The neverending story of shape resonances

Abstract

Abstract Shape resonances, their definition, their nature, their use and supposedly almost miraculous capabilities, have been a rather controversial topic in the scientific literature for quite a long time. There was an upsurge of papers and heated discussions at conferences about these issues more than 10 years ago, the main point of which was whether the shape resonance position in energy above a core level ionization threshold in molecules, either isolated or adsorbed on surfaces, bears some information on bond lengths, with two opposite schools of thought, one maintaining that such connection, if existent at all, is rather loose, the other one ready to use some linear dependence of the shape resonance energy upon bond lengths to actually derive unknown bond distances in adsorbed molecules (the so-called ‘bond-lengths-with-a-ruler’ party). The latest technical and instrumental developments have given rise to another wave of shape resonance papers in the last 3 years. Criteria to assign shape resonances have been reconsidered under the light of new experimental results, and some molecules which were categorized as textbook examples for shape resonances have been shown not to exhibit such continuum phenomena at all. Therefore it is time for a historical survey which hopefully will straighten up some misconceptions still floating around in the literature.