**neutron-induced fission reaction**is the reaction, in which the incident neutron enters the heavy target nucleus (fissionable nucleus), forming a compound nucleus that is excited to such a

**high energy level (E**that the

_{excitation}> E_{critical})**nucleus splits**into two large fission fragments. A large amount of energy is released in the form ofradiation and fragment kinetic energy. Moreover and what is for this chapter crucial, the fission process may produce

**2, 3 or more free neutrons**that are capable of inducing

**further fissions**and so on. This sequence of fission events is known as the

**fission chain reaction**and it is of importance in nuclear reactor physics.

The **nuclear chain reaction** occurs when one singlenuclear reaction causes an average of one or more subsequent nuclear reactions.

**The chain reaction** can take place only in the **proper** **multiplication environment** and only under **proper conditions**. It is obvious, if one neutron causes two further fissions, the number of neutrons in the multiplication system will increase in time and the reactor power (reaction rate) will also increase in time. In order to stabilize such multiplication environment, it is necessary to increase the non-fission neutron absorption in the system (e.g. to **insert control rods**). Moreover, this multiplication environment (the nuclear reactor) behaves like the exponential system, that means the power increase is not linear, but it is **exponential**.

On the other hand, if one neutron causes** less than one** further fission, the number of neutrons in the multiplication system will decrease in time and the reactor power (reaction rate) will also decrease in time. In order to **sustain the chain reaction**, it is necessary to decrease the non-fission neutron absorption in the system (e.g. to **withdraw control rods**).

In fact, there is always a** competition** for the fission neutrons in the multiplication environment, some neutrons will cause further **fission reaction**, some will be **captured** by fuel materials or non-fuel materials and some will** leak out** of the system.

In order to describe the multiplication system, it is necessary to define the **infinite and finite multiplication factor** of a reactor. The method of calculations of multiplication factors has been developed **in the early years** of nuclear energy and is only applicable to **thermal reactors**, where the bulk of fission reactions occurs at thermal energies. This method well puts into the context all the processes, that are associated with the thermal reactors (e.g. the neutron thermalisation, the neutron diffusion or the fast fission), because the most important neutron-physical processes occur in energy **regions that can be clearly separated from each other**. In short, the calculation of multiplication factor gives a good insight in the processes that occur in each thermal multiplying system.