4.4 Tolerable Limits for Light-Element Impurities
163
4.4 Tolerable Limits for Light-Element Impurities
In addition to the possibility of predetonation caused by spontaneous fission, another
danger for weapons designers is that a chain reaction can be initiated by the natural
alpha-decay of the fissile material if that material contains even a small percentage
of light-element impurities. A particular danger in this regard is the presence of
any beryllium in a Pu core.
239 Pu has a fairly short half-life for alpha-decay, about
24,100 years, or 7.605 × 10
11 s. From the decay-rate formula (4.4), this leads to an
enormous rate of alpha-decays:
R α =10
3
N A
A
ln 2
t 1/2
= 10
3
6.022 × 10
23
239
ln 2
7.605 × 10 11
= 2.296 × 10
12 kg
−1 s
−1
.
(4.25)
This figure is much greater than the rate of spontaneous fissions for
240 Pu. For a 10kg core of pure
239 Pu, the alpha-decay rate would be 2.3 × 10
13 s
−1 . If some of these
alphas should find a beryllium nucleus to react with during the time that the bomb
core is being assembled, the result will be a neutron which could go on to initiate
a premature detonation via an (α, n) reaction of the sort involved in Chadwick’s
discovery of the neutron (Sect. 1.4):
4
2 He +
9
4 Be →
12
6 C +
1
0 n.
(4.26)
A similar effect happens with alpha bombardment of lithium:
4
2 He +
7
3 Li →
10
5 B +
1
0 n.
(4.27)
This is a serious issue. As described by Bernstein (2007), plutonium metal at
room temperature is rather brittle and difficult to form into desired shapes unless
alloyed with another metal. But a light alloying metal such as aluminum cannot be
used because of this (α, n) problem; one needs to use an alloying material whose
nuclei have a Coulomb barrier strong enough that they cannot be overcome by alphaparticles of a few MeV. Los Alamos metallurgists alloyed plutonium with gallium to
achieve desirable malleability properties.
Chemical processing of plutonium will inevitably introduce some level of impurities. The question is: What level of impurity can one tolerate if the resulting rate
of neutron production is to be kept below, say, one per 100 μs? For simplicity, we
develop the analysis assuming that only one impurity is present.
To address this issue requires appreciating two empirical ideas from experimental
nuclear physics: (i) The yield (y) of a reaction; and (ii) The stopping power (S) a
material presents against particles traveling through it. Note that y here refers to the
yield of a particular nuclear reaction, not the yield of a bomb as whole, for which
we have used the symbol Y. We discuss these two issue first, and then develop a
163
4.4 Tolerable Limits for Light-Element Impurities
In addition to the possibility of predetonation caused by spontaneous fission, another
danger for weapons designers is that a chain reaction can be initiated by the natural
alpha-decay of the fissile material if that material contains even a small percentage
of light-element impurities. A particular danger in this regard is the presence of
any beryllium in a Pu core.
239 Pu has a fairly short half-life for alpha-decay, about
24,100 years, or 7.605 × 10
11 s. From the decay-rate formula (4.4), this leads to an
enormous rate of alpha-decays:
R α =10
3
N A
A
ln 2
t 1/2
= 10
3
6.022 × 10
23
239
ln 2
7.605 × 10 11
= 2.296 × 10
12 kg
−1 s
−1
.
(4.25)
This figure is much greater than the rate of spontaneous fissions for
240 Pu. For a 10kg core of pure
239 Pu, the alpha-decay rate would be 2.3 × 10
13 s
−1 . If some of these
alphas should find a beryllium nucleus to react with during the time that the bomb
core is being assembled, the result will be a neutron which could go on to initiate
a premature detonation via an (α, n) reaction of the sort involved in Chadwick’s
discovery of the neutron (Sect. 1.4):
4
2 He +
9
4 Be →
12
6 C +
1
0 n.
(4.26)
A similar effect happens with alpha bombardment of lithium:
4
2 He +
7
3 Li →
10
5 B +
1
0 n.
(4.27)
This is a serious issue. As described by Bernstein (2007), plutonium metal at
room temperature is rather brittle and difficult to form into desired shapes unless
alloyed with another metal. But a light alloying metal such as aluminum cannot be
used because of this (α, n) problem; one needs to use an alloying material whose
nuclei have a Coulomb barrier strong enough that they cannot be overcome by alphaparticles of a few MeV. Los Alamos metallurgists alloyed plutonium with gallium to
achieve desirable malleability properties.
Chemical processing of plutonium will inevitably introduce some level of impurities. The question is: What level of impurity can one tolerate if the resulting rate
of neutron production is to be kept below, say, one per 100 μs? For simplicity, we
develop the analysis assuming that only one impurity is present.
To address this issue requires appreciating two empirical ideas from experimental
nuclear physics: (i) The yield (y) of a reaction; and (ii) The stopping power (S) a
material presents against particles traveling through it. Note that y here refers to the
yield of a particular nuclear reaction, not the yield of a bomb as whole, for which
we have used the symbol Y. We discuss these two issue first, and then develop a