Experimental Studies on Electronic Configuration Mixing for the Even-Parity Levels of Gd I Using Isotope Shifts Recorded in the Visible Region with FTS

Abstract

Electronic configuration (4f⁷6s²6p + 4f⁷5d6s6p + 4f⁷5d²6p) mixing studies in the high even-parity energy levels of Gd I spectrum have been carried out on the basis of isotope shift (IS) Δ𝜎^156,160 data recorded in 49 spectral lines partially in the visible wavelength region on Fourier Transform Spectrometer (FTS) and the relevant spectral line IS data available in the literature. We employed “Sharing rule” to the experimentally observed level isotope shifts (LIS) of the even-parity levels for finding the percentage composition of each configuration being mixed. An FTS spectrum of Gd I in the region of 365–495 nm acquired employing the highly enriched Gd isotopes in liquid nitrogen cooled hollow cathode lamp (HCL) as a light source and photomultiplier tube as the detector. The studies of altogether 48 even-levels have revealed that amongst the 20 high even parity levels assigned previously to >95% 4f⁷5d6s6p configuration, 10 levels have agreed very well whereas 7 have exhibited large contribution of 4f⁷5d6s6p configuration compared to 4f⁷5d²6p configuration and 3 levels have equal contribution of 4f⁷5d6s6p and 4f⁷5d²6p configurations. Out of 8 unassigned levels, 6 have dominant 4f⁷5d6s6p configuration compared to 4f⁷5d²6p configuration and the remaining two have dominancy in 4f⁷5d²6p configuration.

1. Introduction

Gadolinium occupies position in the middle of the lanthanide series and has the [Xe] 4f⁷5d6s² ground state configuration generating highly complex first spectrum of neutral gadolinium atom (Gd I) [1]. For the last few decades many successful attempts have been made to investigate the Gd I spectrum. Albertson [2] in 1935 identified 5 low odd-parity levels of ground term and 35 upper even-parity levels comprising 71 classified spectral transitions. Analyses of arc and spark spectra based on wave numbers and intensities by Russell [3] have led to the energy level classification of 1217 transitions of Gd I with identification of some 200 even-parity levels. Although enriched Gd isotopes have been employed by Speck [4] for the first time for studying IS in the Gd I spectrum their data was confined mainly to investigate the nuclear spins and moments of odd isotopes. Odintsova and Striganov [5] reported IS between all pairs of even isotopes in many strong spectral lines for the first time; however the data was limited to the studies of static deformation parameter 𝛽 and internal quadruple moment 𝑄₀ for the nucleus of Gd-152 isotope. Electronic configuration assignment studies have been performed on Fabry-Perot Spectrometer (FPS) employing IS as a tool in this laboratory by Afzal et al. [6] in the region of 3290–3950 Å and also these studies were extended to the regions of 3930–4140 Å [7], 4140–4535 Å [8] and 4535–4975 Å [9]. Venugopalan and Ahmad [10] have carried out reevaluation of term IS data for the levels of 4f⁸6s², 4f⁸6s6p, 4f⁷5d6s7s, and 4f⁷5d³ configurations on the basis of newly published laser spectroscopic data by Miyabe et al. [11, 12]. There were two studies performed by Kronfeldt et al. [13, 14] on 𝐽 dependence of IS in the ground state 4f⁷5d6s² configuration. Such 𝐽-dependences also have been reported by Jin et al. [15–18] in 4f⁷5d6s², 4f⁷5d6s6p, 4f⁷6s²6p, 4f⁷5d²6p, and 4f⁸5d6s configurations. Jung et al. studied high-resolution optogalvanic laser absorption spectroscopy [19] and population density measurements [20] in the meta-stable levels of Gd I. IS and hfs studies have been done by Jia et al. [21] in high lying odd-parity levels of Gd I usig resonantly enhanced Doppler-free two-photon spectroscopy. Childs [22] has measured hfs and IS using laser-rf double resonance spectroscopy. Autoionizing resonances by Bushaw et al. [23] were determined in Gd I spectrum using high-resolution CW laser. A collimated atomic beam laser spectroscopy has been employed by Dutta et al. [24] and by Bushaw et al. [25] to study IS and hfs in some selected transitions of Gd I. Detailed electronic configuration interaction of the type (4f⁷6s²6p + 4f⁷5d6s6p + 4f⁷5d²6p) configurations in 24 high even-parity levels has been established by Kronfeldt et al. [26] employing theoretical and experimental hfs spectrum generated by laser induced resonance fluorescence spectroscopy. An identification of odd-parity energy level at 38024.792 cm⁻¹ of 4f⁷5d6s8s configuration was made by Nörtershäuser et al. [27] in addition to the experimental IS and hfs splitting produced by double resonance-enhanced two-photon transition mass spectroscopic technique. Blaum et al. [28] have measured IS and hfs in all 4f⁷5d6s²⁹D_J → 4f⁷5d6s6p ⁹F_J+1 transitions of Gd I with the aid of high-resolution resonance ionization mass spectrometry. Absorption spectra of Gd I in the region of 560–600 nm have been studied by Niki et al. by means of laser-induced fluorescence spectroscopy using CW dye laser [29] and also using blue diode laser [30]. A violet diode laser spectroscopy has been employed to investigate IS and hfs in two spectral lines by Yi et al. [31]. A high-resolution diode-laser spectroscopy of some rare earths including a 682.83 nm transition of Gd I has been performed by Wakui et al. [32] to derive the field shifts and 6s-electron densities. IS studies carried out by us using FTS in 67 transitions [33] in the wavelength region of 495–535 nm have furnished new IS data in 44 lines and confirmations to previous configuration assignments of many high even levels as well as new assignments of 4f⁸5d6s configuration to some high lying even-parity levels of Gd I. Recently Jin et al. [34] have studied IS and hfs in 5 transitions of Gd I using high-resolution atomic-beam UV laser spectroscopy technique.

Out of 250 odd-parity levels [1] of Gd I approximately 150 carry electronic configurations whereas 70 even-parity levels are without configuration assignments and 30 even-parity levels above the level at 32167.925 cm⁻¹ (𝐽=2) have tentative configurations. Four energy levels of 4f⁷5d³ configuration comprising one (with 𝐽=3) of ⁹P⁰ term and three (with 𝐽=5, 6 and 7) of  ⁹F⁰ term are yet to be identified. Out of 486 even-levels listed of Gd I only 236 levels have definite configuration assignments whereas 161 levels were tentatively assigned and 89 levels are without configuration assignments. The present experimental studies have been taken up to investigate the detailed configuration mixings in the high even-parity levels of Gd I.

2. Experimental

The present investigation reports IS Δ𝜎^156,160 measurements in the 365–495 nm wavelength region carried out using BOMEM DA-8 series FTS. IS data in this region already have been covered in this laboratory on FPS [6–9] and the present studies involve new lines for which IS data were not available in the literature and also some of the lines previously studied. A liquid nitrogen cooled HCL containing highly enriched Gd¹⁵⁶ : Gd¹⁶⁰ isotopes in the oxide form with the ratio of 0.7 : 1.0 has been employed as a source. The source was evacuated to ~10⁻⁶mbar before filling with a Ne as a buffer gas at 2.5 mbar and the discharge was run at 25 mA dc. Detailed procedure of preparation of HCL will be found in [33]. Quartz was used as the beam splitter and a photomultiplier tube (PMT) was used as the detector. The spectrum recorded at the spectral resolution 0.02 cm⁻¹ was analyzed on wave number scale employing a computer program with the help of which each completely resolved spectral component is identified. Magnitude of IS larger than 0.060 cm⁻¹ has accuracy ±3.10⁻³ cm⁻¹ and lower values than quoted one have accuracy ±5.10⁻³ cm⁻¹. Unit of IS data is cm⁻¹. Spectrum of Gd I was calibrated using strong lines of Ne I and Cu I which exhibit wide full width at half maximum (FWHM) of ~0.130 cm⁻¹ and ~0.075 cm⁻¹, respectively, compared to ~0.050 cm⁻¹ FWHM of Gd I lines. Variation of IS Δ𝜎^156,160 values (±5.10⁻³ cm⁻¹) being observed for some lines may be due fluctuation of light intensities from HCL. Figure 1 depicts large IS Δ𝜎^156,160 –0.131 cm⁻¹ in the line at 390.270 nm, the spectral line for which IS data was not available in the literature.

Figure 1 

A high resolution spectrum in the region of 25575–25875 cm−1, recorded on FTS using liquid nitrogen cooled HCL containing highly enriched Gd-156 and Gd-160 isotopes (in 7 : 10 ratio) in the oxide form. Inset-expanded region showing IS Δ𝜎156,160 −0.131 cm−1 in the spectral line at 390.270 nm of Gd I.

3. Results and Discussion

Table 1 lists IS data in 49 spectral lines out of which data was new for 22. Wavelengths listed in Table 1 were taken from Russell [3]. As could be seen all lines are exhibiting negative ISs due to large change in S-electron charge density at the nucleus for the low odd-parity energy levels. On the basis of present IS data, the correct energy level classifications have been provided for the two transitions at 368.501 nm and at 369.693 nm [3]. Energy level classification previously reported by us for the line at 418.2760 nm has been revised on the basis of data published in [3]. IS Δ𝜎^156,160 literature data of 42 spectral lines in the range of 408–775 nm and that of 4 lines listed from our unpublished FTS data have been compiled in Table 2 and employed for the derivation of LIS values of the presently encountered energy levels and also as a supporting data to the results being published.

Table 1 

Wavelengths, line intensities, and energy level classifications have been taken from Russell [3]. IS Δ𝜎^156,160 (cm⁻¹) in the 49 spectral lines (cm⁻¹) of Gd I covering the region of 3646–4936 Å on FTS, source: liquid nitrogen cooled HCL, detector: PMT. Units of measurements were wavelengths (nm), intensities in arbitrary units (A. u.), energy levels (cm⁻¹), and IS (cm⁻¹). The accuracy for lines showing IS greater than 0.060 cm⁻¹ was ±3.10⁻³ cm⁻¹, and for lines with smaller IS than 0.060 cm⁻¹ it was ±5.10⁻³ cm⁻¹.

Table 2 

IS Δ𝜎^156,160 data in the 42 spectral lines of Gd I covering the region of 4087–7749 Å; the listed literature data mostly studied by means of laser spectroscopy have been employed to evaluate the LIS, Δ𝑇^156,160 of the presently involved levels. Units of measurements were wavelengths (nm), intensities (A. u.), energy levels (cm⁻¹), and IS (cm⁻¹).

For a first approximation, all energy levels of a particularly pure configuration should show the same LIS. But in practice levels of the same configuration usually show different LIS values and this may be due to second order effects of ISs, that is, due to 𝐽 dependence, specific mass shift, and configuration mixing (see King [35]). 𝐽-dependence and specific mass shift properties change magnitude of LIS in the case of lanthanides to the order of fraction of wave number (±3.10⁻³ cm⁻¹); however presence of configuration mixing in the levels shows considerable variation in their IS values. For a configuration mixing to take place between a pair of energy levels, the energy levels must be of the same parity and 𝐽, lie relatively close together, must belong to two different configurations that can interact directly, and must contain large component of common parentage (of 4f^𝑛−1 or 4f^𝑛−2, etc.). All these conditions are fulfilled by the energy levels of three 4f⁷6s²6p, 4f⁷5d6s6p, and 4f⁷5d²6p configurations for configuration mixing. There is no other possibility of exhibiting configuration mixing, for example, of (4f⁸6s² + 4f⁸5d6s + 4f⁸6s7s) configurations; this may be because the levels of these configurations lie far away from each other, levels of 4f⁸6s² lie at 10900 cm⁻¹, of 4f⁸5d6s lie between 25000–35000 cm⁻¹, and those of 4f⁸6s7s configuration lie above the 40400 cm⁻¹.

LIS of a level with mixed configuration can be derived by the application of “Sharing rule” given by Bauche and Champeau [36]. To apply a “Sharing rule” LIS “Δ𝑇” value of pure configurations being mixed was chosen from the literature. LIS values of the pure 4f⁷5d6s6p and 4f⁷5d²6p configurations are 0.110 and 0.010 cm⁻¹, respectively, and have been taken from our earlier studies [8] whereas LIS value 0.190 cm⁻¹ for 4f⁷6s²6p configuration has been calculated from experimental IS data of the two near IR transitions which were reported for the first time by Jin et al. [16]. The uncertainty in the present configuration mixing is ±1%. Present results on configuration mixing are more accurate as compared to results published in [26], this may be because the results presented in [26] were based on common features of experimental hfs. Also the contributions of 4f⁷5d²6p and 4f⁷6s²6p configurations have been neglected in [26] during analysis.

According to “Sharing rule,” for a state whose wave function “Ψ” results from mixing of   “𝑛” configurations, the IS “Δ𝑇” equals the sum of ISs Δ𝑇_𝑖 of individual configurations multiplied by the weight 𝐶²_𝑖 of the configuration in “Ψ”, Δ𝑇=^𝑛_𝑖=1𝐶²_𝑖⋅Δ𝑇_𝑖,where𝐶²_𝑖=1. (1)

3.1. LIS Δ𝐓^{𝟏𝟓𝟔,𝟏𝟔𝟎} Values of the Energy Levels of Gd I

22 odd parity levels listed in Table 3, 40 high even-parity energy levels listed in Table 4, and 8 even-parity levels assigned to 4f⁸5d6s configuration listed in Table 5 have been involved in the present investigation. The low odd- parity energy levels and their data encountered repeatedly in our earlier studies [6–9] and also in the present studies have been confirmed and listed in Table 3. The odd- parity energy level lying at 39458 cm⁻¹ (𝐽=6) of 4f⁷5d6s7s configuration, and the couple of levels at 40894 cm⁻¹ (𝐽=5) and 41370 cm⁻¹ (𝐽=4) of 4f⁸6s6p configuration whose LIS, Δ𝑇^156,160 values also have been confirmed in the present investigation.

Table 3 

Odd-parity energy levels (cm⁻¹), their configurations, term, and 𝐽 values have been taken from [1]. LIS Δ𝑇^156,160 (cm⁻¹) have been referred from [6–9].

Table 4 

List of even-parity energy levels with their experimental LIS Δ𝑇^156,160 (cm⁻¹) values encountered in the present studies. Levels, their configuration, term, and 𝐽 values have been taken from [1].

Table 5 

Even-parity energy levels (cm⁻¹) belonging to 4f⁸5d6s configuration are listed separately in Table 5. Configurations, terms, and 𝐽 values have been taken from [1]. LIS Δ𝑇^156,160 (cm⁻¹) values have been referred from [6–9].

Table 4 lists even-parity energy levels along with experimentally derived LIS Δ𝑇^156,160 values given in column 5. Columns 6 and 7 list LIS values evaluated by applying “Sharing rule” to the configuration mixing data reported by Kronfeldt et al. [26] and to the three LIS values of pure 4f⁷6s²6p, 4f⁷5d6s6p, and 4f⁷5d²6p configurations.

The LIS Δ𝑇^156,160 values of the high even-parity levels have been derived with the help of Transition Arrays, that is, by subtracting the known LIS Δ𝑇^156,160 values of low odd-parity levels (described in Table 3) wherever available from the spectral line IS Δ𝜎^156,160 listed in Tables 1 and 2. Figure 2 is the graphical representation of the even-levels against their LIS Δ𝑇^156,160 values. It is seen in Figure 2 that a cluster of low even-levels of 4f⁷5d6s6p configuration is free from configuration interaction whereas levels lying above 25000 cm⁻¹ of 4f⁷5d6s7p and 4f⁷5d²6p configurations have been widely spread and overlapped with each other suggesting strong configuration mixing.

Figure 2 

Even-parity energy levels (cm−1) plotted against their respective experimental LIS Δ𝑇156,160 (cm−1) values. As seen in the Figure levels belonging to 4f75d6s6p and 4f75d26p configurations in the range of 22500–30000 cm−1 have been mixed together suggesting configuration interaction whereas the cluster of extreme low even-levels of pure 4f75d6s6p and extreme high even-levels of pure 4f75d26p configurations is free from configuration interaction.

3.2. Configuration Interaction Analysis of the High Even-Parity Levels of Gd I

3.2.1. The 4f⁷5d6s6p Configuration

10 high even-parity levels between 17318 and 24458 cm⁻¹ of 4f⁷5d6s6p configuration, except the level at 17749 cm⁻¹ listed in Table 4, have experimental LIS Δ𝑇 values in the range of 0.104–0.111 cm⁻¹. The LIS values recalculated according to configuration mixing reported in [26] and also derived by us applying “Sharing rule” to the hypothetical Δ𝑇 values of pure configurations (columns 5, 6, and 7) are consistent with the experimental Δ𝑇 values and confirm the previous configuration assignments. The level at 17749 cm⁻¹ (𝐽=2) with experimental LIS 0.123 cm⁻¹ shows rather large (17%) contribution of 4f⁷6s²6p configuration than earlier (10%) suggested mixing. The level at 24988 cm⁻¹ (𝐽=4) of ⁷D term has LIS value of 0.092 cm⁻¹ suggests 82% and not the 99% 4f⁷5d6s6p configuration. The couple of levels at 26615 cm⁻¹ (𝐽=5) and 26866 cm⁻¹ of ⁷F term have LIS values 0.038 and 0.060 cm⁻¹ respectively and former belonging to the dominant 4f⁷5d²6p and a later has equal contribution of 4f⁷5d6s6p and 4f⁷5d²6p configurations. The levels lying between 23215–25043 cm⁻¹ have LIS values in the range of 0.060–0.068 cm⁻¹ which points out that the contribution of 4f⁷5d6s6p configuration is 50–57% and not ~99% as reported in [26]. The levels at 25376 cm⁻¹ (𝐽=7), 27425 cm⁻¹ (𝐽=4) of 4f⁷5d6s6p configuration, and at 30809 cm⁻¹ (𝐽=3) of tentatively assigned to 4f⁷5d6s6p configuration have LIS values 0.048, 0.092 and 0.080 cm⁻¹ belonging to 38 : 62%, 82 : 18%, and 70 : 30% 4f⁷5d6s6p : 4f⁷5d²6p configurations, respectively.

3.2.2. The 4f⁷5d²6p Configuration

A level at 30505 cm⁻¹ (𝐽=7) has experimentally derived and calculated LIS value 0.010 cm⁻¹ and belongs to 100% pure 4f⁷5d²6p configuration. Four levels of 4f⁷5d²6p configuration between 23103 and 32091 cm⁻¹ and of term ⁹F have LIS values in the span of 0.061–0.005 cm⁻¹ and can be assigned to 49%, 72%, 77%, and 100% of 4f⁷5d²6p configuration. As seen the level at 23103 cm⁻¹ (𝐽=1) studied previously in [26] gives the value 0.109 cm⁻¹; however our experimentally observed and calculated LIS value 0.061 cm⁻¹ suggests the revision of the previously predicted 99.23% 4f⁷5d6s6p configuration to 50 : 49% (4f⁷5d6s6p : 4f⁷5d²6p) configurations. A level at 34836 cm⁻¹ (𝐽=4) assigned to 4f⁷5d²6p? has experimental and calculated LIS value 0.078 cm⁻¹ and can be assigned to 68 : 32% (4f⁷5d6s6p : 4f⁷5d²6p) configurations.

3.2.3. Levels without Electronic Configuration Assignments

Four unassigned even-parity levels of term ⁹F_J? at 28504 cm⁻¹, 28731 cm⁻¹, 29119 cm⁻¹, and at 29426 cm⁻¹ have experimental and calculated LIS values 0.078, 0.042, 0.077, and 0.067 cm⁻¹ and can be assigned to 56–68% 4f⁷5d6s6p configuration except the level at 28731 cm⁻¹ which has contribution of 69% 4f⁷5d²6p configuration. Four more energy levels at 30394 cm⁻¹ (𝐽=2), 33704 cm⁻¹ (𝐽=3), 34147 cm⁻¹ (𝐽=2), and at 36147 cm⁻¹ (𝐽=6) have LIS values 0.100 cm⁻¹, 0.068 cm⁻¹, 0.084 cm⁻¹, and 0.010 cm⁻¹ suggesting 90%, 58%, 74% 4f⁷5d6s6p, and 100% 4f⁷5d²6p configurations, respectively. The level 30394 cm⁻¹ (𝐽=2) has been previously studied by us [33] and the present study enabled us to predict its detailed configuration mixing which is (90 : 10%) 4f⁷5d6s6p : 4f⁷5d²6p.

3.2.4. The 4f⁸5d6s Configuration

Three levels (see Table 5) at 24854 cm⁻¹ (𝐽=6), 25380 cm⁻¹ (𝐽=5) and at 25820 cm⁻¹ (𝐽=4) of ⁹G term and two levels at 27040 cm⁻¹ (𝐽=4), and 27041 cm⁻¹ (𝐽=3) of ⁹F term all belonging to 4f⁸5d6s configuration have been confirmed presently. An unassigned level at 27129 cm⁻¹ (𝐽=1) has LIS value of 0.058 cm⁻¹ and assigned to 4f⁸5d6s configuration. The last two levels at 28414 cm⁻¹ (𝐽=5) and 31327 cm⁻¹ (𝐽=3) assigned tentatively earlier to 4f⁸5d6s configuration [1] have LIS values of 0.037 and 0.048 cm⁻¹ respectively support their previous configuration assignments.

4. Conclusion

Present IS, Δ𝜎^156,160 studies on FTS in 49 spectral lines carried out in the visible region of 365–495 nm yielded new data in 23 lines of Gd I. A detailed analysis of electronic configuration mixing in the high even- parity levels of Gd I has been performed employing experimental and hypothetical LIS data. Configuration mixings reported earlier using experimental hfs and parametric calculations have been reanalyzed presently, providing good consistency for 10 out of 22 even-levels. Percentage compositions of remaining 10 even-levels have been revised. Two levels tentatively assigned to 4f⁸5d6s configuration have been confirmed and a tentatively assigned level earlier to 4f⁷5d²6p? configuration, was revised to 4f⁷5d6s6p configuration. Out of 8 unassigned levels, 6 have exhibited their dominancy in 4f⁷5d6s6p and the remaining two have dominancy in 4f⁷5d²6p configuration.

Acknowledgments

The authors express gratitude to the referees for including [30, 34].