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Jan. 12, 2007 Research Highlight Physics / Astronomy

A force reveals its magic

The inclusion of the long-neglected tensor force into theoretical models revises our understanding of ‘magic numbers’ in the atomic nucleus

The world of nuclear physics is a relatively ordered one. Atoms are made up of a nucleus, surrounded by electrons. The nucleus itself is composed of nucleons, the protons and neutrons, where the number of positively charged protons determines the chemical element and the number of neutrons its isotope.

For radioactive elements, certain isotopes live longer than others before they decay, depending on particular combinations of neutron and proton numbers. Whenever the number of either neutrons or protons adds up to a certain ‘magic number’, the nuclei are particularly stable (Fig. 1a). In the rare case where both the number of protons and neutrons are identical to a magic number, the isotope is very stable and called ‘doubly magic’. An example is lead-208, which consists of the magic numbers of 82 protons and 126 neutrons.

This empirical finding is explained by a theoretical model where the nucleus is structured into different shells that are filled with neutrons and protons. When a magic number of protons and neutrons is reached, the shells are completely filled and therefore very stable. This concept is very similar to an atom’s electronic states, where the electrons are also arranged in shells surrounding the nucleus. Whenever all shells are completely filled, the atomic element is very stable and chemically inert—it is a noble gas.

The nuclear shell pattern is described in detail by a successful class of theories, the mean-field models. Mean-field theory allows the precise calculation of the shell structure and the energy required to add or remove a proton or neutron from the nucleus. This allows the direct determination of the magic numbers, and is of importance to improving our fundamental understanding of the stability of isotopes more generally.

Image of nuclear isotope plot and the reversed shell model Figure 1: (a) A plot of the nuclear isotopes of different elements, which are determined by the composition of protons and neutrons in the nucleus. Stable isotopes are plotted in black and unstable (radioactive) isotopes are given in green (experimentally produced) and blue (predicted). Intersecting lines of the orange grid depict the original magic numbers, as numbered along the axes. (b) In the revised shell model, magic numbers are not constants and may disappear (e.g., within in the pink circles). Instead, for more unstable isotopes, new magic numbers appear (e.g. red bars).

Enter the tensor force

Schematic depiction of the atomic nucleus Figure 2: In the atomic nucleus, protons and neutrons moving in the nucleus (pink and blue spheres), interact with each other through the nuclear forces, among which the tensor force, mediated by a pi meson (yellow), influences the shells and thus changes the magic numbers.

A research team from RIKEN’s Nishina Center for Accelerator-Based Science and the University of Tokyo has now shown these traditional models to be incomplete. Writing in the journal Physical Review Letters, the researchers demonstrate that a force occurring in the nucleus, rooted in a prediction by Hideki Yukawa, does indeed play an important role1.

In 1935, Yukawa, Japan’s first Nobel laureate, postulated the existence of a new type of particle, the meson. And it is by the exchange of a particular meson, the pi meson, that the tensor force manifests itself (Fig. 2). The pi meson acts as a mediator between the nucleons (proton or neutron). This exchange depends strongly on their relative position as well as the spinning motion of these nucleons, so that the tensor force can be either attractive or repulsive.

Such broad variation in the effects of the tensor force means that the force has quite an influence on the arrangement of particles in the nucleus and the structure of the nuclear shells. “Although the tensor force has been known to exist, it has never been studied in connection with magic numbers,” explains Takaharu Otsuka from the RIKEN team. As the force is rather complicated and previously thought to have negligible influence on the magic numbers, it was long-ignored in conventional theories describing the nuclear shells. When included explicitly in the mean-field model, the results differ significantly compared to conventional expectation.

A new magic

The most significant discrepancies to previous results occur away from the region of stability for nuclear isotopes and where the number of neutrons and protons are unbalanced and isotopes are highly radioactive. For those isotopes, the influence of the tensor force is expected to be significant. Consequently, the shape of the nucleus can be different from conventional expectation and the calculated energy it takes to remove a nucleon from the nucleus differs. These findings might therefore lead to the disappearance of conventional magic numbers and the appearance of new ones for exotic isotopes (Fig. 1b). For instance, nickel-78, comprised of 28 protons and 50 neutrons, is a classical example of a doubly magic nucleus, but may now turn out not to be so.

This finding is surprising, as magic numbers were expected to remain stable. “What we have shown is that magic numbers are not constants and that for some rare isotopes, conventional magic numbers may disappear, and new ones may arise,” Otsuka says.

Importantly, estimates for the production and decay rates of certain radioactive isotopes need to be revised, which is relevant for example to understand supernova explosions.

Towards an experimental verification

The aim now is to verify the theoretical predictions. This will be one of the key experiments scheduled for the new RIKEN Radioactive Ion Beam Factory (RIBF) facility that is currently being completed at Wako.

At RIBF, beams of various heavy ions will be generated so that their properties such as nuclear structure and radioactive decay times can be studied. For some of the more exotic isotopes, where significant differences between the existing mean-field models and the new model are expected, RIBF will be ideally suited to study those isotopes in detail.

Although the tensor force has a long history in nuclear physics, in retrospect it seems surprising that its implications for the nuclear shell structure were considered to be only of minor relevance. Indeed, the exciting discovery by the RIKEN researchers fundamentally revises our understanding of the nuclear shells and may lead to a better knowledge of radioactive processes. More generally, these findings are a continuing testament to the influence of the tensor force, reaching far beyond the atomic nucleus.

References

  • 1. Otsuka, T., Matsuo, T. & Abe, D. Mean field with tensor force and shell structure of exotic nuclei. Physical Review Letters 97, 162501 (2006). doi: 10.1103/PhysRevLett.97.162501

About the Researcher

Takaharu Otsuka

Image of Takaharu Otsuka

Takaharu Otsuka was born in Yokohama, Japan, in 1952, and graduated from the University of Tokyo in 1974. He earned his masters degree in 1976 and his Doctor of Science in 1979 from the same university. From 1979 to 1986, he worked as a researcher at the Division of Physics, the Japan Atomic Energy Research Institute. During that time, he did a two-year stint as a postdoctoral researcher at the Los Alamos National Laboratory in the US, from 1983 to 1985. In 1987, he became an associate professor in the Department of Physics, University of Tokyo, and in 1997 he was appointed professor in the same department. He has been concurrently serving as a senior guest researcher at RIKEN since 1994 and as the Director of the Center for Nuclear Study at the University of Tokyo since 2005.

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