The First Three Minutes (2) ...
The free neutron is unstable, but neutrons in composite nuclei can be stable, so
the conversion of neutrons to protons
will continue until the simplest nucleus (deuterium, the
mass-2 isotope of hydrogen) can form. But no
composite nuclei can form yet because the temperature implies an average
energy for particles in the gas of about 2.6 MeV.
Deuterium has a binding energy of only 2.2 MeV and
so cannot hold together at these temperatures. Detailed considerations indicate that deuterium
can only hold together in appreciable quantities when the average energy per particle has dropped to
about 0.07 MeV. This barrier to production of
composite nuclei, which allows the free neutrons to be converted steadily to
protons, is called the deuterium bottleneck (see the right panel).
Time ~ 1 Second
The temperature has dropped to about 10 billion K as the Universe continues to
expand, and the density is now down to about 400,000 times that of water. At this
temperature the neutrinos drop out of thermal equilibrium (This is called weak freeze-out; see
the top right figure of the preceding page). The
deuterium bottleneck still exists so there are no composite nuclei and the
neutrons continue to convert to protons. The proton abundance
is now up to about 75 percent and the neutron abundance has fallen to about 25 percent.
Time ~ 14 Seconds
The temperature has now fallen to about 4 billion K. The average energy of the
particles in the gas has fallen to about 0.34 MeV. This is too low for photons to
produce electron-positron pairs so they fall out of thermal equilibrium and the
free electrons begin to annihilate all the positrons to form photons. The
deuterium bottleneck still keeps appreciable deuterium from forming and the
neutrons continue to decay to protons. At this stage the abundance of neutrons has
fallen to about 18 percent and the abundance of protons has risen to about 82 percent.
Time ~ 3 Min 45 Sec
Finally the temperature drops sufficiently low (about 1 billion K) that deuterium
nuclei can hold together. The deuterium bottleneck is thus broken and a rapid
sequence of nuclear reactions combines neutrons and protons to form deuterium, and
the resulting deuterium with neutrons and protons to form the mass-4 isotope of
helium (alpha particles). Thus, all remaining free neutrons are rapidly "cooked"
into helium. Elements beyond helium-4 are difficult to form in any substantial amount
because of the peculiarity
that there are no stable mass-5 or mass-8 isotopes in our Universe and the next
steps in the most likely reactions to form heavier elements would form mass-5 or
mass-8 isotopes. Although a few isotopes in the mass-5 through mass-8 range
are formed in tiny concentrations in the big bang, essentially all nuclei end up either
as protons or as the mass-4 isotope of helium. That is, the big bang nucleosynthesis
produces primarily hydrogen
and helium. As we have noted in earlier chapters, the heavier elements must be produced later
in stars.
Element Production and the Early Universe
Because deuterium serves as a bottleneck until a critical temperature
is reached and then is quickly converted into helium, which is very stable, the
present abundances of helium and deuterium (and other light elements like lithium
that are produced by the big bang
in trace abundances)
are a sensitive probe of conditions in the first few seconds of the Universe.
The oldest stars contain material that is the least altered from that produced originally in
the big bang. Analysis of their composition indicates elemental
abundances that are in very good agreement with the predictions of the hot big bang.
This is one of the strongest
pieces of evidence in support of the big bang theory.
