1. Experimental and Theoretical He-broadened Line Parameters of CO in the Fundamental Band
Adriana Predoi-Cross1*, Hoimonti Rozario1, Koorosh Esteki1, Shamria Latif1, Franck Thibault2, V. Malathy Devi3, Mary Ann H. Smith4 and Arlan Mantz5
1 Department of Physics and Astronomy, University of Lethbridge, Lethbridge, AB, Canada
2 Institute de Physique de Rennes, Université de Rennes 1, Rennes, France
3 Department of Physics, College of William and Mary, Williamsburg, VA, USA
4 Science Directorate, NASA Langley Research Center, Hampton, VA, USA
5 Department of Physics, Astronomy and Geophysics, Connecticut College, New London, CT, USA. *
71st International Symposium on Molecular Spectroscopy, June 20-24, Paper WB02.

2. Objectives For Our Spectroscopic Study
Extremely precise measurements of spectral line shapes can help us both to understand fundamental processes of molecular dynamics and to interpret remote sensing data. By applying the results of laboratory studies and theoretical models to the analysis of remote sensing measurements, it is possible to determine the chemical composition and physical properties of remote environments such as the atmospheres of the giant planets.

3. Experimental conditions of the spectra used in this study
Gas
Temperature (K)
Cell Pressures (atm)a
Gas mixing ratio
Path Length (m)
Pure CO
296.21
1.0
296.27
CO-He
296.39
0.0107
296.51
0.0098
296.63
230.70
0.0137
230.69
0.0132
0.0135
0.0133
182.56
0.0123
182.55
0.0121
182.53
0.0129
182.52
142.27
0.0105
142.21
142.17
0.0113
142.15
0.0122
79.20
0.0106
a 1 atm =760 Torr= kPa
Note: All spectra were recorded using the high resolution 1-m Fourier Transform spectrometer at the National Solar Observatory on Kitt Peak, AZ. Previous analysis was done by Mantz et al. [J. Mol. Struct. 742 (2005) ] using constrained multispectrum fits with the Voigt line shape.
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4. Expressions for Retrievals of Broadening and Shift Parameters
bL(p,T) is the Lorentz halfwidth (in cm-1) of the spectral line at pressure p and temperature T, and the broadening coefficient bL0(Gas)(p0,T0) is the Lorentz halfwidth of the line at the reference pressure p0 (1 atm) and temperature T0 (296 K), and  is the ratio of the partial pressure of CO to the total sample pressure in the cell. The temperature dependence exponents of the pressure-broadening coefficients are n1 and n2.
Where 0 is the zero-pressure line position (in cm-1),  is the line position corresponding to the pressure p, δ0 is the pressure-induced line shift coefficient at the reference pressure p0(1 atm) and temperature T0(296 K) of the broadening gas (foreign broadener or self broadener), and  is as defined above.
The temperature dependence of the pressure induced shift coefficient (in cm-1atm-1K-1) is δ′. δ0(T) and δ0(T0) represent the pressure induced shift coefficients (in cm-1atm-1) at T and T0 (296 K), respectively. An initial estimate of zero was assumed for δ′ for both foreign- and self-broadening.

5. Limitations of the Voigt Profile
Example: CO-Xe system
Ref: A. Predoi-Cross et al. Can. J. Phys. 87(5) (2009)
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Ref: Ha Tran, private communication

6. Non-Voigt profiles: velocity changing effects
γ(ν) and shift δ(ν) of the line.
In order to compensate for the velocity dependence we can define speed classes based on the Maxwell Boltzmann distribution of velocities. These can then be analysed and combined in order to form profiles that incorporate this speed dependence effect.
Ref. (above): Ha Tran, Université Paris-Est Créteil, France, private communication.
Ref. (right): J.-M. Hartmann, C. Boulet, D. Robert, Collisional Effects on Molecular Spectra (2008) p. 92.

7. Line Mixing Effects
Collisions induce transfers of populations between the levels of the two lines that lead to transfers of intensity between the lines.
Absorption Coefficient
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Ref: Ha Tran, Université Paris-Est Créteil, France, private communication

8. Close-coupled theoretical calculations of broadening, shift, narrowing coefficients
Quantum dynamical calculations were performed on the 3-dimensional potential energy surface (PES) for the 12C16O-He system proposed by Heijmen et al. J. Chem. Phys. (1997).
Most of the close-coupling pressure broadening and shift cross-sections as a function of the relative collisional energies were used from Luo et al. J. Chem. Phys. 115 (2001) in order to provide pressure broadening and pressure shift coefficients in the 0→1 band.
Additional calculations were devoted to purely rotational R lines to predict the odd component of the ro-vibrational shifts.
Assuming that the even component of the shifts has a purely vibrational origin resulting from the isotropic parts of the PES and is therefore J- independent, we are able to determine the shift coefficients in the fundamental (at least at room temperature).
Moreover, since the half width at half maximum is nearly vibrationally independent, we also present some results of our calculations performed in the vibrational ground state to complete our data analysis.
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9. THEORETICAL CALCULATIONS

10. Bottom panel: A section of the 19 overlaid experimental spectra analyzed applying the multispectrum nonlinear least squares fitting technique using the speed dependent Voigt profile with weak line mixing. Top panel: Overlaid observed minus calculated fit residuals.
Author Name, Title
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11. Differences between the line positions retrieved in the present study, those in the HITRAN2012 database, and those resulting from the constrained multispectrum fit analysis reported in Mantz et al. J. Mol. Struct. (2005).
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12. Retrieved line intensities (linear scale) for CO transitions in the 10 band plotted as a function of m (m = −J″ for P-branch and J″+1 for R-branch transitions) for the four line shapes, compared to HITRAN 2012 values.

13. Retrieved CO-He broadening coefficients in cm-1atm-1 at 296 K obtained using the four line shape profiles, overlaid with other published measurements of CO-He broadening coefficients.
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14. Retrieved CO-He broadening coefficients in cm-1 atm-1 at 296 K obtained using the Voigt, Rautian, speed dependent Voigt (SDV), and Rautian with speed dependent line shape profiles.
Measured CO-He broadening coefficients as a function of the rotational quantum index m overlaid with theoretical He-broadening coefficients (CC) and empirical values calculated using a power law polynomial.
Experimental (Voigt with line mixing) and theoretical (CC) broadening coefficients at different temperatures.

15. Temperature dependence exponents for He-broadening coefficients of CO transitions in the fundamental band.
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16. Measured CO-He pressure-induced shift coefficients (cm-1 atm-1 at 296 K) obtained using the four line shape models. Overlaid with our measurement results are other published measurements and the calculated CO-He pressure-shift coefficients ▲.
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17. Experimental He-shift coefficients (Voigt with line mixing) and the close coupled (CC) theoretical He-shifts at different temperatures.
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18. Retrieved temperature dependences for He-pressure shift coefficients (cm-1 atm-1 K-1) overlaid with the results from Mantz et al. J.Mol. Struct. (2005) plotted as a function of m.
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19. Scaling Laws Exponential Power Gap Model - EPG
To calculate the elements of the relaxation matrix we use a nonlinear Marquardt algorithm to optimally fit the parameters a, b and c in the state to state transfer equation. The best fit is found by optimizing the diagonal elements of the relaxation matrix to be equal to the experimentally determined broadening coefficients.

20. Energy Corrected Sudden Calculations for Rotational Transfer
This is a dynamically based scaling law that takes into account the finite durations of collisions through the addition of an adiabaticity factor. The elements of the relaxation matrix are calculated from the following function:

21. Measured, calculated and previously published CO-He collisional line mixing coefficients (in cm-1 atm-1 at 296 K) for transitions in the 10 band of CO.
[F. Thibault et al., J. Chem. Phys. (1992)]

22. Conclusions
We have re-analyzed an existing set of CO-He spectra using a unconstrained multispectrum approach.
The He-broadened line parameters have been retrieved using the Voigt, speed dependent Voigt, Rautian, and Rautian with speed-dependence line shape models.
The best agreement between measured and calculated spectra was found for the speed dependent models when line mixing is accounted for.
We have used theoretical calculations using a potential energy surface to compute the He-narrowing parameters at different temperatures, the He-broadening and He- induced pressure shift coefficients.
All theoretical close coupled results for He-broadening and He-pressure shift coefficients have been compared with our experimentally determined parameters and with previously published results.
Our retrieved He-broadening coefficients were found to agree very well with the corresponding close coupled calculated values at different temperatures.
The weak line mixing coefficients have been compared with results of semi-empirical calculations using the Exponential Power Gap law, the Energy Corrected Sudden approximation, and also with published results obtained from quantum dynamical calculations and were found to be in satisfactory agreement.

23. Acknowledgements Thank you!
The research carried out at the University of Lethbridge is funded by the Natural Sciences and Engineering Research Council of Canada through the Discovery and CREATE grant programs. The part of the research carried out at the College of William and Mary, Connecticut College and NASA Langley Research Center have been funded by cooperative agreements and contracts with the National Aeronautics and Space Administration. We thank A. Mashwood and N. Islam for their contributions in the early stages of this project. Dr. D. Chris Benner at the College of William and Mary is thanked for allowing us to use his multispectrum fitting software in analysing the data.
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