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In August 1920, the British Association for the Advancement of Science
held its annual meeting in Cardiff. Arthur Eddington, a respected physicist
at the time, supposedly the only person apart from Albert Einstein who understood
the general theory of relativity, chose to address the meeting on the subject
of solar energy, drawing on the still recent discovery of the energy stored
within atoms.

At the time, astrophysicists could not explain how the Sun could have
stayed hot for the length of time required by geological evidence and biological
evolution. They knew that, as the star formed, gravitational energy would
have been converted into heat, raising the temperature inside. And from
simply laws of physics, Eddington could calculate the exact temperature
inside the Sun needed to produce the pressure required to hold it up against
its own weight. But what form of fuel was being ‘burnt’ to provide that
heat? The clue came from Einstein’s famous equation relating mass and energy.

Even in 1920s physicists knew that the mass of a hydrogen atom (we would
now refer to the hydrogen nucleus) is 1.008, and four hydrogen atoms (nuclei)
might combine, they guessed, to make one helium atom, or nucleus. But the
mass of the helium atom is 4.004. Eddington pointed out that the ‘lost’
mass would be available as energy to power the Sun and stars. If just 5
per cent of the Sun’s mass were initially in the form of hydrogen, said
Eddington, then its gradual transformation into helium and even heavier
elements – the process now known as nuclear fusion – would be more than
enough to provide all the energy needed.

But Eddington’s comments were ahead of their time for two reasons. First,
in 1920 the idea that even 5 per cent of the Sun’s mass might be in the
form of hydrogen seemed a little extreme. At that time, people thought the
composition of the Sun was rather similar to the composition of the Earth.
Secondly, and even more crucially, the theory of quantum mechanics, which
describes how subatomic particles interact, had yet to be developed.

A key new insight came from a Russian emigre scientist, George Gamow,
at the end of the 1920s. One of the problems with trying to persuade two
atomic nuclei to fuse is that each nucleus carries a positive charge, which
makes them repel each other. In order to fuse, they have to collide fast
enough in a collision to overcome this electrical potential barrier. But
according to standard astrophysical calculations, even the centre of the
Sun is too cold to let this happen. But Gamow showed how quantum processes
effectively smear out the size of a nuclear particle so that interactions
can happen without the two nuclei getting quite as close as classical theory
requires. This allows some interactions even at lower temperatures. This
is known as the ‘tunnel effect’, because particles seem to ‘tunnel through’
the electrical barrier.

Astrophysicists were quick off the mark to follow up Gamow’s insight,
which was published in a paper in 1928. By the next year, the Welsh-born
physicist Robert Atkinson, then working in Berlin with Fritz Houtermans,
had taken up the idea and used it to demonstrate that, in principle, solar
energy could indeed be produced by sticking atomic nuclei together – in
other words, nuclear fusion. Their calculations showed how hydrogen nuclei
(protons) could get close enough to other nuclei for fusion to take place,
even at the kind of relatively low temperatures that straightforward physics
said must exist in the heart of the Sun.

The tunnel effect allows only a small proportion of the protons to fuse,
even at the energies found inside the Sun, but a little fusion goes a long
way – 0.7 per cent of the mass of each hydrogen atom is released as energy
each time four protons are converted into one helium nucleus. This is so
much energy that the reaction can be quite rare, and yet provide enough
energy to keep the Sun hot. To generate its observed output of 4 x 10 ²⁶
watts, the Sun must convert 5 billion kilogrammes of matter into pure energy
every second. But even so, during its life of some 4.5 billion years, it
has lost less than 0.1 per cent of its total mass.

But the 1929 paper was only a first step along the road to unlocking
the secret of what keeps the Sun hot. At that stage, physicists did not
know exactly which form of fusion reactions were at work inside the Sun.
They also had completely the wrong idea about what the Sun was made of.

In 1929, astrophysicists’ ideas about the composition of the Sun were
still based on the natural guess that the composition of the Sun might not
be very different from Earth’s. Although Atkinson and Houtermans had shown
that protons could penetrate other nuclei of heavier elements and fuse with
them under the conditions existing inside the Sun, at the end of the 1920s,
nobody guessed the Sun was, in fact, kept hot by the fusion of protons with
other protons, to make helium nuclei more or less directly. The realisation
dawned only gradually during the 1930s.

In 1928, Albrecht Unsold, in Germany, showed for the first time that
hydrogen is not only the most abundant element in the atmosphere of the
Sun, but also that there are roughly a million times more hydrogen atoms
there than anything else. The evidence was gleaned by measuring the strength
of different lines that corresponded to different elements in the spectrum
of light from the Sun. This was confirmed by William McCrea, in 1929.

Although Unsold and McCrea proved hydrogen is by far the dominant element
in the atmosphere of the Sun, it took a long time for astrophysicists to
appreciate its dominance throughout both the Sun and stars. Even so, clearly
there was ample hydrogen to provide energy by fusion, and in the early 1930s
Atkinson developed the idea that heavier nuclei might absorb protons one
after another until they became unstable and, as a result of a kind of nuclear
indigestion, spat out alpha particles (helium nuclei) instead. This is a
way of turning hydrogen into helium through an intermediary. He was nearly
right – some stars do get their energy in this way, but this is not the
main fusion process at work inside the Sun.

Throughout the 1930s, astrophysicists’ misconceptions about the composition
of the Sun meant they were hamstrung when it came to pinning down the exact
cycle of fusion reactions. Unsold and McCrea had convinced them that there
was a lot of hydrogen in the Sun (at least in its atmosphere), so they knew
there were probably many protons available inside the Sun, with the right
kind of energies, to participate in the right kind of reactions. Using the
standard equations of physics that describe how heat is transmitted outwards
from the interior of a globe of gas like the Sun, Eddington showed how the
flow of heat, and, therefore, the stability of the globe of gas, depended
on the composition of the star.

Electromagnetic radiation interacts strongly with charged particles
such as electrons and protons, and according to these calculations, a star
such as the Sun could be stable only if it contained the right mixture of
electrons and nuclei. Too many charged particles would hold the radiation
in, making the star swell up as the radiation pushed them out of the way;
to few would allow radiation to escape too easily, so the star would deflate
like a pricked balloon. And it makes a difference whether the protons can
roam about freely, as do hydrogen nuclei, or whether they are grouped in
heavier nuclei. In the case of iron, 26 protons are packed together (plus
the appropriate number of neutrons – 30 in the most stable form of iron).

For the same total mass of the Sun, the number of electrons is always
the same as the number of protons. There are most electrons if all the nuclei
are simple protons, and far fewer electrons if a large fraction of the mass
is locked up as neutrons. (For a Sun made of pure iron, less than half the
mass would be protons, and the rest neutrons, so there would be less than
half the number of electrons as in a Sun made of pure hydrogen).

As it turned out, the calculations showed that a globe exactly the size
of the Sun, and with the Sun’s temperature and measured rate of energy generation,
could exist as a stable star, provided that the proportion of hydrogen in
its interior was either about 35 per cent or at least 95 per cent (at least
95 per cent made of hydrogen and helium, in fact, with very little scope
for any heavier elements.) Once again, what ‘everybody knew’ coloured ideas
about the Sun, and held back progress. Until Unsold and McCrea showed otherwise,
‘everybody knew’ that the composition of the Sun was rather like the Earth’s.
Once everybody knew there was a lot of hydrogen inside the Sun, and that
the laws of physics said ‘a lot’ meant either 35 per cent hydrogen and 65
per cent heavy elements, or 95 per cent hydrogen and less than 5 per cent
heavies, it was ‘obvious’ that the lower figure for hydrogen, closer to
what everybody had known before, must be correct.

Once again, Gamow comes into the story. In April 1938, he organised
a conference in Washington DC, bringing astronomers and physicists together
to discuss the problem of energy generation inside stars. One of the young
nuclear physicists at that meeting, who had a thorough understanding of
the conditions required for protons to penetrate more massive nuclei and
was aware of the astrophysical problems, was Hans Bethe. Bethe was born
in Strasbourg (then in Germany, now part of France) in 1906, and worked
at several German universities before moving to Britain in 1933 and on to
the US in 1935, where he worked at Cornell University, in New York.

By 1938, astrophysicists knew that the energy of the stars must originate
from nuclear processes, but they did not know which nuclear processes. The
problem is fairly simple to sum up, using a couple of examples. Some reactions,
such as the interaction between hydrogen nuclei and lithium nuclei, are
far too efficient to explain how the Sun stays hot. Even at a temperature
of 15 million K, if there was a lot of lithium in the Sun’s core it would
be rapidly converted into helium nuclei, releasing so much energy so quickly
that the Sun would blow itself apart. On the other hand, reactions between
protons and, for example, oxygen nuclei are far too slow, at these temperatures,
to produce the right amount of energy on their own. If the Sun depended
on those reactions, it would fizzle out (in fact, it would shrink until
it got hot enough in the centre to make the reactions go faster). Bethe
and the other participants in the conference were asked which nuclear reaction,
or set of reactions, would go at just the right rate at the temperature
inside the Sun to produce the exact amount of energy the Sun actually radiates.

In his book The Birth and Death of the Sun, written just after the conference,
Gamow describes how Bethe decided that this should not be a very difficult
problem to solve, and how he set out to find the secret of stellar energy
on the train back to Cornell. According to legend, Bethe promised himself
he would solve the problem before the steward called the passengers to dinner
– and did so with seconds to spare. At the same time, early in 1938, another
German back in Berlin, Carl von Weizsacker, had identified the same solution
to the stellar energy problem. But he lacked an ebullient Gamow to make
the discovery memorable by spreading the news of a (possible partly apocryphal)
hasty calculation while waiting for dinner on a train.

In its modern version, only slightly improved since 1938, this process
of generating energy is called the carbon cycle, or the carbon-nitrogen-oxygen
(CNO) cycle. It works like this. First, a proton tunnels into a nucleus
of carbon-12 containing six protons and six neutrons. The nucleus produced,
nitrogen-13, is radioactive, and emits a positron and a neutrino, converting
into carbon-13. If a second proton now tunnels into this nucleus, it gives
a nucleus of nitrogen-14. If a third proton tunnels into the nitrogen-14
nucleus, it is transformed into oxygen-15, which is also radioactive and
spits out a positron and a neutrino, transmuting into nitrogen-15 (in every
case, the name of an isotope depends on how many protons it contains; its
number is the combined total of neutrons and protons). But now, if yet another
proton tunnels into the nucleus of nitrogen-15, it ejects an alpha particle
– two protons and two neutrons bound together to form a helium nucleus.
What is left behind is a nucleus of carbon-12, just what the cycle started
with; along the way, four protons have, in effect, been combined to make
one helium nucleus, with a couple of positrons, two neutrinos and a lot
of energy released along the way.

A relatively small amount of carbon-12 in the heart of a star will act
as a catalyst for many cycles of this kind, steadily converting hydrogen
into helium and releasing energy to keep the star hot, even though the overall
amount of carbon, nitrogen and oxygen in the star is unchanged (and if Bethe
really did work all that out on the train before dinner, he deserves all
the credit Gamow gave him).

The process explains beautifully how some stars stay hot. But it turns
out that it is not the most important process for generating energy inside
the Sun. As astrophysicists improved their calculations, and their observational
colleagues obtained more accurate estimates of stellar masses and luminosities,
it became clear that the carbon cycle is the dominant energy source in stars
with more than about one and a half times the mass of the Sun and correspondingly
higher internal temperatures. In the Sun, with its lower temperature, the
reaction can produce only a modest amount of energy. By the time this was
realised, it was no embarrassment to the astrophysicists, because Bethe
had already found the nuclear process that really does keep our Sun hot.

The proton-proton chain

This time, there was no train ride involved, just steady work back at
Cornell, with his colleague Charles Critchfield. Their work on what is known
as the proton-proton chain was also first published in 1938, although it
was not until the 1950s that astrophysicists could say for certain that
most of the Sun’s energy is produced by the proton-proton chain, not the
CNO cycle. One of the main reasons it took so long to sort this out was
the confusion over the Sun’s composition; everything fitted together neatly
once it was realised that the Sun is, indeed, more than 95 per cent hydrogen
and helium. The modern estimate sees the Sun as 70 per cent hydrogen, 28
per cent helium, and just 2 per cent heavy elements.

The proton-proton chain starts with a collision between two protons
brought close enough together to fuse into a nucleus of heavy hydrogen (a
deuteron), emitting a neutrino and a positron in the process. Another proton
can then tunnel into the deuteron, producing a nucleus of helium-3, containing
two protons and one neutron. Finally, when two nuclei of helium-3 collide
they form a stable nucleus of helium-4, spitting out two protons as they
do so. About 95 per cent of the helium-3 nuclei suffers this fate; the other
5 per cent has a choice of two slightly different fates.

Just like the CNO cycle, the proton-proton cycle converts four protons
into one nucleus of helium-4, and energy has been released. But whereas,
as we now know, the CNO cycle needs temperatures above about 20 million
K to work effectively, the proton-proton chain is an efficient energy source
even at a temperature as low as 15 million K.

It is hard to put this in any kind of everyday context. Temperatures
such as 15 million K and densities many times that of lead are simply not
part of our everyday experience. But there are some slightly mind-boggling
features of these nuclear reactions that are worth trying to take on board
(and which, if nothing else, will make you appreciate what engineers are
up against when they try to reproduce fusion processes as a source of energy
for power stations here on Earth).

First, the tunnel effect calculations show that even at a temperature
of 15 million K, the basic proton-proton interaction starting the chain
off happens only if one of the colliding protons is travelling five times
faster than average. And even then, the collision has to be almost exactly
head on – a fast moving proton that strikes another proton only a glancing
blow could not tunnel through the electrical barrier. Inside the Sun, just
one proton in a hundred million is travelling fast enough for even a head-on
collision to do the trick. But there are so many protons inside the Sun
that, even at this incredibly slow reaction rate, and with just 0.7 per
cent of the mass of each set of four protons being converted into pure energy
when a helium-4 nucleus is formed, about five million tonnes of mass is
converted into energy every second inside the Sun.

As the satellite Ulysses now heads towards the Sun (going the long way
round via Jupiter) to find out more about the detailed physics, remember
that just 70 years ago, no one even knew what the Sun was made of. And it
took 20 more years to sort out just what keeps the Sun hot.

John Gribbin is the author of Blinded by the Light, a book about the
Sun to be published early in 1991 by Bantam Press.