Nuclear moments and hyperfine interactions

Abstract

Topics Angular, magnetic and quadrupole moments of the nucleus Magnetic electron-nucleus interaction Quadrupolar electron-nucleus interaction Hyperfine structure and quantum number F Hydrogen atom reexamined: fine and hyperfine structure 5.1 Introductory generalities Until now the nucleus has been often considered as a point charge with infinite mass, when compared to the electron mass. The hyperfine structure in high resolution optical spectra and a variety of experiments that we shall mention at a later stage, point out that the nuclear charge is actually distributed over a finite volume. Several phenomena related to such a charge distribution occur in the atom and can be described as due to nuclear moments. One can state the following: i) most nuclei have an angular momentum, usually called nuclear spin. Accordingly one introduces a nuclear spin operator I¯ h, with related quantum numbers I and M I , of physical meaning analogous to the one of J and M J for electrons. Nuclei having even A and odd N have integer quantum spin number I (hereafter spin) while nuclei at odd A have semi-integer spin I ≤ 9/2; nuclei with both A and N even have I = 0. ii) associated with the angular momentum one has a dipole magnetic moment, formally described by the operator µ I = γ I I¯ h = g n M n I (5.1)