The Cu II Spectrum

Abstract

New wavelength measurements in the vacuum ultraviolet (VUV), ultraviolet and visible spectral regions have been combined with available literature data to refine and extend the description of the spectrum of singly ionized copper (Cu II). In the VUV region, we measured 401 lines using a concave grating spectrograph and photographic plates. In the UV and visible regions, we measured 276 lines using a Fourier-transform spectrometer. These new measurements were combined with previously unpublished data from the thesis of Ross, with accurate VUV grating measurements of Kaufman and Ward, and with less accurate older measurements of Shenstone to construct a comprehensive list of ≈2440 observed lines, from which we derived a revised set of 379 optimized energy levels, complemented with 89 additional levels obtained using series formulas. Among the 379 experimental levels, 29 are new. Intensities of all lines observed in different experiments have been reduced to the same uniform scale by using newly calculated transition probabilities (A-values). We combined our calculations with published measured and calculated A-values to provide a set of 555 critically evaluated transition probabilities with estimated uncertainties, 162 of which are less than 20%.

1. Introduction

The spectrum of singly ionized copper, belonging to the Ni isoelectronic sequence, has a long history of research. The most significant contributions to the analysis were made by Shenstone [1] in 1936 and by Ross [2] in 1969. Interest in this spectrum was mainly due to the fact that it has a large number of sharp distinct lines in the vacuum ultraviolet (VUV) region, as well as an equally large number of lines in the ultraviolet (UV), visible, and infrared (IR) regions, from which accurate wavelengths of the VUV lines can be established using the Ritz combination principle, thus providing a large set of lines usable as secondary VUV wavelength standards. This spectrum is also of considerable interest for astrophysics. Lines of Cu II were observed in the spectra of nebulae by Thackeray [3], Aller et al. [4], McKenna et al. [5], and by Wallerstein et al. [6], and also in interstellar H I clouds, as well as in Ap, Be, and Bp stars (Jaschek, and Jaschek [7], Danezis and Theodossiou [8]) and in the Sun (Samain [9]). Cu⁺ was successfully used as an active lasing medium in various hollow cathodes. Continuous-wave or pulsed lasing has been reported for 28 lines of Cu II in a wide range from UV to IR (McNeil et al. [10,11], Jain [12], Zinchenko and Ivanov [13]). Since copper is an important impurity in tokamaks, the Cu II spectrum has potential applications in fusion research, where its lines can be used for diagnostic purposes.

For several decades after the original analysis by Shenstone [1] the VUV wavelengths of Cu II calculated from the energy levels (i.e., Ritz wavelengths) were widely used as auxiliary wavelength standards. After the refinements of the measured UV wavelengths by Reader et al. [14] and by Kaufman and Ward [15], and after improved and greatly extended measurements by Ross [2] in the UV and visible ranges, the quality of the VUV Ritz wavelengths of Cu II seemed to be so good that no further investigations of this spectrum were needed. The only inconvenience stemmed from the fact that Ross’s thesis [2] was never published, although a large part of it was released with small modifications as a report of the Los Alamos National Laboratory, see Ross [16]. Energy levels and a few strongest lines from Ross [2] were included in the compilations by Sugar and Musgrove [17] and by Sansonetti and Martin [18], but the bulk of the wavelength and line intensity data remains nearly inaccessible. Thus, the initial goal of the present work was simply to digitize Ross’s line lists and include them in the Atomic Spectra Database (ASD; see Kramida et al. [19]) of the National Institute of Standards and Technology (NIST) with consistent energy-level identifications. However, a close examination revealed several problems with Ross’s data.

The first problem is with internal consistency of Ross’s data. An important aspect of ASD is that it requires the observed wavelengths for an atom to be consistent with the energy levels tabulated for that atom. That is, the wavelengths derived from the energy levels (Ritz wavelengths) must agree with the observed wavelengths to within the stated uncertainties. However, in attempting to incorporate the data of Ross into ASD, we found that for a large number of lines the differences between observed and Ritz wavelengths were much greater than the uncertainties. We decided that, because of the importance of Ritz wavelengths for Cu II, this had to be investigated.

The second problem with Ross’s data is the possible presence of systematic shifts in his wavelengths. Nave and Sansonetti [20] showed that Ritz wavelengths below 2400 Å (41667 cm⁻¹) derived from Ross’s Cu II energy levels are systematically too low, the mean relative deviation being about 4 × 10⁻⁷. This error is significantly greater than the average relative uncertainty of Ritz wavenumbers given by Ross, 1.2 × 10⁻⁷. Near 2000 Å (50000 cm⁻¹), it corresponds to an error of 0.02 cm⁻¹, compared to the mean stated uncertainty of 0.006 cm⁻¹. This puts the usability of Ross’s Ritz wavenumbers in the VUV into question.

The third problem is the absence of a consistent description of line intensities throughout the entire range of observed wavelengths. While Ross’s own measurements cover the large range above 1980 Å, most of the observed intensities in the VUV region are furnished by old measurements of Shenstone [1], which were made with seven different instruments and with two different light sources. Additional measurements for some selections of strongest lines were made by Reader et al. [14] and by Kaufman and Ward [15], each with their own intensity scale.

Finally, Ross’s theoretical interpretation of the energy levels, adopted by Sugar and Musgrove [17] and by Sansonetti and Martin [18], is inadequate. Ross used the LS coupling scheme in his analysis, as well as in his final level list. However, the observed fine-structure intervals indicate that the level structure of most configurations is best described by the J₁l (a.k.a. JK) coupling scheme, similar to the isoelectronic Ni I spectrum interpreted by Litzén et al. [21].

Another problem that needs to be addressed is the scarcity of available critically evaluated data on radiative transition probabilities (A-values). At present, the NIST ASD [19] includes only seven A-values of Cu II from the compilation of Wiese and Martin [22]. All of them have large estimated uncertainties (≤40% for six transitions and ≤50% for one transition).

The main purpose of the present work is to solve the above-mentioned problems and construct a self-consistent set of recommended energy levels and wavelengths of Cu II supplemented with a uniform description of line intensities. Re-interpretation of the energy levels, as well as the search for possible classifications of previously unidentified lines, required new calculations, which necessarily produce radiative transition probabilities (A-values). Thus, we also critically evaluate all available data on A-values and extend them with our calculated ones found to be of sufficiently good accuracy.

The usability of the Cu II wavelengths as standards is limited by substantial hyperfine structure (HFS) splitting and presence of two stable isotopes, ⁶³Cu (69.15%) and ⁶⁵Cu (30.85%) in natural copper (Coursey et al. [23]). HFS and isotope shifts (IS) of a few tens of Cu II lines between 2218 Å and 8096 Å were first observed and roughly estimated by Shenstone [1] and then more accurately investigated by Elbel et al. [24,25]. The measured IS was in the range (0.001 to 0.101) cm⁻¹. For singly-excited 3d⁹nl configurations the IS is smaller than 0.05 cm⁻¹, while for the doubly-excited 4d⁸4s² configuration it is about 0.1 cm⁻¹. The HFS constants A_hfs for several [3d⁹]4s, 4p, 4d, 5s, 5p, 5d, 6s and [3d⁸]4s² and 4s5p levels were found to range from 0.022 cm⁻¹ to 0.075 cm⁻¹ except for one level, 3d⁹4s ³D₁, having a very small A_hfs = −0.004 cm⁻¹. The nuclear spin I of both ⁶³Cu and ⁶⁵Cu is I = 3/2 [18]. Thus, depending on the total angular momentum J of the levels, the width of the HFS varies between 0.016 cm⁻¹ and 0.5 cm⁻¹. The ionization energy of Cu⁺ is 163669.2 cm⁻¹ (20.292 39 eV) (Ross [2]). Thus, excitation of this spectrum requires temperatures in excess of 6000 K (0.5 eV). Such temperatures lead to Doppler broadening Δσ_Dop/σ > 4 × 10⁻⁶, resulting in line widths >0.4 cm⁻¹ at wavelengths near 1000 Å, 0.2 cm⁻¹ near 2000 Å, and 0.1 cm⁻¹ near 4000 Å. As a result, most observed lines possess unresolved or partially resolved HFS and IS. The smallness of HFS and IS explains the scarcity of studies of these effects in Cu II. However, these effects should be relatively easy to observe in the infrared region. Such observations would be very valuable.

All wavelength measurements described in the present paper were made with natural copper samples. As we know, there is no such physical entity as an atom of natural copper. Thus, the energy levels and Ritz wavelengths derived from these measurements do not pertain to a real atom, but rather are empirical values that best describe the spectrum as normally observed.

2. Wavelength Measurements

The unfortunate consequence of the thorough analysis made by Ross [2,16] is that, in the 46 years after his thesis, there were no studies devoted specifically to Cu II. Instead, his Cu II Ritz wavelengths were widely used as secondary standards for investigation of other species. In particular, the archive of the NIST Atomic Spectroscopy Group has several tens of photographic plates with VUV spectra obtained with the 10.7 m normal incidence vacuum spectrograph with a 1200 lines/mm concave grating. These plates were recorded for studies of Y, Zr, Ge, La, and other elements. For calibration purposes, separate tracks were exposed on these plates with spectra of copper hollow cathodes. The latter, in addition to copper lines, contain lines of carrier gases (helium, neon, and argon), as well as hydrogen, carbon, oxygen, nitrogen, silicon, and germanium that were present as intrinsic or deliberately introduced impurities. These spectra were obtained in different years from 1969 to 1974. In addition to that, we have several high-resolution spectra recorded with two NIST vacuum Fourier transform spectrometers (FTS) in years 2002 to 2008 using Cu/Ge/Pt/Fe/Ne and Cu/Re/Ar/He hollow cathodes. The “new” measurements described in the Abstract were all made with these old recordings. However, we carried out new reductions of the wavelengths and re-analyzed the uncertainties, so it is in this sense that the measurements can be considered as new. To obtain a consistent and comprehensive description of the Cu II spectrum, we combined these new measurements with the old published data from Shenstone [1], Kaufman and Ward [15], and Ross [2,16], which we re-analyzed to evaluate the wavelength calibration, measurement uncertainties, and observed line intensities. Since this re-analysis depends on our new measurements, we describe them first.

Table 1 lists the exposures used in the present analysis. Since exposures used in grating measurements were taken over a period of several years, several different lamp designs were employed. The design of these lamps was similar to the one described in detail by Reader and Davis [26], except that a special fitting was made to attach them to the NIST vacuum spectrograph. The cathode was solid copper with a cylindrical hole of about 7 mm in diameter. Following Kaufman and Ward [15], small pieces of Ge and Si were placed in the cathode to obtain good reference lines in regions that were not covered well by Cu II. The carrier gas was a combination of flowing helium at a pressure of about 0.5 kPa (4 Torr) and neon or argon at about 70 Pa (0.5 Torr). The entrance slit of the spectrometer separated the lamp from the spectrometer chamber, which was maintained at a residual pressure of about 7 × 10⁻³ Pa (5 × 10⁻⁵ Torr). The demountable high-current lamp made at the University of Hannover, used several tens of years later in the FTS measurements, had a similar design described by Danzmann et al. [27]. Ar at a pressure of 200 Pa (1.5 Torr) with an addition of He at 70 Pa (0.5 Torr) was used as a carrier gas in spectrum 14, while Ne at a pressure of 270 Pa (2 Torr) was used in spectra 12 and 13. Pieces of Ge, Pt, Fe, or Re were placed inside the cathode. The grating spectrograms covered the region (636 to 2682) Å, while the FTS spectrograms covered the region (1792 to 11733) Å.

Table 1. Spectrograms used in the present measurements.

Exposure	Track	Region (Å)	Hollow Cathode Used	Impurities	Equip. a	Wavelength Standards b	Track Label	Date	Fit Poly c	St. Dev. d
1	1	636–827	Cu/He/Ar/Ne		NIVS	Ar II (11), Ne I (1), Cu II (TW-1) e	418	4/3/1974	2	0.0009
2	2	822–1000	Cu/Ge/Si/He/Ar	H, C, O	NIVS	H I (2), O I (9), O II (1), Ar II (2), Ge II (3)	419_tr42	4/4/1974	2	0.0013
	6	977–1166		H, C, N, O	NIVS	C I (2), C II (1), N I (2), O I (7), Ar I (2), Si II (2), Ge II (3)	419_tr42	4/4/1974	2	0.0013
3	5	824–1020	Cu/He	H, O	NIVS	H I (1), O I (5), Cu II (KW66-4, TW-10) f		12/17/1969	2	0.0012
4	7	1181–1360	Cu/Ge/Si/He/Ar	H, C, N, O	NIVS, LiF	C I (6), N I (3), Si II (6), Ge II (1), Cu II (KW66-6, TW-1) g	X431_tr27	10/24/1974	2	0.0024
	8	1339–1527			NIVS, LiF	C I (4), O I (1), Cu II (KW66-48)	X431_tr27	10/24/1974	2, 3 k	0.0021
5	9	1399–1590	Cu/He/Ar	C, N	NIVS	C I (1), Cu II (KW66-62, TW-4) h		12/16/1969	2, 2 l	0.0010
6	10	1398–1584	Cu/Si/He/Ne	C, N	NIVS	C I (3), Si II (1), Cu II (KW66-44, TW-1) i		1/15/1970	2	0.0012
	17	1920–2106			NIVS	C I (1), Cu II (R69-20)		1/15/1970	2	0.0021
7	11	1399–1587	Cu/Ge/Si/He	C, N	NIVS	C I (3), N I (1), Si II (2), Ge II (2), Cu II (KW66-66)	X434_tr52	11/11/1974	3	0.0014
	14	1560–1743			NIVS	C I (5), N I (1), Ge II (3), Cu II (KW66-21)	X434_tr52	11/11/1974	3	0.0016
8	12	1394–1584	Cu/Ge/Si/He	C, N	NIVS	C I (3), Si II (2), Ge II (3), Cu II (KW66-52)	X434_tr27	11/11/1974	2	0.0016
	13	1559–1743			NIVS	C I (1), Si I (3), Ge II (1), Cu I (1), Cu II (KW66-14)	X434_tr27	11/11/1974	2	0.0019
	15	1751–1939			NIVS	Si I (7), Si II (1), Cu I (1), Cu II (KW66-5)	X434_tr27	11/11/1974	2	0.0017
9	16	1790–1980	Cu/Si/He	C	NIVS	C I (1), Cu I (1), Cu II (KW66-4, R69-1, TW-2) j		11/10/1969	4	0.0012
10	18	1977–2162	Cu/Ge/Si/He	H, C, O	NIVS	Si I (2), Ge I (6), Ge II (2), Cu I (I), Cu II (R69-11)	X433_tr27	11/7/1974	2	0.0016
	20	2139–2315			NIVS	Si I (4), Ge I (1), Cu I (4), Cu II (R69-26)	X433_tr27	11/7/1974	5	0.0021
	21	2336–2517			NIVS	Si I (3), Cu I (1), Cu II (R69-13)	X433_tr27	11/7/1974	3	0.0017
	22	2490–2682			NIVS	O I (3), Si I (7), Ge I (3), Ge II (1), Cu II (KW66-2, R69-5)	X433_tr27	11/7/1974	2	0.0011
11	19	2117–2310	Cu/Ge/Si/He		NIVS	Si I (2), Ge I (1), Cu I (4), Cu II (R69-20)	E16-3	6/3/1969	2	0.0019
12	–	1792–3324	Cu/Ge/Pt/Fe/Ne		FTS	Ge I-II (37)		2002	1	1.7 × 10−8
13	–	1825–3324	Cu/Ge/Pt/Fe/Ne		FTS	Ge I-II (37)		2002	1	2.0 × 10−8
14	–	2769–11733	Cu/Re/Ar/He		FTS	Ar II (68)		2009	1	2.0 × 10−9

^a Equipment used: NIVS = Normal Incidence Vacuum Spectrograph (NIST, 10.7 m grating, reciprocal linear dispersion 0.78 Å); FTS = Fourier Transform Spectrometer (NIST, FT700 0.2 m vacuum FTS for spectra 12 and 13, and a 2 m vacuum FTS for spectrum 14); LiF = a LiF window was used to remove higher diffraction orders;

^b The number of spectral lines of each spectrum used as standards is given in parentheses. Unless otherwise indicated, the standard wavelengths used in grating measurements were the Ritz wavelengths taken from the ASD database [19]. For Cu II lines used as standards, the references are as follows: KW66—Kaufman and Ward [15]; R69—Ross [2]; TW—this work. Standards used in the FTS measurements are described in the text;

^c Power of the polynomial used to fit standard lines;

^d For grating spectra (exposures 1–11), standard deviation of the measured wavenumbers of the standard lines from the fitted polynomial (Å); For FTS spectra (exposures 12–14), standard deviation of the correction factor from the linear fit (dimensionless);

^e Cu II line at 826.9946 Å measured in 1^st order on track 2 was used as standard on track 1;

^f Ten Cu II lines measured in 1^st order on track 2 were used as standards on track 5;

^g Cu II line at 1275.5713 Å measured in 2^nd order on track 22 was used as standard on track 7;

^h Four Cu II lines measured in 1^st order on tracks 10–12 were used as standards on track 9;

ⁱ Cu II line at 1407.1688 Å measured in 1^st order on tracks 8, 11, and 12 was used as standard on track 10;

^j Two Cu II lines measured in 1st order on track 15 were used as standards on track 16;

^k Long-wavelength end of track 8 was fitted separately with a cubic polynomial;

^l Short-wavelength end of track 9 was fitted separately with a 2nd degree polynomial.

The grating spectra were photographed on Kodak SWR plates and measured with a Grant semiautomatic comparator. (Commercial products are identified in this paper for adequate specification of the experimental procedure. This identification does not imply recommendation or endorsement by NIST.) Repeated measurements of the same plates were made, from which the measurement uncertainty of line positions was estimated to be 1.6 μm for isolated well-resolved lines, corresponding to statistical wavelengths uncertainties of 0.0012 Å. Most of the lines were measured on two to six different tracks. Thirty-eight Cu II lines were measured in the second order of diffraction, and one (861.9932 Å) in the third order, while the rest of them were measured in the first order. Below 1980 Å, most of the tracks had a sufficient number of impurity lines (H, He, C, N, O, Ne, Si, Ar, Ge), which were used as standards. Cu II lines accurately measured by Kaufman and Ward [15] were also used as standards in the region (860 to 1663) Å. In the region above 1980 Å, we used Ross’s [2] interferometric and grating measurements as standards. Although later we found that Ross’s wavelengths are systematically too long (see below), the average error in the wavelengths we used as standards in the grating spectra was only (−0.0004 ± 0.0008) Å, well below our total measurement uncertainties. Therefore, we did not remove the systematic errors from Ross’s wavelengths used at this stage. The systematic uncertainty of each measured wavelength on our plates was estimated as a combination in quadrature of the standard deviation of the fitted polynomial (given in Table 1) and a mean uncertainty of standard wavelengths in the vicinity of the measured line. These systematic uncertainties were combined in quadrature with the statistical uncertainty (0.0012 Å for sharp isolated lines and up to 0.005 Å for blended or overexposed lines). Multiple measurements of the same line on different tracks were averaged with weights inversely proportional to squares of total uncertainties. The uncertainty of the mean was calculated as a combination in quadrature of the reduced statistical uncertainty and the straight average systematic uncertainty. In total, we have measured 1217 unique spectral lines in the grating spectra between 636 Å and 2682 Å, of which 938 were either identified as Cu II lines or did not have any identification, and the rest were identified as belonging to impurities noted above. The wavelengths determined in the present work have uncertainties ranging from 0.0008 Å to 0.010 Å. A number of lines reported by Kaufman and Ward [15] were overexposed on our plates, which led to significant systematic shifts in determining their positions. Such overexposed lines were not used in the current wavelength measurements.

Our FTS measurements were calibrated assuming a common calibration factor for all wavenumbers in each spectrogram. The value of the calibration factor was determined as a weighted mean of the ratio σ/σ_std, where σ is the measured wavenumber, and σ_std is the tabulated wavenumber of the reference line. For the Ar II and Ge I-II lines used as standards in the FTS spectra, we used the Ritz values from ASD as σ_std. We used reciprocal squared uncertainties of σ_std, combined in quadrature with our measurement uncertainties (see below), as weights in this averaging. Uncertainties of thus obtained calibration factors (given in Table 1) represent the systematic uncertainties in our FTS measurements. Positions of the line centers σ, line widths W, signal-to-noise ratios S/N, and total integrated intensities were evaluated using the XGREMLIN code by Nave et al. [28] either automatically, assuming a Lorentzian profile for isolated symmetrical lines, Gaussian profile for nearly symmetrical but visibly perturbed lines, or manually with a Gaussian profile with a line width fixed at a visually estimated value.

For well-resolved symmetrical lines, statistical uncertainties of FTS measurements can be approximated by Equation (1) of Brault [29]:

$$\delta {\sigma }_{\mathrm{stat}}=\frac{k}{\sqrt{N_w}}·\frac{W}{S/N},$$

(1)

where σ is the wavenumber, W is the full width at half maximum of the line, N_w is the number of statistically-independent points in the line width, and k is a constant depending on the line shape and the algorithm used for fitting the line. For Gaussian profiles, k = 0.693. For an optimally sampled spectrum, the interferogram is recorded to a path difference such that N_w is between 3 and 4 for the majority of the spectral lines. This gives the commonly-used approximation of

$$\delta {\sigma }_{\mathrm{stat}}=\frac{W}{2·S/N}$$

(2)

Using N_w = W/r, where r is the resolution of the spectrum in cm⁻¹, Equation (1) can be re-written as:

$$\delta {\sigma }_{\mathrm{stat}}=\frac{k}{S/N}\sqrt{rW}$$

(3)

Our spectra were taken with r = 0.015 cm⁻¹ for the Cu/Re/Ar/He spectrum and r = 0.13 cm⁻¹ for the Cu/Ge/Pt/Fe/Ne spectra. Typical line widths of symmetrical lines in our spectra range from 0.04 cm⁻¹ around 10000 cm⁻¹ to 0.25 cm⁻¹ around 30000 cm⁻¹, giving values of N_w between 2.5 and 3. The instrumental line shape of the FTS comes from the finite length of the interferogram and is a sinc function of width r. When this is convolved with the Gaussian lines in our spectra, the increase in the width is negligible for a line with N_w = 3 and only 0.2% for a line with N_w = 2 and can thus be ignored in the calculation of the statistical uncertainty.

Many of the Cu lines are affected by HFS and cannot be adequately fitted using Gaussian profiles. For example, Figure 1 shows the profile of the Cu II line at 12852 cm⁻¹.

Figure 1. Profile of the Cu II line at 12852 cm⁻¹ (7778.7 Å) as measured in our Fourier transform spectrometers (FTS) spectrum. This line has a partially resolved hyperfine structure (HFS). The vertical line indicates the center of gravity.

The position of such lines was estimated using the center of gravity. For strong isolated lines (S/N > 150), where it is easy to estimate the range for calculation of the center of gravity, Equation (3) can be used to estimate the uncertainty using k = 1 [29]. However, this uncertainty increases for weaker lines where it is not as easy to estimate the range of calculation for the center of gravity. The measurements are further complicated by the asymmetric HFS. Its precise shape and width is not studied so far for the Cu II spectrum. In our high-resolution Cu/Re/Ar/He spectrogram, HFS patterns are partially resolved in 230 out of total 352 Cu II lines. The average width of the HFS of those lines is W_ave = 0.14 cm⁻¹. Since the shapes of the HFS are unknown, an additional uncertainty in the measured centers of gravity arises from the possible omission (or erroneous inclusion) of a weak HFS component at the far wing of the line profile. The possible error caused by this effect of noise is easy to estimate by calculating the shift of the center of gravity of the structure:

δσ_hfs = 0.5W_hfsI_noise/(I_tot + I_noise),

(4)

where I_tot is the measured integrated intensity, W_hfs is the maximum of W_ave (see above) and the fitted width of the structure, and I_noise is the estimated possible integrated intensity of a hypothetical missed or erroneously included HFS component, equal to the root of mean square of the noise amplitude in the vicinity of the structure multiplied by the average width of sharp Cu II lines (equal to 5 × 10⁻⁶ times wavenumber for this spectrum).

The calibration of exposures 12 and 13, measured with a Cu/Ge/Pt/Ne hollow cathode, was made using 37 Ge I and II lines interferometrically measured by Kaufman and Andrew [30]. The reference wavenumbers from the latter paper have been decreased by 1.4 parts in 10⁸ to put them on the scale of a recent measurement of ¹⁹⁸Hg by Sansonetti and Veza [31], as described in Nave and Sansonetti [32]. Exposure 14, made with a Cu/Re/Ar/He hollow cathode, was calibrated using 68 Ar II standards from Whaling et al. [33]. Uncertainties of the calibration factors were determined as the sum in quadrature of the statistical uncertainty (coming from the different values of the calibration factor derived from different standard lines) and the mean uncertainty of the standard lines.

The total uncertainty of Cu II measurements was determined as the sum in quadrature of statistical and systematic uncertainties. The former was taken as the sum in quadrature of Equations (3) and (4), and the latter is the uncertainty in the calibration factor (given in Table 1) times the wavenumber. Total uncertainties of our Cu II wavelengths measured by FTS range from 0.000025 Å to 0.023 Å.

Kaufman and Ward [15] photographed the VUV spectrum of a water-cooled hollow cathode discharge containing germanium and silicon in the first, second, and third orders of diffraction of the same 10.7 m Eagle-mounting vacuum grating spectrograph as used in the present work (designated as NIVS in Table 1). They reported 141 measured wavelengths of Cu II in the range (861 to 1663) Å. As wavelength standards, they used lines of Cu II, Ge I, and Si I that were either calculated (Ritz) or interferometrically measured. The reciprocal linear dispersion was 0.78 Å/mm in the first order of diffraction. Many of the reported lines were measured on several (up to 11) spectrograms. We estimated their measurement uncertainties by comparing the measured wavelengths with the Ritz values (using Ross’s [2] energy levels) separately for lines measured only in the first order (0.003 Å for a single measurement), measured several times in the 1st order, but only once in the 2nd and/or 3rd order (0.0010 Å), and for lines measured on several spectrograms in several orders of diffraction (varying from 0.0004 Å to 0.0018 Å). These estimates agree well with those given explicitly by Kaufman and Ward for a few lines. Careful work was required to reconstruct the list of observed wavelengths, since some of the values given in Table III of Kaufman and Ward [15] are Ritz wavelengths, but many of them are also given in their Table I including the value of the residual λ_Ritz − λ_obs. Since there is no information regarding the wavelength standards actually used in various wavelength regions, all wavelengths reported by Kaufman and Ward [15] were adopted without corrections.

Ross [2,16] investigated the Cu II spectrum photographically from 1979 Å to 11217 Å using plane and concave grating spectrographs and Fabry-Perot interferometers. The light source was a water-cooled hollow cathode discharge with helium or neon as a buffer gas. Ross [2] noted that intensity of most Cu II lines was greatly enhanced when He at a pressure of about 0.9 kPa (7 Torr) was used as the carrier gas, while if Ne is used, only lines below 3000 Å arising from relatively low levels are excited. The standards for the Fabry-Perot interferograms were the lines of ¹⁹⁸Hg emitted by a water-cooled sealed electrodeless-discharge lamp containing argon carrier gas at a pressure of 33 Pa (0.25 Torr), with vacuum wavelengths 5462.27055 Å and 2537.2687 Å referred to Kaufman [34]. For grating measurements, a 9.2 m concave grating spectrograph with Paschen-Runge mounting was used. The grating had 600 lines/mm, was blazed at 10000 Å, and provided a reciprocal dispersion of ≈1.7 Å/mm. For calibration, interferometrically measured Cu II lines were used as standards.

As noted in the Introduction, subsequent studies reported some systematic errors in Ross’s short-wavelength measurements. This can be explained by the fact that below 2200 Å, Ross encountered severe technical difficulties in his interferometric measurements, caused by strong absorption in the crystalline quartz of the plates and windows. He partially solved the problem by removing the windows, which exposed the interferometer to spectroscopically non-standard air and did not permit thorough temperature control. In addition, Kaufman’s values for the ¹⁹⁸Hg lines Ross used as standards, 5462.27046 Å and 2537.26877 Å [34], have since been re-evaluated. Their currently recommended vacuum wavelengths are 5462.27062(3) Å and 2537.268755(17) Å [35]. Additional errors could have been due to a possibly imperfect match between filling the interferometer’s aperture with light from the hollow cathode and from the mercury lamp. To verify the calibration of Ross’s wavelengths, we compared his reported wavelengths with those measured in our FTS spectra. Similar to FTS measurements, interferometric measurements of Ross can be corrected by a multiplicative factor [20]:

σ_c = (1 + k_eff)σ_u,

(5)

where σ_c is the corrected wave number, σ_u is the uncorrected wave number, and the correction factor k_eff is determined from one or more internal standard lines in the spectrum, in this case from our wavenumbers measured by FTS. Dependence of thus derived k_eff on wavenumber is plotted in Figure 2.

Figure 2. Dependence of calibration factor for interferometric measurements of Ross [2] on wavenumber. The error bars are measurement uncertainties of Ross [2] and our FTS data, combined in quadrature. The solid line is a weighted fit with two cubic polynomials stitched together at about 45000 cm⁻¹. The dashed lines are 68% confidence intervals (±1 standard deviation) of the fit.

It should be noted that Figure 2 includes all Ross’s lines that were also measured in our FTS spectra. Many of those lines were weak in our FTS spectra, resulting in large error bars in Figure 2. However, there was a sufficiently large number of strong lines with small error bars, which explain the very small uncertainties of the fitted curve in Figure 2.

Unlike FTS measurements, where k_eff is a constant over the entire range of measured lines, the calibration correction of Ross’s measurements depends on wavenumber. This dependence is rather weak, and the value of k_eff is small (<10⁻⁷) in the interval (17000 to 38000) cm⁻¹ (6000 Å to 2700 Å), but k_eff notably increases (up to 3.5 × 10⁻⁷) for infrared lines, and varies rapidly for the far-UV lines below 2700 Å. The accuracy of the fitted k_eff values varies from 3 × 10⁻⁸ to 3.5 × 10⁻⁷, depending on the measurement uncertainties in Ross [2] and in our FTS data. It determines the systematic uncertainties in the Ross’s wavenumbers as now re-calibrated.

This re-calibration and increased uncertainty associated with it allowed us to explain only a small part of numerous lines strongly deviating from Ritz wavelengths in Ross’s list, noted in the Introduction. To explain the remaining problematic lines, additional factors contributing to uncertainties, not accounted for by Ross, must be considered. One such factor can be pressure shifts caused by relatively high pressure of He in his discharge, 0.9 kPa (7 Torr). Such shifts could cause quasi-random deviations of measured wavelengths in both directions from unperturbed values. Another contributing factor could be partially resolved HFS. The Doppler width reported by Ross for the sharp line at 2473 Å (40419 cm⁻¹) was about 0.1 cm⁻¹, which is of the same order of magnitude as most of the known HFS widths. He noted that partially-resolved HFS was indeed a problem in his wavelength measurements, and that his tabulated results are centers of gravity of observed HFS structures. However, he did not give any details about the method with which these centers of gravity were determined. Such determination depends on the measurement accuracy of the relative intensities of the HFS components, which might have been distorted by non-linearity of response of photographic plates used by Ross. The shift in the measured center-of-gravity wavenumber caused by errors in intensity measurements would be some fraction of the HFS width. We accounted for both types of such possible shifts (caused by pressure and HFS) by adding in quadrature a constant quantity to the wavenumber-measurement uncertainties of Ross [2]. The value of this constant was found empirically to be 0.007 cm⁻¹. These increased uncertainties are statistically consistent with residuals σ_obs − σ_Ritz of the level-optimization procedure (see Section 3).

Shenstone [1] made the most comprehensive study of the Cu II spectrum prior to Ross [2]. He photographed spectra of a copper hollow cathode (Schuler tube) filled with helium or neon using several spectrographs: 6.4 m and 3 m normal incidence grating spectrographs and two Hilger prism spectrographs for the UV and visible regions, a 2 m normal incidence vacuum grating spectrograph for the VUV region, and another concave grating spectrograph (in NBS) for the infrared region. Since Ross could not observe lines shorter than 1979 Å, Shenstone’s line list remained the only source of information about observed Cu II lines and their intensities in the VUV. We have re-measured many of VUV lines listed by Shenstone with much greater accuracy. Most of his lines in the UV, visible, and infrared regions were re-measured by Ross [2]. However, 94 lines from Shenstone [1] ranging from 836 Å to 6870 Å were not observed in our and Ross’s spectra. For 15 of them, Shenstone did not give a measured wavelength (apparently, because low resolution did not permit accurate measurement), but gave the observed intensity. Wavelength calibration and uncertainties of Shenstone’s measurements were investigated by comparing them with Ritz wavelengths calculated from Ross’s [2] energy levels. Because of the relatively low resolution of Shenstone’s measurements, the small differences of Ross’s Ritz wavelengths from more accurate ones obtained from our final level optimization (see Section 3) did not have any effect on this analysis. Since most of Shenstone’s lines used in the final line list were measured with the vacuum grating spectrograph, we compare his measurements made on this instrument with Ritz wavelength in Figure 3.

Figure 3. Deviations of vacuum ultraviolet (VUV) wavelengths measured by Shenstone [1] from Ritz values from Ross [2]. The solid line is a 2nd degree polynomial fit.

Although Figure 3 includes all wavelengths reported by Shenstone (excluding a few lines with extremely large deviations), assessment of uncertainties was made separately for “good” wavelengths given with three figures after the decimal point (in Å) and having no indication of blending or other perturbations, for wavelengths given with two decimal figures (apparently, deemed less accurate by Shenstone), and for lines indicated as blended or perturbed, or having multiple classifications. The trend indicated in Figure 3 by a solid line was derived from accurately measured lines only. It resulted in a correction to Shenstone’s VUV wavelength varying from +0.003 Å for the shortest wavelengths near 700 Å to +0.010 Å near 1980 Å. After this correction, the uncertainty for each category of lines was estimated as a root-mean-square (rms) of the residuals. These uncertainties were found to vary from 0.006 Å for the best measurements to 0.07 Å for the worst. A similar analysis was made separately for each spectrograph used by Shenstone.

For completeness, we included in our line list one line observed by Wagatsuma and Hirokawa [36] at 4485.3 Å, which was not reported by other observers. Since wavelengths reported by Wagatsuma and Hirokawa are the Ritz ones (owing to low precision of their measurements), we also give only the Ritz wavelength for this line.

In all the laboratory studies described above, only electric-dipole allowed (E1) lines could be observed, since densities in the discharge light sources are high enough to collisionally depopulate metastable levels, from which forbidden lines could emerge. However, four forbidden lines of Cu II were observed in other studies. The first observation known to us is that of Thackeray [3] who identified the line of Cu II at 3806.3 Å as the electric-quadrupole (E2) 3d^{10 1}S₀–3d⁹4s ¹D₂ transition in emission spectra of two nebulae, η Carinae and RR Telescopii. Another E2 transition, 3d^{10 1}S₀–3d⁹4s ³D₂ at 4375.8 Å, as well as the hyperfine-induced 3d^{10 1}S₀–3d⁹4s ³D₃ transition at 4558.7 Å, were observed but not identified in emission of RR Telescopii by Aller et al. [4]. The above-mentioned E2 transition at 3806.3 Å, as well as the magnetic-dipole (M1) 3d^{10 1}S₀–3d⁹4s ³D₁ transition at 4165.7 Å, were observed and identified by McKenna et al. [5] in emission of the same nebula, RR Telescopii. In the laboratory, the two E2 transitions at 3806.3 Å and 4375.8 Å were observed (with an accuracy inferior to astrophysical observations) and their radiative decay rates were measured by Prior [37] in an electrostatic ion trap.

All observed and identified spectral lines of Cu II are collected in Appendix A, Table A1. In addition to observed lines, this table includes several predicted transitions, in particular, six M1 and E2 transitions between the levels of the first excited configuration, 3d⁹4s. This table lists 2557 transitions corresponding to 2494 unique measured spectral lines, 677 of which were measured in this work, and includes 50 additional lines that are either predicted (not observed), observed but not measured, or were masked by stronger neighboring lines in observed spectra. In addition to observed wavelengths, Table A1 gives for each transition the Ritz wavelength with standard uncertainty obtained in the level optimization procedure (see Section 3), energy-level classification, intensity on a unified scale (see Section 5), and a reference to the source of the observed wavelength. For 555 transitions, we also give a critically evaluated transition probability (A-value) with its uncertainty estimate and a reference. Lines on which laser action was reported in the literature are marked with “L” in the Notes column.

In Table A1, wavelengths between 2000 Å and 20000 Å are given in standard air; outside of this region, they are in vacuum. Conversion from air to vacuum was made using the five-parameter formula from Peck and Reeder [38]. Ritz wavelengths and their uncertainties were obtained using the LOPT (level optimization) code [39] as described below in Section 3. Transition probabilities are either calculated in the present work or critically compiled from references [40,41,42,43,44,45,46,47,48,49,50,51] as described in Section 6.

3. Energy Levels

The precise positions of energy levels, as well as the Ritz wavelengths and their uncertainties, were derived from the identified lines listed in Table A1 using the least-squares level optimization code LOPT [39]. The resulting energy levels are listed in Table A2.

Of all 2557 transitions in Table A1, 113 were excluded from the level optimization procedure. Among those, there are 61 transitions that were either predicted (e.g., far-IR forbidden transitions), had poorly measured wavelengths (e.g., astrophysically observed forbidden lines), were severely blended, or were masked by much stronger nearby lines. The remaining 52 lines were excluded because their observed wavelengths deviated too much from the Ritz values. In total, we used 2443 observed transitions in our level-optimization procedure. For comparison, Ross [2,16] used 1691 observed transitions in his level optimization.

If one compares the presently found energy levels with those given by Ross [2,16], the average agreement is good. The mean difference (E_TW − E_Ross) is only 0.007 cm⁻¹ with a standard deviation of 0.016 cm⁻¹ (the subscript “TW” means “this work”). However, a more detailed comparison shows that, of the 347 levels correctly identified by Ross, 156 deviate from those given in Table A2 by more than two (up to 11) combined uncertainties. Uncertainties of our level values are on average greater than those of Ross by a factor of 1.4, owing to our increased estimate of Ross’s wavelength uncertainties. For only 32 levels our uncertainties are smaller than those of Ross (by up to a factor of eight). This improvement is due to our FTS measurements. Similar conclusions can be made for the Ritz wavelengths. Among about 500 Ritz VUV wavelengths listed by Ross, only a few are incorrect because of erroneous identifications described below. If these are excluded, the mean difference (σ_TW − σ_Ross) is 0.012 cm⁻¹ with a standard deviation of 0.019 cm⁻¹. However, for 273 VUV lines (more than half of all given by Ross), Ross’s Ritz wavelengths deviate from ours by more than twice the combined uncertainty. Our Table A1 includes 632 Ritz wavelengths for VUV lines below 2000 Å. Most of the new lines were observed and measured in this work.

The analysis that led to Table A1 and Table A2 was made in an iterative manner. In the first step, after an initial list of all observed lines was constructed, it contained more than 600 unclassified lines, 143 of which were listed by Ross [2,16], 54 by Shenstone [1], one by Kaufman and Ward [15], and the rest were observed in our VUV grating spectra. Twenty-four of these lines (18 in Ross [2,16] and 6 in Shenstone [1]) were found to be due to previously identified transitions in Cu I. To find possible identifications for the remaining unknown lines and to find proper designations for the energy levels, we made a parametric analysis of the Cu II spectrum using Cowan’s suite of atomic codes RCN/RCN2/RCG/RCE [52] (A version of the codes adapted by A. Kramida for Windows-based personal computers is available online: http://das101.isan.troitsk.ru/COWAN). In this analysis, we included the following sets of configurations: 3d¹⁰, [3d⁹](ns, nd) (n = 4–10), ng (n = 5–10), [3d⁸](4s², 4p², 4s4d, 4s5s, 4d², 4s5d) in the even parity, and [3d⁹](np, nf) (n = 4–8), nh (n = 6–8), [3d⁸](4s4p, 4s4f, 4p4d, 4s5p, 4s5f) in the odd parity, 25 configurations in total. All known energy levels from Sugar and Musgrove [17] were included in the least-squares parametric fitting (LSF) with the RCE code. The calculations were made in the relativistic mode (HFR), including Breit corrections and correlation term (explained in the RCN manual). The fitted parameters were substituted as input for the RCG code to obtain a list of predicted lines with calculated A-values. The calculated A-values and energy levels, as well as known experimental levels, were used in the input files for the visual line-identification code IDEN1 originally designed by Azarov [53] and later programmed for Windows-based computers by one of the present authors (AK). Using this tool, we identified 117 previously unclassified lines with transitions between known energy levels, revised four levels and found 28 new energy levels. The revised and newly found energy levels explained 79 previously unclassified lines and involved revised classifications of 24 lines previously identified by Ross [2] and Shenstone [1].

At this stage of the analysis, it was also found that two levels listed by Ross [2] and included in the compilation of Sugar and Musgrove [17] had to be rejected. One of them, an undesignated odd-parity level with J = 1 at 144240.6 cm⁻¹, was retained by Ross from Shenstone’s level list. It was identified by one line measured by Shenstone at 823.802 Å, which we re-measured to be at 823.8361(18) Å and identified with a transition between other previously known levels, 3d⁹4s ¹D₂–3d⁹(²D_5/2)7p ²[5/2]°₂. It was also found that there are no possible unknown odd-parity levels with J = 1 sufficiently close to the value given by Ross to explain this level. Another rejected level is also of odd parity, designated by Ross as 3d⁹6p ³P°₀ (at 141154.164 cm⁻¹). It was based by Ross on two lines, one observed by Shenstone at 853.56 Å and identified by Ross as a transition from this level to 3d⁹4s ³D₁, and another observed by Ross at 3217.641 Å, which he interpreted as a transition from this level to 3d⁹(²D_3/2)5s ²[3/2]₁ (to be consistent with our tables, we use our new JK designations). Both these transitions were predicted to be extremely weak, certainly much weaker than other possible transitions from this level. We re-measured the first line to be at 853.544(2) Å and re-classified both lines as transitions from other levels. In addition, the energy given by Ross deviates too much from that predicted by our parametric fitting.

Two levels listed by Ross as 3d⁹6p ³F°₂ and ³D°₁ at 141244.576 cm⁻¹ and 141734.167 cm⁻¹, respectively, were each based by Ross on several transitions to lower-lying even levels with J = 1 or 2. Most of the corresponding lines were previously observed and similarly identified by Shenstone. However, we found that observed line intensities agree much better with those predicted if assignments of these two levels are interchanged. Further proof for this revision was provided by our identification of two transitions from the lower of these two levels down to levels with J = 3. One of the corresponding lines was newly observed in our VUV spectrum, and another one was present among Ross’s unclassified lines.

Following Shenstone [1], Ross interpreted the level at 137212.765 cm⁻¹ as 3d⁸4s4p ¹P°₁. Sugar and Musgrove [17] gave a more specific designation, 3d⁸(³P)4s4p(³P°) ¹P°₁ based on a parametric calculation made by Roth [54]. We found three transitions connecting this level with even J = 3 levels. Since other combining levels have J = 1 and 2, the only possible J value for this level is 2. We labeled this strongly mixed level as 3d⁸(¹G)4s4p(³P°) ³F°₂, although it represents only 36% of the percentage composition; an equal contribution is from 3d⁸(³F)4s4p(¹P°) ³F°₂, followed by 14% of 3d⁸(³P)4s4p(³P°) ¹D°₂.

Ross found the level at 147491.888 cm⁻¹, which he designated as 3d⁹7p ³F°₃ based on three weak lines at 3360.9941 Å, 9310.353 Å, and 9569.11 Å, identified as transitions from this level down to 3d⁹4d ³G₃, 3d⁹5d ³P₂, and 3d⁹5d ³F₄. Although these three lines indeed perfectly satisfy the Ritz combination principle, our calculations indicate that their intensities should be negligibly small, while much stronger transitions to other even-parity levels should occur, but were not observed by Ross. The strongest predicted transitions from this level are in the VUV region inaccessible to Ross. We have found three lines in our VUV exposures at 824.663 Å, 1609.342 Å, and 1924.548 Å, which have wavelengths and intensities consistent with this level, placing it at our new revised position, 147525.93 cm⁻¹. All other odd-parity levels with J = 3 predicted to occur within ±2000 cm⁻¹ from this energy are experimentally known, which leads us to conclude that the combination of three lines observed by Ross is spurious. We note that the density of observed lines in the UV, visible, and IR regions is sufficiently high to produce several tens of spurious combinations of two, and a few of three lines, which we observed in the combined line list. We could not find alternate identifications for the three lines assigned previously by Ross to this revised level.

Three other levels in Ross’s list were found to be questionable, either because they were based on only one or two weak lines, or because the energy strongly disagrees with our parametric calculation. These levels are at 154838.963 cm⁻¹, 155244.833 cm⁻¹, and 156958.096 cm⁻¹, designated by Ross as 3d⁹8d ³P₁, ³P₀, and ³F₂, respectively.

After the new identifications were made, the new experimental energies were incorporated in the LSF procedure, and the questionable levels removed. We also inserted in the LSF several tens of levels belonging to the [3d⁹]9d, 10d, 8g, 9g, 10g, 7f, 8f, 6h, 7h, and 8h levels whose positions were accurately extrapolated by Ritz-type quantum defect or polarization formulas (see Section 4). These levels were found to be sufficiently pure, unperturbed by interactions with other configurations, and thus the series formulas provided dependable results.

In this final LSF, 218 known even-parity levels were fitted with 38 free parameters with a standard deviation of 40 cm⁻¹, and 241 known odd-parity levels were fitted with 35 free parameters with a standard deviation of 72 cm⁻¹. The fitted (LSF) and ab initio Hartree-Fock (HF) values of parameters are given in Table A3. In both parities, the ζ_3d parameters of the 3dⁿ core were linked together in one group for all configurations, so that their LSF/HF ratio was the same for all members of the group, but was allowed to vary in the fitting. Other parameters, similar in different configurations, such as the effective parameter α_3d, electrostatic parameter F²(3d,3d) of the 3d⁸ core, and configuration-interaction parameters, were also linked in similar groups, which decreased the number of free parameters and made the fitting more stable.

Using the transformation procedures implemented in Cowan’s RCE code, eigenvector compositions were calculated in several coupling schemes. Similar to the spectrum of neutral nickel analyzed by Litzén et al. [21], most of the 3d⁹nl configurations were found to be best described in the J₁l (otherwise known as JK or J_cK) coupling scheme, in which the total angular momentum of the core (3d⁹ in this case) is combined with the orbital momentum of the valence electron to produce the K quantum number, which is then combined with the spin of the valence electron to obtain the final total angular momentum J. In Ni I, Litzén et al. [21] found the lowest [3d⁹]nl configurations, 4s, 4p, and 5p, to be better described in the LS coupling scheme, which is also the best for the 3d⁸4s² and other 3d⁸nln′l′ configurations. In Cu II, our findings are similar, except that the 3d⁹5p configuration is better described by J₁l coupling. The J₁l purity of the 3d⁹nl configurations increases from 65% for 3d⁹6p to 100% for 3d⁹ns, nh (n ≥ 6), and ng (n ≥ 6), and generally increases with increasing n and l. This general trend is disrupted in 3d⁹6p. This configuration strongly interacts with 3d⁸4s4p, unlike 3d⁹5p, for which this interaction is somewhat weaker, resulting in the average J₁l purity of 75%. For the 3d⁸4s4p configuration, in agreement with the previous analysis by Roth [54], we found that the best description is obtained by first combining the quantum numbers of the 4s and 4p electrons with each other to produce an intermediate LSJ term (³P° or ¹P°) of the 4s4p valence shell, and then combine it with LSJ of the 3d⁸ core. Although the average purity of 3d⁸4s4p in this coupling scheme is rather high, 73%, many of its levels are strongly mixed with other configurations, rendering assignment of single-configuration labels arbitrary. Several levels attributed to this configuration have a leading percentage of the composition smaller than 30%. In a few cases, such as the levels at 139331.149 cm⁻¹ (J = 3) and 139710.491 cm⁻¹ (J = 2), we assigned labels corresponding to the second leading term in the composition, in order to preserve uniqueness of the labels within the J manifolds. The labels assigned to the levels do not fully describe their physical nature; percentage compositions given in Table A2 are somewhat better in this regard.

The high J₁l purity of the 3d⁹ng configurations and very small values of parameters describing interactions between 3d⁹ and ng shells allows for accurate prediction of the levels that were missing in Ross’s levels list. This permitted us to find some of these levels from the lines left unclassified in his analysis.

For each level, Table A2 gives a number of observed lines on which this level is based. Most of the levels are based on more than two observed lines. However, 71 of them are derived from only one or two observed lines. Most of them are firmly identified, because the observed lines are the strongest predicted ones, and the level positions are confirmed by trends along series. Five of such levels are marked as questionable, because the corresponding series are strongly perturbed, or because the observed lines are not the strongest predicted to occur from these levels. The absence of predicted stronger lines could be explained by different registration sensitivity in exposures used in different spectral regions.

We identified the previously missing 3d⁸4s^{2 1}S₀ level based on one line observed at 1807.8535 Å in two exposures in our VUV spectra and at 1807.84 Å by Shenstone [1]. We assigned this line to the strongest predicted transition from this level, terminating at 3d⁹4p ¹P°₁. Although this line is observed to be about 20 times stronger than predicted, this was the only unidentified line within the interval of ±3000 cm⁻¹, and it places the 3d⁸4s^{2 1}S₀ level within 25 cm⁻¹ of its predicted position. Therefore, we believe that this identification is correct.

Five odd-parity levels are given in Table A2 with revised designations. The level with J = 3 at 121524.8509 cm⁻¹ was previously labeled by Sugar and Musgrove [17] as 3d⁹5p ³D° with a 53% contribution of this term in the composition, as given by Roth [54]. Although our calculation yields the same leading term in the composition of this level, the total contribution from the 3d⁸4s4p configuration is calculated to be greater than from 3d⁹5p. Therefore, we designated this level by the second largest component, 3d⁸(³F)4s4p(³P°) ¹F°. A marginally larger contribution of the 3d⁹5p ³D° term was found in the J = 3 level at 121079.1501 cm⁻¹, which we attributed to this configuration. The J₁l-coupling designation gives a better description of this level, the leading term being 54% of 3d⁹(²D_5/2)5p ²[5/2]°. In effect, the identifications of these two J = 3 levels at 121079.1501 cm⁻¹ and 121524.8509 cm⁻¹ have been interchanged. This revision is supported by better agreement of observed and calculated line intensities.

The J = 4 level at 134742.863 cm⁻¹ was labeled by Sugar and Musgrove [17] as 3d⁹6p ³F°, and its composition was given as 49% of this term and 39% of 3d⁸(¹G)4s4p(³P°) ³F°. We found the leading term to be 50% of 3d⁸(³F)4s4p(¹P°), which we use as a revised label. We note that Sugar and Musgrove gave the same configuration and term label to another J = 4 level at 139395.786 cm⁻¹ with almost the same percentage composition. We found for the latter level 59% contribution from 3d⁹6p ³F°, but designated it in J₁l-coupling as 3d⁹(²D_5/2)6p ²[7/2]°.

Another J = 4 level at 137938.904 cm⁻¹ was designated by Sugar and Musgrove [17] as 3d⁸(³F)4s4p(¹P°) ³F° with 53% of this term in the composition. We found the leading terms to be 49% of 3d⁸(¹G)4s4p(³P°) ³F°, 39% of 3d⁹6p ³F°, and only 5% of the term given as label by Sugar and Musgrove. We changed the label to the leading term indicated by our calculation.

The J = 3 level at 139331.149 cm⁻¹ was designated by Sugar and Musgrove [17] as 3d⁹6p ³D° with 56% of this term in the composition. In our calculation, the leading LS term is found to be 46% of 3d⁹6p ¹F°. However, in J₁l-coupling adopted for the 3d⁹6p configuration, the leading term is 32% of 3d⁹(²D_5/2)6p ²[7/2]°, which is used to label another level having 62% of this term. Thus, we labeled the level at 139331.149 cm⁻¹ by the second leading LS term of its composition, 3d⁸(¹G)4s4p(³P°) ³F°.

4. Ionization Energy

Ross [2] derived the value for the ionization limit by extrapolation of quantum defects along 12 series of the type 3d⁹nl (two ns, nine nd, and one nf, with n ranging from 4 to 10 for the ns J = 3 series, 4 to 9 for the ns J = 1 series, and 4 to 8 for the rest). Although Ross used LS designations for all the levels involved, the series he chose are almost pure in J₁l coupling, resulting in smooth behavior of quantum defects along the series. Using the RITZPL computer code by Sansonetti [55], we repeated Ross’s derivation with our more accurate level values and obtained slightly different values for the series limits. In the derivation of the limit, we added two more 5-member 3d⁹nd series, in which we found some new identifications. The weighted average of the limits obtained closely agrees with the average value adopted by Ross. In addition, series limits obtained from six three-member series with an exact fit of the polarization formula (Sansonetti [56]) produced values in close agreement with this average. Thus, we adopted the value for the ionization limit given by Ross [2], 163669.2(5) cm⁻¹ or 20.292 39(6) eV, which is now confirmed.

Table A2 includes predicted energies for 89 [3d⁹]nd, nf, ng, and nh levels for which no reliable identification could be found in the observed spectra. These levels are not necessarily those that produce the strongest predicted lines. Rather, they are those that are easier to accurately predict, because the corresponding series have relatively small perturbations. In this derivation, we used predicted positions for centers of gravity of groups of closely located levels along series, using the RITZPL (quantum-defect formula) and POLAR (polarization-formula) extrapolation codes by Sansonetti [55,56], which we combined with fine-structure intervals predicted by the LSF (described in Section 3). Uncertainties assigned to these levels in Table A2 are weighted means of the “observed-calculated” residuals of the LSF, calculated separately for known levels with J₁l purities of ≥99%, (97 to 98) %, and (92 to 96) %. Some of the remaining unclassified lines observed by Ross [2,16], Shenstone [1], and by us may be due to these levels. However, we could not reliably identify them because of lack of observed Ritz combinations.

5. Line Intensities

Procedures used in the present work to adjust observed line intensities to a common scale were described in detail by Kramida [57,58]. In this derivation, line intensities observed in each experiment are roughly modeled as described by Boltzmann level populations with certain effective excitation temperature T_eff. This temperature is found from a Boltzmann plot built using calculated transition probabilities. The ratios of predicted Boltzmann-population intensities are plotted against wavelengths to derive the response function of the registration equipment, which is then removed from the observed intensities to obtain an improved fit for T_eff from the Boltzmann plot. For photographic registration, an additional correction of non-linearity of intensity registration with exposure is deduced from a plot of ratios of calculated and observed intensities versus observed intensity. This procedure is repeated iteratively until convergence is achieved. Then it is easy to scale the reduced intensities observed in experiments with different T_eff and different sensitivity to a common value of T_eff. In this way, we combined intensities observed in our 22 VUV and 3 FTS spectrograms listed in Table 1 with those reported by Shenstone [1], Kaufman and Ward [15], and Ross [2,16] and reduced them to the scale derived from Ross’s observed intensities to produce the average values given in Table A1. This scale corresponds to T_eff = 1.5 eV, which is about average for all experiments included in the analysis. For different experiments, the fitted value of T_eff varied between 0.6 eV in some of our VUV exposures to 11 eV in observations of Kaufman and Ward [15]. It should be noted that in most experiments analyzed here populations of highly excited levels were enhanced by resonant transfer from excited levels of helium or other rare gases used in the discharges. This population transfer is the mechanism leading to population inversion and producing laser action observed in hollow-cathode discharges. Thus, it should be expected and is indeed observed that level populations deviate from the Boltzmann distribution by a factor of three on average and strongly vary depending on discharge conditions. Line intensities are given in Table A1 in terms of total energy flux under the line contour.

As noted in Section 2, only E1-allowed lines were observed in laboratory discharges. Thus, the intensity scale adopted for E1-forbidden lines is different from the allowed lines. It is based on relative intensities observed in nebulae spectra by Thackeray [3], Aller et al. [4], and McKenna et al. [5], modified in such a way that the relative intensities of lines from a common upper level are consistent for different observations.

6. Transition Probabilities

Transition probabilities of Cu II were reported in 42 papers, the full list of which can be found in the NIST Atomic Probability Bibliographic Database (Kramida and Fuhr [59]). In addition, we have calculated them using Cowan’s codes [52] using our LSF parameters described in Section 3. To assess the uncertainties of all available data sets, we used evaluation procedures described by Kramida [57].

The initial reference data set was constructed of 41 A-values determined by Ortiz et al. [50] from branching fractions measured using laser-induced breakdown spectroscopy and lifetimes calculated using the Cowan suite of codes [52], modified by inclusion of core-polarization effects. The high accuracy of theoretical lifetimes used in that work was confirmed by excellent agreement with accurate measurements made by Pinnington et al. [51] and Cederquist et al. [43], as well as with other advanced calculations.

This initial selection was expanded by inclusion of theoretical A-values from Dong and Fritzsche [45] obtained in a large-scale multiconfiguration Dirac-Fock calculation accounting for relaxation effects in the orbitals. Uncertainties of these theoretical data were estimated by comparing the results obtained by those authors in the Babushkin (length) and Coulomb (velocity) gauges. This comparison indicated that the stronger lines with line strength S > 10⁻⁶ a.u. were calculated with uncertainties in A-values of about 12% on average, while for weaker lines the average uncertainty was much larger, 60%. These conclusions are supported by good agreement (less than 10%) of calculated lifetimes with measurements. For 18 transitions the A-values reported by Dong and Fritzsche [45] were normalized to lifetimes of the upper levels measured by Pinnington et al. [51] and by Cederquist et al. [43].

For three transitions representing the sole allowed decay channels of their upper levels, the lifetimes measured by Pinnington et al. [51] and by Cederquist et al. [43] were directly converted into A-values and also added to the reference data set. Further expansion of the reference data set was provided by results of Crespo López-Urrutia et al. [44] obtained by combining their own measurements of emission branching fractions with radiative lifetimes measured in other studies. From this work, the results obtained using the lifetimes reliably measured by Cederquist et al. [43] and by Kono and Hattori [48] were used without adjustments. However, for several transitions we re-normalized their results to lifetimes more accurately measured by Pinnington et al. [51]. Uncertainties of Crespo López-Urrutia et al. [44] were estimated by combining in quadrature systematic contributions from the uncertainties of the lifetimes and statistical uncertainties, which we estimated to vary from less than 5% for the strongest lines to 90% for the weakest lines, which we assumed to have a signal-to-noise ratio about 1.

Kono and Hattori [48] measured radiative lifetimes of some of the 3d⁹4p and 3d⁹5s levels by a delayed coincidence technique and combined them with branching fractions, some of which were measured in a specially designed discharge tube, and some of which were obtained in a single-configuration LSF-adjusted intermediate-coupling calculation. These authors did not report separately their measured branching fractions, which impedes assessment of their results. Instead, they used all of their data, both experimental and theoretical, together, and adjusted the resulting A-values to satisfy the J-file sum rule. We renormalized several of their reported A-values to radiative lifetimes measured more accurately by Brown et al. [42], Pinnington et al. [51], and Cederquist et al. [43] and estimated the uncertainties by a method similar to the one described above in evaluation of results of Crespo López-Urrutia et al. [44].

Assessment of measurements made by Neger and Jäger [49] and by Hefferlin et al. [47] (hereafter referred to as N88 and H71) presented the greatest difficulties, since they grossly disagree with each other. N88 reported relative transition probabilities (A-values) of seven Cu II lines measured by using an axial discharge type of an exploding copper wire. The rather vague description of these measurements does not include the temperature value used in the data reduction. However, Neger and Jäger compare their results with those reported by Lux [60], obtained with similar equipment, and note that Lux determined the plasma temperature to be 26500(3500) K (2.3(3) eV) from a Boltzmann plot using several Cu I lines with known transition probabilities. The relative A-values reported by N88 (using the line at 4555.92 Å as reference) have uncertainties ranging from 18% to 25% and perfectly agree with those of Lux [60]. Thus, we assumed that they used Lux’s temperature value in their data reduction and restored the observed line intensities from the reported line ratios and this temperature. Two of the lines reported in N88 are in common with more accurate measurements of Ortiz et al. [50].

Hefferlin et al. [47] (H71) determined relative intensities of 11 Cu II lines from photoelectric radiance measurements on the Burnout V experimental magnetic-confinement fusion reactor at the Oak Ridge National Laboratory. To derive the relative log(gf) values from these measurements, they assumed the electron temperature to be 67 eV (±50%). Neger and Jäger [49] blamed this large uncertainty in the temperature value for the discrepancy of the H71 results with theirs. We note that Cu⁺ should be completely ionized at this high temperature. Thus, an obvious path would be to dismiss the results of H71 as erroneous. However, their reported relative log(gf) values appear to be internally consistent and agree well with other independent estimates. Thus, we restored the observed line intensities from them, using the 67 eV temperature as reported in H71, and attempted to reconcile the two sets of relative intensities (from H71 and N88) by using the following procedure.

As a first step, to determine initial estimates of the excitation temperatures in H71 and N88, we used Boltzmann plots with reference A-values for the lines at 4043.48 Å and 4227.94 Å from Ortiz et al. [50], and for the line at 4909.73 Å from Cederquist et al. [43], while for all other lines we used our Cowan-code calculations. As a second step, using the temperatures derived from these Boltzmann plots, we determined the adjusted A-values from the H71 and N88 observed line intensities. Then we replaced the Cowan-code A-values in the reference set with logarithmic means of thus obtained H71 and N88 adjusted A-values and found adjusted temperature values from the Boltzmann plots. The second step was repeated iteratively until reasonable convergence, i.e., until the change in the temperature values between iterations decreased below 0.001 eV. The final Boltzmann plots for H71 and N88 are shown in Figure 4a,b, respectively.

Figure 4. Boltzmann plots for relative intensities of observed lines: (a) Measurements of Hefferlin et al. [47] (H71); (b) Measurements of Neger and Jäger [49] (N88). The A-values used in these plots are the final adopted values given in Table A1. The error bars are combined uncertainties of A-values and relative intensities (see text).

The excitation temperatures determined for the H71 and N88 data sets are 0.662(5) eV and 1.4(5) eV, respectively. The latter is somewhat lower than the Lux [60] value used in N88, 2.3(3) eV. The final adjusted A-values deduced from the H71 and N88 data are compared with the adopted A-values in Figure 5. In this plot, the reference A-values used for the two leftmost lines (4043.48 Å and 4227.94 Å) and for the rightmost line at 4909.73 Å are from Ortiz et al. [50] and Cederquist et al. [43], while the rest of the lines use the mean of H71 and N88. The error bars are combined uncertainties of the measured line ratios and reference A-values. This plot shows that the adjusted A-values from H71 and N88 are consistent with each other, as well as with the adopted reference A-values.

Figure 5. Comparison of adjusted A-values deduced from the line ratios reported by Hefferlin et al. [47] (H71) and by Neger and Jäger [49] (N88). The error bars are combined uncertainties of the measured line ratios and adopted reference A-values.

With the reference data set constructed from data described above, assessment of uncertainties in the theoretical study by Biémont et al. [41] was relatively easy to do by plotting the ratio of the calculated values to the reference ones against line strength S and calculating standard deviations for different ranges of S. This procedure resulted in estimated uncertainties of 9% for S ≥ 8.5 atomic units (a.u.), 22% for S = (0.2 to 8.5) a.u., and 120% for S < 0.2 a.u.

Assessment procedures described above resulted in 210 reference A-values with uncertainties less than 25% covering a wide range of line strengths from 0.06 a.u. to 155 a.u., after which it became possible to evaluate the uncertainties of our LSF calculations. Comparison of our calculated A-values with the reference ones is illustrated in Figure 6.

Figure 6. Comparison of transition probabilities calculated in this work (A_TW) with reference values (A_ref, see text). Natural logarithm of the ratio A_TW/A_ref is plotted against our calculated line strength, S_TW (in atomic units).

This plot displays a typical behavior of theoretical transition probabilities. Namely, the strongest lines exhibit the smallest discrepancies from the reference values, while for weaker lines the magnitude of discrepancies grows. A similar comparison was made between A-values produced in our two LSFs (the final and preliminary ones, described in Section 3). From these comparisons, we estimated the uncertainties of our A-values to be ≤10% for S > 200 a.u., ≤15% for S = (50 to 200) a.u., ≤30% for S = (4.3 to 50) a.u., and ≥50% for smaller S. We included 79 of our best calculated A-values in Table A1.

Studies of E1-forbidden transition probabilities of Cu II are very scarce. Garstang [46] calculated A-values for several M1 and E2 transitions from the first excited configuration, 3d⁹4s, down to lower-lying levels of the same configuration and to the ground state, 3d^{10 1}S₀. He used the pseudo-relativistic Hartree-Fock method with superposition of configurations and LSF-adjusted Slater parameters, similar to the one implemented in Cowan’s codes [52] used in the present work, but limited by inclusion of only three low-lying configurations of even parity. Beck [61] made an ab initio restricted non-relativistic multiconfiguration Hartree-Fock calculation for the 3d^{10 1}S₀–3d⁹4s ^1,3D₂ E2 transition and obtained A = 2.33 s⁻¹, somewhat larger than the sum of Garstang’s values for transitions from ¹D₂, 1.7 s⁻¹, and ³D₂, 0.12 s⁻¹. Prior [37] measured the A-value for the 3d^{10 1}S₀–3d⁹4s ¹D₂ transition at 3806.3 Å to be 1.60(24) s⁻¹, in excellent agreement with Garstang’s semiempirical value. The most recent multiconfiguration Dirac-Hartree-Fock calculation of Andersson et al. [40] gave A = 1.937 s⁻¹ for this transition. However, their calculated wavelength is 3724.7 Å, significantly shorter than experimental. Adjustment to the experimental wavelength yields A_adj = 1.74 s⁻¹, in good agreement with Prior [37] and Garstang [46]. A similar adjustment of the value of Andersson et al. [40] for the 3d^{10 1}S₀–3d⁹4s ³D₂ transition at 4375.8 Å (which Andersson et al. [40] calculated to be at 4275.8 Å) gives A_adj = 0.093 s⁻¹, about 30% lower than Garstang’s result. For these two E2 transitions, our A-values calculated with Cowan’s codes are too high by a factor of about 1.7. We assume that our A-value for the predicted 3d⁹4s ³D₃–³D₁ E2 transition at 48318 Å, 9 × 10⁻⁸ s⁻¹, has a similar low accuracy. The 3d^{10 1}S₀–3d⁹4s ¹D₂ transition at 3806.3 Å was observed by Thackeray [3] and by McKenna et al. [5] in emission spectra of nebulae.

It should be noted that, in addition to the two E2 transitions mentioned above, Andersson et al. [40] give calculated A-values for the magnetic-octupole (M3) and hyperfine-induced 3d^{10 1}S₀–3d⁹4s ³D₃ transitions at 4559 Å. The latter are different for various HFS components of the two isotopes (⁶³Cu and ⁶⁵Cu) and are typically on the order of a few times 10⁻⁹ s⁻¹, three orders of magnitude greater than for the M3 transition. This transition, as well as the 3d^{10 1}S₀–3d⁹4s ³D₂ E2 transition at 4375.8 Å, was observed by Aller et al. [4] in the spectrum of the RR Telescopii nebula.

A-values for M1 transitions are relatively easier to calculate than E1 and E2 transitions, since their calculation does not involve radial integrals, but only amplitudes of eigenvector components. We compared our calculated A-values for M1 transitions with those of Garstang [46] and found that all of them agree to better than 15%. We included in Table A1 our A-value for the 3d^{10 1}S₀–3d⁹4s ³D₁ M1 transition at 4165.7 Å, which was not given by Garstang [46]. It turned out to be extremely small, 2.1 × 10⁻¹² s⁻¹. Our calculation indicates that there is no E2 contribution to the total decay rate of the 3d⁹4s ³D₁ level. This makes the identification of the line observed at this wavelength by McKenna et al. [5] with this transition questionable. Possible explanations for this observation could be (1) our calculated M1 A-value is greatly underestimated; (2) there is a considerable contribution of E2 transition to this line, which for unknown reason is computed as negligibly small by Cowan’s codes; (3) hyperfine-induced transition significantly increases the total radiative rate; (4) the population of the 3d⁹4s ³D₁ level in RR Telescopii is many orders of magnitude greater than that of ³D₂ and ¹D₂; or (5) the identification is incorrect, and the observed line is possibly due to some other species. As explained above, the first explanation is rather unlikely. To confirm or disprove the second and third explanations, more extensive atomic calculations are needed, while checking the fourth one requires population-kinetics modeling.

7. Conclusions

The present work provides a comprehensive list of all observed, classified, and predicted spectral lines of Cu II, which includes 2557 transitions with wavelengths from 675 Å to 10.9 μm. Over 600 of them were measured in this work using grating and Fourier-transform spectrometers. Experimental wavelengths of 2443 transitions were used in a least-squares level optimization procedure to produce optimized values for 379 energy levels, of which 29 are newly identified, and nine are revised. The previous analysis of Ross [2,16] is largely confirmed. However, our extended base for the levels optimization results in more dependable level values and Ritz wavelengths that can be used as secondary standards in the vacuum ultraviolet region. An improved theoretical interpretation of the energy levels was made by a parametric least-squares fitting with Cowan’s atomic codes, which included all experimental levels. The fitted Slater parameters were used to calculate radiative transition probabilities for electric-dipole, magnetic-dipole, and electric-quadrupole transitions, which were critically evaluated together with other published data to construct a list of recommended A-values for 555 transitions.