The Theory of Pressure Broadening and Its Application to Microwave Spectra

Abstract

In this paper the calculation of the widths of several absorption lines in the microwave region is attempted. First, the fourier integral formula for transition probability is deduced with the adiabatic assumption. Then the width and the shift of the absorption line are calculated, assuming the well type and the inverse power intermolecular potential. Applying the latter model, the width is calculated for several kinds of self-broadened microwave absorption line. A theoretical formula which gives the width of the ammonia inversion line is obtained as a function of $\frac{K}{{[J(J+1)]}^{\frac{1}{2}}}$, where $K$ and $J$ are the rotational quantum number. It agrees with experiment for large $\frac{K}{{[J(J+1)]}^{\frac{1}{2}}}$, and its temperature dependence is also good. In the microwave absorption of oxygen, the quadrupole interaction is shown to be responsible for the width, and our theoretical result agrees with experiment if the quadrupole moment of this molecule is 2.5 to 2.0\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}26}$. It is also shown that the widths of the rotational lines of linear and symmetric top molecules can be explained by the dipole interaction.