Properties of heavy nuclei

In the context of fission reactors, the properties of nuclei heavier than Thorium are of paramount importance. In particular one distinguishes between fissile and fertile nuclei. This distinction is based on the response of these nuclei to the capture of a slow neutron: while fissile nuclei have a high probability of fissioning after such a capture, as shown on figure 3.1,

  

Figure 3.1: Fission cross section of fissile nuclei

fertile nuclei have not, although they have significant fission cross sections for neutrons with energy in the MeV range, as shown on figure 3.2.

  

Figure 3.2: Fission cross-sections of fertile nuclei

Neutron capture by fertile nuclei leads to the production of a fissile species, usually following beta decay. The best kown examples of fissile nuclei are ²³³U,²³⁵U and ²³⁹Pu. Typical fissile nuclei production processes from neutron capture by fertile species are:

$$^{232}Th+n\rightarrow^{233}Th\underset{22.3\min}{\overset{\be... ...Pa\underset{26.97d}{\overset{\beta_{-}}{\rightarrow} } ^{233}U$$ (4.4)

$$^{238}U+n\rightarrow^{239}U\underset{23.45\min}{\overset{\bet... ...Np\underset{2.35d}{\overset{\beta_{-}}{\rightarrow} } ^{239}Pu$$ (4.5)

Figure 3.3

  

Figure 3.3: Capture cross-sections of ²³²Th and ²³⁸U.

shows that the capture cross-sections , above the resonance region, decrease sharply with energy.

As a rule heavy nuclei with an even number of neutrons are fertile while those with an odd number of neutrons are fissile. This is the result of the even odd effect on neutron binding energies as well as of the fact that fission barriers'heights lie between odd and even neutron binding energies.

Aside from fission and capture cross-sections, the values of $\eta$ are very important in order to assess the potentialities of the nuclei to sustain a chain reaction. Variations of $\eta$ with neutron energy are shown for some nuclei in Figure 3.4.

  

Figure: Energy dependance of $\eta$ for the principal fissile nuclei

The figure shows that ²³³U has a particularly high value of $\eta$ at low neutron energy, while, at high energies, ²³⁹Pu takes the lead. Indeed, only ²³³U has allowed breeding in a thermal neutron reactor, the Molten Salt Reactor Experiment at ORNL[31]. Here the breeding rate was barely 5% per year and was only obtained with an on line extraction of the neutron capturing ²³³Pa. Breeding is obtained much more readily with fast neutron reactors using ²³⁹Pu as fuel, a rate of 18% per year having been reached with Superphenix.