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A New Basis for Nuclear Structure

Evidence being sought that the structure of the bound proton and neutron has changed in a nucleus would herald a new paradigm for the structure of atomic nuclei.

Evidence being sought that the structure of the bound proton and neutron has changed in a nucleus would herald a new paradigm for the structure of atomic nuclei.

By Anthony Thomas

The idea that the internal structure of protons might change under certain circumstances is being put to the test, and could help to explain some inconsistencies in theoretical physics.

At the start of the 20th century Rutherford discovered that the atom was largely empty space, with most of its mass concentrated in a tiny nucleus, just one hundred thousandth of the size of the atom itself. The only particles known at that time were the proton and the electron and there was no way for the laws of physics to bind them into such a small volume.

It took another 20 years, until the discovery of the neutron, to resolve this mystery. Since that discovery, the overwhelming majority of studies of nuclear structure have adopted the hypothesis that the protons and neutrons inside a nucleus are immutable objects whose internal structure never changes. These immutable objects interact through non-relativistic two- and three-body forces and the challenge is primarily to accurately solve the many-body problem.

In the 1970s this pattern was in a sense repeated, with the discovery of the quarks. The proton and neutron, far from being elementary particles, are themselves mainly empty space containing apparently point-like quarks bound by force carriers known as gluons. The proton consists of two "up" quarks and one down and vice-versa for the neutron.

In the early 80s an experiment at CERN by the European Muon Collaboration (EMC) discovered the remarkable result that the distribution of momentum on the quarks in a nucleus were significantly different from that on a free nucleon (i.e., a free proton or a neutron). This discovery certainly suggests that the proton and neutron may not be immutable when immersed in an atomic nucleus. Many hundreds of research papers have been devoted to the so-called EMC effect. Yet, there has been almost no effect on the study of nuclear structure! With few exceptions the approach started in the 1930s, half a century before the discovery of quarks, is still the state of the art.

A notable exception to this has been the work of Pierre Guichon and his collaborators. This group started with the realization that special relativity is also critical in an atomic nucleus and the attractive force that binds nuclei has a particular relativistic character. It is a so-called Lorentz scalar, which means that it acts like a change in the mass of the quarks inside a nucleus. Earlier relativistic treatments taking this into account, notably the model of Walecka, found that the typical scalar potential energy felt by a bound nucleon was of order 500 MeV. This is a huge number; more than half of the mass of the proton. As a consequence, the "effective mass" of the bound nucleon is only one half of its free mass in his model.

The realization that this scalar force was so large led Guichon to propose a dramatically different approach to the binding of nuclear matter, the Quark Meson Coupling (QMC) model, where the effect of the mean scalar potential generated by other nucleons is treated self-consistently in solving for the motion (wave function) of each confined quark.

Philosophically, this approach is radically different from anything done before because the colourless clusters of quarks which occupy single particle levels in nuclear matter may have nucleon quantum numbers but their internal structure is modified. Almost immediately it was
shown by Thomas and collaborators that this change could account for the key features of the famous nuclear EMC effect. Later the model was developed further by Guichon, Rodionov and Thomas to correctly treat the effect of centre of mass motion in the bag. In that same paper the model was also extended to finite nuclei, showing very naturally how one obtains realistic spin orbit forces. Finally, since the model is built at the quark level, using the same quark model, with the same quark-meson coupling constants, one can derive the properties of any strongly interacting particle bound in a nucleus. For example, it shows very naturally why the spin-orbit force for the Λ hyperon is extremely small.

In the last decade a great deal of effort has been devoted to making a connection between the quark-level QMC model and more familiar approaches to nuclear structure involving density functional theory with Skyrme forces. Starting with the QMC model itself, Guichon, Thomas and collaborators have succeeded in deriving a density functional equivalent to it. From this one can use the standard machinery which has proven so successful in all areas of nuclear structure, to investigate finite nuclei.

Very recently, in a landmark paper published in the Physical Review Letters, Stone, Guichon, Reinhard and Thomas carried out a systematic study of the properties of atomic nuclei across the whole periodic table using the new, effective, density-dependent NN force derived from the QMC model. The study began by defining those combinations of the three fundamental couplings in the model couplings to the up and down quarks which reproduce the saturation density, binding energy per nucleon and symmetry energy of nuclear matter within the empirical uncertainties on these quantities. Then, a search was carried out for the set of three parameters satisfying this nuclear matter constraint which best described the ground-state properties of a selection of more than 100 nuclei across the entire periodic table.

The root mean-square deviation of the fit from the actual binding energy for this set of nuclei was just 0.35%. For the superheavy nuclei (with charge larger than 100) where the binding energies are known, the deviation was a mere 0.1%. This level of agreement with the empirical binding energies is remarkable, in that it is comparable with the very best phenomenological Skyrme forces which have typically 11 or more adjustable parameters. Not only does this derived effective nuclear force satisfactorily describe binding energies but going beyond the nuclei used in the fit it accurately describes the evolution of quadrupole deformation across isotopic chains, including shell closures, shape co-existence and so on.

To develop a realistic model of nuclear structure starting at the quark level is a very significant achievement. However, even more important is to find experimental evidence confirming the underlying hypothesis that the structure of the bound proton and neutron has changed in a nucleus. In another recent Physical Review Letter, an Australia-Japan-USA collaboration (involving Bentz, Cloët and Thomas) predicted a remarkable signal of this anticipated change in structure, involving the response of nuclei to inelastic electron scattering.. If confirmed by an experiment already performed at the Thomas Jefferson National Accelerator facility in Virginia (USA), which is expected to announce results soon, this would herald a new paradigm for the structure of atomic nuclei.

The figure below shows the Coulomb sum rule for nuclear matter with a density consistent with that of 12C and 208Pb. It illustrates the role of relativistic effects but most important, at large three momentum transfer a reduction of up to 20% (red solid curve compared with the green dash-dot) resulting from the in-medium modification of the proton electric form factor. If these calculations were to be confirmed in the Jefferson Lab experiment it would provide clear evidence for this very different picture of how atomic nuclei are made; one in which the change of the structure of a bound nucleon is actually essential to understanding nuclear structure.

Coulomb sum rule for the process in which an electron scatters from a nucleus and breaks it up, primarily by knocking out a proton or neutron. In a non-relativistic treatment the quantity should approach unity at large momentum transfer (|q|), as we see in the Monte Carlo calculation shown by the brown points. The green dot-dashed line shows the effect of special relativity but includes no change in the structure of the bound protons and nucleons. The difference between that line and the red solid curve demonstrates the effect of the predicted change in nucleon structure inside an atomic nucleus - from Bentz, Cloët and Thomas, Phys. Rev. Lett. 116 (2016) 032701.

Anthony Thomas is Director of the Adelaide Node of the ARC Centre of Excellence in Particle Physics at the Terascale, and Director of the ARC Special Research Centre for the Subatomic Structure of Matter, School of Chemistry and Physics, University of Adelaide.