The possibility of transmuting and incinerating nuclei depends on the neutron cost of these reactions. The simplest case is that of fission products.

Fission product transmutation

The transmutation of fission products requires, obviously, at least one neutron per nucleus. The production rate of the most important LLFPs, 99Tc and 129I, are given in table 3.8. From this table it appears that at least 0.07 neutron per fission would be required to achieve transmutation of these two nuclei. Ideally the most efficient way to transmute fission products is to use neutrons which

would be lost to captures in the structural elements or which would escape the reactor. This is why it has been proposed to capture neutrons in the resonances of fission fragments, whenever these display strong resonances [57]. In this way, it is hoped that neutrons are captured by the fission products before they reach thermal energies where captures in structure materials are significant. We discuss these ideas in the case of a fast reactor using a lead reflector, such as was proposed by Rubbia et al. [76]. 99Tc is characterized by the existence of a strong resonance at ER = 5584meV, with Г = 149.2meV and a0 = 104 barns. We apply equation (3.64):

which we write, after numerical evaluation (o, = 10 barns for lead)

PSurv(x)=exp("- Е gg^’2 (P1 + x X 103 — 1^ (3.141)

where x is the concentration of 99Tc nuclei with respect to lead. We find that 90% of the neutrons are captured for a 99Tc concentration of 6 x 10-4. In the energy amplifier original design [76], about 6% of the neutrons were captured in the lead. About half of these are captured below 5 eV and could, thus, be captured in the diluted technetium. Since each fission produces 2.5 neutrons, it follows that 7.5 neutrons could be absorbed in technetium per 100 fissions. The volume of lead to consider is that where the neutron flux is high enough, rather than the full volume of the lead pool described in the energy amplifier proposal. The transport length in lead is around 1 m. It is found that the total weight of lead irradiated by a high neutron flux is around 600 tons. The amount of 99Tc which should be dissolved in order to capture 90% of the available neutrons would then be around 180 kg. The number of neutrons captured per year in the 99Tc would be

NTccap) = 8.4 x 1025 (3.142)

assuming a 10 MW beam and a value of ks = 0.98. These captures corre­spond to a transmuted mass of 14 kg. The half-life of the 99Tc in the neutron flux would be 7.5 years.

These data can be compared with those obtained with critical reactors. Calculations have been made both for fast and PWR reactors [66]. In the case of fast reactors the best results are obtained using moderated assemblies where 99Tc is mixed with a hydrogeneous material like CaH2. In the case of fast reactors, the shortest half-life is 15 years, while it is 21 years in the case of PWR. Thus, it appears that capture by adiabatic resonance crossing, like that discussed above, might be advantageous.

For transmutation, the most important parameter is the neutron flux, since the effective lifetime of a nucleus in a neutron flux is inversely
proportional to the flux value. As an example, a set of nuclei with a cross­section of 1 barn, typical of some fission products, needs 200 years in a 1014 neutron/cm2/s flux to be reduced by a factor of 2. Such numbers explain, partly, why projects such as that of Bowman et al. [2] aimed at a thermal neutron flux as high as 1016/cm2/s.