We have said that ﬁssionable elements have a high-
mass nucleus. But is this a sufﬁcient condition as
In nature, heavy elements such as 235U and 239Pu can
be ﬁssioned by a thermal neutron, while others such
as 238U and 243Am are not. Why is that?
In the graph, we see that a nucleus must overcome a
potential maximum at about 5 [fm].
This potential barrier of height Ebmust be overcame
using an external source to produce nuclear ﬁssion.
The energy of the inbound neutron must be at least
as large as Ebto break the nucleus into two sections.
In other words, ﬁssion will occur if the absorbed neu-
tron provides an excitation energy Enat least as large
This condition explains why certain materials are
more susceptible to ﬁssion than others.
But the fact that thermal ﬁssion will not occur does
not mean that you cannot start the process by another
In fact, the process can be started using a fast neu-
tron, which creates fast ﬁssion.
This is the principle behind a nuclear reaction, where
the process is started by fast neutron emitter, that cre-
ate a ﬁrst wave of ﬁssion, that in turn ejects thermal
neutrons that hit other heavy nuclei. This chain reac-
tion continues until all the “fuel” is depleted.
2 Nuclear Reactor
A nuclear reactor is system where a ﬁssion chain re-
action occurs in a controlled manner.
2.1 Preparing the Fissionable Material
Most nuclear reactors use 235U as effective agent
In nature, uranium contains
• ∼ 0.7% of 235U
• ∼ 99.3% of 238U, which is not ﬁssionable by ther-
The ﬁrst task to prepare the reactor is to enrich the
uranium, a process where one increases the propor-
tion of 235U to 3% by artiﬁcially separating the iso-
2.2 Desirable Characteristics of a Working
When designing a working reactor, one needs to take
into account three potential problems:
1. Neutron Leakage. Not all neutrons involved on
the chain reaction will impact 235U atoms.
Leakage can be controlled by using a reactor core
large enough, reducing the surface-to-volume ra-
2. Neutron High Energy. The most effective form
of ﬁssion is produced by thermal neutrons. How-
ever, the neutrons ejected after ﬁssion are highly
energetic, with a kinetic energy on the order of 2
What we need is to slow down these neutrons so
they can become thermal neutrons (on the order
of 0.04 eV).
The solution comes from mixing the effective
agent with another substance, called moderator
•slow down neutrons via elastic collisions.
•not remove neutrons from the core by ab-
In North America most nuclear reactor use water
3. Neutron Nonﬁssion Capture. When neutrons are
being slowed down, they can be captured by 238U
when their kinetic energy is in the 1-100 eV range.
This process, called resonance capture removes
neutrons from the chain reaction as well.