Delayed neutrons

Delayed neutrons are associated with the beta decay of the fission products. 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 for leaving the residual nucleus in such a highly excited state that neutron emission instead of gamma emission occurs. This process is exemplified on figure 3.5.

  

Figure 3.5: Schematic illustration of the delayed neutron emission process. On the right the precursor nucleus(A,Z), in its ground state, beta decays to excited states of the possible neutron emitting nucleus(A,Z+1). The most excited levels of this nucleus may be above the neutron binding energy, and thus, emit neutrons, leaving a residual nucleus (A-1,Z+1)

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 seconds and several tens seconds. Probabilities for delayed neutron emission are of order or less than 1% per fission, or per prompt fission neutron.

Beta delayed neutron emission is enhanced when the emitted neutron binding energy is minimum. This is true when the neutron emitter has an odd neutron number, 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 very important delayed neutron emitters precursors. Examples are ⁸⁷Br and ¹³⁷I.

Beta delayed neutrons are characterized by their yields $\beta_{i}$, relative to the total neutron number per fission, and their decay constants $\tau_{i}.$ The total delayed neutrons yield per fission is $\beta=\sum\beta_{i}$. One may, also, define a mean decay time $\tau_{d}=\sum\beta_{i}\tau_{i}$. Thus the time which determines the time constant of the reactor is $\tau_{nf}+\tau_{d}$ rather than $\tau_{nf}.$ Table 3.3 shows the values of $\beta,\tau_{d}$ and $T_{d}=\tau_{d}/\beta$ 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 lead, generally, to higher values of $\beta,$but, often to smaller values of T_d.

c

	$\beta$	$T_{d}(\sec.)$	$\tau_{d}(\sec.)$	N/A
232Th	0.0203	6.98	0.141	0.612
233U	0.0026	12.40	0.032	0.605
235U	0.00640	8.82	0.056	0.608
238U	0.0148	5.32	0.079	0.613
239Pu	0.002	7.81	0.020	0.607
241Pu	0.0054	104.10	0.054	0.609
241Am	0.0013	10	0.013	0.606
243Am	0.0024	10	0.024	0.609
242Cm	0.0004	10	0.004	0.603

Table 3.3
properties of delayed neutrons

From the table, we see that the doubling time will range between 0.1 and 1 second. The smaller the value of $\tau_{d}$, the more difficult will be the reactor control. In particular reactors fueled exclusively with minor actinides would have low values of $\tau_{d}$.

Because of the important influence of the delayed neutrons fraction $\beta$ on the reactors' safety it is customary to express reacticity in $ units: a positive reactivity of 1 $ is a reactivity equal to $\beta$, corresponding to a multiplication coefficient $k_{eff}=1+\beta.$ Of course reactivities can, also, be expressed in fractions of unity.