Phase diagram of water

Lower ‘control rods’ into reactor to absorb excess neutrons
Materials used: 113 Cd (σ c = 20,000 barns)
10
B (σ c = 4,000 barns)
cross section is for thermal neutrons (~0.025 eV)
[σ c (max) ~ π(λ/2π) 2 ∼ 2.6 10 7 barns]
(withdraw control rods if reactivity gets too low)
In practice control would be virtually impossible but for the existence
of ‘delayed’ neutrons
Delayed neutrons are released only after the β-decay of a fission product
Typically, about 1% of neutrons produced by fission are delayed by
10-20 seconds, which is enough time for small adjustments in the
position of the control rods (automatically controlled)
eg
87
Br β −
t 1/2
54.5 s
n
87
Kr *
86
Kr
137
I β −
t 1/2
21.8 s
n
137
Xe *
136
Xe
Neutron Population Growth
η is number of neutrons emitted per neutron absorbed
Because of losses the mean number is k, where k < η
k is the effective multiplication factor
If all neutrons were prompt the neutron population would grow like
dn/dt = n(k−1)/τ = nq/τ
where q=(k−1) and τ is the average neutron lifetime in the reactor
So
n = n o exp{qt/τ}
eg q = 0.001, τ = 0.001 second gives n = n o exp(t), so after 10 s
n/n o increases by a factor of 22,000
In 235 U the mean lifetime of the
groups of delayed neutrons is
about τ d = 9 s and they represent
a fraction β = 0.65% of the total
neutron emission
235
U delayed neutrons
If q