and charge symmetry. Neutrons, being neutral particles, are not affected much by the electromagnetic force. On the other hand, protons, being charged, feel a much larger electrical force. Charge symmetry is a statement about the strong force: the nuclear force between two neutrons is the same as the nuclear force between two protons. Charge independence is a bigger symmetry, relating a proton-neutron system to a proton-proton or neutron-neutron system: the nuclear force between any two nucleons (be they protons, neutrons, or a combination) is the same, apart from the electroweak contributions. The ideas of charge symmetry and charge independence in nuclear physics led to the marvelous concept of isospin. Isospin is an abstract way of describing the symmetry between neutrons and protons. The theoretical description of isospin is mathematically similar to angular momentum and spin, but isospin is in a completely abstract space in which the axes have something to do with the type of particle or the flavor. This revolutionary theoretical idea is the prototype of techniques for describing all internal symmetries. Charge symmetry and charge independence are not exact symmetries in nuclear systems, and accounting for the observed deviations tests our understanding of the limits of this symmetry. Isospin symmetry is broken by the electromagnetic interaction and because each type of quark has a definite mass. Understanding broken symmetries better is an ongoing goal of modern nuclear physics; the particulars of symmetry breaking are studied with careful measurement of polarization effects in reactions with light nuclear systems at medium-energy nuclear physics accelerators. One recent experiment (shown in Figure 6.2) employed sophisticated methods of polarizing liquid hydrogen targets and highly polarized proton beams.

For a long time, it was assumed that the laws of nature are unchanged by mirror reflection: a process seen in a mirror should be completely consistent with its theoretical description. Experiments had already established that other spatial transformations—translations and rotations—are indeed symmetries obeyed by the laws of physics; furthermore, no evidence for inversion symmetry breaking was evident in the structure of atoms or nuclei, so it was assumed that all physical laws obey mirror symmetry. It came as a tremendous surprise in 1956 when it was discovered that the weak interaction violates mirror symmetry. The associated quantum number, parity, is not conserved in certain fundamental processes. The first clear experimental demonstration was done by a group of nuclear physicists. They studied the beta decay of ⁶⁰Co that had been diffused into a paramagnetic salt and spin-polarized in a high magnetic field at low temperatures. It was found that electrons emitted in this decay are emitted preferentially in the direction of the nuclear spin. But when viewed in a mirror, the relative orientation of the electron momentum to the nuclear spin reverses, as shown schematically in Figure 6.3. The observed asymmetry in the ⁶⁰Co beta decay means that we would be able to tell whether we were viewing the process directly or in a mirror! The observation of parity violation caused physicists to question whether or not other discrete transformations—conjugation of charges (exchanging particles for antiparticles)