On the theory of linear absorption line shapes in gases

Christian J. Bordé

doi:10.1016/j.crhy.2009.10.019

On the theory of linear absorption line shapes in gases
[Sur la théorie de la forme des raies d'absorption linéaire des gaz]

Christian J. Bordé ^1,²

¹ Laboratoire de physique des lasers, UMR 7538 CNRS, université Paris-Nord, 99, avenue J.-B. Clément, 93430 Villetaneuse, France
² SYRTE, UMR 8630 CNRS, observatoire de Paris, 61, avenue de l'observatoire, 75014 Paris, France

Comptes Rendus. Physique, Volume 10 (2009) no. 9, pp. 866-882.

Résumé
Abstract

Une théorie détaillée de la forme des raies d'absorption linéaire des gaz à basse pression est développée. L'objectif est de mieux cerner tous les effets susceptibles d'intervenir dans la détermination de la constante de Boltzmann à partir d'une mesure de la largeur Doppler. On démontre en particulier qu'il n'y a pas d'élargissement supplémentaire lié au temps fini de traversée du faisceau laser par les molécules. Les effets de recul et Doppler du deuxième ordre sont intégrés dans la forme de raie grâce à un traitement quantique complet. L'effet Mössbauer–Lamb–Dicke de rétrécissement des raies Doppler par les collisions est lui aussi incorporé dans la théorie avec comme cas particuliers les profils de Galatry et de Nelkin–Ghatak.

A detailed theory of the line shape in linear absorption spectroscopy of low-pressure gases is developed. The goal is to take into account all effects that come into play in the determination of Boltzmann's constant from measurements of the Doppler width. We demonstrate that there is no additional broadening from finite transit time across the laser beams. The molecular recoil and the second-order Doppler effect are included in the line shape thanks to a complete quantum treatment. The Mössbauer–Lamb–Dicke narrowing of Doppler lines by collisions is also included and the special cases of Galatry and Nelkin–Ghatak profiles are presented.

Publié le : 2009-11-01

DOI : 10.1016/j.crhy.2009.10.019

Keywords: Absorption line shape, Laser spectroscopy, Doppler width, Transit-time broadening, Boltzmann constant, Base units of the SI
Mot clés : Forme de raie d'absorption, Spectroscopie laser, Largeur Doppler, Élargissement dû au transit, Constante de Boltzmann, Unités de base du SI

Affiliations des auteurs :

Christian J. Bordé ^{1, 2}

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     title = {On the theory of linear absorption line shapes in gases},
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     number = {9},
     year = {2009},
     doi = {10.1016/j.crhy.2009.10.019},
     language = {en},
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Christian J. Bordé. On the theory of linear absorption line shapes in gases. Comptes Rendus. Physique, Volume 10 (2009) no. 9, pp. 866-882. doi : 10.1016/j.crhy.2009.10.019. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2009.10.019/

Bibliographie
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[2] Antonio Castrillo; Giovanni Casa; Andrea Merlone; Gianluca Galzerano; Paolo Laporta; Livio Gianfrani On the determination of the Boltzmann constant by means of precision molecular spectroscopy in the near-infrared, C. R. Physique, Volume 10 (2009) no. 9, pp. 894-906 (this issue)

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