TO: Clifford K. Beck
FROM: A. C. Menius, Jr. and R. L. Murray
SUBJECT: Reactor Period vs. Reactivity

The relation between excess reactivity and period (e-folding time) is
given by the inhour equation
where [tau]p is the average time between fissions due to prompt neutrons, [tau] is the
period of the reactor, [gamma]f is the effective fraction of neutron delayed, qi is the
fraction of the delayed neutrons with period [tau]i (mean life).

The half-lives and yields for delayed neutrons in each group are
available.^a1 Experiments at Los Alamos with the "water-boiler" (hypo) have shown
that [gamma]f = 0.0086 and [tau]p = 135 x 10-6 seconds. Theoretically [tau]p = 1/V[sigma]a, thus,
considering only fissionable material we have the ratio of the N. C. State Reac
tor prompt period to Los Alamos given by
[tau]p = [tau]p1 = 135 x 10-6 seconds.

We have, then, for the inhour equation

A plot of this is attached to the original report. With an excess
reactivity at 20°C of 0.0157, which is the calculated value for the N. C. State
Reactor, a minimum period of about 0.02 seconds is obtained. This value should
be used in the design of the ceontraol amplifiers.

cc: Members of the Reactor Committee

^a1Hughes, Dobbs, Cohn and Hall, Physical Review, 73, 111 (1948).