1.9 Leaping the Fission Barrier
35
has a Q-value of 6.53 MeV, but the fission barrier of
240 Pu is only about 6.0 MeV. It
follows that
239 Pu will be fast-neutron fissile as well, and hence like
235 U can serve
as the active ingredient in nuclear weapons, although it does prove to have some
complications. Plutonium production is explored more fully in Sects. 3.3 and 5.3;
the complications are discussed in Sect. 4.2.
To close this section, we make a few follow-up remarks regarding thorium, which
was mentioned in the discussion of the discovery of fission in Sect. 1.5. There is
only one stable isotope of this element,
232
90 Th. This nuclide acts like
238 U as far as
its inelastic scattering and fissility properties are concerned; the Q-value of the n
+
232 Th →
233 Th reaction is 4.79 MeV, but the fission barrier for
233 Th is about
5.5 MeV. Also, the spectrum-averaged fission cross-section of thorium is only about
0.08 barns, so it is only mildly fast-neutron fissile, and is useless as a bomb fuel.
It does have value, however, as a potential component of reactor fuel.
233 Th decays
through protactinium to
233 U, which is fissile and so contributes to power production
while lessening the amount of plutonium produced—a positive aspect for nuclear
non-proliferation efforts.
1.10 A Semi-empirical Look at the Fission Barrier
In this section, we extend the model of the fission process developed in Sect. 1.7 to
show how one can “derive” the general trend of fission-barrier energy as a function
of mass number shown in Fig. 1.8. This derivation is not rigorous, and will require
some interpolation and adoption of a result from Bohr and Wheeler’s 1939 paper.
Also, as fission barriers are now known to depend in complex ways on nuclear shell
effects, pairing corrections, energy levels, and deformation and mass asymmetries,
we cannot expect the simple model presented here to capture their detailed behavior.
Some elements of this model are adopted from Reed (2020).
We saw in Sect. 1.7 that if a nucleus of mass number A and atomic number Z is
modeled as a sphere, its total energy U E can be expressed as
U
orig
E
= a S A
2/3
+ a C
Z
2
A 1/3
,
(1.77)
where a S and a C are respectively surface and Coulomb energy parameters: a S ~
18 MeV and a C ~ 0.72 MeV. Further, if the fissioning nucleus is modeled as two
touching spheres of mass ratio f (f ≥ 1), then the energy of the system at the moment
of fission is given by
U
f iss
E
= a S A
2/3
α + a C
Z
2
A 1/3
(β + γ ),
(1.78)
where
35
has a Q-value of 6.53 MeV, but the fission barrier of
240 Pu is only about 6.0 MeV. It
follows that
239 Pu will be fast-neutron fissile as well, and hence like
235 U can serve
as the active ingredient in nuclear weapons, although it does prove to have some
complications. Plutonium production is explored more fully in Sects. 3.3 and 5.3;
the complications are discussed in Sect. 4.2.
To close this section, we make a few follow-up remarks regarding thorium, which
was mentioned in the discussion of the discovery of fission in Sect. 1.5. There is
only one stable isotope of this element,
232
90 Th. This nuclide acts like
238 U as far as
its inelastic scattering and fissility properties are concerned; the Q-value of the n
+
232 Th →
233 Th reaction is 4.79 MeV, but the fission barrier for
233 Th is about
5.5 MeV. Also, the spectrum-averaged fission cross-section of thorium is only about
0.08 barns, so it is only mildly fast-neutron fissile, and is useless as a bomb fuel.
It does have value, however, as a potential component of reactor fuel.
233 Th decays
through protactinium to
233 U, which is fissile and so contributes to power production
while lessening the amount of plutonium produced—a positive aspect for nuclear
non-proliferation efforts.
1.10 A Semi-empirical Look at the Fission Barrier
In this section, we extend the model of the fission process developed in Sect. 1.7 to
show how one can “derive” the general trend of fission-barrier energy as a function
of mass number shown in Fig. 1.8. This derivation is not rigorous, and will require
some interpolation and adoption of a result from Bohr and Wheeler’s 1939 paper.
Also, as fission barriers are now known to depend in complex ways on nuclear shell
effects, pairing corrections, energy levels, and deformation and mass asymmetries,
we cannot expect the simple model presented here to capture their detailed behavior.
Some elements of this model are adopted from Reed (2020).
We saw in Sect. 1.7 that if a nucleus of mass number A and atomic number Z is
modeled as a sphere, its total energy U E can be expressed as
U
orig
E
= a S A
2/3
+ a C
Z
2
A 1/3
,
(1.77)
where a S and a C are respectively surface and Coulomb energy parameters: a S ~
18 MeV and a C ~ 0.72 MeV. Further, if the fissioning nucleus is modeled as two
touching spheres of mass ratio f (f ≥ 1), then the energy of the system at the moment
of fission is given by
U
f iss
E
= a S A
2/3
α + a C
Z
2
A 1/3
(β + γ ),
(1.78)
where