## Effective Delayed Neutron Fraction – β_{eff}

The delayed neutron fraction, **β**, is the fraction of delayed neutrons in the core **at creation at high energies**. But in the case of thermal reactors, the fission can be initiated **mainly by a thermal neutron**. Thermal neutrons are of practical interest in the study of thermal reactor behavior. **The effectively delayed neutron fraction** usually referred to as **β _{eff}**, is the same fraction at thermal energies.

The effectively delayed neutron fraction **reflects the ability of the reactor** to **thermalize** and **utilize** each neutron produced. The **β** is not the same as the **β _{eff}** due to the fact

**delayed neutrons do not have the same properties as prompt neutrons**released directly from fission. In general, delayed neutrons have

**lower energies**than prompt neutrons.

**Prompt neutrons**have initial energy between

**1 MeV and 10 MeV**, with an average energy of

**2 MeV**.

**Delayed neutrons**have initial energy between

**0.3 and 0.9 MeV**with an average energy of

**0.4 MeV**.

Therefore, in thermal reactors, a delayed neutron **traverses a smaller energy range** to become thermal. It is also **less likely to be lost** by leakage or parasitic absorption than the 2 MeV prompt neutron. On the other hand, **delayed neutrons** are also **less likely to cause fast fission** because their average energy is less than the minimum required for fast fission to occur.

These two effects (**lower fast fission factor** and **higher fast non-leakage probability for delayed neutrons**) tend to counteract each other and form **the importance factor (I)**. The importance factor relates the average delayed neutron fraction to the effectively delayed neutron fraction. As a result, the effectively delayed neutron fraction is the product of the average delayed neutron fraction and the importance factor.

**β _{eff} = β . I**

The delayed and prompt neutrons have a difference in their effectiveness in producing a subsequent fission event. Since the energy distribution of the delayed neutrons also differs from group to group, the different groups of delayed neutrons will also have different effects. Moreover, a nuclear reactor contains a mixture of fissionable isotopes. Therefore, the important factor is insufficient in some cases, and an important function must be defined.

**For example:**

**In a small thermal reactor with highly enriched fuel**, the increase in fast non-leakage probability will dominate the decrease in the fast fission factor, and **the important factor will be greater than one**.

**In a large thermal reactor with low enriched fuel**, the decrease in the fast fission factor will dominate the increase in the fast non-leakage probability, and **the important factor will be less than one (about 0.97 for a commercial PWR)**.

**In large fast reactors**, the decrease in the fast fission factor will also dominate the increase in the fast non-leakage probability, and the **β _{eff}** is less than β by about 10%.

Table of main kinetic parameters.

## Interactive chart – Infinite Multiplying System Without Source and Delayed Neutrons

Press the “**clear and run**” button and try to increase the power of the reactor.

Compare the response of the reactor with the case of Infinite Multiplying System Without Source and without Delayed Neutrons (or set the β = 0).