136 Thermal History of the Universe
favored on energetic grounds already at 2MeV, free nucleons continue to be favored
by the high entropy down to 0.07MeV.
Other nuclear fusion reactions also commence at a few MeV. The npp bound state
(^3) He++is produced in the fusion of two deuterons,
d+d→^3 He+++n, (6.77)
p+d→^3 He+++훾, (6.78)
where the final-state particles share the binding energy
2 푚p+푚n−푚(^3 He++)= 7 .72 MeV. (6.79)
This reaction is also hampered by the large entropy per nucleon, so it becomes ther-
modynamically favored only at 0.11MeV.
The nnp bound state^3 H+,ortritont, is the ionizedtritiumatom,^3 H. It is produced
in the fusion reactions
n+d→t+훾, (6.80)
d+d→t+p, (6.81)
n+^3 He→t+p, (6.82)
with the binding energy
푚p+ 2 푚n−푚t= 8 .48 MeV. (6.83)
A very stable nucleus is the nnpp bound state^4 He++with a very large binding
energy,
2 푚p+ 2 푚n−푚(^4 He++)= 28 .3 MeV. (6.84)
Once its production is favored by the entropy law, at about 0.28MeV, there are no
more훾rays left that are hard enough to photodisintegrate it. From the examples set by
the deuteron fusion reactions above, it may seem that^4 He++would be most naturally
produced in the reaction
d+d→^4 He+++훾. (6.85)
However,^3 He++and^3 H+production is preferred over deuteron fusion, so^4 He++is
only produced in a second step when these nuclei become abundant. The reactions
are then
n+^3 He++→^4 He+++훾, (6.86)
d+^3 He++→^4 He+++p, (6.87)
p+t→^4 He+++훾, (6.88)
d+t→^4 He+++n. (6.89)
The delay before these reactions start is often referred to as thedeuterium bottleneck.
Below 0.8MeV occasional weak interactions in the high-energy tails of the lep-
ton and nucleon Fermi distributions reduce the푛∕푝ratio further, but no longer by