“Carbon Nucleus Imaged through Simulation”

What does the interior of a carbon atom’s nucleus look like? A new study by Forschungszentrum Jülich, Michigan State University and the University of Bonn provides the first comprehensive answer to this question. In the study, the researchers simulated all known energy states of the nucleus.

These include the puzzling case of Hoyle. If it did not exist, then carbon and oxygen would be present in the universe only in small traces. In the end, we also owe our existence to her. The study has now been published in the journal Nature Communications.

The nucleus of a carbon atom usually consists of six protons and six neutrons. But how exactly is it arranged? And how does its composition change when the nucleus is bombarded with high-energy radiation? For decades, science has been searching for answers to these questions. Not least because it may provide a key to a puzzle that has long puzzled physicists: why is there so much carbon in space at all — an atom without which there is no life on Earth?

After all, shortly after the Big Bang, there was only hydrogen and helium. The hydrogen nucleus consists of one proton, and the helium nucleus consists of two protons and two neutrons. All heavier elements were created several billion years later due to aging stars. In them, helium nuclei fused into carbon nuclei at enormous pressure and extremely high temperatures. This requires three helium cores to fuse together.

“But it is very unlikely that this will happen,” explains Prof. Dr. Ulf Messner of the Helmholtz Institute for Radiation and Nuclear Physics at the University of Bonn and the Institute for Advanced Simulations at the Forschungszentrum Jülich. The reason: Together, helium nuclei have much more energy than carbon nuclei. However, this does not mean that they merge particularly easily – on the contrary, it is as if three people want to jump into a merry-go-round. But since they run much faster than roundabouts, they don’t work out.

Simulation on a supercomputer

As early as the 1950s, British astronomer Fred Hoyle hypothesized that the three helium nuclei first coalesced to form a kind of transition state. The Hoyle state has an energy very similar to a helium nucleus. To stay in the picture: It’s a faster spinning version of the Merry-go-round, which all three riders can jump on with ease.

When that happens, the carousel slows down to its normal speed. “Only by looping through the Hoyle state can stars create carbon in any appreciable amount,” says Meissner, who is also a member of the fields “Modeling” and “Material” at the University of Bonn.

About ten years ago, together with colleagues from the United States, Forschungszentrum Jülich and Ruhr-Universität Bochum, he succeeded in simulating this case of Hoyle for the first time. “We already had an idea of ​​how the protons and neutrons are arranged in the carbon nucleus in this case,” he explains. However, we have not been able to validate this assumption with certainty.

With the help of an advanced method, researchers have now succeeded. This mainly depends on confinement: in fact, protons and neutrons – nucleons – can exist anywhere in space. But for their calculations, the team restricted that freedom: “We arranged our nuclear particles on the nodes of a three-dimensional lattice,” Meissner explains. So we only allowed them in strictly defined positions.”

Computing time: 5 million processor hours

Thanks to this restriction, it was possible to calculate the motion of nucleons. Since nuclear particles affect each other differently depending on their distance from each other, this task is quite complex. The researchers also ran their simulations several million times with slightly different starting conditions.

This allowed them to see where the protons and neutrons were most likely to be. “We made these calculations for all known energy states of the carbon nucleus,” says Meissner. The calculations were performed on the JEWELS supercomputer at the Forschungszentrum Jülich. They required a total of about 5 million processor hours, with several thousand processors running simultaneously.

The results effectively provide images of carbon nuclei. They proved that nuclear particles do not exist independently of each other. “Instead, they are grouped into groups of two neutrons and two protons each,” the physicist explains. This means that the three helium nuclei can still be detected after they fused to form a carbon nucleus.

Depending on the energy state, they exist in different spatial configurations—either arranged in an isosceles triangle or like a slightly bent arm, with the shoulder, elbow joint, and wrist each occupied by a mass.

Not only does the study allow the researchers to better understand the physics of carbon nuclei, but also, Meissner concludes, “the methods we have developed can easily be used to simulate other nuclei and will certainly lead to entirely new insights.”