Accuracy in atomic and molecular data

Abstract

Abstract Uncertainty estimates have long been a standard part of experimental physics, but the same has not been true on the theoretical side. However, the culture is now changing, and it is becoming more common to include uncertainty estimates in theoretical calculations of atomic and molecular properties. This tutorial paper discusses the progress that has been made in assessing the accuracy of both theory and experiment in a wide variety of circumstances, ranging from the most fundamental measurements of atomic properties such as the electron anomalous magnetic moment and the proton size puzzle in the hydrogen atom to uncertainty estimates for two- and three-electron atoms (helium and lithium), for many-electron atoms and for electron–atom scattering processes. This is followed by a discussion of uncertainties for molecules, and especially the recent remarkable progress for H 2 + and H2 treated as full three- and four-body problems without the use of the Born–Oppenheimer approximation. The paper includes a discussion of variational methods and the Hylleraas–Undheim–MacDonald theorem, which guarantees variational bounds for excited states as well as for the ground state. This leads naturally to a discussion of the use of pseudostates to perform perturbation sums over intermediate states, and a demonstration calculation for the polarizability of hydrogen. The results of well-defined uncertainty estimates have important implications for both the search for new physics beyond the standard model from high-precision measurements, and for the application of theoretical atomic and molecular data to plasma physics and to astrophysics.