There is nothing magical about the usual six groups of delayed neutrons, other than the fact that the decay characteristics of a shut-down infinite system can be represented adequately by six exponentials and six yields. These do not vary greatly for thermal or fast fission except in the final value of /9.

There has been some attempt to identify the groups with some predo­minant fission product but after 87Br that corresponds to the first group, there has been no success.

Notice the mathematical progression in anyway. (See Table 1.2.) The progression of Я; values (each approximately e times the previous one) arises from a mathematical matching or peeling of the decay curve rather than from actual fission product decay times.

In some problems where the number of equations makes the problem computationally large, say on an analog computer, or where the effect of delayed neutrons is small, then it is usual to take less than six groups.

A smaller number of groups can be arranged to represent the average behavior very well:

No groups (N — 0). One simply modifies the neutron lifetime in equation 1.10 so that

/ = і* + і Wd

t-i

The equation then gives the correct stable period for small reactivity changes. One group (N — 1). Define Д and A so that:

д = І A, m = iwd (i. i7)

1-І t-1

The equation now satifies the high and low frequency response gain and phase (Fig. 1.4). See also Section 1.5.3 for a frequency response discussion.

Two groups (N = 2). The smallest number of groups with which one can represent delayed neutron behavior adequately is two.

The relevant data can be obtained by matching particular transients, from the in-hour equation, or by matching the transfer function in more detail than for a single group. These methods are all discriminatory in that they relate best to particular transients, to steady periods, or to certain frequency disturbances, respectively. However they all give very adequate results.

Table 1.3 shows figures derived from a transfer function match for a plutonium-fueled reactor. The method is general and can be applied to any reactor system.

Figure 1.5 shows the same transient, a $ 0.5 reactivity decrease as a step, represented by Eqs. (1.10), using different numbers of delayed neutron groups. It can be seen that while the modified effective neutron lifetime model at least gives the correct trend, the two-group representation is very adequate for transient calculations.