© ESO 2018

1 Introduction

This work is part of a larger effort to catalog, interpret, and model the photoabsorption spectrum of CO in the 90–155 nm wavelength region. These measurements are performed at the third-generation SOLEIL synchrotron facility in Saint-Aubin, France. We employ the Fourier-transform spectrometer (FTS) installed on the DESIRS beam line, a unique instrument that combines high spectral resolution and a high signal-to-noise ratio (S/N) in the vacuum ultraviolet (VUV) wavelength range.

In the course of our earlier work (2008–2015) on CO photoabsorption spectroscopy in the 90–155 nm region, we were mainly interested in oscillator strengths and perturbations for several CO isotopologues. A large part of this work concerned the Rydberg W–X bands and Rydberg complexes in the 92.5–97.5 nm range: Eidelsberg et al. (2012, 2014, 2017) for ¹²C¹⁶O, ¹³C¹⁶O, ¹²C¹⁸O, and ¹³C¹⁸O, respectively, and perturbations in the W–X bands (Heays et al. 2014) and the f-value measurements of the lowest VUV states (Stark et al. 2014), while another part dealt with the A–X bands for ¹³ C¹⁶O (Gavilan et al. 2013) and ¹³ C¹⁸O (Lemaire et al. 2016). The common goal of these studies was the accurate determination of oscillator strengths, with an absolute calibration made by reference to the unperturbed B¹ Σ ⁺(v′ = 0)–X¹Σ⁺(v′′ = 0) band that was previously well characterized by high-resolution (0.14 cm⁻¹) laser-based measurements (Stark et al. 1999) and by synchrotron-based measurements (Federman et al. 2001). The B¹ Σ ⁺–X¹Σ⁺ bands were already extensively investigated for four isotopologues (¹² C¹⁶O, ¹³ C¹⁶O, ¹² C¹⁸O, and ¹³ C¹⁸O) in both absorption and emission (Eidelsberg et al. 1987) using the Observatoire de Paris (Meudon, France) 10 m VUV grating spectrograph. In that work, term values were derived for the B00, B10, and B20 absorption bands. The uncertainty on the absolute wavenumbers was estimated to be ±0.1 cm⁻¹.

Throughout this paper, the notation is simplified as follows: states are designed by their symmetry (e.g., X¹ Σ ⁺ or E¹ Π), while a band is denoted E¹ Π (v′)–X¹Σ⁺(v′′) or for brevity EXv′v′′, for example, EX20 for v′ = 2 and v′′ = 0, or shorter: E20. The notation indicating the isotopologues is also simplified in tables and figures, where we write, for example, 1216 for ¹² C¹⁶O, etc.

The current investigation describes our high-resolution measurements of the B¹ Σ ⁺, C¹ Σ ⁺, and E¹Π states for six CO isotopologues in the 101–115 nm range. This range encompasses the following absorption transitions: B(v′ = 0, 1 and 2), C(v′ = 0, 1, 2 and 3), and E(v′ = 0, 1, 2 and 3) from the fundamental electronic state X(v′′ = 0).

This work revisits and completes, 25 yr later, part of the CO atlas of transition frequencies started by the Paris-Meudon Observatory team (Eidelsberg et al. 1991; Le Floch 1992), and initiated by the work of Letzelter et al. (1987) and Viala et al. (1988) on the photoabsorption and photodissociation cross sections, either measured or calculated for the four isotopologues ¹² C¹⁶O, ¹² C¹⁸O, ¹³ C¹⁶O, and ¹³ C¹⁸O. It improves and completes calculations derived from the combination of earlier low-resolution measurements of term values and molecular constants of B00 and B10 for ¹² C¹⁶O (Le Floch & Amiot 1985), of C00 and E00 for ¹² C¹⁶O (Le Floch 1992), and of B00, B10, C00 and E00 for ¹² C¹⁸O and ¹³ C¹⁸O (Haridass et al. 1994). Line positions of B20 for ¹² C¹⁶O have been studied by Baker & Launay (1994).

This work also revisits and completes earlier experimental work at low resolution on E00 and E10 (Baker et al. 1993, 1994). Higher resolution work (Cacciani et al. 1995, 2001; Cacciani & Ubachs 2004; Drabbels et al. 1993a,b; Ubachs et al. 1995, 2000) is discussed in detail in Sect. 2.1 as these data are used in this work for the absolute calibration of our data.

It is also worth mentioning the extensive work of Morton & Noreau (1994), which provides a compilation of electronic transitions (including BX00 to BX20, CX00 to CX30, and EX00 to EX20) in the CO molecule (¹² C¹⁶O, ¹² C¹⁸O, ¹³ C¹⁶O, and ¹³ C¹⁸O). Line positions are limited in this work to J′′ ≤ 6. This paper includes all experimental data published up to 1994.

A first detailed model of CO photodissociation, based on laboratory data, including depth-dependent attenuation and isotope-selective self-shielding of photodissociation rates, was developed by van Dishoeck & Black (1988) to model in detail, coupled with a chemical network, the structure and chemistry of a variety of interstellar clouds. This work, updated by measurements produced in the subsequent 20 yr, was revisited by Visser et al. (2009), including self- and mutual-shielding of all isotopologues (in particular, for the first time, ¹² C¹⁷O and ¹³ C¹⁷O) as well as shielding by atomic and molecular hydrogen.

All term values are referenced to the X¹ Σ ⁺(v′′ = 0, J′′ = 0) ground state of the respective isotopologues, according to the ground-state energy levels determined by Guelachvili et al. (1983) and Farrenq et al. (1991).

This work only reports and is based on lines that are observed and clearly identified in spectra, with the exception of the extremely congested Q-branches of the E state (at low J) for which we report in our tables literature values obtained at very high resolution (for E00 and E10) or estimated (for E20) for the sake of completeness.

This article is organized as follows. Section 2 briefly describes the experimental setup and the analysis procedure. Section 3 presents our results: line assignments, term values, and molecular constants for each state (B, C, and E) and bands observed. The last section presents our concluding remarks.

2 Experimental setup and data analysis

CO spectra are recorded at high resolution using the vacuum-ultraviolet Fourier-transform spectrometer (VUV-FTS) available on beamline DESIRS (Dichroïsme Et Spectroscopie par Interaction avec le Rayonnement Synchrotron) of the SOLEIL synchrotron. The beamline and spectrometer have been described in detail in previous publications (de Oliveira et al. 2009, 2011, 2016; Nahon et al. 2012, 2013).

Four bottles of isotopically purified gases, namely ¹² C¹⁶O (Alphagaz, 99.997%), ¹² C¹⁸O (ICON Isotopes, ¹⁸O 99%), ¹³ C¹⁶O (Messer, ¹³C 99.1%; ¹⁶ O 99.95%), ¹³ C¹⁸O (Cambridge Isotopes, ¹³C 99%, ¹⁸ O 95%), and one bottle containing a ¹² C¹⁶O/¹²C¹⁷O/¹²C¹⁸O mixture (ICON Isotopes, 41.5%, 48.5%, and 9.9% respectively), are used to obtain data for five isotopologues. The presence of a sixth isotopologue, the rarely studied ¹³ C¹⁷O, is detected as an impurity in the ¹³ C¹⁶O and ¹³ C¹⁸O bottles, and serves to complete this analysis, which provides a consistent dataset on six natural isotopologues.

Sample gases continuously flow through a 10 cm long windowless absorption cell that is open on both sides through capillary tubes. Most spectra are recorded at room temperature (295 K), but a few are obtained with the central part of the cell cooled by liquid nitrogen; this results in a gas temperature of 90 ± 5 K. In some cases, these cooled spectra are useful for improved line assignations by reducing the number of lines in a spectrum and their Doppler broadening.

A total of 69 spectra, recorded at different pressures and spectral resolutions, were analyzed for this work (amounting to 3327 individual lines). The analysis was performed line by line, determining the line positions by modeling them as Gaussian or Voigt functions (for ~97% of the cases), and at times extracting them from simulations of the spectra of blended lines. In order to improve the accuracy, the present results rely on up to four different records for a given band and a given isotopologue. The bands observed in this work are reported in Table 1.

A key element of this work is the need for absolute wavelength calibration. The first step in the calibration procedure is provided by the FTS team. In summary, the raw FTS interferogram data based on the accurate measurement of the mirror displacement are first phase-corrected and then Fourier-transformed into a frequency spectrum. The resulting spectra are frequency-calibrated using atomic lines from different origins that appear in the spectra (de Oliveira et al. 2011, 2016). The accuracy of individual rovibrational lines is not only dependent on the accuracy of the absolute frequency calibration atomic lines, but also on the spectral resolution and on the strength and blendedness of each measured line. The parameters involved are the number, N, of independent scanning steps for a given line, which depends itself on the width, W, (mainly Doppler) of the measured line, and on the S/N compared to the background continuum signal. The final accuracy of line positions, σ in wavenumbers, reported by de Oliveira et al. (2011), is based on the empirical expression Δ (σ) ~) (see also their reference 20).

Lemaire et al. (2016) reported line positions determined from VUV-FTS spectra with a relative accuracy better than ~ ±0.008 cm⁻¹ at 87 000 cm⁻¹ (or ~±0.01 pm at 115 nm). A comparison of wavenumber measurements of common sets of lines from multiple independent spectra is consistent with this estimated accuracy.

Two methods were used to place all spectra on a unique wavelength scale. First, more than 30 atomic lines (mainly Xe I, Kr I, and sometimes O I) present in the studied range were used with reference frequencies taken from the NIST atomic lines database¹. The presence of these gases is due to unintentional minor contamination or to a column of rare gas introduced on the beamline intended to filter out high-frequency harmonics generated in the undulator. Most of these lines have been measured with an accuracy of 10⁻³ nm and some with an accuracy of up to 10⁻⁶ nm. These latter are O I: 115.21512 nm (Kaufman & Edlén 1974), Xe I: 106.125564 nm, 105.612829 nm, 104.383497 nm (Yoshino & Freeman 1985; Brandi et al. 2001), and Kr I: 100.1060639 nm (Brandi et al. 2002). The positions of these lines are shown in Fig. 1.

Second, the random error associated with calibrating the wavenumber scale via a small number of atomic transitions can sometimes be improved upon by including reference data for molecular lines. For this aim, high-resolution laser measurements of some CO lines (and isotopologues) available in the literature were employed (Cacciani et al. 1995, 2001; Cacciani & Ubachs 2004; Drabbels et al. 1993a,b; Ivanov et al. 2008; Philip et al. 2004; Ubachs et al. 1994, 1995, 2000, and recently Daprà et al. 2016). Most of these measurements, obtained by narrow-band laser spectroscopy in one- or two-photon experiments, rely on the I₂ - or Te₂ -saturation spectrum asprimary absolute calibrators, associated with the marks of an actively stabilized Fabry-Pérot étalon. They are summarized in the next subsection (in alphabetical order) and are cited in the corresponding sections.

To overcome the lack of calibration data for some bands, we considered the overlapping regions of contiguous scans. A given setting of the undulator delivers a quasi-Gaussian beam profile of width ~5 nm at 1/e of the peak signal. An absorption scan encompasses about 3–5 bands, as can be seen in Fig. 1. With the right choice of undulatorsettings, we were able to measure at least three bands in a single scan. In this way, a band with no calibration reference can be surrounded by two bands subject to accurate calibration, for instance, the B20 band surrounded by the B10 and C00 bands.

The final accuracy of our measurements also relied upon isotopologue cross calibrations. These were obtained through mixed isotopologue samples (as is the case for the available ¹² C¹⁶O–¹²C¹⁷O bottle, which contains some small amount of ¹² C¹⁸O, and as in the case of ¹³ C¹⁷O, which was present as an impurity in ¹³ C¹⁶O and ¹³ C¹⁸O bottles). Even with pure gas samples, isotopologue impurities may show up in spectra that were recorded at high pressures. We also prepared and used on purpose mixed isotopologue samples allowing for such cross calibrations.

It is worth noting that more data were collected for this work than are included in papers dedicated to oscillator strength measurements. Those are restricted in pressure range and consequently in number of lines observed, in order to keep optical depths <1.5, or absorption lower than 78%, for the accurate determination of oscillator strengths. For this study we used higher pressures in order to observe high J′ levels and isotopologues present in small amounts. As described above, we also use cooled gases to remove possible ambiguities.

2.1 Laser calibration benchmarks and associated data

An absolute calibration of lines requires the availability of accurately determined standards, either atomic or molecular, as close as possible to the lines under study. There are many reported laser-based measurements of CO VUV transitions with accurate absolute calibrations based on primary standards. Some previous work has been limited to a few lines of each vibrational band, while others offer almost complete bands for use as comparisons for calibration purposes. Data like this exist for most CO isotopologues. They are summarized in detail in this section.

Reports of laser-based measurements that were used to accurately calibrate our spectra often also presented an analysis of the rotational structure of the bands under study, providing associated data such as term values, reduced term values, and molecular constants. These results are also mentioned in detail in this section as they are compared later to our own results.

Depending on the data available, laser calibrated benchmarks could in some cases be derived from transitions other than the one-photon P, R, and Q transitions of this study. When two-photon O, S, or Q transitions were available, the corresponding one-photon transitions for the R- and P-branches were recalculated by way of term values, taking into account that common-J′ term values (TVs) of the excited state calculated from various one- and two-photon transition frequencies, that is, TV(), TV(), TV(), TV(), and TV(), have to be equal.

We summarize below all references providing laser calibration benchmarks that were used for this work, as well as the associated data mentioned above. They are sorted by alphabetical order of authors. With the exception of the first laser high-resolution measurements (Baker et al. at Paris-Meudon Observatory and Drabbels et al. at Nijmegen University), the majority of CO molecular calibration lines used here were measured using ultra-high resolution lasers at VU University Amsterdam (Cacciani et al., Daprà et al., Ivanov et al., Niu et al., and Ubachs et al.).

Baker (1994) This paper reports some perturbations observed in the B20 state of ¹²C¹⁶O that are due to the interaction with the ³Π(F1) spin-orbit component of the k³Π(0)–X¹Σ⁺(0) band. Line positions and term values are given for B20 and kX00.

Baker & Launay (1994) This paper analyzes the k³Π(v′ = 2, 3 and 5)–X¹Σ⁺(0) bands, the first one perturbing the E00 band, and the last one the E10 band. Line positions and term values are given for kX20, kX30, and kX50.

Baker et al. (1993, 1994) These papers provide a study of the E00 and E10 bands for four isotopologues, ¹² C¹⁶O, ¹³ C¹⁶O, ¹² C¹⁸O, and ¹³ C¹⁸O. Spectra were recorded using 2 + 1 resonantly enhanced multiphoton excitation showing the five rotational branches O, P, Q, R, and S at a resolution of ~0.1 cm⁻¹. Spectra were acquired either separately for each isotopologue or with mixtures of several, and were then separated by time of flight mass spectrometry, in order to obtain an accurate relative calibration between isotopologues. Perturbations of E10 were analyzed. Term values (for three isotopologues of E00 and four of E10) and molecular constants (for E10) are also given for the four isotopologues.

Cacciani & Ubachs (2004) This paper gives Q-branch transition frequencies of E00 [Q: J′ = 1–8] for ¹² C¹⁶O and [Q: J′ = 1–7] for ¹³ C¹⁶O and ¹³ C¹⁸O. Measured and calculated transition frequencies for E00 of ¹² C¹⁶O [up to J′ = 34 with gaps] and ¹³ C¹⁶O [up to J′ = 42 with gaps], obtained by three different experimental methods, are accessible as supplementary data.

Cacciani et al. (1995) This paper provides a few term values for ¹²C¹⁶O (the E00 band [J′ = 31, 41, and 44] and E10 band [J′ = 5–13]), focused in both cases around perturbations. Molecular constants are also determined for ¹²C¹⁶O (E00 and E10), ¹³C¹⁶O (E00 and E10), ¹²C¹⁸O (E00 and E10), and ¹²C¹⁷O (E00). Transition frequencies were tabulated in a later paper (Cacciani & Ubachs 2004).

Cacciani et al. (2001) This paper provides transition frequencies for R- and P-branch lines of the C10 band for ¹²C¹⁶O [R: J′ = 0–27; P: J′ = 1–31], ¹²C¹⁸O [R: J′ = 0–13; P: J′ = 1–8, 10], ¹³ C¹⁶O [R: J′ = 0–15; P: J′ = 1–5, 9–20], ¹³ C¹⁸O [R = J′ = 0–5, 8–12; P: J′ = 1, 3, 5–8], and a few for ¹² C¹⁷O [R: J′ = 0–2; P: J′ = 1] and ¹³ C¹⁷O [R: J′ = 0–1, 3–5; P: J′ = 1–3]. Molecular constants are also calculated for the six isotopologues, although at lower accuracy for ¹² C¹⁷O and ¹³ C¹⁷O.

Daprà et al. (2016) This paper is mainly based on data for ¹² C¹⁶O published by the Amsterdam team over several years and gives measured wavelengths (Tables 6–8; called molecular parameters) for the R and P (and Q for E00) J′ = 0–5 transitions of the B00, C00, and E00 bands. Their results are expressed with an accuracy of up to the sixth digit (in nanometers)and an error bar of between 3 and 13 in units of this digit. The restriction to the lowest rotational states (J′ ≤ 5) is due to thefact that this paper is aimed at the comparison with quasar observations. These data are the most accurate to date. They result from measurements and not from calculations, as can be deduced from the fact that term values for a given level, determined through the R- and P-branches, are not strictly equal.

Drabbels et al. (1993a) This paper reports observed transition frequencies for ¹²C¹⁶O of the Q- and S-branch lines of B00 [J′ = 0–14 for Q and 0–1 for S] and of C00 [J′ = 0–6 for Q and 0–1 for S]. Corresponding molecular constants are also calculated from these data.

Drabbels et al. (1993b) This paper completes the previous paper with additional measurements of Q lines for B10 [J′ = 0–2], for ¹³C¹⁶O B00 [J′ = 0–2], and for ¹²C¹⁸O B00 [J′ = 0–1]. There is also a slight revision of ¹²C¹⁶O B00 [J′ = 0–4 for Q and 0–1 for S], but as this paper was submitted earlier than the previous paper, it is not clear which should be considered as the more accurate.

Molecular constants are calculated for these four bands.

Ivanov et al. (2008) This paper reports “extreme-ultraviolet laser metrology of O I transitions” (about 20 lines in the 94.86–102.82 nm range) that are used for absolute calibration purposes, when oxygen is present, for E20 and higher energy states.

Niu et al. (2016) While focused on the spectroscopy and perturbation analysis of the A¹ Π(v = 0) state of ¹³ C¹⁶O, this paper provides deperturbed molecular constants for B00.

Ubachs et al. (1994) This paper summarizes the work performed in the 91.2–115 nm range by the Amsterdam and Nijmegen teams over several years, reporting molecular constants for many states of four isotopologues and, of relevance to the present work, for ¹² C¹⁶O (B00, B10, C00), ¹³ C¹⁶O (B00), and ¹² C¹⁸O (B00).

Ubachs et al. (1995) This is a laser spectroscopic study of ¹² C¹⁷O (observed here for the first time) R- and P-branch lines of C00 [J′ = 10–17 for R and 10–15 for P] and derived molecular constants. The latter are also given for C00 and C10 for ¹² C¹⁶O, ¹³ C¹⁶O, and ¹² C¹⁸O, but no transition frequencies are available.

Ubachs et al. (2000) This paper reports the transition frequencies of E10 for six isotopologues. For ¹²C¹⁶O [R: J′ = 0–26 with three gaps; Q: J′ = 8–21 with two gaps; P: J′ = 5–28 with three gaps], ¹²C¹⁸O [R: J′ = 0–11; Q: J′ = 8–13 with one gap; P: J′ = 2–13 with three gaps], ¹³C¹⁶O [R: J′ = 0–20 with five gaps; Q: J′ = 7–23; P: J′ = 2–20], ¹³C¹⁸O [R: J′ = 0–20 with two gaps; Q: J′ = 1,18; no P], a few for ¹² C¹⁷O [R: J′ = 0–1; Q: J′ = 1–2; no P] and for ¹³ C¹⁷O [R: J′ = 0–12 with six gaps; Q: J′ = 1–12; P: J′ = 3]. The very high resolution (up to ~3 × 10⁶) achieved by a narrow-band laser source allowed assigning the Q-branch lines with an absolute accuracy of 0.003 cm⁻¹ for all six natural CO isotopologues. Molecular constants are also derived for the ground-state X(v′′ = 0), E10 and the perturbing k60 bands.

References to the available absolute high-resolution calibration band or lines we used are summarized in Table 2 for each band and for each isotopologue. The availability of term values and/or molecular constants derived from the laser-based measurements is also noted in the table.

We also mention the mainly theoretical work of Lefèbvre-Brion & Eidelsberg (2012), which presents molecular constants (T_v and B_v) for E00, E10, E20, and E30 derived from our VUV-FTS high-resolution CO datasets, extracted before the absolute wavelength calibration of this work.

2.2 Data analysis

2.2.1 Atlas of measured wavelengths and wavenumbers

In order to place the atlas on an absolute wavelength scale, we compared our measured data with the entire set of calibration references from Table 2 (including all isotopologues when available). The average of their differences provides the value of a shift that was applied to correct the raw experimental wavelengths. As proof of the accuracy of the data delivered by the VUV-FTS team, this correction was usually very small (<3.4 × 10⁻⁵ nm or 0.03 cm⁻¹). Two sets of measured transition energies (including calibration shift corrections from the wavelength standards), R_ms and P_ms, corresponding to the R- and P-branches (and additionally Q_ms for ¹Π states), were the result from this procedure. In order to check the quality of our transition energy determinations, we compared for each J′ the values of

according to the method of combination differences (Herzberg et al. 1950). For each band and for each J′ , we calculated the difference A–B between these two quantities, which we defined as 2 ×δ_P. These differences lead to uncertainties in the term values TV_R and TV_P. Some publications interested in precise term values shared equally for each J′ the difference between TV_R and TV_P (or between R and P, in order to calculate corrected transition energies R_corr = (R_ms − δ_P) and P_corr = (P_ms + δ_P), which produces a single best-term value based on both lines. We did not follow this procedure here, but kept the measured values.

2.2.2 Atlas of term values and molecular constants

For each measured band, we used the line positions of R- and P-branch lines that terminate on the same upper rotational levels to calculate common upper-level term values with uncertainties.

The agreement of the term values calculated from independently measured P- and R-branch transitions with a common upper J-level, TV_R, and TV_P, is never perfect because of experimental noise and in some cases line broadening. However, as we described above, the excellent reproducibility of the measurements obtained with the VUV-FTS for a given band and a given isotopologue from spectra recorded at different times suggests that when the discrepancy is larger than the random fitting errors, it reveals the possible presence of a local perturbation that modifies the shape of one of the lines involved. For each J′ = i + 1 level, the final term value was obtained by averaging the term values TV_R = + and TV_P = + that were calculated from measured line positions of each rotational branch, R_ms and P_ms. The relative difference is again 2 ×δ_P. As a final result, R_ms, P_ms and δ_P values are tabulated for each band and isotopologue. Both R_ms and P_ms are given in wavelengths and wavenumbers (and δ_P in wavenumbers), and are presented in separate tables for ¹² C- and ¹³ C-bearing CO species.

Term values of the upper levels for all six isotopologues were derived from these two independent measurements. They are presented in separate tables for each band. while reduced term values are shown with graphs for better visualization. We must be careful for high J′ term values in two specific cases: (a) a high value of δ_P (we adopted in this work a limit of 0.125 cm⁻¹) might mean that one of the lines is less well identified than the other (or does not belong to the studied band), even if the two R and P lines are both clearly observed, and (b) no δ_P value indicates that only one transition is present, either R or P. In the first case, we kept the TV derived from a single level, while in the second case, erratic TV values had to be rejected. All these tables and graphs are introduced for each state in the following sections. For each band and isotopologue, the statistical uncertainty on term values was obtained by calculating over all J′ , when both R and P levels were measured, the average and standard deviation (at 2σ) of 2 ×δ_P/2. The division by a factor of two takes into account that each term value results from two independent measurements (R_ms and P_ms) and that at least two different records (up to four in some cases, as described above) provide the same line position results. Each average is displayed in statistical tables, alongside its standard deviation (at 2σ), showing thedispersion in our measurements. An average closer to zero means that the δ_P values are randomly distributed, ensuring no bias in our measurements. A standard deviation closer to zero signifies a high probability of the absence of perturbation(s).

The molecular constants T_v, B_v, and D_v were least-squares fitted to the experimental term values using a second-order polynomial. Following the above remarks, only a subset of term values was considered at times, particularly for high J′ term values. Reduced term values were finally calculated for each vibrational level by subtracting a model defined by

for the e-parity levels of the B¹Σ⁺ and C¹ Σ⁺ sates and the f-parity levels of the E¹ Π state, while for the e-parity levels of E¹Π, the additional term

takes the Λ-doubling of this state into account (so that q = B_e − B_f and q_D = D_e − D_f, where the e and f subscripts refer to the parity of the considered levels). For the E¹ Π state, the Λ -doubling components can be either calculated by subtracting the molecular constants deduced from the e- and f-parity levels, or they can be directly obtained by fitting the TV_e –TV_f differences for each level to a second-order polynomial. The results of both methods are presented in Sect. 3.5. Their valueswere graphically compared according to their oxygen isotopic content to check for anomalies that are due to perturbations. In almost every case, our molecular constants were generated by much larger datasets than those referenced in Sect. 2.1 (see also Table 2).

It is worth noting that the lines in the R- and P-branches are in general not observed up to the same J′. It is also possible, in the case of high-pressure spectra, that some lines observed at high J′ values belong to a weak unidentified underlying band. As a consequence, some reduced term value graphs could present a break or jump for the last higher J′ values. This break, however, could correspond in some cases to a real perturbation.

3 Results and discussion

The results presented here constitute the first part of an atlas of the Rydberg states at wavelengths below 115 nm for six isotopologues of CO. They update and complete the previous CO atlas at the higher resolution provided by the VUV-FTS coupled to the SOLEIL synchrotron (Eidelsberg et al. 1991; for revised band origin wavenumbers, see Eidelsberg et al. 1992). They also fill some gaps and provide higher J′ lines that were previously not observed with high-resolution laser methods.

In addition to the atlas of absolute wavelengths and wavenumbers for the B, C, and E states of the six CO isotopologues, we provide for the derived term value atlas for each observed band. As a further step, we calculate reduced term values and molecular parameters. The latter are compared according to their oxygen isotopic content, and when possible, with previous determinations.

Figure 1 shows the bandhead wavelengths of the states and bands studied in this work. Table 1 summarizes the measured bands for each isotopologue. Some isotopologue bands are not recorded because of the combination of low oscillator strengths and low available pressures or partial pressures. Low partial pressure is particularly a problem in the case of ¹³ C¹⁷O, which is observed as a minor contaminant in high-pressure spectra of both ¹³ C¹⁶O and ¹³ C¹⁸O.

For all ¹²C (or ¹³C)-bearing isotopologues, the isotope shift spacing between bandheads increases almost linearly with v′ vibrational number, allowing for an easier differentiation of the lines pertaining to a given isotopologue for increasing v′ and J′ .

3.1 Specific cases of ¹²C¹⁷O and ¹³C¹⁷O

3.1.1 ¹²C¹⁷O

As ¹² C¹⁷O is mixed in almost equal proportions with ¹² C¹⁶O in our sample, the absolute calibration of ¹² C¹⁷O transitions benefits from the absolute calibration of ¹² C¹⁶O (as well as ¹² C¹⁸O, which is also present in a small amount).

3.1.2 ¹³C¹⁷O

The case of ¹³ C¹⁷O is specific because it is observed in the high-pressure spectra of either ¹³ C¹⁶O or ¹³ C¹⁸O. The occurrence of the ¹³ C¹⁷O bands is due to isotopic contamination of the ¹³ C¹⁶O and ¹³ C¹⁸O bottles. Based on the relative strengths of identical absorption features, the ratio of the isotopologues in the ¹³ C¹⁶O gas sample, sorted by concentration, is found to be ¹³ C¹⁶O:¹³C¹⁸O:¹³C¹⁷O:¹²C¹⁶O = 1:0.041:0.073:0:0045. The high CO pressure needed to observe the minor ¹³ C¹⁷O species leads to strong absorption and saturation of the main species spectrum. Combined with the fact that the isotopic shifts of v′ = 0 bands are very small (≤1 cm⁻¹ for B00 and C00 and ≤3 cm⁻¹ for E00), ¹³ C¹⁷O lines for low J′ are difficult to extract because of blending with saturated (broadened) lines. This effect is weaker for increasing J′ because of the difference between molecular constants of the different isotopologues. ¹³ C¹⁷O lines of B00 with J′ > 2 are measured nearly as accurately (~0.04 cm⁻¹) as for the main isotopologue (either ¹³ C¹⁶O or ¹³ C¹⁸O), similarly for C00 lines with J′ > 6. The search for low J′ line positions is facilitated by considering the values extrapolated from the clearly observed high J′ line levels (up to J′ = 23 for B00, J′ = 21 for B10, J′ = 39 for C10, and J′ = 26 for E00), which leads to an accuracy better than 0.08 cm⁻¹ for the low J′. This effect is less noticeable for v′≥ 1 as the spacing of spectra bandheads of the different isotopologues increases with v′ .

All this concerns R- and P-branches, but there is an additional difficulty for Q-branches that we consider in the E-state subsection.

3.2 X¹Σ⁺ state

In order to calculate the term values of all the bands presented here, high-accuracy data provided by Guelachvili et al. (1983) and Farrenq et al. (1991) were used. From their set of Dunham coefficients, rotational levels of the v′′ = 0 X¹ Σ⁺ ground state were calculated up to J′′ = 48 with an uncertainty of 10⁻³ cm⁻¹, which is at least as good as our own high-resolution measurements. Table 9 lists the ground-state rotational levels of the six isotopologues studied here, ¹² C¹⁶O, ¹² C¹⁷O, ¹² C¹⁸O, ¹³ C¹⁶O, ¹³ C¹⁷O, and ¹³ C¹⁸O. For each isotopologue, these J′′ levels are adjusted to a ninth-order polynomial to obtain their molecular constants. They are reported in Table A.31.

For the sake of consistency between all isotopologues, we did not use the data on the ¹² C¹⁶O ground state by Varberg & Evenson (February 1992), which were published a few months after Farrenq et al. (October 1991). The latter provide data for six isotopologues, and a check on ¹² C¹⁶O B00 revealed a better agreement at high J′ between the term values TV_R and TV_P derived for the R- and P-branches.

3.3 B¹Σ⁺ state

The B00 and B10 bands were observed for all isotopologues, while B20 was observed for all bands except for ¹² C¹⁷O and ¹³ C¹⁷O. The lack of the B20 band in the ¹² C¹⁷O spectra is explained by the low pressure used in scans of this isotopologue. For ¹³ C¹⁷O, the absence is due to the combination of a very low partial pressure and the decreasing oscillator strength with v′.

A total of 19 CO laser-calibrated lines (14 for ¹² C¹⁶O, 2 for ¹² C¹⁸O, and 3 for ¹³ C¹⁶O) were used to determine a shift correction of −7.5 × 10⁻⁶ nm (0.006 cm⁻¹) for B00 and 3 lines for B10, resulting in a shift correction of −1.2 × 10⁻⁵ nm (0.0095 cm⁻¹). These low values attest to the accuracy of our measurements. These corrections were applied to all isotopologues as their spectra are placed, as mentioned above, on a unique scale. Our term values are consistent within the uncertainty with those calculated by Le Floch & Amiot (1985) and Haridass et al. (1994), the latter resulting from the combination of B–A data with high-resolution A–X data obtained with the former Ottawa 10.6 m vacuum-grating spectrograph. For ¹² C¹⁶O B00, the average difference between our values and the Daprà et al. (2016) values is 5.0 × 10⁻⁶ nm. For ¹² C¹⁷O, the present results complete a preliminary version of our B00 data that was incorporated in Hakalla et al. (2016) in order to perform the deperturbation analysis of the A¹Π state of ¹² C¹⁷O, for which earlier optical measurements of B–A and C–A transitions were combined with our vacuum ultraviolet B–X results. Similarly, for ¹³ C¹⁷O, our results of B00 and B10 were used in Hakalla et al. (2017) to perform the deperturbation analysis of the A¹ Π state of ¹³ C¹⁷O.

The data for ¹³ C¹⁸O are slightly better calibrated than in our recent paper (Lemaire et al. 2016) for B00 and B10. In addition, they are extended to higher J′ levels for B10.

As indicated above, the B20 band was calibrated using the surrounding B10 and C00 bands, leading to a common shift correction of +1.0 × 10⁻⁵ nm (−0.0083 cm⁻¹) that was applied to all isotopologues. Figure A.3 illustrates for the four observed isotopologues the perturbations observed in B20 (also studied in ¹² C¹⁶O and ¹³ C¹⁶O by Baker 1994).

For ¹² C¹⁶O, ¹² C¹⁸O, ¹³ C¹⁶O, and ¹³ C¹⁸O, our absolutely calibrated data provide transition frequencies and term values for B00, B10, and B20 that are consistent at slightly higher accuracy with those measured by Eidelsberg et al. (1987), which were obtained with the Observatoire de Paris (Meudon, France) 10 m VUV grating spectrograph. The same remark applies to the line positions obtained by Baker (1994) for B20 of ¹² C¹⁶O with the same instrument.

Table 3 lists table and figure numbers associated with the BX bands. Table 4 gives the statistical uncertainty on the term values for the BX bands (see text in Sect. 2.2.2).

3.4 C¹Σ⁺ state

C00, C10, C20, and C30 were observed for ¹² C¹⁶O, ¹² C¹⁸O, ¹³ C¹⁶O, and ¹³ C¹⁸O. For ¹² C¹⁷O, all bands were observed except for C20, for the same reason as for B20. For ¹³ C¹⁷O, only C00 and C10 were observed; C20 and C30 are not observed for the same reason as for B20.

It is worth noting that for ¹² C¹⁸O, the C30 band does not appear in the same room-temperature spectra obtained at pressures where C20 is observed. It is only observed in a low-temperature spectrum recorded at 90 ± 5 K, showing a limited number of J′ levels.

Sixteen CO laser-calibrated lines were used to determine a shift correction of 1.3 × 10⁻⁵ nm (−0.011 cm⁻¹) for C00. Seventy-two laser-calibrated lines were considered (not including ¹² C¹⁷O and ¹³ C¹⁷O, for which the number of lines in Cacciani et al. 2001 is limited) to determine the shift correction of 3.4 × 10⁻⁵ nm (−0.031 cm⁻¹) for C10.

Our term values are consistent with those calculated by Haridass et al. (1994), which were obtained from the combination of C–A data with high-resolution A–X data obtained with the former Ottawa spectrograph. For ¹² C¹⁶O C00, the average difference between our values and the values of Daprà et al. (2016) is 4.4 × 10⁻⁵ nm (−0.037 cm⁻¹).

For C00, the present results complete a preliminary version of our ¹² C¹⁷O data (as for B00) and provide new data on ¹³ C¹⁷O. Both were used in order to perform the deperturbation analysis of the A¹ Π state of ¹² C¹⁷O (Hakalla et al. 2016) and of ¹³ C¹⁷O (Hakalla et al. 2017).

As for B00 and B10, the present data for ¹³ C¹⁸O are slightly better calibrated and extend to higher J′ levels than in our recent paper (Lemaire et al. 2016) for C00.

The absolute calibration for C20 and C30 was obtained using the two surrounding primary atomic standards as calibrators (the Xe I line at 104.383497 nm for C20, and the Kr I line at 100.1060639 nm for C30, see Fig. 1) and checking that the numerous secondary standards (in the case of C20) are in agreement with each other (at an accuracy higher than 0.01 pm) for the five isotopologues.

Table 5 lists table and figure numbers associated with the CX bands. Table 6 gives the statistical uncertainty on the term values for the CX bands (see text in Sect. 2.2.2).

3.5 E¹Π state

E00, E10, E20, and E30 [the latter formerly labeled as the V (A²Π) ³Π state by Eidelsberg & Rostas (1990), with the present assignment confirmed by Lefèbvre-Brion & Eidelsberg (2012)] were observed for all isotopologues, with the exception of E20 and E30 for ¹³ C¹⁷O (as for B20 because of the combination of a very low partial pressure and decreasing oscillator strength with v′).

For E20 and E30 of ¹² C¹⁸O, the same remark holds as for C30. These two bands do not appear in spectra taken at room-temperature at pressureswhere E10 is observed. It is only observed in low-temperature spectra recorded at 90 ± 5 K, showing a limited number of J′.

For all isotopologues, the rotational spacing is extremely small for the Q-branch of E00, E10, and E20, giving rise to congested spectra that require better resolution than available with the VUV-FTS and smaller Doppler broadening. This is particularly noticeable for the Q-branch of E10, where the lines are very slightly blueshifted with J′ compared tothe Q-branch of E00, which is slightly blueshifted, and the Q-branch of E20, which is slightly redshifted. Only with the use of a very narrow-band laser were Cacciani & Ubachs (2004) able to separate the Q-branch of E00, and Ubachs et al. (2000) did this in combination with a deperturbation analysis for E10. The Q-branch of E30 has a very different aspect (similar to A–X transitions) with a redshifted Q-branch and a returning limb for the R-branch with increasing J′ (see for comparison Figs. A.12, A.17, and A.25 vs. A.28, and also Figs. A.15, A.16, A.24, and A.27 vs. Figs. A.30–A.36).

A careful analysis is required to distinguish the lines in the E00 bands of the different isotopologues. Spectra recorded at different pressures were used for this purpose. Figure A.16 illustrates the difficulty of this task for E00 with three spectra for ¹³ C¹⁸O and 2 for ¹³ C¹⁶O. Figure A.27 shows the easier example of E20 for ¹³ C¹⁶O and ¹³ C¹⁸O, and Figs. A.30–A.36 show the example of E30 for ¹³ C¹⁸O.

There is very good agreement for the R- and P-branch line positions between our present results and other high-resolution measurements (Cacciani et al. 1995; Cacciani & Ubachs 2004 for E00 and Ubachs et al. 2000 for E10). E00 was calibrated using a few levels observed by Cacciani et al. (1995) for ¹² C¹⁶O [3 lines] and a large set of R and P levels (Cacciani & Ubachs 2004) for ¹² C¹⁶O [60 lines] and ¹³ C¹⁶O [32 lines] obtained by their methods labeled 1 and 0 (these data have to be calculated from the supplementary data, but no data are available for ¹³ C¹⁸O). The resulting shift correction is estimated as 2.3 × 10⁻⁵ nm (−0.020 cm⁻¹). Comparisonto Daprà et al. (2016) shows an average difference of 3.8 × 10⁻⁵ nm for E00. For ¹² C¹⁸O and ¹³ C¹⁸O, our term values for E00 (e- and f-parity) match those calculated by Haridass et al. (1994) well, which were obtained from the combination of E–A data with high-resolution A–X data collected with the former Ottawa spectrograph. For the Q-branch of ¹² C¹⁶O, ¹³ C¹⁶O, and ¹³ C¹⁸O, which we cannot separate, we report the Cacciani & Ubachs (2004) observed transition frequencies (see their Table 1). We merged the Cacciani et al. data with our higher-J′ measurements. For the other isotopologues, ¹² C¹⁷O and ¹² C¹⁸O, the Q bandhead up to J′ ≈ 9 was simulated to reproduce the observed spectra. These calculated data were merged with our measured data at higher J′ . For the last isotopologue, ¹³ C¹⁷O, the Q-branch was simulated by interpolation of the ¹³ C¹⁶O and ¹³ C¹⁸O transitions (but these data are not reported in the table) in order to assign the few observed high J′ Q-lines.

E10 was calibrated by a few lines observed by Cacciani et al. (1995) for ¹² C¹⁶O [9 lines] and a large set by Ubachs et al. (2000) of R and P lines for ¹² C¹⁶O [42 R and P lines], for ¹² C¹⁷O [2 R lines], ¹² C¹⁸O [24 P and R lines], ¹³ C¹⁶O [25 P and R lines], and ¹³ C¹⁸O [18 R lines]. The absolute calibration for E10 obtained with the R and P levels is also confirmed by the presence of closely surrounding Xe I atomic lines (see Fig. 1). The resulting shift correction is estimated to be 5.0 × 10⁻⁶ nm. As it is not possible to distinguish the Q-branch of E10 for all isotopologues, we report in the tables the values obtained by Ubachs et al. (2000), merged with our measured data at higher J′. Our dataset for R- and P-branches extends those of Ubachs et al. (2000) to high J′ values. Sample spectra are shown for ¹² C¹⁶O in Fig. A.20, ¹² C¹⁷O in Fig. A.21, ¹² C¹⁸O in Fig. A.22, ¹³ C¹⁶O in Fig. A.23, and ¹³ C¹⁸O in Fig. A.24. All of them show additional lines, and among them, lines that belong to the perturbing state k³ Π (v′ = 5 and 6)–X¹Σ⁺(v′ = 0) (Baker & Launay 1994; Ubachs et al. 2000). The lower panel of Fig. A.21 shows the simulated absorption spectrum of ¹² C¹⁷O at room temperature.

For E20 and E30, only low-resolution spectra without absolute calibration are available (Ogawa & Ogawa 1974 for ¹² C¹⁶O E20) and the Eidelsberg et al. (1991) atlas for ¹² C¹⁶O, ¹² C¹⁸O, ¹³ C¹⁶O, and ¹³ C¹⁸O for both E20 and E30, with either measured or extrapolated or calculated line positions. Consequently, the absolute calibration of E20 and E30, for which there are no previous high-resolution measurements, was obtained in the same way as for C20 and C30, using the two surrounding primary atomic standards as calibrators and checking that the numerous secondary standards (in the case of E20)are in agreement with each other (at an accuracy higher than 0.01 pm) for five isotopologues (with the exception of ¹³ C¹⁷O). For E20, the Q-branch up to J′ = 6 or 7 was obtained in the same way as for E10 by simulating our recorded spectra and merging them with the higher measurable J′ , up to ~10–20, depending on the isotopologue. Figure A.27 shows the simulated absorption spectra of ¹² C¹⁶O at 90 K and at room temperature. Finally, as indicated above, all branches of E30 have well-resolved transitions for all observed isotopologues. Figures A.30–A.36 show spectra for all five isotopologues; in some cases, the results obtained at 293 K and 90 K are compared, which are useful to separate the R-branch lines.

In order to verify the quality of our frequency determinations for the Q-branch, we use a method similar to the combination differences. We compared the values of the Λ -type doubling of the upper state obtained through the R- and P-branches, Λ _R (J) and Λ _P (J) (for J ≥ 1) with

For all isotopologues and all bands (E00, E01, E02, and E03), the results are consistent with the value of Λ _d provided in the term value tables. The Λ doubling of the upper state is graphically represented for all isotopologues in each band, E00, E10, E20, and E30, in Fig. A.37 together with polynomial fits (linear in most cases).

Table 7 lists table and figure numbers associated with the EX bands. Table 8 gives the statistical uncertainty on the e-parity term values of the EX bands (see text in Sect. 2.2.2).

4 Concluding remarks

Our work presents a comprehensive and homogeneous set of absolutely calibrated line positions from which term values and molecular constants are derived. In most cases, these were obtained from larger sets of data than earlier determinations. Our data complete previous determinations and fill many gaps, particularly concerning the B20, C20, C30, E20, and E30 bands of all isotopologues. We also provide new data, particularly for the ¹² C¹⁷O and ¹³ C¹⁷O isotopologues.

A final verification of the absolute accuracy of our whole set of results is provided by comparison with the data reported by Daprà et al. (2016). These datasets were not considered as calibrators because they were derived from others cited in Sect. 2.1, but we verified that they are in good agreement (at least for the six J′ levels included therein) with our own results on B00, C00, and E00 for ¹² C¹⁶O.

In conclusion, the overall uncertainty of our data is a combination of the relative fitting accuracy in line positions (for a well-resolved typical line ~0.008 cm⁻¹) and of the accuracy in the calibrators and in the ground state (up to ~0.003 cm⁻¹). Most of the line positions are thus determined to an accuracy of ~0.009 cm⁻¹. For some weak (mainly at high J′) or a few blended lines, the fitting errors are estimated to be as large as 0.10–0.15 cm⁻¹. Uncertainties on term value data are reflected in the δ_P values presented in the term value tables.

Molecular constants are compiled in Table A.31 for all states and bands. In this table the E state e- and f-parity are treated independently, and we calculate in Table A.32 T_v (1) (average of T_v for e- and f-parity), q_v = B_e − B_f, and q_Dv = D_e − D_f. These molecular constants are also obtained by a quadratic fit of the Λ -doubling data shown in Fig. A.37 and reported in Table A.33.

In order to check the consistency of our term values, we compare their trends for the six CO isotopologues in Fig. A.38. The term value differences between ¹⁶ O and ¹⁸ O bearing isotopologues are compared both for ¹²C and ¹³C versus the B, C, and E states. Term values are also compared as a function of v′ for each states, and a linear fit is drawn through all isotopologues present in each (T_V, v′) data point. Both comparisons show a similar behavior.

The statistical table for the term values (see Tables 4, 6, and 8) can reveal the possible presence of perturbations when there is a large spread in the standard deviation (>0.043 cm⁻¹, namely for ¹² C¹⁶O (E30), for ¹² C¹⁷O (C30), for ¹² C¹⁸O (C20 and C30), for ¹³ C¹⁶O (C10, C20 and C30), for ¹³ C¹⁷O (C10), andfor ¹³ C¹⁸O (C30). Anomalies in the molecular constants also reveal evidence of perturbations, as shown in Fig. A.39, which illustrates this point more clearly than Table A.31. While T_v mainly depends on the absolute calibration, B_v and especially D_v are very sensitive to perturbations, as shown in Fig. A.39.

Perturbations will be discussed in detail in a subsequent paper. Another forthcoming development of this work will be a comprehensive atlas of oscillator strengths and cross sections for the states, bands, and isotopologues presented here.

Acknowledgements

We acknowledge SOLEIL for providing the synchrotron radiation facilities. All the data have been obtained on beamline DESIRS using the VUV-FTS spectrometer during proposals 20140051, 20120715, 20110121, 20100018, 20090021, and 20080025. We acknowledge assistance from the SOLEIL beamline staff (L. Nahon beamline manager), NdO (VUV-FTS manager and coauthor), and D. Joyeux (designer and builder of the VUV-FTS). This research was supported by NASA (grants NNG 06-GG70G and NNX10AD80G to the Univ. of Toledo and NNX09AC5GG to Wellesley College). J. R. L. and G. S. thank the NASA Origins of Solar System program (Grant NNX14AD49G) for funding. A. H., while in the Amsterdam team, acknowledges support from the Dutch astrochemistry network (DAN) from the Netherlands Organisation for Scientific Research (NWO) under grant 648.000.002 and the research fellowship program of PSL Research University Paris. J. L. L. thanks the ISMO-CNRS (Institut des Sciences Moléculaires d’Orsay at Université Paris-Sud) for hosting him as visiting researcher.

Appendix A Additional figures and tables

References

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All Tables

All Figures