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VUV-synchrotron absorption studies of N2 and CO at 900 K M. L. Niua , A. N. Heaysb , S. Jonesb,c , E. J. Salumbidesa,d , E. F. van Dishoeckb , N. De Oliveirae , L. Nahone , W. Ubachsa,∗ a Department
of Physics and Astronomy, LaserLaB, VU University, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands b Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands c School of Physics and Astronomy, The University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom d Department of Physics, University of San Carlos, Cebu City 6000, Philippines e Synchrotron Soleil, Orme des Merisiers, St. Aubin BP 48, 91192, Gif sur Yvette cedex, France
Abstract Photoabsorption spectra of N2 and CO were recorded at 900 K, using the vacuum-ultraviolet Fouriertransform spectrometer at the DESIRS beamline of synchrotron SOLEIL. These high-temperature and high-resolution measurements allow for precise determination of line wavelengths, oscillator strengths, and predissociative line broadening of highly-excited rotational states with J up to about 50, and also vibrational hot bands. In CO, the perturbation of A 1 Π − X 1 Σ+ vibrational bands (0, 0) and (1, 0) were studied, as well as the transitions to perturbing optically-forbidden states e 3 Σ− , d 3 ∆, D 1 ∆ and a′ 3 Σ+ . In N2 , we 3 observed line shifts and broadening in several b 1 Πu −X 1 Σ+ g bands due to unobserved forbidden states of Πu symmetry. The observed state interactions are deperturbed and, for N2 , used to validate a coupled-channels model of the interacting electronic states. This data is appropriate for use in astrophysical or (exo-)planetary atmospheric applications where high temperatures are important and in future spectroscopic models of these molecules. Keywords: Synchrotron radiation, Fourier-transform spectroscopy, Carbon monoxide, Molecular nitrogen 1. Introduction The technique of Fourier-transform spectroscopy is typically applied to the infrared and optical wavelength domains. The interferometric principle requires a beam-splitter for which no materials exist in the far vacuum ultraviolet (VUV) part of the electromagnetic spectrum. At the DESIRS beamline of the SOLEIL synchrotron  this problem was solved by developing a VUV Fourier-transform spectrometer (FTS) based on beam-splitting by wave-front division, thus enabling high-resolution spectroscopy at ∗ Corresponding
Preprint submitted to Journal of Molecular Spectroscopy
wavelengths in the range 40 − 200 nm [2, 3]. In recent years, this unique instrument has been used to perform high resolution spectroscopic studies on a number of small molecules in the gas phase that exhibit strongly-structured multi-line spectra, such as H2 , HD , N2 , and CO ; as well as for molecules with more continuum-like spectra, such as CO2 . These studies amply demonstrate the multiplex advantage of the Fourier-transform technique by revealing many hundreds of absorption lines in a single-scan window of some 5 nm, determined by the bandwidth of the beam line undulator source. Alternatively, the setup was used to determine photo-absorption cross sections  and predissociation linewidths (and hence rates) of excited states of small molecules [6, 10].
January 15, 2015
The FTS-VUV setup has been used for gas-phase absorption spectroscopy under varied measurement conditions. Most studies have been performed in a quasi-static gas environment where the gas sample effusively flows through a narrow capillary-shaped absorption cell, with the absorption path aligned with the VUV beam emanating from the undulator. This cell was not equipped with windows, to permit passage of the VUV beam through the sample gas into the FTS-VUV instrument for spectroscopic analysis. For this geometry, differential pumping maintains an ultrahigh vacuum in the FTS and DESIRS beam line. The column density of absorbing gas is limited by the pumping conditions and vacuum requirements of the beam line. In any case, there is a pressure gradient over the cell length falling off toward both ends, complicating any absolute column density calibration. In further studies dedicated to crosssection measurements, a movable gas cell was used of ∼ 19 mm length and sealed by either MgF2 or LiF wedged windows. This allowed for somewhat-higher pressures and controlled gas column densities . Studies using this cell are limited in wavelength range to λ > 105 nm  by the short-wavelength opacity of the windows. In some experiments requiring the simplification of congested spectra, a molecular jet expansion was employed as well as cooling of the quasi-static gas cell with liquid-nitrogen or liquidhelium. A comparison between these techniques was performed in a study of the D2 spectrum  which also demonstrated improved spectral resolution and accuracy through reduction of the Doppler width under these conditions. For the present study a heated cell is implemented, allowing for the recording of spectra at temperatures of ∼ 1000 K. The high-resolution FTS allows for the measurement and analysis of severely congested spectra at these elevated temperatures. Such spectra bear significance for the modeling of astrophysical shock-wave regions , or other high-temperature astrophysical regions where the spectroscopy of small molecules is key to understanding the phenomena, such as e.g., in the photospheres of white dwarfs . Another goal of performing spectroscopy of hot samples is to follow rotational progressions to high Jquantum numbers, where perturbations due to non-
Figure 1: (a) Cross-section drawing of the gas sample chamber mounted in the FTS-branch of the DESIRS beam line at SOLEIL. The high temperature windowless cell is located in the center of the chamber and is separated from the ultra-high vacuum of the beamline by two stages of differential pumping. (b) The inset shows details of the cell and the shielding where half of the cylindrical shell has been removed for clarity. The heating element is wrapped all over the cylindrical cell inside a groove in order to increase surface contact with the cell. The gas is flowing through a 7.5 × 4.5 mm tube into the heated cell. The copper base can be cooled down with a thermalized water circulation system.
Born-Oppenheimer effects are abundantly present. Some pertinent perturbation features specifically occurring at high rotational quantum numbers will be shown here in VUV-absorption spectra of CO and N2 recorded at 900 K.
temperature (for the cell) and never went beyond a maximum of 200oC with no visible consequence or damage. A thermocouple is connected at one end of the cell to obtain an indication of the gas temperature. The quasi-static gas density inside the heated cell was monitored from outside the vacuum by a 1 mbar range capacitive gauge. The gas column density was adjusted by a needle valve in order to have a constant continuous flow through the cell during the photoabsorption measurements. The effective column density along the absorption path inside the cell varied from 4 × 1014 to 1.2 × 1017 cm−2 and was adjusted according to the cross sections of the recorded bands. In the present study, the FTS-VUV was set to provide an instrumental linewidth of 0.27 cm−1 . The Doppler broadening corresponds to 0.28 cm−1 at a frequency of 65 000 cm−1 , temperature of 900 K, and molecular mass of 28 amu. After convolution with the instrument width, a spectral linewidth of 0.39 cm−1 is anticipated for unsaturated and non-predissociationbroadened N2 and CO lines. The FTS spectra are intrinsically wavelength calibrated by monitoring the movement of the travel arm in the interferometer which is controlled by a HeNe-laser [2, 3]. Additional and improved calibration can be derived from co-recording special calibration lines, e.g. resonance lines of noble gases [16, 17]. In the present case of the CO spectra the very accurate laser-calibration data of the low-J rotational lines in the A − X bands, accurate to ∆λ/λ = 3 × 10−8 , were used . For the present high-temperature measurements with larger Doppler-broadening the FTS was not used in its very highest resolution mode and the spectral accuracy typically reached is estimated at 0.02 cm−1 . The accuracy is somewhat lower for weaker and blended lines.
2. Experimental The VUV Fourier-Transform spectrometer at the DESIRS beamline is a permanent end station dedicated to high-resolution photoabsorption studies in the range 4 − 30 eV . The instrument has been described in detail previously [2, 3]. In short, the spectrometer is based on wave-front division interferometry using reflective surfaces, thus allowing the extension of the FTS technique into the far VUV spectral range. The undulator white beam is used as the background, feeding the FTS branch and permits the recording of a spectral bandwidth ∆E/E = 7%, corresponding to 5 nm, on each scan. The typical integration time for a single scan is less than 30 minutes to obtain a signal-to-noise ratio for the background continuum level of ∼ 400. The windowless absorption cell is a 40 cm long T-shaped tube with a rectangular cross section, installed under vacuum inside the multi-purpose gas sample chamber of the FTS branch (Fig. 1). The cross section of the tube (7.5 × 4.5 mm) is adapted to the astigmatic shape and dimensions of the undulator source in this section of the beam line. An Inconel heating element (thermocoax) is wrapped around the tube sitting in a groove designed to maximize the contact surface between the heating wire and the cell, and ensuring the gas flowing in the tube is uniformly heated. Two semi-cylindrical shells are pressed around the cell in order to improve the thermal contact during the heating operation. An extra stainless steel box is also installed to shield radiation originating from the cell. Inconel allows for heating the cell up to 1000 K, although, the present measurements were done at a maximum temperature of 900 K. The cell is mounted on a copper base plate that can be cooled by water circulation, although during the experiments the setup was operated without the cooling system. The temperature of the base-mount was carefully monitored within the covered range of
3. Absorption spectra of N2 Five N2 vibrational bands were analysed appearing in our spectrum between 100 400 and 108 500 cm−1 (99.6 and 92.2 nm). These bands are spectroscopi′ ′′ ′ cally denoted b 1 Πu − X 1 Σ+ g (v , v = 0) for v = 0, ′1 + 1 + ′ ′′ 1, 2, and 10, and c4 Σu − X Σg (v = 0, v = 1) 3
b − X(2, 0)
Transmittance (arb. units)
12 8 0
Q(J ′′ )
32 P (J ′′ )
10 13 16
P (J ′′ ) 51 Q(J ′′ ) 12 8 0 R(J ′′ ) 9
25 21 17139 5 1
P (J ′′ ) c′4 − X(0, 1) 29 0 2518 R(J ′′ )
b − X(1, 0)
R(J ′′ )
Transition wavenumber (cm
Figure 2: Photoabsorption spectrum showing the bands b − X(2, 0), c′4 − X(0, 1), and part of b − X(1, 0); and further absorption lines arising from H2 contamination, high-J ′ lines of b − X(3, 0), and of unknown origin (circles). The lower trace indicates the residual error after subtracting a model spectrum.
(where v ′ and v ′′ are upper- and lower-state vibrational quantum numbers, respectively; and hereafter we neglect electronic-state term symbols); and have been previously observed in room-temperature or expansion-cooled synchrotron- or laser-based experiments [19, 20, 21, 22, 23, 24]. Part of our photoabsorption spectrum showing three of these bands is plotted in Fig. 2. A listing of the deduced term values for the e and f components of the observed b(v ′ ) levels is given in Table 1. The analysis of DESIRS FTS spectra of molecular nitrogen has been discussed previously . This involves simulating each observed absorption line with a Voigt profile defined by a Gaussian Doppler width, Lorentzian natural line width, transition wavenumber, and integrated cross section. A summed cross section is then transformed into an absorption spectrum by the Beer-Lambert law and convolved with a sinc function simulating the instrumental resolution of the FTS. All parameters defining the model absorption spectrum are then automatically optimised to best agree with the experimental scan.
In many cases a more useful measurement of the strength of a line than the integrated cross section is a derived band f -value, calculated by factoring the ground-state rotational thermal population as well as rotation-dependent H¨ onl-London linestrength factors. Band f -values are only weakly dependent on upper-state J ′ for unperturbed bands. The main difficulties encountered while analysing the hot-cell N2 spectrum were the significant contamination from highly-excited rotational structure of nearby bands and obtaining a correct calibration of the temperature in the cell. Groups of lines from the same vibrational band were sometimes analysed while assuming correlated wavenumbers, widths and strengths to facilitate the analysis of blended spectral regions. That is, P (J ′′ − 1) and R(J ′′ + 1) transitions are connected to a common excited state so the difference in their transition wavenumbers was fixed to known ground-state energy levels  and a common linewidth assumed. A weak J ′ -dependence (or J ′ independence) was also assumed for some linewidths or f -values. 4
Table 1: Experimental upper term valuesa for observed lines in N2 indexed by excited state angular-momentum, J ′ .
a With units of cm−1 and parenthetical 1σ fitting uncertainties in terms of the least-significant digit. The estimated absolute calibration uncertainty is 0.04 cm−1 . b No splitting of e- and f - parity levels was observed (apart from for J ′ = 18) and these were assumed identical. c A splitting of e- and f - parity levels was observed, with term values 108 829.02(1) and 108 828.82(3) cm−1 , respectively.
Lines with natural widths below about 0.05 cm−1 full-width half-maximum (FWHM) are not reliably measured in our experiment due to concurrent instrument and Doppler broadening by 0.27 and about 0.4 cm−1 FWHM, respectively. No linewidths are then measurable from our spectrum for transitions to the weakly-predissociated c′4 (0) level . We compare our measured f -values and linewidths with those calculated from an existing model of N2 photoabsorption and dissociation, including photoabsorbing 1 Πu and 1 Σ+ u excited states and spinforbidden but dissociative 3 Πu states [6, 26, 27, 28, 29]. This model solves a coupled-Schr¨odinger equation (CSE) for the nuclear motion of the excited molecule, where the necessary potential-energy curves and state interactions have been optimised with respect to a large body of room-temperature experimental data. This model has been successfully employed previously in applications of atmospheric  and astronomical photochemistry [31, 32], including temperatures as high as 1000 K. Here, we seek to validate the extrapolation of the CSE model to high temperature by comparison to our new measurements.
3.1. Temperature calibration The f -values of b − X(v ′ , 0) transitions were used to calibrate the ground-state rotational temperature and N2 column density in the hot cell by comparison with previously-measured absolutely-calibrated f -values for v ′ = 0, 1, 2, and 10 [23, 24]. The resultant values are (6.35±0.64)×1015 cm−2 and 901±26 K, respectively. The reference data was recorded at room temperature, included rotational levels as high as J = 23, and themselves have an absolute column density uncertainty of 10% which is also the dominant systematic uncertainty of our f -values. The final agreement between the present measurements and the reference data, shown in Fig. 3, is very good despite the factor-of-5 difference in ground state populations, for example, at J ′ = 20. The c′4 − X(0, 1) band appears quite weakly in our spectrum and was analysed in order to estimate the vibrational temperature in the hot cell. For this, constant band f -values were assumed over
Figure 3: Band f -values of all transitions observed in our experiment as a function of excited-state angular-momentum quantum number, J ′ , and with 1σ random fitting uncertainties (circles with error bars). A 10% systematic error also applies and some f -values were analysed assuming J ′ -independent ranges (horizontal error bars). Also shown are previouslymeasured f -values [23, 24] (crosses), and calculated by the CSE model (solid black curves).
a well-known localised perturbation by the crossing ′ rotational term series of b′ 1 Σ+ u (v = 1) . ′ The newly-measured c4 − X(0, 1) f -values are somewhat smaller than the simulated values and an alternative model adopting an 800 K distribution of ground-state levels leads to the better agreement indicated in Fig. 4. This may indicate incomplete thermalisation of the N2 in our experiment leading to a lesser degree of vibrational excitation than rotational. A similar result is found in Sec. 4 for the CO rotational and vibrational temperatures. As a final check on the temperature of our sample of N2 , the Doppler broadening in our experiment was measured by reference to lower-J ′ levels of the b − X(1, 0) absorption band, whose predissociation broadening is known to be below our resolution limit [21, 26]. We find a kinetic temperature from this of about 930 K, with an uncertainty estimated to be significantly greater than for our deduced rotational temperature.
c′4 − X(0,1)
Figure 4: Band f -values of all c′4 − X(0, 1) transitions observed in our experiment as a function of excited-state angularmomentum quantum number, J ′ , and with 1σ random fitting uncertainties (circles with error bars). A 10% systematic error also applies and some f -values were analysed assuming J ′ -independent ranges (horizontal error bars). Also shown are alternative experimental f -values assuming an 800 K ground state excitation (dashed lines, open circles) and reference values calculated from a combination of CSE and experimental data (solid curve).
3.2. Results Transition wavenumbers for all observed b − X(v ′ , 0) bands were reduced to term values using accurate N2 ground-state molecular constants . Term values for these bands have been deduced previously for rotational levels with J ′ as high as 36 and with about 0.1 cm−1 uncertainty. Our term values are listed in Table 1 and have statistical uncertainties of around 0.01 cm−1 . The absolute calibration of our experiment was made by comparison of argon resonance lines appearing in our spectra with the NIST database and has an estimated uncertainty of 0.04 cm−1 . Our deduced band f -values are plotted in Fig. 3. The decrease of b − X(v ′ , 0) f -value with J ′ continues to the highest-excitation lines that we observe and is in perfect agreement with values predicted by the CSE model. This decrease is effectively due to a decreasing Franck-Condon overlap of b(v ′ ) and X(0) vibrational wave functions with increasing centrifugal distortion. Measured natural linewidths and comparable values from previous photoabsorption and resonantlyenhanced photoionisation experiments [19, 22, 23] are shown in Fig. 5. The widths of b(0), b(1), and b(2)
small ranges of most P (J ′′ ) and R(J ′′ ) lines as indicated piecewise in Fig. 4. Simulated c′4 − X(0, 1) f -values are also shown, with magnitude calculated from the ratio of c′4 − X(0, 0) and c′4 − X(0, 1) f values deduced by electron-excited fluorescence , f(0,0) /f(0,1) = 6.3 ± 0.4, and an absolute c′4 − X(0, 0) absorption f -value measurement . The stated uncertainties of the two experimental values used in this comparison are 6%  and 10% , respectively, although the latter should be neglected because our experimental column-density is calibrated to the same reference. We used the CSE model to simulate the significant rotational dependence of c′4 − X(0, 1) f values and assumed a 900 K distribution of groundstate rovibrational levels. This simulation then correctly reproduced the observed splitting of P - and R-branch f -values for c′4 − X(0, 1) transitions with increasing J ′ . This splitting is also known to occur for the c′4 − X(0, 0) fundamental band  and is the result of a rotational-perturbation of c′4 (v ′ = 0) by nearby 1 Πu levels . Additionally, c′4 − X(0, 1) transitions to J ′ = 11, 12, and 13 levels are significantly weakened relative to their neighbours due to 7
averaged over their J ≤ 5 levels have been previously deduced from laser-based lifetime or linewidth measurements [19, 21, 22]. The rotationally-resolved J-dependent broadening of b(2) and b(10) levels have been measured in synchrotron-based experiments [23, 24], and an increasing b(1) predissociation width with J ′ has also been experimentally deduced [35, 36]. Our newly-measured widths show good agreement with all reference data but with generally reduced scatter. Two interesting new pieces of information are discussed below. First, the decreasing b(2) widths are now shown to pass through a minimum at J ≃ 28. This complex behaviour is well-reproduced by the CSE model which includes a mechanism for predissociative line broadening by including unbound electronic states amongst its coupled channels [26, 27]. The critical interactions in this case are the spin-orbit coupling of b(2) with vibrationally-bound levels of the C 3 Πu state and their subsequent electronic interaction with the unbound continuum of the C ′ 3 Πu state. The dominant perturber of b(2) is the C(8) level which lies only 100 cm−1 lower in energy and has been previously identified in a photoabsorption spectrum  and found to have a linewidth of 18 cm−1 for J ′ less than about 10, despite the nominally spin-forbidden nature of this transition. All other bound 3 Πu states are too remote in energy to contribute significantly to the predissociation of b(2)  and the observed J ′ -dependence of its widths must then closely scale with the broader widths of C(8). Second, there is a sharp peak in the linewidths of b(10) shown in Fig. 5. Increasing widths beginning around J ′ = 15 were known from a poorer signalto-noise-ratio room-temperature spectrum , but are now better resolved and to higher-J ′ . There is also a perturbation of b(10) rotational energy levels near J ′ = 19, as shown in Fig. 6 as a 0.8 cm−1 deflection of its reduced term values. The localised perturbation of b(10) energies and widths indicates a level crossing with a predissociation-broadened level of 3 Πu symmetry, as is known to occur elsewhere in the N2 spectrum . One candidate for the role of b(10) perturber is the v ′ = 16 level of the C 3 Πu state, which has been observed for J ′ ≤ 10  and has a band
J Figure 5: Natural linewidths of e- and f -parity excited-state levels accessed in our experiment as a function of their angularmomentum quantum number, J ′ , and with 1σ random fitting uncertainties (circles with error bars). Some linewidths were analysed assuming J ′ -independent ranges (horizontal error bars). Also shown are previously-measured linewidths [19, 21, 22, 23, 24] (yellow lines and crosses), and linewidths calculated by the CSE model (solid black curves) and a two-level local interaction model (dashed black curve).
Reduced term values (cm−1 )
CO A(v) - X(v=0)
300 K 900 K
0.4 0.2 CO A(v) - X(v=0)
CO A(v) - X(v=1)
66000 Frequency (cm
Figure 6: Experimental f -parity term values of b(10) reduced by the subtraction of a cubic polynomial of best fit in terms of J ′ (J ′ + 1) (circles). Also shown are reduced term values from the b(10)/3 Πu interaction model (curve).
Figure 7: Overview spectrum of the CO A1 Π − X 1 Σ+ system including (0,0), (1,0), and (2,0) bands, and some hot bands. The top panel shows the spectrum which is measured at room temperature (300 K). In the bottom panel is the hot spectrum (900 K). The sharp absorption line in the upper spectrum at 68045.156 cm−1 is a xenon resonance line.
origin only 80 cm−1 below that of b(10). However, a rotational constant calculated from the observed C(16) levels, 1.153 cm−1 , is too low to cross the b(10) term series where the observed perturbation peaks at J ≃ 18. Alternatively, the v = 2 level of the G 3 Πu state has been observed  to lie nearby, 340 cm−1 below b(10), and undoubtedly has a larger rotational constant more characteristic of N2 Rydberg levels, about 1.9 cm−1 . A crossing between G(2) and b(10) is then conceivable. The observed widths of C(16) for J ′ ≤ 10 are less than 0.5 cm−1 FWHM, whereas G(2) is predicted to be much broader, about 90 cm−1 FWHM, by the CSE model of Lewis et al. . To analyse the width and term value perturbation of b(10) further we defined a two-level model of b(10) interacting by the spin-orbit operator with a 3 Πu level (including all triplet sublevels) and optimised its various parameters to match our experimental data. This was done in an identical fashion to similar deperturbations of N2 3 Πu /1 Πu interactions by Lewis et al. . Comparisons of experimental widths and reduced term values with this model are shown in Figs. 5 and 6 and find overall good agreement when adopting a 3 Πu state with a term origin of approximately 108 150 cm−1 , a rotational constant of 1.6 cm−1 , and a spin-orbit splitting of 30 cm−1 (where the sign of the latter is unconstrained). Two further
model parameters are the strength of the b(10) and Πu spin-orbit interaction, 7 cm−1 , and the deperturbed predissociation widths of 3 Πu levels. Good agreement could only be found when assuming the latter increases linearly in term of J ′ (J ′ + 1) from 20 cm−1 at J ′ = 18, to 60 cm−1 at J ′ = 29. All of these deduced values are intermediate between those known or predicted for C(16) and G(2), [28, 37, 38], indicating that the perturber of b(10) is an electronic admixture of the C 3 Πu and G 3 Πu states. Indeed, the coupled-channels model of Lewis et al.  predicts this, as well as a further significant admixture of the F 3 Πu Rydberg state into the nominal C(16) and G(2) levels. 3
4. Absorption spectra of CO A−X(0,0) and (1,0) bands The novel hot cell configuration was employed for the further investigation of the A1 Π − X 1 Σ+ system of CO for the lowest vibrational bands in the excited state. Figure 7 shows an overview spectrum of some bands recorded at 300 K and 900 K. With the higher gas temperature, the rotational envelope of each band includes higher J-quantum numbers and hot bands 9
Table 2: Observed high-J transition frequencies (in vacuum cm−1 ) of the CO A1 Π − X 1 Σ+ (0,0) and (1,0) bands obtained with the hot cell. Lower-J transitions are listed in Ref. . The estimated uncertainty (1σ) is 0.02 cm−1 except for weak or blended lines. J ′′ 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 51
Figure 8: (Preferably printed in two-column) The spectrum of the CO A1 Π − X 1 Σ+ system in the range 63 700 – 64 900 cm−1 measured using the hot cell in combination with the FTS-VUV. Rotational lines in the A−X (0, 0) and (1, 1) bands are assigned by the sticks. Transitions to the e3 Σ− perturber state are also assigned. The slope on the background continuum is due to the spectral profile of the undulator emission.
appear that originate from X 1 Σ+ (v ′′ = 1). Figure 8 displays a more detailed spectrum of the (0, 0) and (1, 1) bands of the A1 Π − X 1 Σ+ system of CO. Note that the strongest transitions in Figs. 7 and 8 are saturated. A number of spectra were recorded at various gas densities so that transition frequencies for all lines could be analysed in unsaturated recordings. The observed high-J transition frequencies in the A1 Π − X 1 Σ+ (0, 0) and (1, 0) bands are collected in Table 2. While in a previous room temperature study of the same bands their rotational progression could be followed up to J = 21 and J = 23, respectively , the present spectrum reveals lines up to J = 51 and J = 53 for the two bands. Accurate transition frequencies for low-J transitions were already given in Ref.. In the observed region, between 63 500 − 67 500 cm−1 , many lines were observed that excite perturber states of the A1 Π (v = 0) and (v = 1) levels, and are examined in the present study. Lines pertaining to the e3 Σ− −X 1 Σ+ (1,0) band, clearly visible in Fig. 8, are listed in Table 3. Data for the e3 Σ− −X 1 Σ+ (1,0)
band had previously been reported by Simmons and Tilford  and, at higher accuracy and also up to J = 22, by Lefloch et al. . On average the data are offset by 0.04 cm−1 with respect to present values, which is within the error margins claimed in Ref. . Term values of the e3 Σ− (v = 1) level can also be obtained via measurement of lines in the B 1 Σ+ − e3 Σ− system, with observations of the (0,1) band  at accuracies in the range 0.001−0.02 cm−1 combined with the measurements of the B 1 Σ+ − X 1 Σ+ (0,0) band, accurate at 0.003 cm−1 . In comparison with the present data set the overall offset on the term values is within 0.015 cm−1 , which is well within the quoted uncertainties. Observed lines associated with the d3 ∆ − X 1 Σ+ system are listed in Table 4 for the (4,0) band, observed for rotational angular momenta of J = 26−36, and in Table 5 for the (5,0) band, with observation of J = 0 − 17. In an investigation by Herzberg et al.  rotational levels up to J = 22 were observed in both bands at low accuracy. The observations in the d3 ∆ − X 1 Σ+ (4,0) band were superseded by those
Table 4: Observed transition frequencies (in vacuum cm−1 ) of the CO d3 ∆ − X 1 Σ+ (4,0) band obtained with the hot cell. The estimated uncertainty (1σ) is 0.02 cm−1 except for weak or blended lines. F1
Table 5: Observed transition frequencies (in vacuum cm−1 ) of the CO d3 ∆ − X 1 Σ+ (5,0) band obtained with the hot cell. The estimated uncertainty (1σ) is 0.02 cm−1 except for weak or blended lines. F1 J ′′ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Table 3: Observed transition frequencies (in vacuum cm−1 ) of the CO e3 Σ− − X 1 Σ+ (1,0) band obtained with the hot cell. The estimated uncertainty (1σ) is 0.02 cm−1 except for weak or blended lines. F1 Q
Table 7: The updated molecular constants for the A1 Π (v = 0) and (v = 1) states of 12 C16 O and the perturber states d3 ∆ (v = 4) and D 1 ∆ (v = 1) following from the perturbation analysis. In cases where an uncertainty is specified in () parentheses the value was determined from the fit; in cases where this is not specified a value was taken from literature. For the A1 Π states, the Tv and B parameters are fixed to the previous work, because these parameters are predominantly determined by the low-J transition frequencies. All values in vacuum cm−1 .
d3 ∆(v = 4) Table 6: Observed transition frequencies (in vacuum cm−1 ) of other CO electronic-vibrational bands obtained with the hot cell. The estimated uncertainty (1σ) is 0.02 cm−1 except for weak or blended lines.
a′3 Σ+ − X 1 Σ+ (9,0) D1 ∆ − X 1 Σ+ (1,0) P
P(26) P(27) Q Q(24) Q Q(25) Q Q(26) R R(25) R R(27) P
Tv 65101.90 (3) Tv 66462.11 (9) B 1.23381 (8) B 1.2373 (3) A -16.52 (1) λ 1.15 (3) γ (×103 ) -8.54 D (×106 ) 6.80 (6) D (×106 ) 8.8 (4) H (×1012 ) -0.8 H (×1012 ) -0.3 AD (×104 ) -1 η0 -21.72 (1) ξ0 0.040 η1 ξ1 0.077 (1)
of Lefloch et al.  at higher accuracy. Comparison with the latter and the present data set yields agreement within 0.04 cm−1 , hence within the quoted error margin of 0.06 cm−1 in Ref. . The d3 ∆ − X 1 Σ+ (5,0) band had been investigated by VUV laser-induced fluorescence measurements . Accurate data on this band were also reported from classical spectroscopic studies by Lefloch ; for this set the agreement with the present data is within 0.02 cm−1 . The d3 ∆ (v = 5) levels were also observed in emission in the B 1 Σ+ − d3 ∆(0,5) band . In the present study the F1 and F2 fine structure components in the d3 ∆ state were observed, while in the study of Choe et al.  the F3 components were seen as a result of different intensity borrowing, In addition two lines in the d3 ∆ − X 1 Σ+ (5,1) band were observed and listed in Table 6. Additional lines observed were assigned to the D1 ∆ − X 1 Σ+ (1,0) band, the I 1 Σ− − X 1 Σ+ (2,0) band, and the a′3 Σ+ − X 1 Σ+ (9,0) band, and listed in Table 6. Some of these transitions probing perturber states were observed previously by Lefloch et al. [40, 45], although not all, and at a lower accuracy of 0.06 cm−1 . Herzberg et al. observed states up to J = 22 in the I 1 Σ− − X 1 Σ+ (2,0) band . Despite the fact that information on the intermediate J-levels is missing, an unambiguous assignment of the transitions originating in J = 34 − 35 could nevertheless be made based on the perturbation patterns. The same holds for the newly observed lines in the D1 ∆ − X 1 Σ+ (1,0) band, for which rotational lines up to J = 17 were observed in the past , and for which new lines originating from J = 24 − 26 are found. A reiteration of a previous deperturbation analysis for the A1 Π (v = 0) and (v = 1) states  is performed including the additional data points for highJ levels. A comprehensive fit was performed based on the diagonalisation of a series of matrices containing J-dependent deperturbed energy levels and interaction energies of multiple states. The entire set of experimental A1 Π − X 1 Σ+ (0,0) and (1,0) lines were reproduced and all lines exciting perturber states. The form of these perturbation matrices is kept the same as that defined in Table 6 of Ref. , keeping the
same labels for the parameters. For the A1 Π states, the Tv and B parameters are fixed to the previous work, because these parameters are predominantly determined by the low-J transition frequencies. Most of the molecular constants resulting from this procedure did not undergo a significant change except for the values pertaining to the states D1 ∆(v = 1) and d3 ∆(v = 4). These values are listed in Table 7. The main difference for the d3 ∆ state entails the inclusion of a quartic centrifugal distortion D and a spin-spin coupling constant, λ. Values for the D1 ∆ state were previously kept constant but are now optimized in the present fit. The rotational temperature Trot = 927 ± 20 K is determined by fitting the transition intensities of transitions with different J–quantum numbers, assuming a Boltzmann distribution of ground state populations. This fitting considers perturber states borrowing intensity from the A1 Π-X 1 Σ+ transitions. The vibrational temperature, Tvib ∼ 845 K, is calculated by comparing the intensities of the strong A1 Π−X 1 Σ+ (1, 0) band and the weak (1, 1) hot band. For this analysis pressure saturation effects must be considered that prevent a direct comparison of intensities of these two vibrational bands with very different cross sections. Instead, spectra recorded at different column densities are used, also involving a comparison with the A1 Π− X 1 Σ+ (0,0) band of intermediate strength. Further, Franck-Condon factors of the (1, 0) and (1, 1) vibrational transitions must be considered, which are taken from Ref. . The kinetic temperature, associated with Doppler broadening, is determined at Tkin ∼ 900 K. 5. Conclusion Vacuum-ultraviolet photoabsorption spectra of N2 and CO were recorded at 930 K using a heated free-flowing gas cell and the Fourier-transform spectrometer end station of the DESIRS beamline at the SOLEIL synchrotron. This novel setup allowed for the measurement of rotational transitions with angular-momentum quantum numbers, J ′ , as high as 51 and also from the first excited ground state vibrational level, which is well beyond the limit of roomtemperature experiments. The high-resolution spec-
trometer permitted quantification of rotationallyresolved transition energies, f -values, and predissociation broadening for many vibrational bands. In CO, we deduce new high-J ′ level energies for the upper states of the A 1 Π − X 1 Σ+ (v ′ , v ′′ = 0) bands with v ′ = 0 and 1, as well as observe new forbidden transitions to levels of the e 3 Σ− , d 3 ∆, D 1 ∆ and a′ 3 Σ+ states. The forbidden transitions appear due to intensity-borrowing from the A − X bands and the new data permitted an improved estimate of molecular parameters describing the forbidden levels and their perturbing interactions. We measure new level energies, f -values, and predissociation linewidths of the N2 bands b 1 Πu − ′ ′′ ′ X 1 Σ+ u (v , v = 0) for v = 0, 1, 2, and 10. These ver′ ify the high-J predictions of a CSE model which was constructed with respect to room-temperature experimental data. This validates the use of photodissociation cross sections calculated from this model in atmospheric or astrophysical applications at high temperatures. No forbidden levels are observed for the case of N2 . Instead, the J ′ -dependent widths of b(v ′ ) provide new indirect information on an interacting dissociative manifold of 3 Π levels. The analysis of perturbed b(10) level energies and linewidths permitted the characterisation of its level crossing with a 3 Πu level of mixed electronic character. There is some indication that for both target molecules the rotational and vibrational temperatures are not identical, 930 and 800–830 K, respectively. The incomplete equilibration of vibrational and rotational excitation will not affect our conclusions regarding the perturbation of high J ′ levels but introduces uncertainty into any determination of hotband absolute f -values. The present measurements of high-temperature cross sections and line lists have a direct application to the study of astrophysical environments and planetary atmospheres. It also provides detailed extra information on the underlying electronic states of the molecules and their non-Born-Oppenheimer interactions. This information, when incorporated with the larger experimental record, is necessary for constraining predictive models of the photoabsorbing and dissociating excited states; and will allow for improvements to the N2 CSE model, and similar theoretical
developments for the case of CO. Acknowledgements This work is financially supported by the Dutch Astrochemistry Network of the Netherlands Foundation for Scientific Research (NWO). We wish to thank JF Gil, technician on the DESIRS beam line for the mechanical conception of the hot cell. We are grateful to the general and technical staff of SOLEIL for providing beam time under project no 20120653. References
 L. Nahon, N. de Oliveira, G. A. Garcia, J. F. Gil, B. Pilette, O. Marcouille, B. Lagarde, F. Polack, J. of Synchtron Rad. 19, 508-520 (2012).  N. de Oliveira, D. Joyeux, D. Phalippou, J.-C. Rodier, F. Polack, M. Vervloet, and L. Nahon, Rev. Scient. Instr. 80, 043101 (2009).  N. de Oliveira, M. Roudjane, D. Joyeux, D. Phalippou, J.-C. Rodier, and L. Nahon, Nat. Phot. 5, 149-153 (2011).  G. D. Dickenson, T. I. Ivanov, M. Roudjane, N. de Oliveira, D. Joyeux, L. Nahon, L. TchangBrillet, M. Glass-Maujean, I. Haar, A. Ehresmann, and W. Ubachs, J. Chem. Phys. 133, 144317 (2010).  T. I. Ivanov, G. D. Dickenson, M. Roudjane, N. de Oliveira, D. Joyeux, L. Nahon, W.-.L. Tchang-Brillet, and W. Ubachs, Mol. Phys. 108, 771-786 (2010).  A. N. Heays, G. D. Dickenson, E. J. Salumbides, N. de Oliveira, D. Joyeux, L. Nahon, B. R. Lewis, and W. Ubachs, J. Chem. Phys. 135, 244301 (2011).  M. L. Niu, E. J. Salumbides, D. Zhao, N. de Oliveira, D. Joyeux, L. Nahon, R. W. Field, W. Ubachs, Mol. Phys. 111, 2163–2174 (2013).
 L. E. Archer, G. Stark, P. L. Smith, J. R.  P. F. Levelt and W. Ubachs, Chem. Phys. 163, Lyons, N. de Oliveira, L. Nahon, D. Joyeux, D. 263-275 (1992). Blackie, J. Quant. Spectr. Rad. Transfer 177,  J. P. Sprengers, W. Ubachs, A. Johansson, 88-92 (2013). A. L’Huillier, C.-G. Wahlstr¨om, R. Lang, B. R.  G. Stark, A. N. Heays, J. R. Lyons, P. L. Smith, Lewis, and S. T. Gibson, J. Chem. Phys. 120, M. Eidelsberg, S. R. Federman, J. L. Lemaire, 8973-8978 (2004). L. Gavilan, N. de Oliveira, D. Joyeux, L. Nahon,  J. P. Sprengers, W. Ubachs, and K. G. H. BaldAstroph. J. 788, 67 (2014). win, J. Chem. Phys. 122, 144301 (2005).  M. Eidelsberg, J. L. Lemaire, S. R. Federman, G. Stark, A. N. Heays, Y. Sheffer, L. Gavilan, J. H.  G. Stark, K. P. Huber, K. Yoshino, P. L. Smith, and K. Ito, J. Chem. Phys. 123, 214303 (2005). Fillion, F. Rostas, J. R. Lyons, P. L. Smith, N. de Oliveira, D. Joyeux, M. Roudjane, L. Nahon,  G. Stark, B. R. Lewis, A. N. Heays, K. Yoshino, Astron. Astrophys. 543, A69 (2012). P. L. Smith, and K. Ito, J. Chem. Phys. 128,  L. Gavilan, J. L. Lemaire, M. Eidelsberg, S. R. 114302 (2008). Federman, G. Stark, A. N. Heays, J.-H. Fillion, ¨ L. J. R. Lyons, and N. de Oliveira, J. Phys. Chem.  W. Ubachs, R. Lang, I. Velchev, W.-U. Tchang-Brillet, A. Johansson, Z. S. Li, V. A117, 9664-9652 (2013). Lokhnygin, and C.-G Wahlstr¨om, J. Chem.  S. R. Federman, M. Fritts, S. Cheng, K. M. MenPhys. 270, 215-225 (2001). ningen, D. C. Knauth, and K. Fulk, Astroph. J.  B. R. Lewis, S. T. Gibson, W. Zhang, Suppl. Ser. 134, 133138 (2001). H. Lefebvre-Brion, and J. M. Robbe, J. Chem.  A. de Lange, G. D. Dickenson, E. J. Salumbides, Phys. 122, 144302 (2005). W. Ubachs, N. de Oliveira, D. Joyeux, L. Nahon, J. Chem. Phys. 136, 234310 (2012).  V. E. Haverd, B. R. Lewis, S. T. Gibson, and G. Stark, J. Chem. Phys. 123, 214304 (2005).  A. N. Heays, R. Visser, R. Gredel, W. Ubachs, B. R. Lewis, S. T. Gibson, E. F. van Dishoeck,  B. R. Lewis, A. N. Heays, S. T. Gibson, H. Astron. Astrophys. 562, A61 (2014). Lefebvre-Brion, and R. Lefebvre, J. Chem. Phys. 129, 164306 (2008).  J. Bagdonaite, E. J. Salumbides, S. P. Preval, M. A. Barstow, J. D. Barrow, M. T. Murphy,  A. N. Heays, J. M. Ajello, A. Aguilar, B. R. and W. Ubachs, Phys. Rev. Lett. 113, 123002 Lewis, and S. T. Gibson, Astroph. J. Suppl. Ser. (2014). 211, 28 (2014).  F. Brandi, I. Velchev, W. Hogervorst, and W. Ubachs, Phys. Rev. A 64, 032505 (2001).
 P. Lavvas, M. Galand, R. V. Yelle, A. N. Heays, B. R. Lewis, G. R. Lewis, and A. J. Coates, Icarus 213, 233-251 (2011).  E. B. Saloman, J. Phys. Chem. Ref. Data 33, 765–922 (2004).  X. Li, A. N. Heays, R, Visser, W. Ubachs, B. R. Lewis, S. T. Gibson, and E. F. van Dishoeck,  E. J. Salumbides, M. L. Niu, J. Bagdonaite, Astron. Astrophys. 555, A14 (2013). N. de Oliveira, D. Joyeux, L. Nahon, and W. Ubachs, Phys. Rev. A 86, 022510 (2012).  A. N. Heays, R, Visser, R. Gredel, W. Ubachs, B.  W. Ubachs, L. Tashiro, and R. N. Zare, Chem. R. Lewis, S. T. Gibson, and E. F. van Dishoeck, Phys. 130, 1-13 (1989). Astron. Astrophys. 562, A61 (2014). 16
 X. Liu, D. E. Shemansky, C. P. Malone, P. V.  G. Herzberg, J. D. Simmons, A. M. Bass, and Johnson, J. M. Ajello, I. Kanik, A. N. Heays, S. G. Tilford, Can. J. Phys. 44, 3039-3041 B. R. Lewis, S. T. Gibson, and G. Stark, J. Geo(1966). phys. Res. 113, A02304 (2008).  J. D. Simmons and S. G. Tilford, J. Chem. Phys. 45, 2965-2968 (1966).  S. Edwards, J. Y. Roncin, F. Launay, and F. Rostas, J. Mol. Spectrosc. 162, 257-267 (1993).  L. W. Beegle, J. M. Ajello, G. K. James, D. Dziczek, and M. Alvarez, Astron. Astrophys. 347,  B. R. Lewis, S. T. Gibson, J. P. Sprengers, W. 375-390 (1999). Ubachs, A. Johansson, and C.-G Wahlstr¨om, J. Chem. Phys. 123, 236101 (2005).  C. Y. Robert Wu, D. L. Judge, M.-H. Tsai, Y.-C. Lin, T.-S. Yih, J.-I. Lo, H.-S. Fung, Y.-Y. Lee, B. R. Lewis, A. N. Heays, and S. T. Gibson, J. Chem. Phys. 136, 044301 (2012).  B. R. Lewis, K. G. H. Baldwin, J. P. Sprengers, W. Ubachs, G. Stark, and K. Yoshino, J. Chem. Phys. 129, 164305 (2008).  A. B. van der Kamp, P. C. Cosby, and W. J. van der Zande, Chem. Phys. 184, 319-333 (1994).  J. D. Simmons and S. G. Tilford, J. Res. Nat. Bur. of Standards, 75A, 455-467 (1971).  A. C. Lefloch, F. Launay, J. Rostas, R. W. Field, C. M. Brown, K. Yoshino, J. Mol. Spectr. 121, 337-379 (1987).  J.-I. Choe, D.-K. Lee, A. C. Lefloch, and S. G. Kukolich, J. Mol. Spectrosc. 136, 173-184 (1989).  M. Drabbels, J. Heinze, J. J. ter Meulen, and W. L. Meerts, J. Chem. Phys. 99, 5701-5711 (1993).  G. Herzberg, T. J. Hugo, S. G. Tilford, and J. D. Simmons, Can. J. Phys. 48, 3004-3015 (1970).  A. Du Plessis, E. G. Rohwer, and C. M. Steenkamp, J. Mol. Spectrosc. 243, 124-133 (2007).  A. C. Lefloch, Ph.D. thesis, Univ. Paris-Sud (1989). 17