Continuous Spectra ofH2andD2

Abstract

A complete theoretical calculation has been made of the continuous spectra of ${\mathrm{H}}_2$ and ${\mathrm{D}}_2$ arising from transitions from the lower vibrational levels of the $1s\sigma 2s\sigma {}_{}{}^3{}_{}{}^{}\Sigma _g^{}{}_{}{}^{}$ state to the unstable $1s\sigma 2p\sigma {}_{}{}^3{}_{}{}^{}\Sigma _u^{}{}_{}{}^{}$ state. Use of the Franck-Condon approximation has been avoided by a direct computation of the electric moment of the electronic transition, as a function of nuclear separation; this quantity is found to decrease rapidly with increasing nuclear separation. Spectra are computed for transitions from each of the vibrational levels separately, and absolute mean lives are determined for the various levels. Relative probabilities of excitation from the ground state of the molecule by electron impact are estimated, and the intensity in the spectrum due to excitation by electron impact is computed for a range of energies of the electrons. The Franck-Condon approximation is found to be more satisfactory than was indicated by a previous investigation. There is sharp disagreement of the results with the observations of Smith. This apparently arises from errors in Smith's intensity standard, and emphasizes the need for a more satisfactory intensity standard in the ultraviolet. Agreement with the results of Finkelnberg and Weizel is obtained, but its significance is weakened by uncertainties in the experimental conditions.