ANDERSON THEORY CALCULATION OF ROTATIONALLY –INVARIANT RELAXATION RATES FOR DENSITY MATRIX ELEMENTS OF A SPATIALLY-DEGENERATE TWO-LEVEL $SYSTEM^{*}$

$^{*}$This work was supported by the National Science Foundation. $^{1}$R.H. Schwendeman and T. Amano, J. Chem. Phys. 70, 962 (1979). $^{2}$R. H. Schwendeman, to be published.Author Institution:The application of two recently-derived $expressions^{1,2}$ for the lineshape of power-broadened microwave transitions depends on the validity of approximations concerning the magnitudes of ratios of relaxation rates for combinations of density matrix elements of different spherical tensorial order. The linewidth theory of Anderson, usually used for calculation of relaxation rates for combinations of off-diagonal density matrix elements of order $1 (T_{2}^{-1})$, has been modified to allow direct calculation of rates for combination of diagonal density matrix elements of even tensorial order and calculation of rates for combinations of off-diagonal elements of odd order greater than 1. A computer program has been written to perform calculations with the equations of the modified theory. The results of calculations for self-broadening in a linear molecule (OCS) and in a symmetric top with inversion ($NH_{3}$) will be presented and the implications of these results with respect to the new lineshape functions and to the determination of relaxation rate by measurements of power-broadened lineshapes will be discussed