Collision Broadening of Rotational Spectrum

The problem studied is the rotational absorption spectrum of linear molecules of moment inertia I in a simple nonpolar buffer gas. The focus is on the behavior of the spectrum as the buffer gas pressure and the associated collision frequency ν is increased. Four regions are distinguished. (1) $\mathrm{\nu \ll \hslash /I}$ , there are sharp lines with a van Vleck‐Weisskopf line shape; (2) $\mathrm{\nu \simeq \hslash /I}$ , the contributions from overlapping lines are summed analytically. The ratio of minimum to maximum absorption in the weakly oscillatory spectrum is computed. (3) ${\text{ℏ/I<ν<(2kT/I)}}^{\text{1/2}}$ , This is the classical inertial region where there is a single maximum in the absorption per cycle. We compute its position as it moves from an angular frequency (2kT/I)^1/2 to lower frequencies with increasing collision frequency. (4) ${\text{ν>(2kT/I)}}^{\text{1/2}}$ , this is the region where the Debye frequency profile is valid, with the peak of absorption at an angular frequency (1/ν) (2kT/I). The calculations are based on a kinetic equation for the density matrix with a single relaxation time, no position change, collision model. We also compute the time dependent correlation functions needed in the theory of the rotational Raman effect of linear molecules.