Moments of the spectra for rotational transitions induced by collisions or by external perturbations

Considered first is the cross section for the rotational transition J'<-J of a linear rotator in collisions. The set of cross sections for a given J and for all J' defines a discrete spectral distribution as a function of the transition energy. In both the classical and the quantum mechanical sudden approximations the moments S(μ; J) of orders μ=2n and μ=2n+1(n=0, 1, ...) are polynomials of degree n in the rotational energy E(J). The special cases for n=0 indicate that S(0; J) and S(1; J) are independent of J. This is a theorem proved elsewhere. Explicit expressions for S(μ; J) of low orders are presented. They are derived on the assumption of equal relative velocities upsilon and upsilon' before and after the collision. (orig.)