Life, Bent Chains, and the Anthropic Principle (by Dr N M Clarke, 1999)

You would not be reading these web pages were it not for nuclear physics in general, and in particular for the remarkable properties of the nucleus of the isotope carbon-12. It is a special energy state of this nucleus which enables all life to exist and whose structure looks like a bent chain of three alpha particles connected together. This particular state is unique, because its existence was predicted by the Anthropic Principle before it was discovered by nuclear physicists - but more about that later!

All living organisms rely on the chemistry of the element carbon, whose ability to form complex 'organic' molecules is so vital for the construction of the "Double Helix" of the DNA which determines the genetic blueprint of every life form. But where does all the carbon come from in the Universe?

The last years before the second world war saw a rush of interest in the role of nuclear fusion reactions and their role in the formation of the elements (nucleosynthesis) at the beginning of the Universe and as a producer of energy in stars. There was controversy about whether there was a 'Big Bang' or a 'steady state' Universe, but general agreement that at some point in time, some primordial nuclear fusion reactions had occurred to form the element helium from the hydrogen which comprises most of the matter in the Universe.

Present models tell us that about 0.1 seconds after the Big Bang, the primordial elements of our Universe were formed- the lightest element, hydrogen, consisting of a single proton and an electron, together with about 25% of the element helium, whose nucleus we call an 'alpha' particle and which has two electrons. In addition there were tiny quantities of deuterium - a heavy isotope of hydrogen, as well as traces of the element lithium.

But how were the other elements formed? How was the carbon made to build our bodies? Whence came the oxygen to create our seas and the atmosphere we breathe? What about the silicon in the sand and in the microchips inside this computer, or the calcium in our bones, and the iron which courses around our arteries carrying the precious oxygen to our cells?

The clues lay in the stars; by the 1930s it was clear that it was the enormous energy locked up inside the nucleus which provided the heat of the stars, and enabled them to burn for periods approaching the lifetime of the Universe which is more than ten thousand million years! The burning (fusion) of hydrogen in stars was studied by Hans Bethe and Chas. Critchfield [Phys. Rev. 54(1938) 248 +862] who proposed that two protons could react together to form deuterium. This reaction is extremely unlikely (nuclear physicists say that it has 'a small cross section'), but this is offset by the huge number of protons available in the average star.

The deuterium is rapidly destroyed by reacting with another proton to form a light isotope of helium called helium-3. The helium-3 in turn reacts with more helium-3 to create a helium-4 (an 'alpha' particle) and two protons. These reactions are called the 'hydrogen cycle' or 'proton-proton cycle'. Later, Weizsäcker [Physikalische Zeitschrift 39 (1938) 633] and Bethe [Physical Review 55 (1939) 434] proposed the 'carbon cycle' which also burned hydrogen with the same release of energy as the 'hydrogen cycle', but with the carbon nucleus acting as a catalyst as it was destroyed and re-created during the cycle.

But where did the carbon come from in order to act as a catalyst?

In 1946 George Gamow had suggested that nucleosynthesis was associated with events at the origin of the Universe, whilst Fred Hoyle and others had suggested that ALL the elements heavier than helium had been made in the furnaces of stars, but nobody could see a way in which these heavy elements could be formed, nor was there any experimental evidence of nucleosynthesis in stars.

The 'smoking gun' was discovered in 1952 when Paul Merrill identified the spectrum of the element of technetium in certain S type (red giant) stars. The element technetium is special- it is unknown in the crust of the Earth, because it has NO stable isotopes! Even its most stable isotopes, technetium-97 and 98 have half lives of only a few million years, so that during the long age of the solar system, this element has vanished from the Earth. But its existence was discovered by Perrier and Segre in 1937 in a sample of molybdenum sent by E O Lawrence from the Berkeley cyclotron, and it became the first element to be produced by artifical means. The observation of technetium in stars showed that nucleosynthesis was not confined to the early period of the Universe, but was happening now!

Later observation of supernovae explosions showed that the output of light from the star followed the characteristic curve associated with radioactive decay - in particular the 6 day half life of nickel-56 and the 77 day half life of cobalt-56. Here was direct evidence of the production of elements in exploding stars.

So nucleosynthesis was taking place in stars, but how? Here is the problem:- the fusion of hydrogen to make helium seemed to lead to a 'dead-end'. Once helium was made, it appeared impossible to fuse enough protons or heliums together to make heavier elements. For example, if one tries to fuse a proton with a helium-4 to make lithium-5 then the lithium-5 decays immediately into an alpha particle and a proton! Similarly, if one tries to fuse two alpha particles to make the nucleus beryllium-8, the beryllium-8 immediately decays into two alpha particles again with a lifetime of less than 10-16 seconds.!

These gaps in the stable nuclei at mass-5 and mass-8 were the stumbling block; a new process was needed to 'hop' over these gaps so that one could create the carbon nucleus, and hence all nuclei heavier than carbon.

One idea was that if THREE alpha particles could simultaneously come together, then a nucleus of carbon-12 might be created, but the probability of this happening was calculated to be so small, that it could never reproduce the amount of carbon in our Universe.

The solution was suggested by an astrophysicist, Ed Salpeter, in 1952, and is perhaps the first example of what is now called a 'two-step process' and has been shown to occur in many nuclear reactions. Ed suggested that if two alpha particles fused to form beryllium-8, then there was a short time before the beryllium decayed again; if, during this short time, a third alpha particle collided with the beryllium-8 then there was a small chance of creating the carbon-12 nucleus.

This seemed like a good idea, but there was another problem, this time with the final carbon-12 nucleus. In order for the beryllium-8 and the alpha particle to form a nucleus of carbon-12 the combined mass-energies of these two components have to be very close to an energy state in carbon-12 which has a similar mass-energy. In detail, the combined mass-energy must not be larger than the mass-energy of the carbon-12 state, but can be slightly smaller, because the energies of the particles rushing around inside a hot star enables them to bridge the gap. The state in carbon-12 is then called a 'resonance' in the beryllium-8 + alpha-particle system. Once the resonant state is formed it may then decay to the lowest energy or ground state of carbon-12 to create the stable nucleus.

But no resonance was known in carbon-12! Enter Fred Hoyle. Hoyle calculated the temperature inside a large star to be about 100 million degrees and worked out how much kinetic energy this would give to the particles rushing around in the star's atmosphere. Knowing the masses of both beryllium-8 and the alpha particle, he was able to predict that there must be an excited state at an energy of 7.6 million electron volts in the nucleus carbon-12. His certainty of the existence of this state was based on what we now call the 'Anthropic Principle' - since he, Fred Hoyle, a life form based upon carbon molecules, existed, then the resonance must also exist to create the carbon. A team at Cal. Tech. led by Willy Fowler (later a Nobel Prize winner) began the search for the mysterious resonant state in carbon-12, and discovered it - just a few percent above Hoyle's prediction. To this day, the 7.6MeV state in carbon-12 is known as the 'Hoyle resonance', and Hoyle's prediction of its existence is possibly the only proven example of a scientific prediction using the 'Anthropic Principle'.

If you think that the two-step process that forms the excited state at 7.6MeV is an amazing coincidence, then the decay of this state is even more remarkable! Because the mass-energy of this state is larger than than the combined masses of a beryllium-8 and an alpha particle, the state tends to decay by simple breaking up into a beryllium-8 and an alpha particle! However for every ten thousand decays, four result in the emission of two gamma rays which takes the excited carbon-12 nucleus to its stable ground state! So it is that rare two-step process and those 4 in 10,000 decays which enable me to write this piece and for you to read it!

This remarkable prediction transformed nuclear astrophysics; once the element carbon had been formed the production of heavier elements fell into place, and there was no longer a problem of the 'carbon-cycle' as the dominant mode of energy production in heavier stars.

In 1957, a famous paper was published describing the synthesis of the elements inside stars by Geoffrey and Margaret Burbidge, Willy Fowler and Fred Hoyle and now known by the initial letters of the author's surnames as BBFH [Reviews of Modern Phys. 29 (1957) 547].

What about the excited state at 7.6MeV in carbon-12? It still attracts interest, and the Birmingham nuclear group have studied many nuclear reactions in which this state is involved. It is difficult, because the excited nucleus flies apart into three alpha particles before they reach our detectors, so that the detection systems need to be able to detect many particles simultaneously, and also be able to reconstruct the energy and position of each particle.

Theoreticians have now calculated that the carbon nucleus in its ground state looks rather like a triangle of three alpha particles, but the famous "Hoyle resonance' is an example of a 'chain-state' consisting of three alpha particles in a kind of bent chain. Of course, beryllium-8 is an example of a two-alpha chain state (though very short lived!), but there are theoretical predictions that there may be other states in other nuclei which consist of chains of alpha particles, because of the stability of the alpha particle.

Recent calculations of highly excited states in light nuclei have indicated that many states may look like chains of alpha particles which are bound together by neutrons or protons, rather like the covalent bonding of atoms by electrons to form molecules. This area of research is known as Nuclear Molecular Analogues, and the Birmingham nuclear group is now actively searching for such states.

A last thought; it is estimated that each atom in your body has passed through about eight stars since the beginning of the Universe. Only the hydrogen in the water in your cells is an exception, since most of it was formed after the Big Bang, but all other elements were created by a succesion of stars which condensed, formed, burned, died or exploded again and again over thousands of millions of years!

Finally, a worthy successor to the famous BBFH paper has appeared in Reviews of Modern Physics, Vol. 69, no. 4 (1997) 995 by Wallerstein et al. This reveals our growing knowledge over the last 40 years, but also higlights much that we do not understand; so the quest continues.

N M Clarke, 18th November 1999 (edited for this web-page by C. Wheldon June 2010).