Reactivity

If there are N_o neutrons in the preceding generation, then there are N_o(k_eff) neutrons in the present generation. The numerical change in neutron population is (N_ok_eff - N_o). The gain or loss in neutron population (N_ok_eff - N_o), expressed as a fraction of the present generation (N_ok_eff), is shown below.

This relationship represents the fractional change in neutron population per generation and is referred to as reactivity (ρ). Cancelling out the term N_o from the numerator and denominator, the reactivity is determined as shown in the equation below.

(1-1)

From Equation (1-1) it may be seen that ρ may be positive, zero, or negative, depending upon the value of k_eff. The larger the absolute value of reactivity in the reactor core, the further the reactor is from criticality. It may be convenient to think of reactivity as a measure of a reactor's departure from criticality.