Researchers have made the best calculations yet to show why there are no nuclei composed of five or eight particles in nature. A team used a series of increasingly complex and realistic models for the force between two nuclear particles to compute the stabilities of light nuclei, allowing them to tease apart the components of the force responsible for destabilizing the absent nuclei. The result, appearing in the 28 October print issue of PRL, argues against the suspicion of many undergraduates that nuclear physics is needlessly complicated.
The strong nuclear force between protons and neutrons has a complicated mathematical expression because nuclear particles reveal themselves as composites at short distances. Researchers believe that the quarks within protons and neutrons obey a theory called quantum chromodynamics (QCD), but “nobody knows how to calculate [the force] yet from that level,” says Robert Wiringa of Argonne National Laboratory in Illinois. “We have to make up forces to fit the data.” As experimenters gathered more data over the decades from collisions between two nuclear particles, or nucleons, the deduced force became increasingly accurate, and correspondingly baroque. But until recently, no one could apply a realistic model of the force to solve problems with more than a few nuclear particles.
Now, Wiringa and his Argonne coworker Steven Pieper have extended a numerical technique to encompass nuclei made from up to 10 particles. Armed with this powerful technique, they attacked a basic question that involves an entire nucleus: Why are there no stable 5- or 8-body nuclei? Lacking these nuclei, the big bang created nothing heavier than lithium, and the Sun has shone long enough for humans to evolve. Wiringa and Pieper wondered if such a complex force law is required to explain the simple fact of the two missing nuclei.
A nucleus is unstable if it contains more energy as a whole than it would in pieces. For example, two 4-body nuclei are lower in energy than one with eight particles. The researchers started with a complete version of the nuclear force and removed levels of complexity in stages, like Russian dolls, calculating the energies of 7 of the lightest nuclei at each step. The missing nuclei remained unstable when they deleted the so-called spin-orbit term from the force law. But when they took the next step and removed the tensor force, which is similar to the force felt by two magnets side by side, the energies of the two unnatural nuclei suddenly dropped, meaning they would be stable in the absence of that force. The relative importance of the tensor force is predicted by theory, Wiringa says, “and here we’re seeing it really is essential for making nuclei the way they are.”
“A lot of [these] ideas have been around for a long time, but people couldn’t evaluate them,” says John Millener of Brookhaven National Laboratory in Upton, New York. With the improved calculations, he says, “you can really trace what’s happening there.”