502
J. Apostolakis
The detailed treatment of energy deposition in scintillators may also require a more
detailed treatment of neutrons than provided by the simpler interaction models.
Simulating neutrons below 20 MeV relies on measurements of cross-sections for
key processes, which have been assembled into established data libraries. Libraries,
such as JEFF [87], ENDF/B VII [88], ENDF/B VIII [89], JENDL [90] and CENDL
[91], include evaluations of cross sections and distributions of secondaries for key
reactions based on a combination of measurements and estimates from nuclear
model codes. They cover all measured interactions, from inelastic and capture at
low energies; through inelastic interactions resulting in the emission of one or two
neutrons (plus gammas); to multi-neutron production at tens of MeV. For some
elements, data is available for several individual isotopes, while for others only
the values for the natural composition are measured. Cross sections have many
resonances in the keV–MeV region, complicating precise treatment.
For reactions that result in more than two outgoing particles, in most cases only
spectra are available; i.e. information on the correlations of products is not included.
As a result, sampling secondaries for one interaction in a way that conserves energy
and momentum requires complex algorithms and additional computation. This has
recently been introduced in PHITS; other codes rely on uncorrelated sampling and
conserve energy only on average.
This detailed treatment consumes significant CPU and memory, because the full
set of cross sections for all isotopes of all elements is required. Variants of this
approach are utilised in MCNP/MCNPX (the gold standard for neutron simulation)
and in the GEANT4’s NeutronHP package.
A simpler approach averages cross sections over chosen sets of nuclei and
fixed bins of energy. This ‘multi-group’ approach provides savings in memory use
compared with the detailed approach and is adopted in FLUKA, as the option for
precise treatment of low-energy neutrons. Accuracy is determined by the number of
sets of nuclei and of the intervals of energy—and also the choice of the grouping.
In addition to the purely electromagnetic interactions of charged particles, and
the interactions of hadrons with matter, it is necessary also to simulate the interaction
of electrons, positrons and gammas with nuclei which result in hadronic final states.
These photo-nuclear and electro-nuclear interactions account for a small portion
of the total cross-section of gammas or electrons, below one percent at its peak. Yet
they are the only interactions that convert electromagnetic energy into hadronic final
states in typical HEP experiments.
Models for photo-nuclear and electro-nuclear interactions are provided in all
multi-particle codes discussed [92].
Given the diversity of hadronic interactions, there is a need to focus on
essential aspects. What most influences the accuracy of the description of the
energy response, energy resolution of calorimeters and missing energy for hadronic
calorimeters?
For HEP applications (in particular calorimeters) some of the key features are:
• most energy is deposited by low-energy particles, and its spectrum is independent
of the type of projectile particle [93];
J. Apostolakis
The detailed treatment of energy deposition in scintillators may also require a more
detailed treatment of neutrons than provided by the simpler interaction models.
Simulating neutrons below 20 MeV relies on measurements of cross-sections for
key processes, which have been assembled into established data libraries. Libraries,
such as JEFF [87], ENDF/B VII [88], ENDF/B VIII [89], JENDL [90] and CENDL
[91], include evaluations of cross sections and distributions of secondaries for key
reactions based on a combination of measurements and estimates from nuclear
model codes. They cover all measured interactions, from inelastic and capture at
low energies; through inelastic interactions resulting in the emission of one or two
neutrons (plus gammas); to multi-neutron production at tens of MeV. For some
elements, data is available for several individual isotopes, while for others only
the values for the natural composition are measured. Cross sections have many
resonances in the keV–MeV region, complicating precise treatment.
For reactions that result in more than two outgoing particles, in most cases only
spectra are available; i.e. information on the correlations of products is not included.
As a result, sampling secondaries for one interaction in a way that conserves energy
and momentum requires complex algorithms and additional computation. This has
recently been introduced in PHITS; other codes rely on uncorrelated sampling and
conserve energy only on average.
This detailed treatment consumes significant CPU and memory, because the full
set of cross sections for all isotopes of all elements is required. Variants of this
approach are utilised in MCNP/MCNPX (the gold standard for neutron simulation)
and in the GEANT4’s NeutronHP package.
A simpler approach averages cross sections over chosen sets of nuclei and
fixed bins of energy. This ‘multi-group’ approach provides savings in memory use
compared with the detailed approach and is adopted in FLUKA, as the option for
precise treatment of low-energy neutrons. Accuracy is determined by the number of
sets of nuclei and of the intervals of energy—and also the choice of the grouping.
In addition to the purely electromagnetic interactions of charged particles, and
the interactions of hadrons with matter, it is necessary also to simulate the interaction
of electrons, positrons and gammas with nuclei which result in hadronic final states.
These photo-nuclear and electro-nuclear interactions account for a small portion
of the total cross-section of gammas or electrons, below one percent at its peak. Yet
they are the only interactions that convert electromagnetic energy into hadronic final
states in typical HEP experiments.
Models for photo-nuclear and electro-nuclear interactions are provided in all
multi-particle codes discussed [92].
Given the diversity of hadronic interactions, there is a need to focus on
essential aspects. What most influences the accuracy of the description of the
energy response, energy resolution of calorimeters and missing energy for hadronic
calorimeters?
For HEP applications (in particular calorimeters) some of the key features are:
• most energy is deposited by low-energy particles, and its spectrum is independent
of the type of projectile particle [93];