Neutron-to-proton ratio
After one second, the Universe had cooled to 10
13
K.
The Universe was filled with protons, neutrons, electrons, and neutrinos. The
temperature was high enough that they interconverted through the weak reaction in
equilibrium.
As the temperature cools, the equilibrium is shifted in favour of protons due to their
slightly lower mass. After one second the temperature is too low to maintain any
interconversion and the n/p ratio was set at 1/6.
Neutron half-life
After the neutron-to-proton ratio is fixed at about 1/6 at freezeout, the neutrons begin
to decay into protons.
The half-life of the isolated neutron is 10.4 min. If the neutrons remain isolated much
longer than this time then they will all decay into protons.
Today most of the baryonic mass in the Universe is in hydrogen and helium in gas
and stars. This is 75% hydrogen 25% helium by mass.
There is therefore three times as much hydrogen by mass today, corresponding to
twelve times as much by number. Therefore there are 2 neutrons for every 14
protons, so the current n/p ratio is 1/7. This is close to the freezeout value,
suggesting that after a few minutes all the neutrons were incorporated into atoms.
Periodic table
Atoms are identified by their numbers of neutrons and protons. The number of
protons determines which chemical element.
Different atoms of the same element with different numbers of neutrons are isotopes.
The periodic table lists the elements organised according to their chemical
properties. The number of electrons in an atom is the same as the number of
protons.
Band of stability
Stable isotopes occupy a band of stability, according to their numbers of neutrons
and protons.
Elements with too many or too few neutrons lie off the band of stability and are
radioactive.
Beta minus decay moves an atom downwards to the right on the n-p plot.
Beta plus decay moves an atom upwards to the left on the n-p plot.
Alpha decay moves an atom downward to the left with gradient 1 on the n-p plot.
Big Bang Nucleosynthesis
After freezeout the neutrons need to be incorporated into larger nuclei before they
decay.
The first nuclear reaction is combining with a proton and make deuterium.
Deuterium can then combine with other neutrons or other species to make other
elements.
The first larger isotope in the band of stability is helium-4. This is the final location for
almost all neutrons at the end of nucleosynthesis.
Only subsequent nucleosynthesis in stars generates larger isotopes than helium-4.
Deuterium bottleneck
Any deuterium that is produced before the Universe has cooled below about 0.1
MeV is immediately destroyed by energetic photons.
Therefore nucleosynthesis cannot begin in earnest until after 10 seconds.
After 10 seconds, sufficient deuterium remains that nucleosynthesis of larger nuclei
can proceed.
After about 20 minutes, the temperature is too low to support any nuclear reactions.
Helium-4
Once deuterium nuclei can survive, they react with other nuclei, eventually forming
helium-4. This is the first stable nucleus with a nucleon number greater than one.
Helium-4 may form from deuterium through two distinct channels.
The deuterium could form tritium by capturing a neutron. the tritium nucleus can then
form helium-4 by capturing either a proton or another deuterium nucleus and then
releasing a neutron.
Tritium may also be formed by combining two deuterium nuclei and releasing a
proton.
Alternatively, deuterium can form helium-3 either by capturing a proton or by
combining with another deuterium nucleus and releasing a neutron.
Helium-3 can then form helium-4 either by capturing a neutron or by combining with
a deuterium nucleus and releasing a proton.
that form the very stable nuclide helium-4 (
4
2
He, He-4). Note, there are only four
types of reactions to consider:
– Neutron captured, photon emitted.
– Proton captured, photon emitted.
– Deuteron captured, neutron emitted.
– Deuteron captured, proton emitted.
• In one reaction the isotope tritium (
3
1
H) was formed by:
2
1
H + n →
3
1
H + γ
2
1
H +
2
1
H →
3
1
H + p
and the newly formed tritium could then undergo reactions to produce He-4:
3
1
H +
2
1
H →
4
2
He + n
3
1
H + p →
4
2
He + γ
• However, through another set of reactions deuterium also reacted to produce helium-
3 (He-3):
2
1
H +
2
1
H →
3
2
He + n
2
1
H + p →
3
2
He + γ
and this isotope of helium could undergo reactions to form He-4:
3
2
He + n →
4
2
He + γ
3
2
He +
2
1
H →
4
2
He + p
• Other reactions can occur but are less significant (even direct fusion of two deuterons).
The major product of primordial synthesis was He-4, and not large quantities of
higher elements for two reasons:
– The fusion rate is temperature dependent, and we get what is referred to as
the Deuterium Bottleneck i.e. higher temperatures are required to fuse nuclei of
higher atomic number, but lower temperatures are required to reduce photodis-
integration (energetic photons rip nuclei apart) of deuterium, which is a basic,
or building block, for nucleosynthesis. So by the time deuterium is available in
sufficient quantities, the temperature is too low for significant fusion rates of
elements higher than hydrogen and helium. Eventually, the temperature falls
too low for nucleosynthesis, and all fusion reactions cease.
8
Lithium-7 and larger elements
Elements larger than helium can be produced in trace amounts by rare nuclear
reactions.
The reason these reactions are rare is that extremely high temperatures are required
to overcome large Coulomb barriers and we are on the low-temperature side of the
deuterium bottleneck.
The primordial abundance of lithium is very low, one part per billion in terms of mass
as opposed to 0.25 four helium. Primordial beryllium is about a factor greater than
1000 lower.
Larger elements were not produced in the Big Bang, only in stellar nucleosynthesis.
Calculation of abundances
The temperature dependence on the rate of nuclear reactions is complicated
because there are several nucleon-nucleon interactions.
From the reaction rates and equilibrium dynamics, the production of different
isotopes can be calculated as a function of cosmic time.
This can then be integrated over time, to determine the final abundances and
compare with observations.
Stellar nucleosynthesis and Big Bang nucleosynthesis
comparison
In stellar nucleosynthesis, helium is made by the CNO cycle, not by combining
protons and neutrons.
Primordial abundances
Helium-4
Helium 4
From extragalactic HII regions. Need to estimate contamination, but most estimates give about Y=0.24
Helium-3
heliumhelium
The primordial solar system ratio he3/he4 can be inferred from trapped mantle gases released in eruptions when
volcanoes pass over hotspots in the mantle.
Uncertainties large, that ratio consistent with nucleosynthesis.
Deuterium from high redshift gas clouds
Spectrum of gas cloud
Primordial deuterium abundance
Lithium
Primordial lithium abundance
Population II stars
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