498
J. Apostolakis
Inelastic interactions, which excite the nucleus, typically become relevant at
energies of order MeV. They are modeled with a statistical approach for energies
up to about 100 MeV. The original Weisskopf evaporation model [63] describes the
emission of protons and neutrons from nuclei in thermodynamic equilibrium. It is
supplemented by several additional de-excitation channels, which compete to occur.
These include the multi-fragmentation model for highly excited nuclei [64], Fermi
breakup of light nuclei, fission of heavy nuclei and photon evaporation.
In an alternative approach, following the Generalised Evaporation Model (GEM)
of Furihata [65], nuclei with up to 28 nucleons are evaporated directly. This
improves greatly the description of the emission of light and medium fragments,
with an extra computational cost. GEM is an option in MCPNX, in GEANT4 and
a similar approach is used in FLUKA. Fragments heavier than 4 He, though emitted
infrequently, are important for specific applications, such as the response of silicon
devices and damage to them; using the GEM approach is recommended for these.
At energies up to about 300 MeV a simple algorithm can be used to count
the number of excited nucleons and holes of missing nucleons in the Cascade
Exciton Model (CEM) model [66]. Such models are called pre-compound (or
pre-equilibrium) models. A pre-compound model of this type is implemented in
GEANT4. And CEM.03 [67], which is included in MARS, MCNPX and MCNP 6,
is an improved CEM descendant.
These models are also used to calculate the de-excitation of nuclei after
interactions at the higher energies, important in many applications. For example,
they determine the energy that is lost to nuclear breakup, and the partitioning of
energy between the low-energy protons, neutrons and gammas that are produced.
These processes produce the majority of neutrons, whatever the initial interaction,
and as a result affect substantially the escaping energy, lateral shower profiles and
compensation of calorimeters—amongst other observables.
11.3.8 Cascade Models of Hadron–Nucleus Interactions
at Intermediate Energy
At energies above about 100 MeV an intranuclear cascade model is used for nucleon
and pion projectiles. In a cascade the interaction is modeled as a succession of
independent collisions of the projectile (and secondaries) with individual nucleons
inside the target nucleus [68].
In a cascade, the nucleus is described in two ways. It can be an ensemble
of nucleons positioned at random locations, sampled from a model of nuclear
density—as used Quantum Molecular Dynamics (QMD) models such as UrQMD
[69], in the GEANT4 Binary cascade model [70] and in the Liege cascade INCL.
Else, the nucleus can be composed of a number of shells of constant density, as in
the original cascade of Bertini, in FLUKA, and in INUCL and its descendant, the
J. Apostolakis
Inelastic interactions, which excite the nucleus, typically become relevant at
energies of order MeV. They are modeled with a statistical approach for energies
up to about 100 MeV. The original Weisskopf evaporation model [63] describes the
emission of protons and neutrons from nuclei in thermodynamic equilibrium. It is
supplemented by several additional de-excitation channels, which compete to occur.
These include the multi-fragmentation model for highly excited nuclei [64], Fermi
breakup of light nuclei, fission of heavy nuclei and photon evaporation.
In an alternative approach, following the Generalised Evaporation Model (GEM)
of Furihata [65], nuclei with up to 28 nucleons are evaporated directly. This
improves greatly the description of the emission of light and medium fragments,
with an extra computational cost. GEM is an option in MCPNX, in GEANT4 and
a similar approach is used in FLUKA. Fragments heavier than 4 He, though emitted
infrequently, are important for specific applications, such as the response of silicon
devices and damage to them; using the GEM approach is recommended for these.
At energies up to about 300 MeV a simple algorithm can be used to count
the number of excited nucleons and holes of missing nucleons in the Cascade
Exciton Model (CEM) model [66]. Such models are called pre-compound (or
pre-equilibrium) models. A pre-compound model of this type is implemented in
GEANT4. And CEM.03 [67], which is included in MARS, MCNPX and MCNP 6,
is an improved CEM descendant.
These models are also used to calculate the de-excitation of nuclei after
interactions at the higher energies, important in many applications. For example,
they determine the energy that is lost to nuclear breakup, and the partitioning of
energy between the low-energy protons, neutrons and gammas that are produced.
These processes produce the majority of neutrons, whatever the initial interaction,
and as a result affect substantially the escaping energy, lateral shower profiles and
compensation of calorimeters—amongst other observables.
11.3.8 Cascade Models of Hadron–Nucleus Interactions
at Intermediate Energy
At energies above about 100 MeV an intranuclear cascade model is used for nucleon
and pion projectiles. In a cascade the interaction is modeled as a succession of
independent collisions of the projectile (and secondaries) with individual nucleons
inside the target nucleus [68].
In a cascade, the nucleus is described in two ways. It can be an ensemble
of nucleons positioned at random locations, sampled from a model of nuclear
density—as used Quantum Molecular Dynamics (QMD) models such as UrQMD
[69], in the GEANT4 Binary cascade model [70] and in the Liege cascade INCL.
Else, the nucleus can be composed of a number of shells of constant density, as in
the original cascade of Bertini, in FLUKA, and in INUCL and its descendant, the