains the only source of values for these Ta lines, and these values are of doubtful accuracy, since SALm et al. [335] indicated limitations arising from energy-dependent errors. Apparent lifetimes deduced from Ref.[50] A-values were exaggerated, with respect to their own, towards lower energy. This may indicate a temperature measurement error in CORLISS and BOZMAN'S arc. A plot of the ratio of lifetimes (direct LIF to inferred Ref.[50] values) vs level energy would yield corrections to the Ref.[50] apparent lifetimes, from which branching ratios [50] (not subject to this type of error) would yield absolute A-values (cf. Ref.[342]), but such a correction would be crude and possibly subject to fairly large error. The f-values of 43 W lines were listed by OBBARIUSand KOCK [345] with an absolute scale from preliminary "r values of z7D~ and z7P~ s t a t e s of KWIATKOWSKIet al. [344] (from LIF on a thermally evaporated atomic beam). As the former paper [345] shows, agreement of the various f-values from Refs[342, 345] is quite good. Some new

REVIEW

245

lifetimes were also given by DEN HARTOC et al. [342]; a comparison with results for W levels in common with those measured by PLEKnOTKIN and VEROLAINEN[305] shows good agreement for levels with "r shorter than -1800 ns. None of the lifetime papers [305,342-344] give lifetimes for the 39,183 cm -1 level (for the sensitive 255.135 nm line); nor do the arc measurements of OBBAPOUSand KocK [345] extend that far towards the UV. Table 44 gives f-values for some less sensitive resonance lines of W. Rhenium [50, 346]. The first direct lifetime measurements for nine levels of Re were made by DUQUEI"rE et al. [346]. Their lifetimes, together with branching fractions derived from the Ref.[50] intensities, gave f-values for certain lines (Table 44), as derived by them. The astronomically interesting lines used to revise the solar Re abundance also include the strongest resonance lines used for AAS (Table 44). Osmium [50, 347]. Lifetime data were combined with Ref.[50] intensities by KWIATKOWSKI et al. [347] to give values for two lines (Table 44). Accuracy for the 330.2 nm line is probably better than for h305.87 nm because of many fewer branches for the former. Iridium [348]. GOUCH et al. [348] have reported LIF lifetimes in Ir. Their values differed considerably from those inferred from the Ref.[50] A-values, indicating systematic errors in the Ref.[50] values, although the exact nature of the error was unclear. From their lifetimes and branching ratios, f-values for two of the strongest lines used in AAS analysis are given in Table 44. As can be seen from Table 44, even the most sensitive Ir resonance lines have quite modest f-values. Platinum [349-353]. Accurate Pt wavelengths are of relevance for studies with the Hubble Space Telescope and three recent studies [349-351] of Pt list intensities, wavelengths and terms. GouGH et al. [352] have reported an f-value for the 265.95 nm resonance line, from LIF lifetimes and Ref.[50] intensities. A study by READER et al. [349] indicates a higher branching fraction (77%, compared to 68% in Ref.[50]) and this later study may well be more accurate. From this "r and the BF of READER et al., f(265.95 n m ) = 0.12 (Table 44), but the error may exceed - 1 0 % , because of the uncertain BF. For other lines of Pt, results are from a branching study [353], and lifetimes of GOU~H et al.; BRs of these lines (Table 44) agree fairly well in Refs[353] and [349], so the f-values are probably more reliable than for h265.9 nm.

2.1.11. Lanthanum and lanthanides (La through Lu) Most of the abundance data for astronomy of lanthanides are from ion lines, except for some neutral atom lines seen in sunspots [354]. Absolute AAS determinations are limited to Er, Eu and Yb [10, 16]. Refs [355-357] summarise studies by PENI~IN and colleagues of lanthanide f-values. Ref.[355] lists lines in the first and second spectra of Nd, Eu, Gd, Tb, Dy, and Er, with absolute scales for hook f-values from DCM lifetimes. Relative f-values for Nd, Sm, Eu, Gd, Dy, Tm, and Yb are also listed in another paper from the same group [356], with absolute values for a few lines from hook/absorption and lifetime (DCM) measurements. The values of PENKIN and colleagues remain the only data for some of these elements and more recent work is summarised by KOMAROVSt
246

P . S . DO1DGE

+1 +1

0

•

.

,.~-

~

+1 +1

E

66

I ~6

~6~

66

+1 +1

+1 +1 +1

~6

~ 6

~oo

E E

,

,

~

~

~.

77 *77 ~*?~

8

e~ o e~

+1

e¢ Ill

o6~

.

.

.

.

.

.

.

.

.

.

.

.

oca~

Z<<

REVIEW

247

Table 45. Lanthanum and ianthanide f-values*

Term combination

Energies (cm -~)

f-Value (recommended)

550.134 418.732 494.977 602.4193 583.1912 520.1369 520.0406 520.0108 495.137 513.344 492.4521 463.4208 429.674 511.716 459.403 462.722 466.188 368.413 407.870

2D3t2 - y2D~/2 2D3/2 - w2F~/2 2D3/2 - y21~1~ (J = 4) (J -- 5) ° (J = 4) (J = 5) ° (J = 4) (J = 4) ° (J = 4) (J = 3) ° (J = 4) (J = 4) ° 4I~/2-(J = 9/2) 4Ig/2-(J = 11/2) 514-5K ~ 514- 5H~ 7F6 - 7G~ 7F4 - Sl:~ asS~/2-YaP9/2 asS~/z-ySPw2 asS.~r2-ySPs/2 6s z 9D~- 6s6p9p 3 6s 2 9D~- 6s6pgD5

0-18172.4 0 - 23875.0 0 - 20197.4 3196.61-19791.74 3196.61-20338.89 0-19220.36 2437.63-21661.54 3100.15-22325.16 0-20190 0-19474 0-20300.875 0 - 21572.61 4020.66- 27287.58 2273.09- 21809.74 0-21761.26 0-21605.17 0-21444.58 533-25044 0-27136

0.24 0.23 0.16 0.12 0.085 0.032 0.031 0.023 0.31 - 0.04 0.18 ± 0.004 <0.40 -+ 0.10~: <0.21 -+ 0.05¢ <0.32¢ <0.133¢ 0.63 -+ 0.04 0.49 -+ 0.03 0.35 -+ 0.02 0.26 0.18

421.172 410.384 400.796 386.285 371.792 374.406 398.799 555.6466 451.857

5Is-(SIs)('P1) g 411 5/2- (J = 17/2) ° 6s 2 3H6-6s6p(J = 7) ° 6s 2 3H6-6s6p(J = 5) ° 2F~7/2-268899/2 ZF~7/2- 267017/2 6s 2 1So-6S6 p 1P~l 6s 2 1So-6S6 p 3Py1 6s 2 2Da/2-6s6p2F~5/2

0-23736.6 0 - 24361 0-24943.3 0-25880.3

h (nm)

La

Ce

Pr

Nd Sm Eu

Gd Tb Dy Ho Er

Tm Yb

Lu

(no listing)?

0-25068.23 0-17992.01 0-22124.70

0.54 + 0.05 0.44 0.48 0.26 0.35 0.195 1.36 -+ 0.06 0.0159 - 0.0004 0.067 -+ 0.003

* See text for references. t no recommended value. ¢ Maximum values only (see text).

[50] and, with lifetimes from Ref.[359], give the f-values for several lines given in Table 45. Cerium [361,362] A paper by BISSON et al. [361] is the source for the f-values listed here (Table 45). The method involved lifetime determination (by time-resolved pumping to the ionisation continuum) and emission branching ratio measurements. The lines 463.232 and 566.997 nm, known to be sensitive for A A analysis [362], did not have values listed by BISSON et al., because of blending. Other lines like k583.19 nm and h602.42 nm (Table 45) are likely to be comparably sensitive in A A to these, if the combination of gf-value and Boltzmann factor is considered [362]. Praseodymium [357, 363]. Lifetimes and f-values in Pr were listed by GoRsnrov and KOraAROVSKn[363]. Lifetimes were by DCM and no branching was reported from the levels investigated. For two sensitive A A lines, f-values are listed in Table 45. Neodymium [355, 357, 364-366]. Table 45 lists f for two lines of Nd, taken from Refs[355,364], again based on the combined lifetime/hook method. Lifetimes from these studies agree well with those of MAREK and STAHNKE[365], who also used DCM detection but with laser excitation. These f-values [355] are to be regarded only as upper limits, since the study by BLAISE et al. [366] indicates existence of weak infrared branches, with several from the 20,300.88 cm -1 level. Samarium [356, 357, 367-370]. Although low-lying levels of Sm I have been closely studied (see HANNAFORD and LOWE [367] and references therein), the higher energy levels giving the lines of greatest interest to A A S (the 429.7 and 476.0 nm resonance lines---see Table 45) are much less studied. The f-values in Table 45 are from delayed coincidence/hook results of PENKIN et al. [356, 368, 369]. Lifetimes reported by

248

P.S. DOIDGE

BLAGOEV et al. [368] agree very well with those reported in Ref.[367] for four levels in common, (all below 20,713 cm-1), as do those of GORSHKOVet al. [369], suggesting that the DCM results of Ref.[368] are reliable for all the levels studied there. The relative f-values tabulated by PENKIN and KOMAROVSKII[356] have been converted to absolute ones using a conversion factor (= 1.8 × 10 -4) from Ref.[368]. Again, fvalues in Table 45 are upper limits because of known weak infrared branches [370]. Europium [355-357, 371-374]. Lifetime values reported in Ref.[371] were combined with hook data [372] to give absolute f-values. Lifetimes of ySp states reported by PENKIN et al. [355] and by MEYER et al. [373] (by DCM) agree within 5%. As indicated by FECHNERet al. [374], branching was neglected in Ref.[371], although for the 459 nm line (Table 45) this neglect appears justified. The value here is a mean from lifetimes in Refs[371,373]. Gadolinium [355-357, 375,376]. The f-values in Table 45 are, again, from PENKIN et al. [355, 375], from hook relative values [and DCM lifetimes]. Combined errors of the relative f-values [355] and lifetimes were stated [355] not to exceed 25%. (One may note that the f-values deduced from individual lifetimes and branching ratios (inferred from the hook values [356]) can differ by more than 30% from the Ref.[355] values, e.g. for ~368.413 rim). Recently, Gd f-values revised from emission BRs were reported [376]. Terbium [357,377-379]. GogsrlgOV et al. [377] reported Tb lifetimes (DCM) but these lifetimes were not converted to f-values, apparently because of a problem with incomplete classification of lines; the spectrum is complex and apparently not yet analysed completely [378]. "Semiabsolute" values of CORLISS [379] are erroneous [377]. Dysprosium [355-357,380-384]. Lifetimes measured by HOTOP and MAREK [380] and GORSHKOVet al. [381] have been converted to an absolute f-value for the 421.17 nm line (Table 45). Since the "r values from these studies [380, 381] agree well (identically for the 23,737 cm -1 level), it is perhaps surprising that for other lines originating from the ground state whose absolute f-values were derived [355, 381] by combining the lifetimes [381] with relative hook values [382], rather modest accuracies (10-30%) were claimed [381]; an accuracy of -+10% has been assumed for the 421 nm line (Table 45). Holmium [50, 357]. Besides Ref.[50] for three lines, Ho f-values are given by KOMAROVSKn [357]. An f-value for one sensitive line is given in Table 45 from the latter work [357]. Erbium [355-357, 365, 384-386]. Absolute f-values of the 400.8 nm line (Table 45) were reported by PENKIN et al. [355, 384] from DCM lifetimes and relative hook fvalues. Their lifetimes for the 24,943 cm -~ level agree well with those of MAREK and STASNKE [365] (DCM with laser excitation) so that there follows a m a x i m u m value of 0.50 for f(400.8). This is much lower than a calculated (Hartree-Fock) value by COWAN [385] (f = 1.31), and an absorption result (f = 0.72) [386], which must both be erroneous. It is worth noting that the lifetimes [365, 384], if accurate, set upper limits to the A-values of three lines (400.8, 411.1,386.3 nm) that are much less than the values given by FUHR and WIESE [26]; these latter should be regarded as possibly overestimated. Thulium [356, 357,387-390]. BLAGOEVet al. [387] listed relevant lifetime data and gave a revised conversion factor for the calculation of absolute f-values for Tm I from earlier relative hook values [388], as was done in Ref.[356]. Comparisons with earlier lifetime data largely support the BLAGOEVet al. values, although there is a two-fold difference between their value for the 26,8899/2 cm -1 level and those from Hanle effect experiments [389, 390]. Nevertheless, the Ref.[387] data are used for the Table 45 f-values; they are almost identical to those given earlier [356]. Ytterbium [97, 356, 357, 391-398]. The lifetimes of several excited states in Yb I were measured by BLAGO~Vet al. [391] by the DCM. Earlier lifetimes of the 6s6plP~ state by the Hanle effect [392, 393] and beam-foil method [394] are in fair agreement with theirs (Table 46). This state gives the strong 398.799 nm resonance line and the mean of Hanle effect and beam-foil lifetimes, shown in Table 46, with a 100%

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249

Table 46. Ytterbium radiative lifetimes State

• (ns)

Method

Authors, reference

6p ~P~ 5.50 - 0.25 5.2 -+ 0.6 5.12 + 0.12 5.8 + 0.8

Hanleeffect beam-foil Hanleeffect electron-photonDCM

Baumann, Wandel [392] Andersen et al. [394] Rambow, Shearer [393] Blagoev et al. [391]

827 --+40 850 -+ 80 820 - 20 875 --- 20

Hanle effect electron-photonDCM Hanle effect photon-photonDCM

Baumann, Wandel [392] Burshtein et al. [398, 391] Rambow, Shearer [393] Gustavsson et al. [395]

6p 3p~

branching fraction, give f = 1.36-+ 0.06. This compares fairly with a value (f = 1.12 --+ 0.04) previously listed by PENKIN [97] (by simultaneously measuring hooks and absorption--see section 2.2.1). For the weaker intercombination resonance 15-3p (h = 555.6 nm), a lifetime (Table 46) reported by GOSXAVSSONet al. [395] can probably be regarded as accurate [396] and is used for the Table 45 f-value: confirming lifetimes come from Refs [391-393]. L u t e t i u m [26, 50, 357, 399-402]. Branches in Lu were identified from KLINKENBERG'S analysis [399], though he listed little more than 100 lines. Lifetimes in Lu were reported by GORSHKOV et al. [400]. It is to be noted that the A-value from Ref.[26] for the line 451.86 nm is consistent with three lifetimes [400-402], the excited state (6s6p2D~/2) presumably having one dominant branch, while A-values of other lines (e.g. 337.65 nm) indicate lifetimes (e.g. for the 29,608 cm -1 (2F~5/2) level) that are much shorter (by - 4 0 % ) than the values of GORSHKOV et al. Confirmation of the latters' results would be desirable. In view of this uncertainty about the lifetime values of Ref.[400], f-values for more sensitive A A lines than the 452 nm one have not been listed, though they can be derived from these lifetimes; e.g., a value f(337.7 nm) = 0.24 follows from a BF of 99.5% [26] and a lifetime of 7.2 ns [400]. 2.1.12. A c t i n i d e s Only one element from this series is considered here. U r a n i u m [403-413]. A listing by BIENIEWSKI [403] gives comprehensive f-values in U for lines below 360 nm, while a study by HENmON et al. [404] lists values for lines above 380 nm. The former's study (by the atomic beam absorption method) is more relevant for A A analysis, and the values from both are to be compared with those listed by CORLISS [405] and the lifetimes of KLOSE and VomT [406]. The latters' lifetimes, by electron-excitation/DCM, were corrected for radiation trapping, and are presumably fairly accurate, since their value for the level 16,900 cm -1 (the 591.5 nm line) agrees well with independent measurements [45,407-409] and a correction [45] to the value for this level reported by CARLSON et al. [407], by time-resolved optical pumping to the photoionisation continuum. There is, however, considerable disagreement between BmNIEWSm'S f-values and those for common lines listed by KLOSE and VOIGT; f-values for the latter are derived from relative f-values [410, 411] and DCM lifetimes. A comparison for two resonance lines, including the most sensitive for A A analysis [53], is shown in Table 47. Clearly, further study is needed to resolve these discrepancies. The listing of CORLISS uses a lifetime, apparently erroneous, for the 27,887 cm -1 level to set the absolute scale: KLOSE and VOlGa" [406] discuss accurate measurement of this lifetime. CORLISS'S emission (arc) results can be compared with the absorption values (see Table 47). If his A-values are scaled using the value (= 10.9 -+ 0.8 ns) [406] for this level, the Table 47 (column 6) values are found; these differ from the others [403,406]. There are obvious problems with the scale of CORLISS'S values, as may be seen from

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Table 47. Some gf-values for uranium gr h (nm)

Ji

Ju

Energies(cm t)

a

b

c

358.4877 591.540

6 6

7 7

0- 27887.0 0-16900.4

0.56 --

2.2t 0.12

1.6 0.35- 0.36

* a = Ref.[403]; b = Ref.[405]; c = Ref.[406]. t Scale of Ref.[405] adjusted using revised lifetime [406] for normalisation. the f-value for the 591.540 nm line calculated from his gA value and the value deduced from the lifetime of the 16,900 cm -1 (7M7) level, established at 200 -+ 10 ns from no less than five measurements [45, 406-409], together with a branching ratio of 0.86-0.90 [405,406]. mki values of (0.43-0.45) × 107s-1 result from these values, compared to 0.156 × 107s-1 from Ref.[405]. The f-values of HENRION et al. [404] are also too low by this reckoning. By contrast, absorption results of BIENIEWSKI [403, 412], derived from two thermodynamic systems, for the 358.49 nm normalising line ( f - - 0 . 0 4 1 [412] or 0.043 [403]) are somewhat lower than a value (f = 0.17) derived from ,r(27,887 cm -1) = 10.9 ns [406] and a branching fraction of - 0 . 8 2 [405]. (The 358.488 nm transition dominates decays from this level.) It is possible that infrared decays may make up a much larger fraction of decays from this state, but confirming evidence is still lacking. BIENIEWSKI [403] pointed to the difficulties in determining branching ratios in so complex a spectrum as that of U, since infrared branches, though individually weak, may contribute a large fraction to the total branching; with no less than 1,600 levels [413] and an average of 250 U I and U II lines per nm in the ultraviolet and visible [410], the task of minimising blends and identifying branches is formidable. Thus, absorption values [403,412], derived from two different thermodynamic systems, seem preferable.

2.2. DISCUSSION 2.2.1. Overview o f the f-values In the three decades since publication of the CORLISS/BOZMANmonograph [50], great advances have been made in the field of f- and A-value measurement. Some of the milestones can be briefly mentioned. Lifetime measurements have given highly accurate A values, especially for unbranched radiative decays. Since the 1960s, problems with lifetime measurements have been understood and overcome, thereby opening the door to a wealth of accurate measurements. For example, studies of LURIO et al. (e.g. Refs[137, 146, 172] etc.) led to better understanding of the effects of radiation trapping on Hanle effect lifetimes and allowed accurate measurement of the Group 2a and 2b resonance terms. Especially impressive has been the progress made in the last 15 years on lifetime measurement. Beam-laser measurements by the Berlin and Kaiserslautern groups on Li, Na, and K [60, 80], and data of the Lund group for Na, Cu and Ag [43, 100, 124] push the accuracy of experimental lifetimes, and thus of f-values, to better than one per cent. For the group 2a and 2b elements, accuracies of resonance line f-values are generally defined to somewhat better than ± 5 % , mainly from Hanleeffect lifetimes: the Hanle effect is ideally suited to measurement of short lifetimes [Eqn (4)]. For other elements, excited state lifetimes accurate to better than -+5% exist in the literature, mainly from LIF data, but accuracies of many of the f-values derived from these lifetimes are limited by the branching ratio measurements. For two of 67 elements surveyed (Ta, Tb), no reliable data for strong A A lines could be found. Nevertheless, there remain a few elements for which resonance line f-values are apparently defined with somewhat worse accuracy than the <-+ 10% possible with the lifetime/branching ratio method. These are Ge, Pd and some of the lanthanides.

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Lifetime results for the 4s3p ° levels of Ge from two sets of measurements differ widely. Further work is needed on Ge. (A discrepancy between meteoritic and solar Ge abundances by up to 1.8-fold has been noted [22]). The lifetime method is just one (though far the most important and effective) way of getting around the problem of detemining N. Other methods, such as the magnetorotation/absorption [75, 94] and absorption/hook [143] methods, rely on the circumstance that absorption, magnetic rotation and anomalous dispersion are all related to the complex index of refraction. Magnetic rotation in the wings of absorption lines yielded fairly accurate results for Na, K, and Rb [75]. In the 1950s, PENmN and coworkers [143] developed a method for determining f, independently of column density (NO by exploiting the fact that expressions for hook separation and equivalent absorption width can both be written in terms of Nil. The latter can then be eliminated, and the remaining expression contains only the radiation damping; from the hook separations and equivalent widths, the damping constant and thus f follow. Their results [143, 163,414] of Group 2a (Mg, Ca, Sr, Ba) resonance line f-values are, however, considerably lower than modern values from lifetimes (e.g. Ref.[127]); the differences are much bigger than the combined errors estimated for the respective techniques. Except for Mg (as discussed in the Element data section), for which the hook method gave problems, apparently because of Mg2 formation, the reason for this discrepancy is not clear. Lumo et al. noted [146] that the accuracy of the combined method depends on the validity of the assumption that in measuring the equivalent width, the absorption profile is a Lorentzian in the line wings at more than three Doppler widths from line centre, whereas this assumption had never been tested. Although f-value measurement from lifetimes has a long history--methods summarised in the Introduction are based on techniques originating in the 1920s and early (historical) data have been summarised by MITCHELL and ZEMANSKY [36]---the widespread measurement of lifetimes did not begin until the 1960s. Indeed, some early lifetime values are of poor accuracy, such as a Hanle-effect value for Ca (41p~) [415], underestimated because of undercompensation for collisions. The most accurate fvalues are now based on lifetimes. Before lifetime methods began to dominate, however, variants of the atomic absorption method furnished data of good accuracy. It is worth considering briefy atomic absorption methods. As a method for measuring f-values, the atomic beam absorption method came to prominence in the late 1940s (e.g.[296]) and efforts with it have persisted until recently; the work of KING, LAWRENCE, BELL and others is noteworthy here. The method is subject to errors that arise from uncertainties in the beam density determination (often effected by depositing the beam on a glass slide and weighing it), either because of adsorption of gaseous impurities or desorption or incomplete adsorption of the atoms, besides which the vapour temperature must be known. As well, the equivalent width measurement may be subject to error, through the well-known problems of measuring the complete line profile [31]. The equivalent width (proportional to Nil) is easily underestimated, because of the effects of Lorentz broadening on the line wings [31] and some errors in atomic absorption f-values may be traced to this problem. On the other hand, atomic absorption measurements can furnish data of very high (<0.5%) relative accuracy, as the work at Oxford of BLACKWELLand colleagues shows (e.g., Ref.[307]). There are often discrepancies between older literature f-values from atomic absorption measurements and more recent values from lifetimes. One example is Cu: BELL and TuaBs [101] argued that underestimated f-values in atomic beam absorption experiments may have been caused by inaccuracies in measured beam density. Other studies have indicated discrepancies between values derived from lifetimes and absorption for Group V and VI elements, and tried to explain the differences in terms of molecule formation. This possibility was explicitly mentioned by LOTmAN et al. in their studies of Sb [259] and Bi [262], and by ISJBELIS and BF-RZINSH, in studying Te [270]. The former authors suggested that neglect of dimer formation in absorption or emission measurements leads to underestimation of f-values. This possibility was considered to

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be especially important in accounting for the difference between their results and those of L'Vov [3], from a graphite cuvette. This argument for molecule formation [259, 262, 270] is not wholly convincing, however, as it is at odds with data reported by FRECH et al. [416], from high temperature equilibrium calculations; FRECH et al. included dimers of Bi, Sb, and Te in their calculations and concluded that the degree of dimer formation in carbon furnaces was negligible above 1100 K for Bi, 1500 K for Te, and 1600 K for Sb. (A temperature of 1900 K was used in Ref.[3].) The real reason for the discrepancy remains unclear. Problems with branching ratio measurements can be briefly mentioned. Great advances have also been made in this area, as some recent literature indicates. For example, a paper on branching transitions in Ar I and Ar II [417] indicates that accuracy of the relative intensities is now good enough to allow use of such ratios as secondary intensity standards for spectrometer calibration over a wide range of wavelengths. Much of this work has been facilitated by Fourier Transform Spectrometry in conjunction with the National Solar (Kitt Peak) Observatory, the Fourier transform method being ideally suited to the near-simultaneous collection of spectral information from many lines, thus overcoming one problem with branching ratio measurement on hollow cathode discharges, that of source drift. The CORLISS/BOZMANintensities [50] are known to be subject to at least three kinds of error: "wavelength-dependent" [51], "excitation-dependent" [52], and "intensitydependent" (radiation trapping) [336] errors. Branching ratios from a given level are, of course, not dependent on the second of these kinds of error, and rough correction can be made for the first [51]; for these reasons Ref.[50] remains a useful source of branching ratios (BRs) for some elements, especially in 4d and 5d periods, even if BRs inferred for strong lines can sometimes be in error because of radiation trapping [336]. An example of the care needed in using Ref.[50] to derive BRs is provided by Pd. The f-values for three strong lines derived from the lifetimes and Ref.[50] intensities are quite evidently in error, since much the lowest gf-value is thereby given to the line (244.7 nm) which is the most sensitive in AA analysis [53, 54]. Further work is needed on Pd. A detailed discussion will now be made of TI, since the discussion in §2.1.5 indicated the desirability of establishing more accurately the value f(h276.8 nm). 2.2.2. Accuracy of the TI h276.8 nm (62p~/z-62D3/2) f-value The case of T1 is interesting, because of a suggestion [419] that it may be a good reference element for flame atomic absorption; there is also evidence [11] that it is completely atomised in graphite furnaces. Although there exist accurate f-values for the first lines of the sharp series, derived from the 72S lifetime and branching ratios, as well as values for r(6ZD), the latter values are less extensive and consistent than for 7zS; as well, there is apparently no branching ratio, from emission measurements, for the 276.8 nm line. Moreover, the f-value of the 276.8 nm line is given a confidence of only "C" [+(10-25)%] in some NBS compilations (e.g.Ref.[19]). It will be suggested here that greater confidence can be attached to the value f(276.8) = 0.29 than implied by the NBS listing, from considerations of internal consistency among lifetimes when the ratios of hook f-values for lines with common lower levels are used. Reference is made to Fig. 2. These lines and levels define a "bowtie" (see Ref.[290]), with the proviso that spectral information required for that technique (i.e. emission and absorption measurements on all four lines of the bowtie [290]) is incomplete. First, one obtains a value f(~377.6) from the mean weighted "r from Table 25 and the mean branching fraction. From the four values in Table 26, a mean BF of 45% follows and f(377.6) = 0.127. Then, from the ratio off(377.6)/f(276.8) = 0.43 reported by PENIaN and SHABANOVA[228] the value f(276.8) = 0.295 follows. This is almost identical to the value of 0.29 given by both GALLAGVlER and Luvao [222] and in Ref.[228]; the slight difference arises because in the analysis in Ref.[222], a different value (0.461), originally reported by PROKOF'EV and FILIpPov [227], for the ratio f(377.6)/f(276.8) was used, together with slightly different branching fraction and "r(/S),

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62D

5,2

62D 3,2

l'z

=E

vo

62p ° ~z

62po Fig. 2. Schematic energy levels and wavelengths of the strongest absorption lines of Tl I.

while in the measurements of Ref.[228], the value f(377.6) = 0.125 was used, which is slightly less than the value derived from this analysis• Such small differences can be resolved by noting, first, that the values for f(377.6nm) =0.125 and f ( 5 3 5 . 0 n m ) = 0 . 1 3 5 given in Ref.[224] imply that -r(72S) = 8.2 ns which is - 1 0 % longer than the experimental ~" vdlue-(7.55 ns, from Ref.[224]). The value f(535.0 nm) = 0.156 follows from the latter "r and 55% branching to 62p (J = 3/2). Second, the PROKOF'Ev/FILIPPOVvalue f(377.6 nm)/f(276.8 n m ) = 0.461 was considered [228] to be erroneous because of an experimental defect. (PENmN [97] later used the mean of these two values when tabulating T1 f-values.) If the PENKIN/ SHABANOVAvalue is accepted as the more accurate one, then consistent f-values follow. From the other side of the "bowtie" (Fig. 2), the value "r[62D(j = 3/2] can be combined with A(352.94 nm), from the hook ratios of Ref.[228], to yield A(276.8 nm), by difference. Since the latter transition dominates the branching, large variations in A(352.9 nm) affect the value of A(276.8 nm) only slightly. From ,r = 6.9 ns (Hanle effect results in Table 25 are neglected for reasons discussed in the element data, (§2.1.5)), and f(535.0 nm)/f(352.9 nm) = 3.72 [228], A(352.9 nm) = 2.25 x 107s -1, and, by difference, A(276.8 nm) = 1.23 x 108s-~ and f = 0.28. As a third calculation, the lifetime of 62D (J = 5/2) inferred from f(535.0 nm) = 0.156 and the hook ratio [228] f(351.9 nm)/f(535.0 nm) = 2.29 is 7.8 ns, in fair agreement with the Table 25 values. The data further support the supposition that the lifetime difference between the J = 3/2 and J = 5/2 terms of 62D is definite. The accuracy of the value f(276.8 nm) seems still limited by the lack of relative intensity (branching) data but as the foregoing discussion indicates, a good accuracy (<-+10%) can probably be placed on that value and the confidence limit implied by NBS listings (e.g.[19]) is almost certainly too conservative. PENKIN and SHABANOVA [228] concluded that the relative f-values of nZP(J = 3/ 2)-nED(j = 3/2,5/2) were very close to theoretical expectation (for LS coupling); nevertheless, the wide splitting of the ground 2p term (-7800 c m -1) m e a n s that great care is needed for accurate temperature measurements (necessary for their method) and such results must be interpreted with care.

254

P.S. DOIDGE

2.2.3. Application to some problems in Graphite Furnace Atomic Absorption Analysis It is of interest to consider these data in light of the requirements for standardless (absolute) atomic absorption analysis. This problem in spectrochemical analysis exactly parallels that in astronomy: solar abundance measurements, for example, can only be made from accurately known f-values and atomic absorption analysis benefits greatly from the advances in measurement accuracy of these data for astronomy. (The summary by BII~MONT and GREVESSE [22] of the relevance of f-values to abundance studies, though dated by the many data since made available, can nevertheless be read with profit by spectrochemists using f-values.) The f-values recommended here are in some cases considerably higher than values used in studies of atomisation efficiencies by ETAAS [10-12]. This is especially the case for Mg (see discussion below), Si, and V. For V, f-values of some resonance lines from lifetimes and branching ratios are some two-fold higher than earlier values (see §2.1.9); as with many other 3d, 4d and 5d elements for which revised data have become available, the newer f-values are preferred as they lead to excellent agreement between solar and meteoritic abundances [294]. It would be worth analysing more carefully the data of Refs [10-12] to assess the effect of the more accurate f-values on apparent atomisation efficiencies with ETAAS. The results above for Mg, Si, and V suggest somewhat lower efficiencies than previously reported for these elements [11, 12]: e.g., the figure for Mg would drop to - 6 7 % , instead of -103% [11]. The efficiencies of - 1 0 0 % originally reported may then have been optimistically high, suggesting that atomisation of these elements in graphite furnaces is actually incomplete. The author agrees with MAGYAR[418], who suggested that the standardless method, while unlikely to replace the calibration graph (if only because the method with calibration graph is so deeply entrenched in analytical practice), does nevertheless serve as an invaluable check on the validity of the method for a particular element and as a means for optimising experimental conditions. The notion of reference elements is also worth pursuing. This was discussed by ALKEMADE et al. [419]; their emphasis was on elements for flame AAS analysis and among the elements they mention, Ag, Cu, and T1 seem the most promising. This is because the various optical characteristics (f-value, damping (a) parameter, h.f.s. component separations etc.), taken as a whole, are almost as well defined for these elements as for the alkali and alkaline earth elements, whereas problems of incomplete atomisation or ionisation are less important for Cu, Ag, and Tl. Nevertheless, ALKEMADE et al. pointed to a grave problem for Cu, which is that in using the most accurate values for f(324.7 rim), atomisation in the air-acetylene flame still seemed incomplete. Beyond noting that the differences in chemistry of a flame and that of the graphite electrothermal atomiser imply that such results for Cu in the flame do not of necessity prove incomplete atomisation in the furnace, the treatment here must be limited to some remarks on the applicability of the concept to the graphite furnace. It seems worth finding whether there are elements that are sufficiently completely, or consistently, atomised in graphite furnaces to serve as reference elements over useful temperature ranges. As MANNING and SLAVIN have noted [420], Ag is sufficiently well-behaved, in terms of the consistency of response (characteristic mass) from one setup to another to warrant consideration. The h.f.s, of Ag resonance lines is well known [107, 117, 124], as apparently also is collision broadening by Ar [3,421], so that determination of Nl should be straightforward. (It should be emphasised that accurate f-values still only allow measurement of Nl and some problem will exist in absolute GFAAS with knowing the length, l, of vapour; naturally, this may be different to the furnace geometric length. Progress in determining l might be achieved with longitudinally isothermal tubes [12, 13].) As well, careful study of such a small group of supposedly well behaved elements, together with three-dimensional atom distributions, should point the way to correction of anomalies and put the absolute furnace method on a

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surer basis. It is the author's belief that progress towards this goal will only be attained by study of those elements for which the most accurate physical data are available. There are also many reliable f- and A-value data for singly ionised atoms. Although these are more relevant to plasma emission studies, ratios of ionic to atomic f-values have been used in atomic absorption analysis to measure atom-to-ion ratios (e.g. of Ba [11,422]). Lifetimes in Ba II have been reported in several papers: KELLY and MATHUR [423] summarised them. We assume here a value "r(6p2p~/2) = 6.24 ns, with less than 1% error. The branching fraction for the 455.5 nm line is from recent work [424], and is smaller than an earlier value [425] (70% vs 74%). The revised value is f(455.4) = 0.70. Recent work by a density-independent method of optical nutation [426] gave f = 0.66 -+ 0.06, but suffers from only fair accuracy. Since the ion-to-atom ratio is proportional to f(atom)/f(ion), then from these new f-values for Ba I [f(553.6) = 1.64] and Ba II [f(455.5) = 0.70], and the f-values used previously, e.g. by L'vov [11], a slight revision upwards, from 0.35 to 0.38, of the degree of ionisation of Ba in the furnace reported in Ref.[11], is inferred. 2.2.4. Determination of relative Ni f-values by flame atomic absorption One can mention also the use of flame atomic absorption to measure relative fvalues. This has been done by many workers, like L'vov [427], and comments here are restricted to Ni, mainly because Ni has been used as the thermometric species for two-line temperature measurement. The ratio f(232.00 nm)/f(341.477 n m ) = 3.1 was derived by L'vov [11], and used with the absolute value f(341.477) = 0.12 to obtain a value for the 232.0 nm line. This ratio differs appreciably, however, from that reported by HUBER and SANDEMAN(= 5.5; see Table 37) for the same line pair. Both are strong lines and the hook method, used in Ref.[317], should therefore give reliable results. On the other hand, relative values measured by VAN DEN BROEK et al. [428] for the 228.998/232.579 nm pair agree well with HUBER and SANDEMAN'S values: gf(232.58)/ gf(229.00) = 2.24 from Ref.[428], while the ratio is 2.18, as reported in Ref.[317]. (In connection with L'vov's absorption f-value measurements [3], it is interesting to note that his furnace values for Pb (283 nm) and T1 (276.8 m) coincide exactly with the fvalues recommended from this analysis.)

2.2.5. Remarks in summary This survey was undertaken to find out whether the accuracy of f-values is limiting for the determination of atomisation efficiencies in AA analysis. It is clear that, apart from a few elements for which better data are needed, it is not. Resonance line fvalues are, on the whole, well characterised. The large majority of these data come from lifetimes and branching ratios, attesting impressively to the power of this method. Except for a few lines, there are insufficient grounds for now holding, as did WILLIS [7], that the accuracy of these values is limiting. On the other hand, other kinds of data, like collision damping ('a-') parameters, may be limiting. Summaries of aparameter and hfs data (also needed for modelling concentration curves in AAS [429]) seem more scarce; to the author's best knowledge, the only compendia of recent data are those by ARIMONDO et al. [430] of alkali hfs data and the collision cross sections and shifts for Groups la and 2a atom/noble gas pairs listed by ALLARD and KIELKOPF [431]. Apparently, any other data remain in the primary literature. (One may also note, pace LOVETr [432], that hfs data exist for some elements that were noted [432] as having incomplete information available: e.g. for Sr [147] and Te [433], both from level-crossing experiments.) 3. CONCLUSIONS

The lifetime/branching ratio method furnishes f-values of high accuracy for many atomic resonance lines, including the sensitive lines used for spectrochemical analysis. Several exceptions, requiring further study, are suggested by the survey (Ge and Pd being notable). It is concluded that the accuracy of f-values is not limiting for

256

P.S. DOIDGE

application of these data to determination of atomisation efficiencies by atomic absorption analysis. Acknowledgements--The author wishes to thank particularly Dr P. Hannaford, who read a first draft of this survey almost in its entirety and offered many suggestions for improvement. Thanks are also due to him for drawing attention to some recent papers, to P. L Larkins, for kindly communicating results on Pd, to Prof. A. Gil'mutdinov for supplying Reference [25], and to J. B. Willis for helpful conversations.

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