Effective field theory ( 6, 7) has also been applied to tensor polarization observables at low momentum. For example, at Q 2⩽0.5 (GeV/ c) 2, the theory of Arenhövel and colleagues ( 1, 2, 3, 4, 5) successfully describes cross-section data. Sophisticated theoretical frameworks have been developed to describe electron scattering from few-body nuclei at low Q 2. For more than 50 years, a major goal of electromagnetic nuclear physics was to determine the neutron charge distribution with a precision comparable to that for the proton. In particular, the determination of the intrinsically small neutron electric form factor G n E( Q 2) was highly uncertain. In addition, at high neutron momenta, the effect of the D state of the deuteron is sizable. Further, the neutron in the deuteron is not at rest but has Fermi motion, which produces both momentum-dependent and binding effects. Experimentally, electron beams were pulsed with a duty factor typically no higher than 1%, so a poor signal-to-background ratio was a strong limitation. However, the determination of the neutron elastic form factors was plagued by systematic uncertainties. Nature does not provide a free neutron target, so experiments were carried out to measure the cross section in quasi-elastic ( e, e′ n) scattering from the deuteron. However, the determination of the neutron form factors was problematic. Since the 1960s, the proton elastic form factors have been well determined at low and moderate Q 2. The Sachs form factors, denoted as electric G E( Q 2) and magnetic G M( Q 2), are defined for both the proton and the neutron and are functions of the four-momentum transfer squared, Q 2. Represented by a perturbative expansion in powers of α EM, in leading order the cross section is well described by single-photon exchange and the definition of two functions, known as elastic form factors, that contain the distribution of charge and magnetism. Elastic electron-nucleon scattering, in which the final-state electron and nucleon are the same as in the initial state, is the most basic process by which to study hadron structure. Thus, progress in seeking a fundamental explanation of the elementary properties of the proton and neutron, such as mass, spin, distribution of charge, and magnetism, in terms of quarks and gluons relies on QCD-inspired models, lattice gauge theory, and of course experiment.Įxperimentally, the structure of the nucleon is best elucidated in terms of its constituents by means of lepton scattering, which utilizes the electroweak force, the most precisely tested interaction in physics. Unfortunately, at this time exact solutions of QCD in the nonperturbative regime, that is, at the relatively low energy scales of the universe around us, are not available. The Standard Model theory of the strong interaction, quantum chromodynamics (QCD), provides a successful, fundamental description of the protons and neutrons in terms of the interactions between light, point-like quarks via colored, massless gluons. The structure and properties of atomic nuclei are successfully explained by strong interactions among the constituent protons and neutrons by use of quantum many-body theory. The mass of the visible matter consists almost entirely of atomic nuclei. Understanding the fundamental structure of matter in the universe, both visible and dark, is a central goal of physics.
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