2.3 Critical Mass: Tamped Core
71
used a tungsten-carbide tamper, extending this analysis to lower masses shows that
a core of 16.17 kg would be rendered critical by such a tamper with a mass of
552 kg (beyond the range of the left side of Fig. 2.7). This mass is close to the
actual Little Boy tamper mass (see the Preamble), so we can conclude that Little Boy
utilized about (53/16.17) ~ 3 tamped threshold critical masses of
235 U. Table 2.2 lists
values of λ
tamp
trans for some common materials that might be used as tampers. Beryllium
oxide is a very desirable tamper material on account of its very low neutron-capture
cross-section. In computing these mean-free-paths for materials with more than one
isotope, effective cross-sections need to be computed from weighted averages; also,
if a material is molecular (e.g., BeO or WC), the cross-sections of all contributing
elements have to be added. Figure 2.8 shows an equivalent plot for uncompressed
239 Pu.
Table 2.2 Adopted parameters for common tamper materials. Lead and tungsten both have several
naturally-occurring isotopes; values given here are abundance-weighted averages
Material
A gr mol -1
ρ gr cm -3
σ el bn
λ
tamp
trans cm
Infinite tamper
critical mass (kg)
235 U
239 Pu
Al
26.982
2.699
2.967
5.595
21.9
9.6
BeO
25.01
3.02
5.412
2.541
8.9
3.9
DU ( 238 U)
238.05
18.95
4.804
4.342
16.4
7.2
WC
195.85
15.63
6.587
3.159
11.4
5.0
DU = Depleted Uranium
WC = tungsten carbide
0
0.5
1
1.5
2
2.5
3
0
25
50
75
100
125
150
10
11
12
13
14
15
16
Tamper mass (kg)
Tamper mass (kg)
Core mass (kg)
Pu-239
no compression
WC
BeO
DU
Al
Fig. 2.8 Mass of snugly-fitting tampers which will just render threshold critical a given core mass
of uncompressed pure 239 Pu. The dashed curve for BeO is to be read on the right axis; all others
are read on the left axis
71
used a tungsten-carbide tamper, extending this analysis to lower masses shows that
a core of 16.17 kg would be rendered critical by such a tamper with a mass of
552 kg (beyond the range of the left side of Fig. 2.7). This mass is close to the
actual Little Boy tamper mass (see the Preamble), so we can conclude that Little Boy
utilized about (53/16.17) ~ 3 tamped threshold critical masses of
235 U. Table 2.2 lists
values of λ
tamp
trans for some common materials that might be used as tampers. Beryllium
oxide is a very desirable tamper material on account of its very low neutron-capture
cross-section. In computing these mean-free-paths for materials with more than one
isotope, effective cross-sections need to be computed from weighted averages; also,
if a material is molecular (e.g., BeO or WC), the cross-sections of all contributing
elements have to be added. Figure 2.8 shows an equivalent plot for uncompressed
239 Pu.
Table 2.2 Adopted parameters for common tamper materials. Lead and tungsten both have several
naturally-occurring isotopes; values given here are abundance-weighted averages
Material
A gr mol -1
ρ gr cm -3
σ el bn
λ
tamp
trans cm
Infinite tamper
critical mass (kg)
235 U
239 Pu
Al
26.982
2.699
2.967
5.595
21.9
9.6
BeO
25.01
3.02
5.412
2.541
8.9
3.9
DU ( 238 U)
238.05
18.95
4.804
4.342
16.4
7.2
WC
195.85
15.63
6.587
3.159
11.4
5.0
DU = Depleted Uranium
WC = tungsten carbide
0
0.5
1
1.5
2
2.5
3
0
25
50
75
100
125
150
10
11
12
13
14
15
16
Tamper mass (kg)
Tamper mass (kg)
Core mass (kg)
Pu-239
no compression
WC
BeO
DU
Al
Fig. 2.8 Mass of snugly-fitting tampers which will just render threshold critical a given core mass
of uncompressed pure 239 Pu. The dashed curve for BeO is to be read on the right axis; all others
are read on the left axis