Focus: Left-Handed Nuclei

Phys. Rev. Focus 7, 4
Certain asymmetrically shaped nuclei can be left-handed or right handed.
Figure caption
K. Starosta/SUNY
Nuclear potato. When a nucleus with odd numbers of protons and neutrons has axes of three different lengths, it can show a “handedness,” depending on the orientations of the unpaired proton and neutron orbits. Both the handedness and the potato shape are newly demonstrated asymmetries for nuclei.Nuclear potato. When a nucleus with odd numbers of protons and neutrons has axes of three different lengths, it can show a “handedness,” depending on the orientations of the unpaired proton and neutron orbits. Both the handedness and the potato shape... Show more

Many molecular structures have two forms that are mirror images of one another, often called left- and right-handed forms. Now a collaboration reports in the 5 February PRL that potato-shaped atomic nuclei can also have a “handedness” when they spin about an asymmetric axis. The shape of these nuclei has been uncertain, and the results simultaneously demonstrate that nuclei can be rigidly “triaxial”–ellipsoidally shaped, with axes of different lengths in all three dimensions. Since symmetries are fundamentally related to basic interactions, experts are excited about evidence that nuclei are less symmetric than previously thought and expect it to lead to a deeper understanding of nuclear structure.

Physicists have always looked for symmetries–and broken symmetries–because they can lead to fundamental principles. For example, the fact that any experiment will come out the same way today as it will tomorrow (“time translation symmetry”), leads to the classical conservation of energy. Once, nuclei were assumed to be spheres, the ultimate symmetric shape, until research showed they could be extremely elongated like cigars. In the 1960s theorists first speculated that nuclei could be triaxial in shape–and therefore even less symmetrical–but there was no direct way to observe it.

Theoretical work by Stefan Frauendorf of the University of Notre Dame in Indiana and the Rossendorf Research Center in Dresden, Germany, and his colleagues [1] showed that triaxial nuclei with odd numbers of both protons and neutrons (“odd-odd” triaxial nuclei) could have handedness. According to their results, observing the so-called chirality would provide solid evidence for stable triaxial shapes, while also establishing handedness as a new property of nuclei.

Nucleons like to pair up and form a shell structure, just as electrons do in atoms. In some odd-odd nuclei, the unpaired proton and neutron can orbit independently, above the remaining “core” nucleons, which spin as a single unit. If the proton and neutron in a football-shaped nucleus orbit around the same axis on which the core spins, the nucleus is highly symmetric, like a vertically oriented top. But for triaxial nuclei with the right numbers of protons and neutrons, the two independent nucleons can orbit about the shortest and longest axes, while the core spins about the third, intermediate-length axis. In this case, the three sources of rotation can be oriented in two different ways with respect to one another–left-handed and right-handed–and the total spin is askew to the three principal axes.

Krzysztof Starosta of the State University of New York at Stony Brook and other experimentalists have now collaborated with Frauendorf and found evidence for handedness in odd-odd nuclei. They aimed beams of heavy ions at targets of selected elements to produce nuclei with 75 neutrons and 55, 57, 59, and 61 protons (cesium, lanthanum, praseodymium, and promethium) in a wide variety of spin states. In experiments at Stony Brook and Yale University, the team detected the energies and directions of gamma rays emitted by the nuclei and found the energies of each spin state. “Our experimental techniques were not revolutionary,” admits Starosta, but no one had attempted the tests previously, in part because of the complexities of untangling the data for odd-odd nuclei.

The team found a long series of “doublets”–pairs of closely spaced energy states with the same amounts of angular momentum that corresponded to otherwise identical nuclei. The simplest explanation, the team concluded, was that the pairs of states arose from the two different types of handedness.

“The question of whether stable triaxial nuclear shapes exist has been debated for decades,” says Mark Riley of Florida State University in Tallahassee. Starosta and his colleagues have “hit upon the first direct evidence,” which Riley says is causing quite a stir in the nuclear physics world.


  1. S. Frauendorf and J. Meng, Nucl. Phys. A617, 131 (1997)
  2. V.I. Dimitrov, S. Frauendorf, and F. Dönau, Phys. Rev. Lett. 84, 5732 (2000)

Subject Areas

Nuclear Physics

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