Hopping Electron Models: an Appetizer

Abstract

Often we treat excited levels as discrete, as they appear in low resolution or in some simple approximation. Sooner or later, however a closer analysis always shows that when all the degrees of freedom are considered they are in a continuum. Thus, the 2p level of H, H(2p), is coupled to a continuum of H(1s) + 1 photon, and thereby gains a width and a structure. The 2p state of H is discrete only if you accept to neglect its interaction with a continuum of photon modes that eventually take the H atom to the ground state while producing photons. In 1952, Fermi discovered a peak in the pion-proton (π⁺ − p) elastic cross section for center-of-mass kinetic energies 1.2 to 1.4 GeV; since the half width at half maximum (∼ 100 MeV) implies a lifetime τ ∼ 10⁻²³s, which is very short, the strong interaction was implied in the formation and also in the decay. This was christened the doubly charged Δ⁺⁺ resonance. Such high-energy Physics contents are pertinent to this book: hundreds of resonances are familiar by now to particle physicists, but Fermi’s concept of resonances is important in quantum problems at all energy scales. Firing 500 eV electrons on Helium and measuring the loss spectrum, one observes[31] an asymmetric resonance in the ionization continuum al ∼ 60 eV which has been identified as the 2s2p¹P state of He. Many more are known by now, and they are all due to the neutral, twice excited He atoms in auto-ionizing states.