Journal of Spectroscopy

Volume 2018, Article ID 2098625, 6 pages

https://doi.org/10.1155/2018/2098625

## Retrieval of Total Scattering Cross Sections of Molecules from Inhomogeneously Broadened Absorption Lines

^{1}Laboratory of Theoretical Spectroscopy, V.E. Zuev Institute of Atmospheric Optics, Siberian Branch, Russian Academy of Sciences, 1, Academician Zuev Square, 634021 Tomsk, Russia^{2}Laboratory of Molecular Spectroscopy, V.E. Zuev Institute of Atmospheric Optics, Siberian Branch, Russian Academy of Sciences, 1, Academician Zuev Square, 634021 Tomsk, Russia^{3}Department of Physics, Tomsk State University, 36, Lenin Ave., 634050 Tomsk, Russia

Correspondence should be addressed to V. P. Kochanov; ur.oai@hcok

Received 20 June 2018; Revised 18 July 2018; Accepted 28 July 2018; Published 15 October 2018

Academic Editor: Jose S. Camara

Copyright © 2018 V. P. Kochanov and L. N. Sinitsa. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

A new method of retrieving quantitative information on the hard, soft, and diffraction collision’s frequencies from inhomogeneously pressure-broadened line profiles was proposed and tested. The essence of the method lies in the processing of recorded profiles using various profiles’ models containing these frequencies treated as adjustable parameters in different manners. Three self-broadened H_{2}O absorption lines free of an instrumental function were processed with the use of four model line profiles. Retrieved set of pressure line broadening and narrowing constants allows finding out the sought frequencies. The estimation of the total scattering cross section, ∼630 Å^{2}, in pure water vapor was made.

#### 1. Introduction

Various models for spectral line profiles allow retrieving information on collision processes that affect the line shape. The simplest Lorentzian and Voigt profiles provide retrieving only the homogeneous collision line half-width *γ* and the line shift Δ. With the aid of more complicated profiles [1–4], where the Dicke line narrowing [5, 6] is taken into account, it is possible to find out an additional parameter—the frequency of elastic velocity-changing collisions. In the conventional approach [1–6], this frequency is expressed via the diffusion coefficient *D* aswhere is the most probable thermal speed of absorbing molecules. Thus, exploitation of the collision line narrowing makes it possible to obtain the data on from processing recorded line profiles, which is still nonconventional information for spectroscopy. Similarly, involvement of other physical mechanisms of forming the line shape increases the number of the profile’s adjustable parameters. Certain parameters may have a direct physical meaning, and thus they can serve as a source of valuable additional information extracted from a line shape. Such are the frequencies of soft and hard velocity-changing collisions.

Let us detail the latter assertion. The matter is that the structure of the collision integral implies division of its kernel onto three parts related to hard (hard collisions are mainly large-angle scattering collisions [9] that lead to establishing the equilibrium distribution of molecules over velocities after each collision, soft collisions are caused by classical scattering on small angles less 0.3 rad [10], and the diffraction-scattering collisions occur when scattering angles are ∼0.01 rad [8–10].), soft, and diffraction-scattering collisions [7–11]. These three types of collisions function to a great extent additively due to considerable difference in widths of the corresponding differential scattering cross sections. Consequently, the total output frequency of the collision integral *ν*_{t} can be represented as a sum [7–11].where , , and are the input collision integral frequencies of the elastic hard, soft, and diffraction scattering collisions, respectively, and the Lorentzian collision half-width at half-height contains the contributions of elastic and inelastic collisions. If the above frequencies enter into a model collision integral explicitly, then the line profile derived from the respective muster equation for a density matrix will contain these frequencies as adjustable parameters [9, 10]. This opens a possibility to retrieve the newly introduced parameters from processing experimental line profiles.

It was shown earlier [12–14] that the output frequency can be measured directly as a collision-broadening constant of nonlinear resonances at sufficiently low gas pressures. The theory [14, 15] allows expressing the frequency through the total collision cross section. Thus, qualitatively new fundamental information can be obtained from nonlinear spectroscopic measurements. On the contrary, in this paper, we intend to show that the value of also may be obtained by means of linear spectroscopy. Namely, correct account of the combined effect of hard and soft collisions [8–11] performed on the basis of the quantum-mechanical collision integral kernel [7] and the inverse-power intermolecular interaction potentials provides the presence of all the frequencies specified in (2) in the model line profiles [8–11]. Therefore, in principle, it is possible to retrieve these frequencies from processing recorded spectra with the profiles [8–11]. Though, such retrieval is not guaranteed to be a priori successful because of a strong correlation between some of the profile’s parameters [10]. At the same time, certain parameters of the collision integral can be calculated theoretically for different intermolecular interaction potentials [9, 10]. In particular, such is the ratio of soft to hard collision frequencies, which also can be used in the fitting. Thus, we can assume that the ambiguity caused by marked above correlation of the parameters can be eliminated, and the retrieving different collision integral frequencies will be possible. Ascertainment of a principal scheme of the estimation of the discussed frequencies and testing its operability form the goals of this paper.

#### 2. Experimental Setup

The high-resolution spectra of H_{2}O were recorded with the use of the photoacoustic (PhA) spectrometer based on a single-mode Ti-sapphire laser pumped by an Ar-ion laser. The Ti-sapphire laser had the output power of 1 W and the 50 kHz linewidth. It was able to tune in the 11300–12800 cm^{−1} spectral range with the 20 MHz frequency step. This provided the spectral resolution better than 0.001 cm^{−1} and the negligible contribution of the laser bandwidth to recorded line profiles (the Doppler HWHM was ∼0.018 cm^{−1} or 542 MHz). The high power of the laser provided a high threshold absorption sensitivity of the spectrometer, ∼1⋅10^{−8} cm^{−1}. The body of the PhA cell was made of stainless steel. The length of the cell was 10 cm. The acoustic signal in the PhA cell was detected by high-sensitive laboratory-made capacitor microphone with a preamplifier. A signal of the photoacoustic detector is directly proportional to the absorption coefficient of the gas as opposed to the spectrophotometric method where a signal is proportional to the transmittance of the medium. This circumstance allows recording a weak absorption with a higher accuracy. Wavelength calibration was carried out with the use of the Fourier spectrometer “Bruker DA 003”. The measurement technique is described in more detail in [16, 17].

Three H_{2}O lines centered at 12415.204, 12413.977, and 12411.404 cm^{−1} (≈805 nm) were used to perform the estimations outlined in Introduction. Parameters of these lines taken from [18] are presented in Table 1. The self-broadening of these lines was registered within the pressure range 1 Torr ≤ ≤ 20 Torr.