108 The hot universe
pnpn
DDD1DD2DγDpTD(^3) Hen
(^3) He D (^3) He (^4) He
(^4) He T
(^7) Lip
(^7) Ben
(^7) Be
(^7) Li
(^4) He
(^3) He
T
Fig. 3.6.
The general picture is as follows. Until the temperature drops to 0.08 MeV, the
p,nand D reservoirs are in equilibrium with each other and decoupled from the
rest (the deuterium bottleneck). However, as soon as the temperature drops to 0.08
MeV, the DD pipes become very efficient, rapidly converting the deuterium supply
from thenpreservoir into heavier elements. Finally, nearly all free neutrons have
been bound in nuclei. Around this time the concentrations of the elements in the
various “reservoirs” freeze out at their final abundances. Now we consider the
build-up of each element in detail.
3.5.3 Helium-4
Once deuterium reaches the abundanceXD(bn)the bottleneck opens and nucleosyn-
thesis begins. However, at the beginning, deuterium production in the reaction
pn→Dγ is still greater than its destruction in DD reactions. The ratio of the
corresponding rates is
λpnXpXn
λDDX^2 D104
(
10 −^4
XD
) 2
, (3.135)
where the experimental value forλpn/λDDis about 10−^3 atTMeV 0 .07–0.08 and
we have setXn 0. 16 ,Xp 0. 84 .Because of the very high supply rate, deu-
terium remains in chemical equilibrium with nucleons until its abundance rises to
XD 10 −^2 .After that, two-body DD reactions become dominant andXDbegins to
decrease−see Figure 3.7, where the time dependence of abundances forη 10 7
is shown. (Note that the deuterium photodestruction can be ignored now because it