Knowledge Bank

Recent experimental investigations of the far infrared rotational spectra. of ozone and sulfur $dioxide1,2$ suggested a theoretical study of these spectra. This study revealed the appearance of groups of high J-low K lines, either of the type $RR(J0),RP((J-1)2),RR((J-2)2),Rp((J-3)4)\dots$ $orRP(J)1),RR((J-1)1),RP((J-2)3),RR((J-3)3)\dots$ within surprisingly narrow frequency intervals. The width of these intervals decreases, in general, with increasing J. In the $SO2$ spectrum, for instance, the number of lines of such multiplets within frequency intervals of width $0.1cm-1$ is two for $J\ge 32$, three fur $J\ge 45$, four for $J\ge 58$, etc. Some of the peaks in Gebbie’s absorption curves appear to be due. to such multiples. The formation of such multiplets was not expected An attempt to understand the reason for their occurence led to the development of algebraic approximation procedures for the evaluation of high J-low K lines. Some of the formulas thus obtained are surprisingly simple, and might prove useful in the interpretation of experimental results. Sets of such formulas for high J-low K rigid rotor energy levels, centrifugal distortion corrections, and line strengths are in preparation.