The Triple Alpha Process

Shashwat Udit
May 25, 2017

Submitted as coursework for PH241, Stanford University, Winter 2017


Fig. 1: Diagram of the Triple Alpha Process. (Source: Wikimedia Commons)

Humans are carbon-based lifeforms. Without an abundance of carbon to form its building blocks, life as we not it could not exist. However, for astrophysicists in the middle of the 20th century, carbon posed a problem. It wasn't clear how carbon, or any other heavier element, could have been created from a fusion process involving either of the two light elements hydrogen, with its atomic mass of 1, and helium, with its atomic mass of 4, since there are no stable isotopes with atomic mass of 5 or 8. A potential solution was first proposed by Edwin Salpeter in 1952. [1] The vast majority of carbon in the universe is produced in red giant stars, through a fusion process known as the triple alpha process in which three helium nuclei or alpha particles fuse to form C-12. The triple alpha process takes part in two steps (Fig. 1). In the first step, two alpha particles combine to form Be-8, a highly unstable isotope with a lifetime of approximately 10-16 seconds. In short order, a third alpha particle joins in order to form C-12. [2]

The Hoyle State

Salpeter's hypothesis had an issue when it was proposed: it wasn't clear that the somewhat unlikely triple alpha process, involving the near-simultaneous collision of three particles, would have a reaction rate sufficient to explain the rate of carbon produced, even given the enormous estimated temperature and pressure within the core of red giant stars. To resolve the issue, the British physicist Fred Hoyle built on Salpeter's work. With a temperature of 108 degrees kelvin and density of 105 grams per cubic centimeter as his estimated conditions within the core of a red giant, Hoyle estimated that a non-resonant reaction rate would be unable to explain the amount of carbon produced. Hoyle then predicted that there was a resonance state of C-12 around 7.7 MeV. [3] This state, now known as the Hoyle state, describes that state of the carbon formed immediately after the collision of an alpha particle with the Be-8 nucleus, and the triple alpha reaction is completed when the Hoyle state electromagnetically decays to the ground state of C-12, passing through a spin-2 state along the way. [4] After making his prediction of this state, Hoyle then worked with a team of physicists at the California Institute of Technology led by William Fowler and confirmed that this resonant state existed. With the existence of the Hoyle State, the triple alpha reaction rates could explain observed fraction of carbon, and through further reactions involving additional alpha captures the nucleosynthesis of heavier elements such as oxygen and nitrogen. In 1957, Fred Hoyle together with William Fowler, Margaret Burbidge, and Geoffrey Burbidge published the influential paper titled Synthesis of the Elements in Stars in the journal Review of Modern Physics, showing that the elements that made up the world had mainly be made in stars from hydrogen in a series of fusion reactions, including the triple alpha process. [3] In 1983, William Fowler would receive a Nobel Prize for his contribution. Hoyle did not; some suspect he was passed over because of his abrasiveness to fellow scientists and willingness to promote ideas well outside the scientific mainstream. [5]

While the existence of Hoyle state has been known since the 1950s, little was known about the state itself for several decades. In 2012, a group performed calculations of the structure of the Hoyle State on the Julich Supercomputing Centre, using a theoretical approach called chiral effective field theory to represent the interactions between nucleons. The group calculated a shape that involved a "bent-arm" or obtuse triangle configuration of the three alpha clusters with the Hoyle state of the carbon nucleus. [4]

Fine Tuning?

The triple alpha process is extremely important is determining the elemental composition of the universe and allowing life as we know it to exist. Yet that the process occurs at all is somewhat improbable, as its discovers showed it was only made possible by the complex interplay of physical constants that cause the excited resonance of C-12 to occur where it does. The philosophical and scientific implications of this have prompted much discussion.

Since we exist, the laws of the universe must be compatible with our existence. As a philosophic argument, this is known as the anthropic principle and occasionally used as explanation after the facts are determined for why the laws of the universe are what they are. Using it to make testable predictions is another matter; it has been claimed that the prediction of the Hoyle state is the only successful case of anthropic argument to predict a physical phenomena in the history of science. [5] This is disputed, based on the fact Hoyle's papers in the 1950s do not mention the anthropic argument, and it was only associated with the prediction of the Hoyle State by various figures, including Hoyle, decades later. [6] While answering such questions may be outside the domain of science, one area that can be examined is just how fine-tuned the triple alpha process is, or how much it would vary if universal constants did. The answer appears to be that the triple alpha process is actually quite fine tuned, with one group estimating in 2000 that variation in the strong force and Coulomb forces outside a narrow window would drastically affect the production in the universe of carbon, oxygen, or both. [2] However, it is important to note that while the prevalence of the triple alpha process in its current form may require finely tuned universal constants, by itself that not necessarily mean that the Universe or life requires finely tuned universal constants. It has been argued that with different universal physical constants, a stable isotope with atomic mass 8 could exist, possible eliminating altogether the need for the triple alpha process in order to produce carbon or heavier elements. [7]

© Shashwat Udit. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.


[1] N. B. Nguyen, F. M. Nunes, and I. J. Thompson, "Investigation of the Triple-Alpha Reaction in a Full Three-Body Approach," Phys. Rev. C 87, 054615 (2013).

[2] H. Oberhummer, A. Csótó, and H. Schlattl, "Stellar Production Rates of Carbon and Its Abundance in the Universe," Scence 289, 88 (2000).

[3] E. M. Burbidge et al., "Synthesis of the Elements in Stars," Rev. Mod. Phys. 29, 547 (1957).

[4] E. Epelbaum et al., "Structure and Rotations of the Hoyle State," Phys. Rev. Lett. 109, 252501 (2012).

[5] R. McKie, "Fred Hoyle: The Scientist Whose Rudeness Cost Him a Nobel Prize," The Guardian, 2 Oct 010.

[6] H. Kragh, "An Anthropic Myth: Fred Hoyle's Carbon-12 Resonance Level," Arch. Hist. Exact Sci. 64, 721 (2010).

[7] F. C. Adams and E. Grohs, "Stellar Helium Burning in Other Universes: A Solution to the Triple Alpha Fine-Tuning Problem," Astropart. Phys. 87, 40 (2017).