Vibrational excitation of H2 and HCl by low-energy electron impact. An isotope scaling law *

We examine the mass dependence of cross sections for resonant vibrational excitation by electron impact (from z+ to ur) in H2 and its isotopes. Excitation cross sections, for both inelastic and superelastic ollisions, using numerical potential curves in a nonlocal resonance theory are presented and seen to obey the scaling law ucc,~~“~-“~~~*, where n is the reduced nuclear mass of the isotope. This scaling law is also observed to hold for HCI, DCI, and TCl. We also present a supporting analytical argument for this isotope scaling law using a simple resonance model in which the neutral and resonant anion nuclear potential energy curves are taken as equal-frequency linear harmonic oscillators. Cross sections for vibrational excitation by low-energy electron impact of Hz [ l-5] and of HCl [ 6-9] have been measured by several different inves-tigators. The absolute cross section values for exci-tation from the y = 0 level of Hz are fairly consistent with each other to within 20%30%. Vibrational ex-citation of the heavier isotopes of H2 and HCl has been much less studied experimentally. Vibration-ally excited D2 and other isotopes of H2 are of in-terest as a source of production of negative ions H-and D- through the process of dissociative lectron attachment. It is therefore desirable to understand the dependence of vibrational excitation cross sec-tions on the isotope mass. The purpose of this paper is to present an isotope scaling law for vibrational excitation of H2 and its isotopes from an arbitrary low-lying vibrational evel. We also observe that this relationship holds approximately for the family of isotopes XCl, where X is one of H, D, or T. The cross sections are obtained by treating vibrational exci-tation as a resonant process which occurs through the formation of a temporary anion state, and nu-merically solving the nonlocal integrodifferentia