5 - Centrifugal barrier effects

Summary

Introduction

Centrifugal barrier effects have their origin in the balance between the repulsive term in the radial Schrödinger equation, which varies as 1/r², and the attractive electrostatic potential experienced by an electron in a many-electron atom, whose variation with radius differs from atom to atom because of screening effects. In order to understand them properly, it is necessary to appreciate the different properties of short and of long range potential wells in quantum mechanics.

As the energy of the incident photon is increased above the ionisation threshold, centrifugal barrier effects often come to dominate the response of many-electron atoms, which totally alters the spectral distribution of oscillator strength in the continuum from what might be anticipated by comparison with H. This applies not only to free atoms, but also to the same atoms in molecules and in solids: many of the changes due to centrifugal effects occur within a small enough radius that they are able to survive changes in the environment of the atom.

Since the centrifugal term is present in the radial Schrödinger equation for all atoms, we must explain why centrifugal effects only dominate the inner valence spectra of fairly heavy atoms. Centrifugal barrier effects are present even in H. However, they act differently in transition elements or lanthanides.

One reason is straightforward: the ground state of H has ℓ = 0, and therefore only p states are accessible directly by a dipole transition from the ground state.