ABSTRACT
Both of the MC codes mentioned above, MCNPX and Geant4, propose different physical models for the simulation of interactions between charged particles or neutrons and materials at the energies typically used for NP activation (around a few tens of MeV for ions and around 10-9 to 10 MeV for neutrons). Interestingly, the models that provide optimal accuracy are the same in both codes; therefore, they will be discussed together. 14.3.2.1 Ion physicsAs explained in Chapters 11 and 12, protons and deuterons are the ions of choice for the activation of NPs. The nuclear interactions of these particles can be described in different phases. In a first phase, termed the intranuclear cascade, the incident particle interacts with individual nucleons, which are considered to be a cold free gas confined within an electric potential that describes the nuclear density as a function of the radius. The subsequent de-excitation of the residual nucleus can be described using a multistage, multistep, pre-equilibrium model in which the excited nucleus may emit a neutron, proton, deuteron, triton, 3He, or alpha particle at each stage or may evolve towards equilibrium by increasing the exciton number through the formation of one particle-hole pair. After this step, an evaporation model, or Fermi breakup model if the number of nucleons is below 15-20, is applied to the residual nucleus with the remaining excitation energy. Finally, the extra energy of the nucleus is released by the emission of a set of gamma rays.MCNPX and Geant4 offer several models to simulate these processes, which are based on theoretical calculations together with parameterisations of available experimental data. Unfortunately, these models have suboptimal accuracy at low energies (a few tens of MeV) of the incident particle. Within this energetic range, the optimal models are those based on the use of evaluated databases. Each of these databases includes a large set of experi-mental data for incident particle energies up to 150-200 MeV; experimental data are completed using theoretical calculations performed with dedicated codes such as TALYS [10] or EMPIRE [11]. Before being included in the database, the data are reviewed and validated by a committee of experts in order to achieve a complete and coherent dataset for each isotope. The information contained in the databases includes cross-section values for the interaction
of ions with a large set of isotopes and the energy and angle distributions of the emitted secondary particles. The available databases can be grouped into two different
categories. The first includes the so-called “activation databases”, the most exhaustive ones being the EAF (European Activation File) for neutrons, protons, and deuterons and the PADF (Proton Activation Data File) for protons. These databases contain cross-section values of the most relevant reaction channels for all stable isotopes producing stable or metastable isotopes, but contain no information about the emitted particles. The second set of databases, which may be considered general databases, such as ENDF-proton, ENDF-deuteron, or TENDL, only contain information on stable isotopes and include a smaller set of isotopes (except TENDL, which contains all stable isotopes and a few metastable ones). These databases do not provide channel-by-channel information; instead, they contain data about total cross-section values and production yields of secondary particles. For example, the cross-section values for the nuclear reactions 56Fe (p,np)55Fe and 56Fe(p,d)55Fe are not collated individually (as in the activation databases); only the 56Fe(p,X) cross-section values and the average number of neutrons, protons, and deuterons produced are included. Of note, the advantage of general databases is that they also contain double differential cross sections of the secondary particles (cross sections as a function of the energy of the secondary particles and the angle between the primary and secondary particles).It is worth mentioning that the cross sections provided by different databases are different, and these differences can even be found when comparing different versions of the same database. The reason for this is because: (i) they are based on different experimental data, which in some cases may differ substantially, and (ii) they use different theoretical models to complete absent experimental data. Despite the differences between the data provided by two databases being small in most cases (less than a few per cent), such differences can be significant in some situations. It is therefore recommended to test different databases and compare the results. A useful tool to compare cross-section values from different databases is JANIS [12], provided by the Nuclear Energy Agency (NEA) of the Organisation for Economic Co-operation and Development (OECD). A comparison of the experimental data
and the TENDL 2009 database for the cross-section values corresponding to the nuclear reaction 48Ti(p,n)48V using JANIS is shown in Fig. 14.1. It can be seen that the differences between the different sets of experimental data and between experimental data and the TENDL database are not negligible.
