1.10 A Semi-empirical Look at the Fission Barrier
39
0
5
10
15
20
25
30
35
40
45
50
0
5 0
1 0 0
1 5 0
2 0 0
2 5 0
Fission barrier (MeV)
Mass number A
Fig. 1.13 Fission barrier energy of (1.89)–(1.92) for fission-product mass ratio = 1. Compare to
Fig. 1.8
Figure 1.13 is satisfyingly similar in shape to Fig. 1.8, although with a lower peak
value (~ 45 MeV instead of ~ 55). This indicates that (1.89) does not accurately model
the run of the fission barrier over all mass numbers, but this is not too surprising as
Bohr and Wheeler’s purpose was to try to estimate fission barriers for nuclei with
x-values similar to that of the
239 U compound nucleus in an effort to predict the
fissility behavior of heavy nuclei. More detailed fission barrier models can be found
in Hyde (1964). For elements lighter than uranium, the fission barrier is too great to
be overcome by release of binding energy alone, and it is for this reason that common
elements such as aluminum or iron cannot be used to fuel nuclear weapons.
1.11 A Numerical Model of the Fission Process
Material in this section is adopted from Reed (2011).
In Sects. 1.7 and 1.10, the fission process was studied analytically via a simplified
“two-sphere” model. While that model does a respectable job of reproducing the
overall characteristics of the fission barrier as a function of mass number A (Figs. 1.8
and 1.13), it does have some artificial features and leaves some questions unanswered.
Physically, if one imagines a situation midway between panels (a) and (b) of Fig. 1.4,
that is, at some point when the nucleus is partially fissioned, there will be a neck
joining the product nuclei. Nuclear physicists model surface energies in a manner
akin to describing surface tension; a discontinuous curvature would correspond to an
infinite force, so the model can be criticized as unrealistic on this aspect alone. More
important, perhaps, is the question of the behavior of the energy of the system when
the nucleus is only partially fissioned. Does the system energy reach a maximum early
39
0
5
10
15
20
25
30
35
40
45
50
0
5 0
1 0 0
1 5 0
2 0 0
2 5 0
Fission barrier (MeV)
Mass number A
Fig. 1.13 Fission barrier energy of (1.89)–(1.92) for fission-product mass ratio = 1. Compare to
Fig. 1.8
Figure 1.13 is satisfyingly similar in shape to Fig. 1.8, although with a lower peak
value (~ 45 MeV instead of ~ 55). This indicates that (1.89) does not accurately model
the run of the fission barrier over all mass numbers, but this is not too surprising as
Bohr and Wheeler’s purpose was to try to estimate fission barriers for nuclei with
x-values similar to that of the
239 U compound nucleus in an effort to predict the
fissility behavior of heavy nuclei. More detailed fission barrier models can be found
in Hyde (1964). For elements lighter than uranium, the fission barrier is too great to
be overcome by release of binding energy alone, and it is for this reason that common
elements such as aluminum or iron cannot be used to fuel nuclear weapons.
1.11 A Numerical Model of the Fission Process
Material in this section is adopted from Reed (2011).
In Sects. 1.7 and 1.10, the fission process was studied analytically via a simplified
“two-sphere” model. While that model does a respectable job of reproducing the
overall characteristics of the fission barrier as a function of mass number A (Figs. 1.8
and 1.13), it does have some artificial features and leaves some questions unanswered.
Physically, if one imagines a situation midway between panels (a) and (b) of Fig. 1.4,
that is, at some point when the nucleus is partially fissioned, there will be a neck
joining the product nuclei. Nuclear physicists model surface energies in a manner
akin to describing surface tension; a discontinuous curvature would correspond to an
infinite force, so the model can be criticized as unrealistic on this aspect alone. More
important, perhaps, is the question of the behavior of the energy of the system when
the nucleus is only partially fissioned. Does the system energy reach a maximum early