If q is very large then a>0 is large and greater than the largest Thus:

Q = (/*со<Де<r) + £ Pi so "о = (б — P) keaH* (1.16)

І=1

Now the neutron lifetime is all important and the delayed neutrons have no effect beyond reducing the reactivity q by /3 to (q — /fJ).

1.2.1 Delayed Neutron Data

The decay constants of the delayed neutron groups do not differ markedly among fissionable isotopes, but the yields (l do (4). A comparison of /3 for different fuels is shown in the accompanying tabulation. Thus an

effective /3 must be calculated before reactor kinetics calculations can pro­ceed. The value of /3 depends not only on the fuel in the system but on a large number of other system variables:

(a) The isotopic concentrations in the system and the fission rate in each isotope affect /3. In a fast reactor 238U may have 15% of the fissions.

(b) Delayed neutrons are slower than prompt neutrons and thus their importance with respect to leakage and fission is different (5). Their slow­ness reduces the effective /3 value in the fast core.

(c) The geometry of the system and the blanket fission rate effect /3 (6). In a fast system 10% of the fissions can occur in the blanket.

(d) Neutron hold-up in a reflector is sometimes represented by another delayed neutron group, although it is better represented by a modified neutron lifetime. This effect is particularly important in heavy water thermal systems but does not apply in a fast reactor system.

(e) Variation with burn-up also changes the balance as far as /9 is con­cerned. The plutonium is enhanced; thus the effective /9 decreases in a thermal system that may start with /9 ~ 0.0075, but in fast cores where 239Pu gives way to 241Pu the effective /9 increases. A fast reactor typically has a /9 of about 0.0035.