Compound Nucleus Formation
If a neutron enters a nucleus—instead of scattering from its surface as in potential scattering—a compound nucleus is formed, and it is in an excited state. There are two contributions to this excitation energy. The first derives from the kinetic energy of the neutron. We determine excitation energy as follows. Suppose a neutron of mass m and velocity v hits a stationary nucleus of atomic weight A and forms a compound nucleus. Conservation of momentum requires that
mv= (m+ Am)V. (2.38)
Kinetic energy, however, is not conserved the formation. The amount lost is
where V is the speed of the resulting compound nucleus. Eliminating
V between these equations then yields
whichmay be shown to be identical to the neutron kinetic energy before
the collision measured in the center ofmass system. Hence we hereafter
denote it by Ecm. The second contribution to the excitation energy is the
binding energy of the neutron, designated by EB. The excitation energy of
the compound nucleus is Ecm + EB. Note that even very slow moving
thermal neutrons will excite a nucleus, for even though Ecm <<>B, the
binding energy by itself may amount to a MeV or more.
The effects of the excitation energy on neutron cross sections
relate strongly to the internal structure of the nucleus. Although the
analogy is far from complete, these effects can be roughly understood
by comparing atomic to nuclear structures. The electrons surrounding
a nucleus are in distinct quantum energy states and can be excited to
higher states by imparting energy from the outside. Likewise, the
configurations of nucleons that form a nucleus are in quantum states,
and the addition of a neutron accompanied by its kinetic energy create
a compound nucleus that is in an excited state. Following formation of
a compound nucleus one of two things happen: the neutron may be
reemitted, returning the target nucleus to its ground state; this scattering
is elastic, even though a compound nucleus was formed temporarily
in the process. Alternately, the compound nucleus may return to
its ground state by emitting one or more gamma rays; this is a neutron
capture reaction through which the target nucleus is transmuted to a
new isotope as the result of the neutron gained.
With higher incoming neutron energies the compound nucleus may
gain sufficient excitation energy to emit both a lower energy neutron and
a gamma ray; thus inelastic scattering results, and at yet higher energies
other reactions may result as well. In fissile and fertile materials, of
course, the fission reaction is the most important consequence of compound
nucleus formation. Before considering these reactions in detail,
we first examine the resonance structure of compound nuclei and the
effect that it has on scattering and absorption cross sections.
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mv= (m+ Am)V. (2.38)
Kinetic energy, however, is not conserved the formation. The amount lost is
where V is the speed of the resulting compound nucleus. Eliminating
V between these equations then yields
whichmay be shown to be identical to the neutron kinetic energy before
the collision measured in the center ofmass system. Hence we hereafter
denote it by Ecm. The second contribution to the excitation energy is the
binding energy of the neutron, designated by EB. The excitation energy of
the compound nucleus is Ecm + EB. Note that even very slow moving
thermal neutrons will excite a nucleus, for even though Ecm <<>B, the
binding energy by itself may amount to a MeV or more.
The effects of the excitation energy on neutron cross sections
relate strongly to the internal structure of the nucleus. Although the
analogy is far from complete, these effects can be roughly understood
by comparing atomic to nuclear structures. The electrons surrounding
a nucleus are in distinct quantum energy states and can be excited to
higher states by imparting energy from the outside. Likewise, the
configurations of nucleons that form a nucleus are in quantum states,
and the addition of a neutron accompanied by its kinetic energy create
a compound nucleus that is in an excited state. Following formation of
a compound nucleus one of two things happen: the neutron may be
reemitted, returning the target nucleus to its ground state; this scattering
is elastic, even though a compound nucleus was formed temporarily
in the process. Alternately, the compound nucleus may return to
its ground state by emitting one or more gamma rays; this is a neutron
capture reaction through which the target nucleus is transmuted to a
new isotope as the result of the neutron gained.
With higher incoming neutron energies the compound nucleus may
gain sufficient excitation energy to emit both a lower energy neutron and
a gamma ray; thus inelastic scattering results, and at yet higher energies
other reactions may result as well. In fissile and fertile materials, of
course, the fission reaction is the most important consequence of compound
nucleus formation. Before considering these reactions in detail,
we first examine the resonance structure of compound nuclei and the
effect that it has on scattering and absorption cross sections.
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