Calculating the elements of life
Life depends on carbon and carbon was created in stars. But just how did that carbon come to be, given raw fuel of hydrogen and helium? A paper in Physical Review Letters describes some calculations from first principles that, for the first time, show how carbon can come into being in the heart of a star.
In one sense, carbon-12 is easy to create. Just combine three alpha particles–helium-4 nuclei. However, the fusion of three alpha particles is highly suppressed at the temperatures of stars. You can get part of the way there–two alpha particles will fuse easily to create beryllium-8. It’s just that adding the third is tricky. Fred Hoyle proposed in 1954 that the extra fusion process could be made easier if there were only an excited state of carbon with certain properties. Soon after, Caltech physicists found this “resonance” in the lab.
The experimental evidence is all there to explain the process but theory has had a hard time catching up. Until now, no nuclear theory has been able to predict just how the carbon-12 comes into being. A series of attempts at simplifying the process have revealed essentially properties of the process but there has been no ground-up approach that has worked.
In this approach, the physicists used a combination of techniques. First they used something called an effective field theory, which expands out the interactions between the particles in order of strength and you can get more accurate results by including more terms in the sequence. In many cases, particular terms correspond to physical phenomena. For example the second order terms in this process correspond to electromagnetic forces and a factor to account for the difference in mass between up and down quarks.
The next step was to do the calculations on a lattice. That means breaking spacetime up into a discrete grid and calculating forces and motions on that grid instead of using a full continuous spacetime. This approach is much more amenable to high-powered computing and has shown its value in many other fields.
To make sure the simplifications are working correctly, the scientists use their scheme to predict the values of properties of helium-4 and then beryllium-8 and compare the results with experiment. When they can show that the calculations are in good agreement it gives them confidence that their more complicated calculation of carbon-12 will be accurate.
From the simulations, it looks like the excited state, called the Hoyle state of carbon-12, comes from an arrangement of three alpha particles effectively in a line, but bound together to form carbon-12. This takes more energy to do than the ground state where all the protons are clustered together, but the additional other properties of the state make it more likely that beryllium and helium can fuse in this way to make carbon.
The authors point out that this idea of a linear state of three alpha particles could potentially be an artifact of using lattice calculations, but that can be resolved in the future with calculations on a finer lattice. Positively, the calculation, starting from nothing, ends up predicting properties of carbon-12 that are measured in experiment, and therefore opens a new window on the creation of elements in the stars.