32
1 Energy Release in Nuclear Reactions, Neutrons, Fission, and Characteristics …
excellent fuel for nuclear weapons. Other isotopes of this element are also created in
reactors, but those of masses 236, 237, 238 and 241 have such short half-lives against
various decay processes as to render them too unstable for use in a weapon (2.87-year
alpha-decay, 45-day electron capture, 88-year alpha-decay and 14-year beta-decay,
respectively).
240 Pu turns out to have such a high spontaneous fission rate that its very
presence in a bomb presents a serious danger of causing an uncontrollable premature
detonation; this issue is analyzed in Sects. 4.2 and 4.3.
239 Pu is the only isotope of
that element suitable as a weapons material.
A pattern of alternating high-and-low Q−E Barrier values is evident for both
elements in Fig. 1.9. All stable nuclei have lower masses than one would predict
on the naïve basis of adding up the masses of their Z protons and A-Z neutrons;
the difference goes into binding energy. Nuclear physicists have known for many
decades that in this mass-energy sense, so-called even/odd nuclei such as
235 U or
239 Pu are inherently less stable than even/even nuclei such as
238 U; the underlying
cause has to do with the way in which nuclear forces act between pairs of nucleons.
Expressed qualitatively, even/even nuclei are of even lower mass than the naive massaddition argument would suggest when compared to what happens with even/odd
nuclei. Hence, when an even/odd nucleus such as
235 U captures a neutron, it becomes
an even/even nucleus of “very” low mass; the mass difference appears as excitation
energy via E = mc
2 . When an even/even nucleus takes in a neutron it liberates massenergy as well, but not as much as in the even/odd case (we might call the result a
“relatively” low mass in comparison); the different Q−E Barrier values are reflected
in the jagged lines in Fig. 1.9.
The issue of the unsuitability of
238 U as a weapons material is, however, more
subtle than the above argument lets on. We saw in Sect. 1.8 that the average energy
of secondary neutrons liberated in fission of uranium nuclei is about 2 MeV, and
that about half of these neutrons have energies greater than the ~1.4 MeV activation
energy of the n +
238 U →
239 U reaction. In view of this, it would appear that
238 U
might make a viable weapons material. Why does it not? The problem turns out
to depend on what happens when fast neutrons such as those liberated in fissions
encounter
238 U nuclei.
The inelastic-scattering cross-section for fission-liberated neutrons against
238 U
nuclei is about 2.6 barns. In inelastic scattering, the kinetic energy of the system
is not conserved, and the incoming particle typically suffers a serious reduction in
kinetic energy; this is quantified below. In contrast, in elastic scattering the kinetic
energy of the system is conserved, and in the case of a low-mass particle such as
a neutron striking a much higher mass target nucleus, the neutron loses very little
kinetic energy. The 2.6-bn figure for inelastic scattering by U-238 is derived from
averaging the cross-section over the energy spectrum of the neutrons, a so-called
“fission-spectrum average,” a concept we will invoke on a number of occasions. On
the other hand, the spectrum-averaged fission cross-section for neutrons on
238 U is
about 0.31 bn. Thus, a fast neutron striking a
238 U nucleus is about eight times as
likely to be inelastically scattered as it is to induce a fission. Experimentally, neutrons
of energy 2.5 MeV inelastically scattering from
238 U have their energy reduced to
a most probable value of about 0.275 MeV as a result of a single scattering; see
1 Energy Release in Nuclear Reactions, Neutrons, Fission, and Characteristics …
excellent fuel for nuclear weapons. Other isotopes of this element are also created in
reactors, but those of masses 236, 237, 238 and 241 have such short half-lives against
various decay processes as to render them too unstable for use in a weapon (2.87-year
alpha-decay, 45-day electron capture, 88-year alpha-decay and 14-year beta-decay,
respectively).
240 Pu turns out to have such a high spontaneous fission rate that its very
presence in a bomb presents a serious danger of causing an uncontrollable premature
detonation; this issue is analyzed in Sects. 4.2 and 4.3.
239 Pu is the only isotope of
that element suitable as a weapons material.
A pattern of alternating high-and-low Q−E Barrier values is evident for both
elements in Fig. 1.9. All stable nuclei have lower masses than one would predict
on the naïve basis of adding up the masses of their Z protons and A-Z neutrons;
the difference goes into binding energy. Nuclear physicists have known for many
decades that in this mass-energy sense, so-called even/odd nuclei such as
235 U or
239 Pu are inherently less stable than even/even nuclei such as
238 U; the underlying
cause has to do with the way in which nuclear forces act between pairs of nucleons.
Expressed qualitatively, even/even nuclei are of even lower mass than the naive massaddition argument would suggest when compared to what happens with even/odd
nuclei. Hence, when an even/odd nucleus such as
235 U captures a neutron, it becomes
an even/even nucleus of “very” low mass; the mass difference appears as excitation
energy via E = mc
2 . When an even/even nucleus takes in a neutron it liberates massenergy as well, but not as much as in the even/odd case (we might call the result a
“relatively” low mass in comparison); the different Q−E Barrier values are reflected
in the jagged lines in Fig. 1.9.
The issue of the unsuitability of
238 U as a weapons material is, however, more
subtle than the above argument lets on. We saw in Sect. 1.8 that the average energy
of secondary neutrons liberated in fission of uranium nuclei is about 2 MeV, and
that about half of these neutrons have energies greater than the ~1.4 MeV activation
energy of the n +
238 U →
239 U reaction. In view of this, it would appear that
238 U
might make a viable weapons material. Why does it not? The problem turns out
to depend on what happens when fast neutrons such as those liberated in fissions
encounter
238 U nuclei.
The inelastic-scattering cross-section for fission-liberated neutrons against
238 U
nuclei is about 2.6 barns. In inelastic scattering, the kinetic energy of the system
is not conserved, and the incoming particle typically suffers a serious reduction in
kinetic energy; this is quantified below. In contrast, in elastic scattering the kinetic
energy of the system is conserved, and in the case of a low-mass particle such as
a neutron striking a much higher mass target nucleus, the neutron loses very little
kinetic energy. The 2.6-bn figure for inelastic scattering by U-238 is derived from
averaging the cross-section over the energy spectrum of the neutrons, a so-called
“fission-spectrum average,” a concept we will invoke on a number of occasions. On
the other hand, the spectrum-averaged fission cross-section for neutrons on
238 U is
about 0.31 bn. Thus, a fast neutron striking a
238 U nucleus is about eight times as
likely to be inelastically scattered as it is to induce a fission. Experimentally, neutrons
of energy 2.5 MeV inelastically scattering from
238 U have their energy reduced to
a most probable value of about 0.275 MeV as a result of a single scattering; see