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Gordon DrakeGordon Drake is part of a team of physicists who determined the exact critical charge for two-electron atoms that form elements like helium.

Physicists settle great debate over two-electron atoms

Going back to the days of Sir Isaac Newton, there have always been certain problems of physics and mathematics that seem all-but unsolvable.

Many of those persist today, and the list is a lengthy one. What is dark matter made of? What causes a supernova to explode? Is there a grand unification theory, or a ‘theory of everything,’ which explains all fundamental physical constants?

Well, physicists everywhere can scratch one of the big unsolved problems off their list, thanks to the work of physics professor Gordon Drake and some of his colleagues.

Along with Camille Estienne, a PhD student in Germany working under the supervision of Nobel Prize winner Theodor Hänsch, and Windsor graduate students Michael Busuttil and Amirreza Moini, Dr. Drake has finally defined a mathematical number – or the critical nuclear charge – that describes just how low the positive charge of the nucleus in two-electron atoms like helium can be, without those electrons flying apart from the nucleus around which they orbit.

“It’s been a subject of great debate in the literature because no one could do an accurate calculation,” said Drake, a fellow of the Royal Society of Canada and former president of the Canadian Association of Physicists. “But this settles the argument. No one will need to do a better calculation.”

Helium is one of the simplest atoms in the periodic table because the atoms contain only two electrons, but unlike planets orbiting the sun, the two electrons repel one another as they orbit the nucleus, Drake explained.

“If you took away the nucleus, the electrons would fly apart,” explained Drake. “It’s inherently a less stable system than a one-electron atom.”

Scientists have always wanted to know how much you could decrease the positive charge of the nucleus while keeping the electrons bound to the atom, he said.

 “It’s like skating along the edge of stability,” he said.

Using a variety of calculations and mathematical models, Drake and his team defined that critical charge number. For the record, it’s 0.91102822407725573(4) times the electron charge.  The result is surprising because any number less than one is not even enough to offset the electrostatic repulsion between the two electrons.

Defining that critical charge threshold provides scientists with a better understanding of quantum mechanics, especially phenomena like quantum tunneling, which basically allows for particles to burrow their way through a barrier of electrostatic repulsion. That principle is one upon which many electronic devices are made, Drake said.

“It’s an important demonstration of what can be done with the use of mathematical models in the study of matter,” he said, adding that the next logical step would be to define the same figure for more complex three-electron atoms.

Besides the obvious rush that comes with solving a difficult dilemma, Drake was especially excited because a paper he co-authored describing how his team arrived at that figure was published in the journal Physical Review Letters, and was selected as an editor’s choice on its website.

“It’s one of the most prestigious journals in physics, and only one in eight articles get selected as an editor’s choice,” he said.

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