Units of Reactivity
Mathematically, reactivity is a dimensionless number, but it can be expressed by various units. The most common units for research reactors are units normalized to the delayed neutron fraction (e.g. cents and dollars), because they exactly express a departure from prompt criticality conditions.
The most common units for power reactors are units of pcm or %ΔK/K. The reason is simple. Units of dollars are difficult to use, because the normalization factor, the effective delayed neutron fraction, significantly changes with the fuel burnup. In LWRs the delayed neutron fraction decreases with fuel burnup (e.g. from βeff = 0.007 at the beginning of the cycle up to βeff = 0.005 at the end of the cycle). This is due to isotopic changes in the fuel. It is simple, fresh uranium fuel contains only 235U as the fissile material, meanwhile during fuel burnup the importance of fission of 239Pu increases (in some cases up to 50%). Since 239Pu produces significantly less delayed neutrons (0.0021 for thermal fission), the resultant core delayed neutron fraction of a multiplying system decreases (it is the weighted average of the constituent delayed neutron fractions).
βcore= ∑ Pi.βi
The unit of reactivity in percents of the effective multiplication factor. For example, the subcriticality of keff = 0,98 is equal to -2% in units of %ΔK/K. Since this is very large amount of reactivity, these units are usually used to express significant quantities of reactivity like power defects, xenon worth, integral worth of control rods or shutdown margin. For operational changes that affect the effective multiplication factor this unit is inappropriate, because these changes are of the lower order.
keff = 0.99 ρ = (keff – 1) / keff = -0.01 ρ = -0.01 * 100% = -1 %