How is the steady-state loss of reactivity due to Xe poisoning calculated for a high-power reactor?

The correct approach to calculate the steady-state loss of reactivity due to fission products such as xenon-135 (Xe) in a high-power reactor involves understanding the balance between production and absorption in the reactor core.

The formula used for this calculation includes several important parameters:

1. σX: This represents the microscopic absorption cross-section for xenon-135. It quantifies how effectively xenon-135 captures neutrons, which significantly contributes to the reactivity loss in the reactor.

2. ν: This is the average number of neutrons produced per fission event. It is crucial because it indicates how many neutrons are available to sustain the fission chain reaction.

3. Σ_f: This is the macroscopic fission cross-section, representing the probability of fission occurring in the reactor per unit volume.

The equation ρ = - (σX)/(ν Σ_f) indicates that the loss of reactivity (ρ) due to xenon poisoning is directly related to the absorption characteristics of xenon-135 compared to the neutron economy of the reactor. As xenon absorbs neutrons more efficiently, the reactivity decreases, resulting in a negative value for ρ.

This calculation is essential for