Sum rules for the rotational structure in the molecular transition spectrum

Publisher Website
Google Scholar
Abstract
This paper is concerned with the spectra, such as the oscillator strength distribution for transitions of linear, symmetric-top or asymmetric-top molecules, induced by any external perturbation. The sum over a rotational structure in the spectrum for a fixed initial rotational state Gamma is expressible in a simple form independent of Gamma . This sum rule is a general form of a theorem proved recently by the present author for the mean-energy-loss cross section. The theorem is a geometrical statement, and is valid regardless of the physical mechanism of the transition. A proof different from that given previously shows that the geometrical meaning of the theorem is the second cosine formula J'2=J2+Jt2+2J.Jt for the addition of the initial rotational angular momentum J and the angular momentum J'. As examples, sum rules for the dipole and generalised oscillator strengths for both discrete and continuum transitions are discussed. Also, sum rules for the rate constant and for the integral and differential cross sections for the mean energy loss hold for the collision of a molecule with any particle having or not having an internal structure, if the adiabatic-rotation approximation is valid.

This publication has 12 references indexed in Scilit: