Highly Excited Singlet Ungerade States of H₂ and their Theoretical Description

Summary

Introduction

Dipole absorption to excited states of diatomic hydrogen lying above 13.6 eV is not usually considered in the discussion of interstellar photophysical processes. The purpose of this contribution is to provide a brief survey of these states, their structure and decay dynamics, and in particular of the theoretical methods used to describe them.

Above about 14.6 eV excitation energy the density of electronic states of H₂ increases dramatically so that above 14.8 eV the spacing of successive electronic states becomes smaller than a vibrational quantum, and at an energy about 0.04 eV below the ionization potential (I.P. = 15.4254 eV) it becomes even smaller than a rotational quantum of energy. This means that the usual Born-Oppenheimer description of molecular structure becomes inadequate: rather than considering the rotational/vibrational motion of the nuclei as being slow and determined by the average field of the rapidly moving electrons, one must also take account of the opposite limit, corresponding to a rapidly rotating and vibrating ion core interacting with a highly excited, distant, and slowly orbiting electron. In terms of the level structure this means that for given electronic inversion symmetry (g/u) and electron spin (0/1) the electronic states n,(l),∧ with associated vibrational structure v,N and parity (– 1)^p (p = 0, 1) are progressively reordered and eventually form Rydberg series. These series are appropriately labelled n, v⁺,N⁺ for each (l), N and parity (– l)^p. l is the electron orbital quantum number which is is put into brackets because (albeit useful for book-keeping purposes) it is not always a good quantum number.