General rotational relaxation matrix: Its properties, M dependence, and relation to experiment

Abstract

A general rotational relaxation matrix, R, is introduced which governs relaxation among density matrix elements. A definition of R in terms of the scattering S matrix is made which has the properties of conservation of mass and detailed balance at equilibrium. The relation between R and S shows that the only nonzero elements of R are those which connect density matrix elements with approximately the same time dependence. Using only spatial invariance of the S matrix, the dependence of R on M, the space projection quantum number for rotational angular momentum, is found to lead to important information about the qualitative physical nature of collisions. Linewidth experiments, saturation experiments, and double resonance experiments are discussed in terms of what parts of R they measure and how they might yield information about the M dependence of R.