Artificial hydrogen poses heavy challenge to quantum theory

Another piece for Nature’s online news, and while this is pretty hardcore, it is also a gorgeously bold experiment.

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Analogues of hydrogen made with exotic particles test quantum chemistry to its limits.

Scientists have made new ultralight and ultraheavy forms of the element hydrogen, and investigated their chemical properties.

Donald Fleming of the University of British Columbia in Vancouver, Canada, and his coworkers have created artificial analogues of hydrogen that have masses of a little over one tenth and four times that of ordinary hydrogen. These pseudo-hydrogens both contain short-lived subatomic particles called muons, superheavy versions of the electron.

The researchers looked at how these new forms of hydrogen behave in a chemical reaction in which a lone hydrogen atom plucks another out of a two-atom hydrogen molecule – just about the simplest chemical reaction conceivable. They find that both the weedy and the bloated hydrogen atoms behave just as quantum theory predicts they should [1] – which is itself surprising.

The experiment is a ‘tour de force’, says Paul Percival of Simon Fraser University in Burnaby, Canada, a specialist in muonium chemistry.

‘I would never attempt such a difficult task myself’, Percival admits, ‘and when I first saw the proposal I was very doubtful that anything of value could be gained from the herculean effort.  Don Fleming proved me wrong. I doubt if anyone else could have achieved these results.’

A normal hydrogen atom contains a single, negatively charged electron orbiting a single positively charged proton in the nucleus. About 0.015 percent of natural hydrogen consists of the heavy isotope deuterium, in which the atoms also contain an electrically neutral neutron in the nucleus. And there is a third isotope of hydrogen (tritium) with two neutrons, produced in some nuclear reactions, but which is too dangerously radioactive for use in such experiments.

Because the chemical behaviour of atoms depends on the number of electrons they have, the three hydrogen isotopes are chemically almost identical. But the greater mass of the heavy isotopes means that they vibrate at different frequencies, and quantum theory suggests that this will produce a small difference in the rate of their chemical reactions, such as the one examined by Fleming and colleagues.

If lighter and heavier versions of hydrogen could be made, that theory could be subjected to more rigorous testing. Fleming and colleagues did this using muons produced by collisions in the Canadian particle accelerator TRIUMF in Vancouver.

Muons are related to electrons, but are more massive. “A muon is an overgrown electron – an electron on steroids – with a mass about 200 times that of an electron”, explains Richard Zare, a physical chemist at Stanford University. “But unlike the free electron the free muon falls apart, with a mean lifetime of about 2.2 microseconds.” This meant that the researchers had to work fast to study their pseudo-hydrogen.

To make the ultralight form, they substituted the proton for a positively charged muon, which has just 11 percent of the mass of a proton. And to make ultraheavy hydrogen, they replaced one of the electrons in a helium atom with a negative muon.

Helium has two electrons, two protons and two neutrons. But because it is more massive, the negative muon orbits much more tightly around the nucleus, and so in effect the atom becomes a kind of composite nucleus – the existing two-proton nucleus plus the muon – orbited by the remaining electron. So it has a mass of a little over four times that of hydrogen.

Fleming and colleagues found that the reaction rates calculated from quantum theory were close to those measured experimentally. “This gives confidence in similar theoretical methods applied to more complex systems”, says Fleming.

The good agreement wasn’t necessarily to be expected, since the calculations rely on the so-called the Born-Oppenheimer approximation which assumes that the electrons adapt their trajectories instantly to any movement of the nuclei. This is generally true for electrons, which are nearly 2000 times lighter than protons. But it wasn’t obvious that it would hold up for muons, which have a tenth of the proton’s mass.

“It surprises me at first blush that the theoretical treatments hold up so well”, says Zare. “The Born-Oppenheimer approximation is based on the small ratio of the mass of the electron to that of the mass of the nuclei. Yet suddenly the mass of the electron is increased by two-hundred-fold and all seems to be well.”

Because the muon has such a short lifetime, extending such studies to more chemically complex systems is even more challenging. However, Fleming and his colleagues propose now to look at the ‘hydrogen’ exchange reaction between the superheavy ‘hydrogen’ and methane (CH₄).

References

1. Fleming, D. G. et al. Science 331, 448-450 (2011).