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Life, Bent Chains, and the
Anthropic Principle

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,
Weizacker [ Phys. Zs 39(1938) 633] and Bethe [ Phys. Rev. 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 Burbage, Willy Fowler and Fred Hoyle and now
known by the initial letters of the author's surnames as BBFH [ Rev. Mod.
Phys. 29 (1957) 547].

What about the
excited state at 7.6MeV in carbon-12? It still attracts interest, and the
CHARISSA
collaboration 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 co-valent bonding of atoms by
electrons to form molecules. This area of research is known as Nuclear
Molecular Analogues, and the CHARISSA
collaboration 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

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