Two teams of nuclear physicists have carried out the most sensitive measurements yet of how an excited form of carbon-12 known as the Hoyle state breaks down into its three constituent alpha particles. The results provide a better picture of the structure of excited states in carbon and other nuclei and improve our understanding of the fusion processes that forge new elements inside stars, say the researchers.

Carbon is essential for life on Earth and is created via nuclear fusion within red-giant stars. In what is known as the triple-alpha reaction, one helium nucleus (alpha particle) joins to another to create beryllium-8, which then combines with a third helium nucleus to form carbon-12. But there is a problem with this basic picture. Beryllium-8 appears too short lived to account for the large amounts of carbon in the solar system – its decay within a mere 8 ×10–17 s giving it only a miniscule chance of merging with an alpha particle before it disappears.

In 1953 the British astronomer Fred Hoyle proposed that this problem could be overcome if the fusion of beryllium-8 with an alpha particle generates an excited state of carbon-12 that very quickly decays to carbon’s ground state via the emission of a pair of gamma rays. Known as the Hoyle state, this was subsequently observed in the energy spectra of nuclear collisions carried out in the laboratory. To this day, however, the structure of the Hoyle state remains a puzzle.

Clusters or shells?

The conventional model of nuclear structure tells us that protons and neutrons act as individual particles that fill up “shells” like electrons in an atom. But this model comes nowhere close to correctly predicting the Hoyle-state energy level. An alternative scheme in which protons and neutrons cluster together to form three alpha particles within the carbon nucleus gets much closer to the correct excitation energy. But it remains unclear whether carbon-12 is made up entirely of clusters or whether it is partly cluster-like and partly a collection of individual protons and neutrons. There is also uncertainty over how the clusters interact with one another.

One way of trying to clear the fog is to dismantle the Hoyle state into its three constituent alpha particles to find out the relative frequency – or “branching ratio” – of two competing decay routes. One route is the (much more common) two-step route in which the excited carbon-12 nucleus first gives off a single alpha particle to create beryllium-8, which then breaks up in two further alphas. The other route is a single step in which the original nucleus breaks apart into three alpha particles simultaneously. The reason for doing this is that different models of the Hoyle state predict different values for the branching ratio.

Measuring the branching ratio involves creating multiple Hoyle states by firing a beam of nuclei at a suitable target and measuring the alpha particles given off. Distinguishing between the one-step and two-step processes relies on being able to determine the relative energy and orientation of the various alpha particles. Groups carrying out these measurements in the past, however, have had to contend with background effects caused by two particles of a similar energy hitting the same silicon detector.

Careful detection

The latest research overcomes this problem through a carefully chosen arrangement of detectors that ensure each alpha particle from the break-up of carbon-12 hits a separate piece of silicon. The two groups involved did so using different nuclear reactions – Robin Smith and colleagues at the University of Birmingham in the UK fired helium nuclei at a carbon target while Daniele Dell’Aquila of the University of Naples and team employed a reaction involving nitrogen and deuterium. Both arrived at very similar results: establishing, respectively, that the single-step process occurs no more than 0.047%/0.043% of the time. That represents a more than fourfold improvement in sensitivity compared with the previous best result, which put an upper limit on the single-step occurrence of 0.2%.

“It is certainly encouraging that they get basically the same result,” says David Jenkins of the University of York in the UK. “It refutes some recent (presumably mistaken) experimental work which identified a substantial branch for the three-alpha decay mode.”

Smith and his colleagues argue that the new results begin to put pressure on the idea that the Hoyle state consists entirely of alpha-particle clusters. He notes that theorists who carried out full three-body calculations of the Hoyle state decay in 2014 arrived at a value for the single-step process of 0.1%, while a model assuming that the three alpha particles condense into the nuclear equivalent of a Bose–Einstein condensate arrives at a similar value: around 0.06%. “We believe that the data provide good evidence that the alpha-condensate interpretation of the Hoyle state is problematic,” he says.

Dell’Aquila adds that the improved constraints on the one-step decay process can help refine our understanding of how elements are made in stars. He points out that in stars that burn helium at low temperatures, the existence of the one-step process significantly affects production of carbon-12.

Detection limit

Both groups say that they have pushed the sensitivity of conventional solid-state detectors to their limit, and that further improvement will require developing gas target detectors. Smith explains that the new detectors would image the paths of the alpha particles as they separate during the decay, so allowing “the unambiguous identification of a direct decay based on their relative directions”.

Both sets of results are described in separate papers in Physical Review Letters.