A **nuclear fission** reaction is the splitting of an atom when bumbarded with neutrons (following absoprtion). The fission can occur from a fast or thermal (slow) neutron and
can also occur spontaneously (particularly in very heavy elements). The atom splits into two smaller atoms called **fission fragments** and ejects neutrons which can
cause subsequent fissions. This is called a **chain reaction**.

A **fissile** nuclide can fission from a neutron of any energy. A **Fissionable** nuclide can fission but only from neutrons which sufficient energy above a threshold.
Examples are given below. Notice that fissile nuclides are generally have an odd value of atomic mass because the binding energy is larger for pairs of nucleons. A **fertile**
nuclide can be converted to a **fissile** material through nuclear reactions/decay. This process is referred to as **breeding**.

Fissile | \(^{235}U, \; ^{233}U, \; ^{239}Pu, \; ^{241}Pu\) |

Fissionable | \(^{238}U, \; ^{240}Pu\) |

Fertile | \(^{232}Th, \; ^{234}U, \; ^{238}U\) |

On average, 2-3 neutrons are released form fission. This quantity is denoted \(\nu \) and depends on the fissioning nuclide and incoming neutron energy. When a neutron is absorbed, it is either captured,
followed by decay, or causes fissioning. The **capture-to-fission ratio** is given by \( \alpha = \frac{\sigma_\gamma}{\sigma_a} \) where \(\sigma_i \) is a cross section representing
the probability of the different interactions. The **reproduction factor** is the number of neutrons emitted per absorption and is given by \( \eta = \frac{\nu}{1+\alpha} \).

Nuclear fission reactions are **critical** when one nuetron produced from fission goes on to induce another fission. This reaction is stable. The **criticality**
is a measure of how close the reactor is to a self-sustaining, critical reaction. It is given by:

\(k_{eff} = \frac{\text{rate of neutron production}}{\text{rate of neutron loss by absorption and leakage}}\)

A reactor can be **critical**, **subcritical** (eventually shuts down) or **supercritical** (rate of power increases drastically).
The **Reactivity** is closely related to criticality and is defined as:

\(\rho = 1-\frac{1}{k_{eff}}\)

The units of reactivity are \([mk]\) or one part in one thousand. Although small, nuclear reactions occur very quickly, thus dangerous power levels can occur for small supercritical reactivities.

Subcritical | \(k_{eff} < 1\) | \(\rho < 0\) |

Critical | \(k_{eff} = 1\) | \(\rho = 0\) |

Supercritical | \(k_{eff} > 1\) | \(\rho > 0\) |

A reactor is operating at \(k_{eff} = 0.99965\). What is the reactivity? Is the reaction critical?

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