hydrogen and helium burning
We turn now to look at the most important nuclear reactions which
occur in stars.
hydrogen burning reactions
The most important series of fusion reactions are those converting
hydrogen to helium in a process known as hydrogen burning.
The chances of four protons fusing together to form helium in one
go are completely negligible. Instead, the reaction must proceed
through a series of steps. There are many possibilities here, but we
will be looking at the two main hydrogen-burning reaction chains: the
proton-proton (PP) chain and the carbon-nitrogen
The PP chain divides into three main branches, which are called the
PPI, PPII and PPIII chains. The first reaction is the interaction
of two protons (p or 1H) to form a nucleus of heavy
hydrogen (deuteron, d, or 2H), consisting of one
proton and one neutron, with the emission of
a positron (e+) and a neutrino
The deuteron then captures another proton and forms the light isotope of
helium with the emission of a -ray.
The 3He nucleus can then either interact with another
3He nucleus or with a nucleus of 4He
(an particle), which has either already been
formed or has been present since the birth of the star. The former case
is the last reaction of the PPI chain, whereas the latter reaction
leads into either the PPII or the PPIII chain, as shown below:
this starts with reactions 1 and 2
||this starts with reactions 1, 2 and 3'
p + p <!img src=arrow.gif width=12> -->
d + e+ + e
3He + 4He <!img src=arrow.gif width=12> -->
7Be + p <!img src=arrow.gif width=12> -->
d + p <!img src=arrow.gif width=12> -->
7Be + e- <!img src=arrow.gif width=12> -->
7Li + e
8B <!img src=arrow.gif width=12> -->
8Be + e+ +
3He + 3He <!img src=arrow.gif width=12> -->
4He + p + p
7Li + p <!img src=arrow.gif width=12> -->
4He + 4He <!img src=alpha.gif width=12>
8Be <!img src=arrow.gif width=12> -->
4He + 4He
It can be seen that there is another choice in the chain when
7Be either captures an electron to form 7Li
in the PPII chain or captures another proton to form 8B
in the PPIII chain. At the end of the PPIII chain, the unstable nucleus
of 8Be breaks up to form two 4He nuclei.
The PP chain reactions are summarized pictorially in
The proton-proton chain.
The reaction rate of the PP chain is set by the rate of the slowest
step, which is the fusion of two protons to produce a deuteron. What
actually happens in this reaction is that the two protons fuse to form
a highly unstable nucleus composed of two protons
(a diproton), which immediately decays back into two
protons. On rare occasions, however, one of the protons in the
diproton will undergo a + decay,
p <!img src=arrow.gif width=12> -->
n + e+ +
forming a deuteron, which is stable. This reaction occurs via the weak nuclear
force and the average proton in the Sun will undergo such a reaction
approximately once in the lifetime of the Sun, i.e. once every
1010 years. The subsequent reactions occur much more
quickly, with the second step of the PP chain taking approximately 6
seconds and the third step approximately 106 years in the
Sun. Note that the neutrino produced by the
+ decay will most
probably leave the star without interacting again, whereas the
positron will annihilate with an electron to produce a photon. Note
also that the fusion of a free proton with a free neutron to form a
deuteron directly is not an important energy source in stars due to
the fact that free neutrons decay into protons with a half-life of
only 15 minutes.
The relative importance of the PPI and PPII chains depend on the
relative importance of the reactions of 3He with 3He
in PPI as compared to the reactions of 3He with 4He
in PPII. For temperatures in excess of 1.4x107K,
3He prefers to react with 4He. At lower temperatures,
the PPI chain is more important.
The PPIII chain is never very important for energy generation, but it does
generate abundant high energy neutrinos.
The other hydrogen burning reaction of importance is the CNO cycle:
1 12C + p <!img src=arrow.gif width=12>
--> 13N +
2 13N <!img src=arrow.gif width=12>
--> 13C + e+ +
3 13C + p <!img src=arrow.gif width=12>
--> 14N +
4 14N + p <!img src=arrow.gif width=12>
--> 15O +
5 15O <!img src=arrow.gif width=12>
--> 15N + e+ +
6 15N + p
<!img src=arrow.gif width=12>
--> 12C + 4He
The reaction starts with a carbon nucleus, to which are added four
protons successively. In two cases the proton addition is followed
immediately by a +
decay, with the emission of a positron and a neutrino, and at the end
of the cycle a helium nucleus is emitted and a nucleus of carbon
remains. The reactions of the CNO cycle are shown pictorially in figure 18.
The CNO cycle.
Note that there are less important side reactions of the CNO cycle
which are not listed here. Carbon is sometimes described
as a catalyst in the above reaction because it is not destroyed by
its operation and it must be present in the original material of the star for
the CNO cycle to operate. When the cycle is working in equilibrium, the rates
of all of the reactions in the chain must be the same. In order for this to
be so, the abundances of the isotopes must take up values so that those
isotopes which react more slowly have higher abundances.
It can be seen from figure 18 that the
slowest reaction in the CNO cycle is the capture of a proton by
14N. As a result, most of the 12C is converted
to 14N before the cycle reaches equilibrium and this is the
source of most of the nitrogen in the Universe.
helium burning reactions
When there is no longer any hydrogen left to burn in the central regions
of a star, gravity compresses the core until the temperature reaches the
point where helium burning reactions become possible. In such reactions,
nuclei fuse to form a 8Be nucleus, but this is very unstable
to fission and rapidly decays to two 4He nuclei again.
Very rarely, however, a third helium nucleus can be added to
8Be before it decays, forming 12C by the
so-called triple-alpha reaction:
4He + 4He <!img src=arrow.gif width=12> -->
4He <!img src=arrow.gif width=12> -->
12C + |
The triple-alpha reaction is shown pictorially in figure 19. It can be seen that the reaction
leaps from helium to carbon in one go, by-passing lithium, beryllium
and boron. It is no coincidence, therefore, that these three elements
are over 105 times less abundant by number than carbon in
The triple alpha reaction.
Once helium is used up in the central regions of a star, further
contraction and heating may occur, and that may lead to additional
nuclear reactions such as the burning of carbon and heavier elements.
We will not discuss these reactions here as the majority of the possible
energy release by nuclear fusion reactions has occurred by the time that
hydrogen and helium have been burnt.
©Vik Dhillon, 3rd December 2013