Application of Quantum Defect Theory to the Associative Ionisation Reaction Between Two Laser-Excited Sodium Atoms

Abstract

As explained in several papers in the present book, Quantum Defect Theory (QDT) is based on the similarity which may be invoked between hydrogen atom and more complicated systems with one “external” electron. In QDT, an electron is assumed to be “external” when it spends most of the time outside any complicated atomic or molecular structure to which it is bounded. In other words, the electron interacts mainly with a quasi-ponctual electric charge. For instance, such situations occur in excited states of alkali atoms: the external electron moves in the field of a positively charged electronic core. The energy levels are described by a Rydberg-type law: $$ E\left( n \right) = {E_0} - \frac{{Ry}}{{{{\left( {n - \mu } \right)}^2}}}$$ where E0 is the ionization energy of the atom, Ry the Rydberg constant. The index “n” labels the states inside the so-called Rydberg series converging to the ionization threshold E0. The quantum defect t holds for the deviation in the behaviour of the atomic system from the hydrogen picture, induced by the short excursions of the external electron inside the complicated electronic core where strong interactions take place. µ is constant over the whole series, as electronic interaction within the core are much larger than the asymptotic energy of a Rydberg level n.