The time dependence of the extinction probability with delayed neutrons

The calculation of the time-dependent extinction probability (EP) in an infinite medium of fissile material is calculated including delayed neutrons. This extension of the model reveals some interesting consequences, one of which is the appearance of an initial plateau in the EP in the range 10−6 to 10−4 s which is significantly less than the final asymptotic plateau value reached as time tends to infinity; i.e. the steady state EP. This steady state is delayed by the presence of the delayed neutrons by a time of the order of 3/λ (∼36 s) where λ is the mean decay constant of the precursors. The presence of the initial plateau is due specifically to delayed neutrons and has not been commented on before. Several other situations are considered, with differing initial conditions, and are illustrated by numerical results.