Izospin

Izospin, commonly called isospin, is an internal quantum number used to describe the near-identical behavior of protons and neutrons under the strong interaction. Originating with Werner Heisenberg in the 1930s, it treats protons and neutrons as two states of a single nucleon doublet, in a way analogous to how electron spin describes two spin states. Isospin is described by the SU(2) group. In some contexts and languages, the term izospin is used as an alternate spelling.

The nucleon has total isospin I = 1/2. The third component, I3, distinguishes proton and neutron: I3 = +1/2 for the proton and I3 = −1/2 for the neutron. Two-nucleon systems can combine to total isospin I = 1 (triplet) or I = 0 (singlet). Pions form an isovector with I = 1, with π+ (I3 = +1), π0 (I3 = 0), π− (I3 = −1).

In the quark model, up and down quarks form an isospin doublet with I = 1/2, I3(u) = +1/2, I3(d) = −1/2. The proton consists of two up and one down quark (uud) giving I3 = +1/2; the neutron (udd) gives I3 = −1/2. Strong interactions preserve isospin to a good approximation because they depend mainly on the flavor structure of the quarks, not electric charge.

Isospin is an approximate global SU(2) flavor symmetry of quantum chromodynamics (QCD). It is exact in the limit of equal up and down quark masses and in the absence of electromagnetism. In reality, small quark mass differences and electromagnetic effects break isospin, causing small mass splittings within isospin multiplets and slightly different reaction rates.

Historically a foundational organizing principle in nuclear and particle physics, isospin continues to provide selection rules and multiplet classifications within the broader SU(3) flavor symmetry. Today it is viewed as an approximate symmetry of low-energy QCD that remains useful for describing hadron structure and interactions.