Spectroscopic models of the rotational energy relaxation based on a projection operator technique are proposed. An exact expression for the memory function is obtained and used to derive formulas for parameters describing the intensity of polarized Raman and CARS bands as a function of frequency and gas pressure. It is shown how to construct a quantum relaxation matrix when data on pressure line broadening are available. The shapes of the fundamental band of pressurized nitrogen are simulated and compared with room-temperature measurements. The formulation allows extension of the proposed models, but the resulting shape function expressions remain analytic and need much less computation than existing fitting-law models. © 1992.