the Dirac equation In 1928, Paul Dirac developed a relativistic wave equation, now termed the Dirac equation, which predicted the spin magnetic moment correctly, and at the same time treated the electron as a point-like particle. Solving the Dirac equation for the energy levels of an electron in the hydrogen atom, all four quantum numbers including occurred naturally and agreed well with experiment. Total spin of an atom or molecule For some atoms the spins of several unpaired electrons (s1, s2, ...) are coupled to form a total spin quantum number S. This occurs especially in light atoms (or in molecules formed only of light atoms) when spin–orbit coupling is weak compared to the coupling between spins or the coupling between orbital angular momenta, a situation known as LS coupling because L and S are constants of motion. Here L is the total orbital angular momentum quantum number. For atoms with a well-defined S, the multiplicity of a state is defined as (2S+1). This is equal to the number of different possible values of the total (orbital plus spin) angular momentum J for a given (L, S) combination, provided that S ≤ L (the typical case). For example, if S = 1, there are three states which form a triplet. The eigenvalues of Sz for these three states are +1ħ, 0 and -1ħ. The term symbol of an atomic state indicates its values of L, S, and J. As examples, the ground states of both the oxygen atom and the dioxygen molecule have two unpaired electrons and are therefore triplet states. The atomic state is described by the term symbol 3P, and the molecular state by the term symbol 3Σ. Nuclear spin Atomic nuclei also have spins. The nuclear spin is a fixed property of each nucleus and may be either an integer or a half-integer. The component of nuclear spin parallel to the –axis can have (2 + 1) values , –1, ..., . For example, a 14N nucleus has = 1, so that there are 3 possible orientations relative to the –axis, corresponding to states = +1, 0 and −1. The spins of different nuclei are interpreted using the nuclear shell model. Even-even nuclei with even numbers of both protons and neutrons, such as 12C and 16O, have spin zero. Odd mass number nuclei have half-integral spins, such as 3/2 for 7Li, 1/2 for 13C and 5/2 for