Delayed neutrons are associated with the beta decay of fission fragments. Indeed, after prompt fission neutron emission the residual fragments are still neutron rich. They undergo a beta decay chain. The more neutron rich

the fragment, the more energetic and faster the beta decay. In some cases the available energy in the beta decay is high enough to leave the residual nucleus in such a highly excited state that neutron emission instead of gamma emission occurs. This process is illustrated in figure 3.5.

The eventually emitted neutron is said to be delayed (with respect to the fission). The delay is determined by the beta decay time constant. Delays vary between fractions of a second and several tens of seconds. Probabilities for delayed neutron emission are of the order of or less than 1% per fission, or per prompt fission neutron.

Beta-delayed neutron emission is highest when the emitted neutron binding energy is small. This is true when the neutron emitter has an odd number of neutrons just above a neutron shell closure. In particular beta decaying nuclei with neutron numbers equal to 52 (N = 50 closed shell) and 84 (N = 82 closed shell) are good delayed neutron emitter precursors. Examples are 87Br and 137I.

Beta-delayed neutrons are characterized by their yields flb relative to the total neutron number per fission, and their decay constants rt. The total number of delayed neutrons yield per fission is fl = 22 fli. One may, also, define a mean decay time Td = fliTi)/fl. Thus, in first approximation,

the time which determines the time constant of the reactor is rnf(1 — fl) + flTd rather than rnf. Table 3.6 shows the values of fl, Td and rd = flTd for a number of nuclei. The data are for fast neutron fission. We have also given the values of N/A for these nuclear species, since the more neutron rich fissioning nuclei generally lead to higher values of fl, but often to smaller values of Td.

From table 3.6 and using equation (3.101), we see that the doubling time will range between 0.1 s and 1 s. The smaller the value of rd, the more difficult

will reactor control be. In particular reactors fuelled exclusively with minor actinides would have low values of rd.

Because of the important influence of the delayed neutron fraction ft on reactor safety it is customary to express reactivity in $ units: a positive reactivity of 1 $ is a reactivity equal to ft, corresponding to a multiplication coefficient keff ~ 1 + ft. Of course reactivities can also be expressed in fractions of unity.

The importance of the delayed neutrons in reactor safety can be seen better examining a modified neutron kinetic equation that includes the effect of delayed neutrons.