After studding this lecture, the student should be able to: define
main processes of neutron interaction with nuclei of a medium; define
the microscopic and macroscopic cross sections and mean free path.
There are two main mechanisms of the neutron interaction with nuclei
of a medium: the first is scattring.
Scattering — it is an interaction of a neutron with a nucleus
which results only in a redistribution of the kinetic energy and the angular
momentum between neutron and nucleus.
The second absorption. Absorption – it includes all interactions of a neutron with
a nucleus resulting in the appearance of new nucleus and new particles
(including neutrons). Further, the term collision of a neutron
with a nucleus will be understood as the scattering and absorption.
For a better understanding of the nature of nuclear reactions, it is very
useful to implement representation of nucleus as a finite potential well.
There are energy levels in the potential well which characterize
the exited states of the nucleus. The bottom of the potential
well characterizes the stable state. When the neutron
is colliding to collide with a nucleus with the velocity v,
it has the kinetic energy T. When the neutron’s energy is close
to the energy of an excited state the neutron can penetrate into the nucleus and
create the compound state. All nuclear reaction occurs though
the mechanism of compound nucleus except one – the potential
elastic scattering (scattering on a nucleus potential without penetration).
The potential elastic scattering — occurs when neutron is deflected
by a nucleus without being absorbed. Potential elastic
scattering conserves kinetic energy and is often visualized as
a "Billiard Ball" type of collision. In this case, some kinetic energy
of the neutron is transferred to nucleus of the target atom. The momentum
is conserved. An important role in explaining the mechanism of many
nuclear reactions played the assumption of N. Bohr (1936) about
two stages of nuclear reactions. The first stage is capturing by the nucleus
of a neutron (at the characteristic distance for nuclear forces ~ 10 in the power minus 15 m),
and the formation of the intermediate nucleus which is called
compound (or compound-nucleus). When the neutron penetrates
into the nucleus, it adds the excitation energy (E_ex), which is the sum of
its kinetic energy and binding energy. The compound nucleus
lives as usual 10 in the power minus 17 seconds and subsequently the excitation energy
has to be removed. The second stage — a decay of the compound nucleus.
There are different ways to remove the excitation energy — the one which
we called nuclear reactions undergoing by the mechanism of compound
nucleus. What happeneds next depends on the probability of
nuclear reactions. The first case — neutron can escape with the
same energy (not direction), this is the resonance elastic scattering.
The second – the neutron can drop down to a lower energy level
(not lower than the binding energy) and escape with a lower
kinetic energy. The residue part of the excitation energy is removed by
the γ-emission. It names the inelastic scattering.
The others the neutron absorption reaction
is the most important type of reactions that take place
in a nuclear reactor. The third option, the neutron can drop down
to the bottom of the potential well and create a new stable state.
All excitation energy is removed by the γ-emission.
It's name the radioactive capture, (n, γ) reaction.
The neutron can drop down to the bottom of
the potential well, but the excitation energy goes to the split the nucleus — fission,
(n, f) reaction; the creation of new particles — reactions of nucleus spallation.
In summary all nuclear reaction occurs with the mechanism of compound
nucleus generation. Except of the only one — the potential elastic scattering.
The next step is to learn how to calculate the probability of the reactions.