The Far Infrared Spectrum of Water Vapor

Abstract

The rotation spectrum of water vapor has been measured with high dispersion from 18μ to 75μ. The spectrometer employed echelette gratings and higher spectral orders were successfully removed through the use of filters and selective reflection. The positions of single lines were determined with an accuracy of about 0.05 ${\mathrm{cm}}^{-1\mathrm{}}$ throughout the entire region while neighboring lines as close together as 0.5 ${\mathrm{cm}}^{-1\mathrm{}}$ could be separated and measured. The analysis of the spectrum was accomplished in the following manner. From the values of the moments of inertia found by Mecke the energy levels were calculated from the asymmetric rotator equations. However, these computed levels are often far from the actual energy levels due to the presence of a large correction arising out of the centrifugal force stretching of the molecule. An estimate of this correction, which amounted in some cases to over 200 ${\mathrm{cm}}^{-1\mathrm{}}$, was made, thus furnishing energy levels with which to begin the analysis. The intensities of the rotation lines were calculated by using as an approximation the symmetric rotator amplitudes. By comparing the expected spectrum with the observed spectrum it was then possible to identify the lines and through them to determine the actual energy levels of the water vapor molecule. Combination relations as well as the formation of analytic series from analogous lines, served as important checks on the identifications. Through these methods the rotational energy levels of the water molecule have been found up to and including the group of $J=11\mathrm{}$ with an accuracy around 0.1 ${\mathrm{cm}}^{-1\mathrm{}}$. The highest level determined, possesses an energy of over 3200 ${\mathrm{cm}}^{-1\mathrm{}}$, while all the rotational levels with energies less than 2000 ${\mathrm{cm}}^{-1\mathrm{}}$ have been obtained. Finally all the allowed transitions together with their intensities are calculated and these are plotted directly above the observed spectrum. The agreement is remarkably good. All the essential features of the spectrum and indeed most of the finer details are correctly reproduced.