Introduction to Cosmology

Big Bang Nucleosynthesis 137

the exponential factor in Equation (6.73). The neutrons also decay into protons by
beta decay,

n→e−+휈e+p, (6.90)

liberating
푚n−푚p−푚e−푚휈= 0 .8 MeV (6.91)

of kinetic energy in the process. This amount is very small compared with the neutron
mass of 939.6MeV. In consequence the decay is inhibited and very slow: the neutron
mean life is 887s. In comparison with the age of the Universe, which at this time is
a few tens of seconds, the neutrons are essentially stable. The protons are stable even
on scales of billions of years, so their number is not going to decrease by decay.
At 0.1MeV, when the temperature is 1. 2 × 109 K and the time elapsed since the Big
Bang is a little over two minutes, the beta decays have reduced the neutron/proton
ratiotoitsfinalvalue:

푁n

푁p

≃^1

7

. (6.92)

The temperature dependence of this ratio, as well as the equilibrium (Maxwell–
Boltzmann) ratio, is shown in Figure 6.4.
These remaining neutrons have no time to decay before they fuse into deuterons
and subsequently into^4 He++. There they stayed until today because bound neutrons
do not decay. The same number of protons as neutrons go into^4 He, and the remain-
ing free protons are the nuclei of future hydrogen atoms. Thus the end result of the
nucleosynthesis taking place between 100 and 700s after the Big Bang is a Universe
composed almost entirely of hydrogen and helium ions. But why not heavier nuclei?
It is an odd circumstance of nature that, although there exist stable nuclei com-
posed of퐴=1, 2, 3 and 4 nucleons, no nucleus of퐴=5, nor really of퐴=8, exists.
In between these gaps, there exist the stable nuclei^6 Li and^7 Li and also^7 Be which

1.0

0.1 0.1

Equilibrium Present

Neutron / proton ratio

10 1

T (MeV)

0.1 0.01

Figure 6.4Theneutron/protonratio from 10 Mev to the present≈10 keV. The equilibrium푛∕푝
ratio is also shown.