Line Width of Rotational Spectra of Some Symmetric Top Molecules Due to Nuclear Quadrupole Moments

The hyperfine structure of rotational spectra is sometimes so complicated that it cannot be analyzed easily. In many other cases it is difficult to resolve the hfs and the whole spectrum is observed as a somewhat broad single line. In these cases the line width or the mean-square frequency deviation may have a more practical significance. In this paper explicit formulas are given for the mean-square frequency deviation as a function of the nuclear quadrupole coupling constant and the quantum numbers $I$, $J$, $K$. Thus by means of these formulas we shall be able to obtain the nuclear quadrupole coupling constant from the line width of the rotational line without analyzing hfs. Calculations were made on symmetric top molecules which have one or three identical nuclei with electric quadrupole moments. The effect of other nuclei which have electric quadrupole moments can be easily taken into account. The method of separating the present line width from that of the pressure broadening and that due to the centrifugal distortion is discussed.