## Delayed Neutrons Fraction

**The total yield of delayed neutrons per fission**, v_{d}, depends on:

**An isotope that is fissioned**(see table).

**The energy of a neutron induces fission**(see chart).

**delayed neutron fraction (DNF)**. At the steady-state condition of criticality, with k

_{eff}= 1,

**the delayed neutron fraction is equal to the precursor yield fraction (β)**.where

**β**is defined as the fraction of the neutrons which appear as

_{i}**delayed neutrons in the i**. In contrast to the prompt neutrons emitted with a continuous energy spectrum, the delayed neutrons in each group appear with a more or less well-defined energy.

*th*group**In general, the delayed neutrons are emitted with much less energy than the most prompt neutrons.**The distinction between these two parameters is obvious. The delayed neutron fraction is dependent on the certain reactivity of the multiplying system. On the other hand,

**β**is not dependent on reactivity. These two factors,

**DNF and β,**are not the same things in case of a rapid change in the number of neutrons in the reactor.

In LWRs, the delayed neutron fraction **decreases with fuel burnup**. This is due to isotopic changes in the fuel. It is simple. Fresh uranium fuel contains only ^{235}U as the fissile material. Meanwhile, during fuel burnup, the importance of fission of ^{239}Pu increases (in some cases up to 50%). Since ^{239}Pu produces significantly **less delayed neutrons**, the resultant **core delayed neutron fraction** of a multiplying system **decreases** (the weighted average of the constituent delayed neutron fractions). This is also the reason why the neutron spectrum in the core **becomes harder with fuel burnup**.

**β _{core}= ∑ P_{i}.β_{i}**

where P_{i} is fraction of power generated by isotope i.

**Example:**Let say the reactor is at the beginning of the cycle and approximately

**98%**of reactor power is generated by

^{235}U fission and

**2%**by

^{238}U fission as a result of fast fission. Calculate the core delayed neutron fraction.

β_{core}= ∑ P_{i}.β_{i} = 0.98 x β_{235} + 0.02 x β_{238}

= 0.98 x 0.0065 + 0.02 x 0.0157

= 0.0064 + 0.0003

= 0.0067