Nuclear Processes in Stars
pp Chain
pp Chain equations
CNO cycle
CNO equations
Stars are the Universe's principal engines of creation. The Universe began with very few atoms of elements
heavier than hydrogen and helium. Generations of stars used some of this hydrogen and helium as fuel,
burning it into heavier elements, including the carbon that builds the bodies of living things like you! In addition,
the energy the produce is harnessed by living systems, such as by the process of photosynthesis on Earth.
Stars are the givers of life! Here we look at the reactions that occur inside stars and see how they produce the
materials and energy that we depend upon.

Nuclear Fusion

The diagram above shows the main hydrogen fusion pathway in a dwarf star like the Sun, the proton-proton
chain (actually a set of branched chains connected together). In this chain, we begin with protons and produce
helium-4 nuclei, positrons (the antimatter equivalent of electrons), neutrinos and photons. In this process two
hydrogen nuclei, which are protons, fuse together into a deuteron (D) which is the nucleus of heavy hydrogen
(deuterium) consisting of one proton and one neutron bound together. Deuterons and protons then fuse into
helium-3 nuclei, consisting of 2 protons and one neutron, and these in turn produce helium-4 nuclei, which are
alpha-particles each consisting of two neutrons and two protons. In essence, lighter atomic nuclei are fused into
heavier atomic nuclei, producing heavier elements from hydrogen. Note that in the Sun the atoms are all ionised
into plasma, so these reactions all involve atomic nuclei, the nucleus of a hydrogen atom is simply a proton.

In terrestrial nuclear power stations energy is generated by the process of nuclear fission - the splitting of
atomic nuclei, which converts a small fraction of the mass in the atoms into a vast amount of energy. This
process, however, is inefficient compared to nuclear fusion. Nuclear fusion is cleaner, producing no long-lived
radioactive waste, and also converts more of the mass into available energy - it is much more energetic.

The list of nuclear reactions embodied in the p-p chain (diagram) are shown below. Some heavier atoms are
produced as reaction intermediates, such as beryllium (Be), lithium (Li) and boron (B). The superscript attached
to these atom symbols is the atomic mass number, e.g. 7 for beryllium, 3 for helium-3, and 4 for helium-4. The
atomic number gives the number of neutrons plus the number of protons in the nucleus. Protons and neutrons
are nucleons, so the mass number is also the nucleon number. The intermediates are transient, the only net
products being helium-4, neutrinos, photons and positrons. Photons (produced in the p-p chain and other
processes) of course, give the Sun most of its luminosity.
Fusing two Protons into Deuteron

The first reaction:
is a nuclear fusion reaction, followed by the decay of a proton into a neutron:
Since a neutron has no net electric charge, and the proton has one unit of net positive charge, it loses its
charge by radiating a positron. An electron neutrino is also produced, which ensures that momentum is
conserved.

The problem with the first nuclear fusion reaction is that protons, like all atomic nuclei, have a net positive
electric charge and
like electric charges repel. The electric force between charged particles is called the
Coulomb force and this repulsive force is Coulomb repulsion. The problem then is how to bring together two
particles that are repelling one-another! First of all, if the protons are hot enough and hence moving fast
enough (thermal energy is the result of the kinetic energy of particles due to their random thermal motion) then
they may collide with sufficient force to come very close together before they bounce off or repel one-another
and if they react in this time, with one becoming a neutron, then a stable deuteron may be formed. However, it
turns out if the Sun relied on this mechanism alone, then it would simply not undergo sufficient fusion, it just isn't
hot enough.

The importance of Nuclear Fusion is Stellar Cores

In the cores of stars like the Sun, nuclear fusion generates important energy, including thermal energy that
replaces the thermal energy radiated away into space. However, it is not correct to say that stars are hot
because of nuclear fusion! Stars are born when cold nebula, clouds of gas and dust, contract under the pull of
their own gravity (which is directed towards the centre of mass of any gas cloud). As the cloud contracts, the
gas particles lose
gravitational potential energy (just as a ball does as it falls to Earth) as they fall inwards
under gravity. Just like a falling ball, the particles of gas accelerate, however, as they move about faster and
faster and the cloud's density increases a sit contracts, so they collide more and more with one-another and
this kinetic energy becomes thermal energy - the cloud heats up! Essentially, gravitational potential energy has
been converted into heat. If the cloud is very massive, its gravity field may be so strong that nothing can escape
it and it could condense into a black hole. This rarely happens, however, since the cloud fragments as it
collapses, and each fragment contracts independently to possibly become a star. Something, however, must
resist gravity if a stable star is to be born. (If the Sun had continued contracting in free-fall, then it would have
collapsed in a further 30 minutes or so!). Thermal energy resists gravity, as gravity pulls the particles inwards,
so there random thermal motions tend to disperse them again. When the particles are hot enough they resist
further collapse. However, collapse would continue at a much slower rate since the cloud would continually lose
heat as radiation to outer space. Fortunately, when temperatures in the hot core of the cloud reach about 10
million Kelvin, nuclear fusion of protons switches on. This converts a small fraction of matter into radiation and
heat, which replaces the energy lost to space and the star becomes stable, neither contracting nor expanding, it
is in equilibrium. Thus,
nuclear fusion does not make stars hot, rather it prevents further collapse and
so actually stops stars getting any hotter
! Thanks to this process, a star as massive as the Sun can exist in
a stable state for about 10 billion years, before its proton (hydrogen) fuel becomes too depleted.

So how do enough protons fuse?

The protons need another way to overcome Coulomb repulsion, other than brute force alone! Quantum
mechanics provides the solution in a bizarre trick called
quantum tunnelling. According to quantum
mechanics particles can pass through barriers and walls by tunnelling through them, or by teleporting across
them! This phenomenon does not occur on the large scale of matter - throw a tennis ball at a sturdy wall and it
will never pass through the wall. The atomic world is very different, however, and often an atom may bounce of
an atomic wall, but occasionally it will, by chance, simply pass straight through whilst leaving the wall intact! The
thinner the wall, the more likely this is to happen. With our protons, what happens is that they are hot enough
and energetic enough to approach quite close, but not close enough to fuse, and they will usually bounce off
one-another's electric force-fields, however, occasionally one of them will teleport across the Coulomb repulsion
barrier, disappearing on the far side and reappearing on the inside! Now the protons are very close together
and so fuse, as if by magic! (It isn't magic of course, since quantum tunnelling is a well understood phenomenon
permitted by the laws of quantum physics).

The CNO bi-cycle

The p-p chain provides about 98.4% of the Sun's energy output, the remaining 1.6% is generated by another
cycle of nuclear reactions, called the CNO cycle or CNO bi-cycle, the
carbon-nitrogen-oxygen cycle. Atoms,
or rather nuclei, of carbon, nitrogen, oxygen and fluorine are produced in this cycle, but these are only transient
intermediates. In stars greater than about 1.5 times the Sun's mass, the CNO cycle is the dominant means of
hygrogen fusion (hydrogen burning), the p-p chain dominating in dwarf stars, including the Sun. The CNO cycle
is illustrated below:
Notice that once again the inputs are protons and helium-4 nuclei, photons, positrons and neutrinos are the
end-product, along of course with the energy these product particles carry!

The p-p chain and CNO cycle can keep the Sun burning as long as it has sufficient hydrogen in its core. Once
the core hydrogen is depleted, however, the Sun leaves the main sequence and becomes a
red giant, burning
hydrogen still in a shell around the core. In a few thousand years still other processes, like helium-burning, will
kick-in, at which point the Sun becomes a
red supergiant.

In hydrogen-burning about 0.66% of the mass of the protons is converted into energy (according to the
equation E = mc^2) and a star enters the red giant phase when about 10% of its hydrogen has been burnt
(most of the hydrogen is not in the core and never gets burnt). Helium-burning converts only 0.065% of the
helium mass into energy and so supplies only about a tenth as much energy, per kg of helium, as
hydrogen-burning and the helium-burning stage is short-lived in comparison to the hydrogen-burning phase.
Helium-burning initiates when the helium core contracts (since it has exhausted its hydrogen and is not
producing energy to counteract gravity) and so heats up further to the threshold temperature of about 100
million K for helium ignition.

Helium burns by the
triple-alpha process shown below:
Carbon burning
Note that the triple-alpha process involves three fusion reactions with helium nuclei and produces carbon and
oxygen. The first of these is between two helium nuclei to produce a beryllium-8 nucleus which exists on
average for a tiny fraction of a second, but sometimes another helium-4 nucleus fuses with the beryllium
before it breaks apart back into two helium-4 nuclei, to produce a carbon-12. The carbon-12 nucleus is
produced in an excited state, and emits a gamma-ray photon as it decays into a stable carbon-12 nucleus.

A helium (helium-4) nucleus is an alpha-particle, consisting of two protons and two neutrons. The higher
temperature needed to burn helium is because the nuclei each have a net electric charge of +2 units and so
more energy is needed to push them together close enough for quantum tunnelling to be effective (the
probability of quantum tunnelling reduces exponentially with distance between the particles). Even so, the
reaction would be extremnely rare, except that carbon-12, the product nucleus, just happens to have an
excited state whose energy exactly equals that of a helium-4 + beryllium-8 nucleus! This is fortunate, since
organic life relies on this reaction to produce the carbon needed to build living bodies!

Very small dwarfs may never reach sufficient temperatures and will end their lives as helium white dwarfs.
Stars like the Sun undergo a helium-burning phase and end their lives as slowly cooling carbon-oxygen white
dwarfs. Once helium burning ends the core contracts further, until it either reaches a high enough
temperature to fuse the carbon and oxygen into still heavier elements, as occurs in massive stars, or until the
matter is compressed into the degenerate matter that supports white dwarfs against gravity.

Carbon and Oxygen Burning

Helium-burning lasts about 500 thousand years. After this phase, if temperatures in the core exceed the
threshold of 500 million K, then carbon can ignite and carbon (C) atoms can fuse into elements such as
magnesium (Mg), sodium (Na), Neon(Ne) and oxygen (O). The scheme of carbon-burning is shown below:
Heavier nuclei require higher temperatures to overcome the greater Coulomb repulsion between them.
Heavier atomic fuels also burn more quickly. Carbon-burning lasts about 600 years only. Neon burning may
last one year and oxygen burning only one day! Oxygen atoms require very high temperatures, in excess of
one billion degrees K in order to fuse!
Photodisintegration and Silicon-Burning

The most massive stars will reach the end-point when their oxygen-burning ceases! They still have one
fuel left, however, two silicon nuclei can fuse to form a nucleus of iron-56, the most stable element and the
end-point of nuclear fusion. However, the Coulomb barriers are simply too great. Before temperatures
become high-enough for silicon burning,
photodisintegration occurs - intensely energetic photons
bombard nuclei, breaking them up into smaller nuclei. Many of these reactions are reversible reactions, for
example:
This reaction proceeds mostly in the forwards direction at one billion K, producing neon, but at 1.5 billion
K the reverse reaction is favoured, breaking the neon into oxygen and helium. Silicon photodisintegrates
at and above 3 billion K. Statistical equilibrium results, with some atoms in the broken-down state whilst
some do make it to the stable iron-56 state. Since iron-56 is the most stable, there is a gradual
accumulation of iron-56, and also of cobalt and nickel which are stable below 7 billion K. This is how
'silicon-burning' occurs to produce heavy elements like iron, nickel and cobalt. Once a supermassive star
has a core of iron, no more nuclear fusion is possible and the core implodes in a
supernova explosion!

Synthesis of Superheavy Elements

If iron-56 is the end-point of nuclear fusion, then where did the elements heavier than iron come from?
They were still synthesised by stars, but by different processes. Note that carbon and oxygen burning
produce free neutrons, as does silicon burning, by photodisntegration resulting in neutrons as nuclear
fragments. Stable nuclei can undergo
neutron capture, fusing with a neutron (which is relatively easy as
a neutron has no electric charge and so there is no Coulomb barrier) to produce heavier nuclei of the
same isotope. (The number of protons determines the element, but atoms of the same element may have
different numbers of neutrons, and these are called isotopes). If the isotope resulting from neutron
capture is also stable, then it may capture another neutron. Eventually, however, the neutron to proton
ratio in the nucleus becomes too high and the nucleus becomes unstable, it is a
radioactive isotope.

A radioactive isotope will randomly decay, undergoing
beta decay (emitting a high-energy electron) and
becoming a lighter atom of a different element. For example:
In this example, strontium-87 captures a neutron (n) to form the stable isotope Sr-88, which captures
another neutron to form the radioactive isotope strontium-89. Sr-89 may capture another neutron before
it decays, forming Sr-90, or it may undergo beta-decay to yttrium (Y). During beta-decay, a neutron in its
nucleus decays into a proton, emitting an energetic electron (beta particle) and an antineutrino.

Neutron-capture and beta-decay are competing processes operating on the Sr-90 nucleus. In
s-processes, neutron capture is slower than the beta-decay, whereas in r-processes the rate of
neutron-capture is faster than beta-decay. Thus, an s-process favours beta-decay, whilst an r-process
favours neutron-capture. However, these processes remain branch-points in which either reaction is
possible. Operating together, s and r-processes produce many elements, including trace amounts of the
superheavy and radioactive elements. When the star reaches the end of its life, it enters either planetary
nebula phase or undergoes a supernova explosion, either way most of its matter is shed into space,
where it may form the building blocks of future stars and planets.