This article has been reviewed according to Science X's editorial process and policies. Editors have highlighted the following attributes while ensuring the content's credibility: When identical charges repel each other but are confined to the surface of a sphere, they seek the arrangement with the lowest possible energy. The idea is simple, but the problem gets harder to solve with every charge added.
The so-called Thomson problem dates back to the "plum-pudding" model of the atom, which Nobel laureate Joseph J. Thomson proposed in 1904. The atomic model has long been superseded, but the mathematical problem has endured.
In 1998, mathematician Stephen Smale listed it as Problem No. 7 among his 18 major mathematical challenges for the 21st century. Exact solutions still exist only for a few small systems. The question also matters well beyond mathematics—for example, for the structure of viruses, fullerenes and colloidal shells.
At the Department of Ion Physics and Applied Physics at the University of Innsbruck, Paul Scheier's team has now brought this abstract optimization problem into the lab. The researchers produce nanodroplets of superfluid helium, just a few tenths of a degree above absolute zero, and charge them multiple times with an electron beam. The charges move to the droplet surface and arrange themselves there almost undisturbed.
The droplets then pass through gold vapor. Gold atoms attach to the charge centers and grow into singly charged nanoparticles of about 700 atoms each. "Superfluid helium nanodroplets give us an exceptionally clean and cold environment in which up to several thousand charges can organize on a curved surface with very little external disturbance," says Scheier.
When the droplets land on a transmission electron microscopy grid, the helium evaporates. The gold particles remain as an imprint of the original charge arrangement. "By tagging the charge centers with gold nanoparticles, we can preserve and image these arrangements after the helium has evaporated," Scheier explains.
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