The Physics of Spallation Processes

4.3. MODELING OF TRANSPORT PROCESSES 39in Fig. 4.1 can be viewed as a convolution of two types of cascades, such that particlesreleased in a primary intra-nuclear cascade (INC) [Ser47] give rise to an inter-nuclearcascade of secondary and higher-order reactions in the surrounding target material.INC versions currently on the market model the multi-body problem numerically[Ber63, Cug87, Cug97a, Cug97b, Gol88, Yar81, Pra88b, Pra89, Pra97] using Monte-Carlotechniques. They all use the following simplifying assumptions:The hadron-nucleus interaction is a sequence of independent collisions of primaryand secondary particles with the nucleons of the nucleus.Cascade particles follow classical trajectories and do not interact with each other.The interaction is based on free elementary cross sections. In-medium effects aregenerally not taken into account. These cross sections have been derived fromempirical approximations ofπN → πN (elastic)NN → NN (elastic)NN → N ∗ N → NπNNN → N ∗ N ∗ → NπNππN → πN ∗ → πNπN ∗ N → NN (delta absorption)πN → πN (charge exchange)data; Pauli blocking 1 , the Fermi motion of the target and projectile nuclei 2 , pionproduction, and the effects of the target mean field are included.The nucleus is viewed as degenerate Fermi gas of neutrons and protons.The assumptions for which the fundamental presumptions (within the INC) are valid are:1. the De-Broglie-wavelength λ of cascade particles is smaller than the average distanceof nucleons in the nucleus (δ ≈ 1.3fm) and the mean free path length L in nuclearmatter: λ ≪ δ, λ ≪ L. For high energies this presumption is certainly valid andthe interacting nucleons do not “see” the nucleus as whole but as an assembly ofindividual nucleons bound together by their mean field.1 In Bertini and ISABEL models, the nucleus is a continous medium in which the incident particlecollides according to its mean free path with a nucleon. This nucleon is than set into motion and canundergo further collisions. In the INCL2.0 code, all the nucleons are moving according to an initial Fermidistribution and collide as soon as they reach their minimum distance of approach or are reflected on thewall of the nuclear potential. The cascade propagation is followed as a function of time in the INCL2.0and ISABEL, but not in the Bertini model, as will be discussed in sect. 4.4.3.2 In the Bertini model, all collisions leading to a particle momentum below the Fermi level are forbidden,irrespective of the progressive depletion of the Fermi sea during the process. In the INCL2.0 and ISABELmodels, attempt is made to take into account the real occupation rate. In the INCL2.0 model, forinstance, this is done statistically by allowing the collisions of two nucleons with a probability equal tothe occupation rate in a small phase space volume around the nucleons.