- Multiple scattering
Special transport algorithm [1], based on Moli??re's theory of multiple
Coulomb scattering improved by Bethe [19,20,21], with account of several
correlations:
* between lateral and longitudinal displacement and the deflection angle
* between projected angles
* between projected step length and total deflection
Accurate treatment of boundaries and curved trajectories in magnetic fields
Automatic control of the step length
Path length correction
Spin-relativistic effects at the level of the second Born approximation
Nuclear size effects (scattering suppression) on option (simple nuclear
charge form factors are implemented, more sophisticated ones can be supplied
by the user).
Fano correction for heavy charged particle multiple scattering
- Single scattering: The algorithm is based on the Rutherford formula with a
screening factor in the form used by Moliere (for consistency with the
multiple scattering model used by FLUKA), integrated analytically without any
approximation. Nuclear form factors and spin-relativistic corrections at the
first or second Born approximation level are accounted for by a rejection
technique.
- Photoelectric effect and fluorescence:
Interactions are sampled separately for each component element and for each
edge. The edge fine structure is taken into account.
The angular distribution of photoelectrons is obtained according to the
fully relativistic theory of Sauter [6].
Parametrizations/tabulations for photoelectric cross sections including all
known edges up to Z=100 and down to a few eV
Fluorescence and approximate Auger electron emission are simulated for all K
and most L lines
- Stopping power:
dE/dx Bethe-Bloch theory [13,14,15,16,17].
- Improved ionization potential, handling of porous substances, ranging out
particles below energy cutoff [2].
Charged particle energy loss fluctuations below an (arbitrary) explicit
ray production threshold are obtained from a sophisticated statistical
approach which includes "close" collisions, plus a two-oscillators model
for "distant" collisions [3].
Ionization fluctuations including corrections for particle spin and
electrons/positrons and "distant collision" straggling corrections (similar
to Blunck-Leisegang ones). Original approach making use of very general
statistical properties of the problem. Within this framework "practical"
solutions have been implemented into the code with very satisfactory
results. This approach exploits the properties of the cumulants of
distributions, and in particular of the cumulants of the distribution of
Poisson distributed variables [3].
Ionization potentials and density effect parameters by Sternheimer, Berger
and Seltzer: [4,5]
Radiative energy losses for e+, e- made to be consistent with Berger &
Seltzer bremsstrahlung data [8].
Shell corrections derived from Ziegler [18]
Differences between positrons and electrons are taken into account
concerning both stopping power and bremsstrahlung [9].
- Barkas effect
- Bloch term
- Heavy ion dE/dx: energy loss straggling according to
* "normal" first Born approximation
* charge exchange effects (dominant at low energies, ad hoc model
developed for FLUKA)
* Effective charge parameterization
* Nuclear form factors at high energies
* Direct e+/e-production
- Delta ray production and transport with account for spin effects.
The variations with energy of the discrete event cross sections and of the
continuous energy loss in each transport step are taken into account exactly.
Bhabha and Moller scattering for e+ and e- : [7]
- Bremsstrahlung
Very accurate electron-nucleus and electron-electron bremsstrahlung
cross-sections, differential in photon energy, were published by Seltzer and
Berger for all elements up to 10 GeV [8].
Those data were obtained at low energy by numerical phase-shift calculations,
and above 50 MeV using the DBMO formulae with screening based on
Hartree-Fock form factors and several corrections.
In FLUKA the full set of Seltzer and Berger cross-sections has been
tabulated, with extra points computed close to the finite value at "tip"
energy. The energy mesh has been concentrated, especially near the photon
spectrum tip, and the maximum energy has been extended to 1000 PeV taking
into account the Landau-Pomeranchuk-Migdal (LPM) suppression effect
[22,23,24,25] and the Ter-Mikaelyan polarization effect [26] in the soft
part of the bremsstrahlung spectrum .
Positron bremsstrahlung is treated separately with ad hoc spectra at low
energies, using below 50 MeV the scaling function for the radiation integral
given by Kim et al. [9] and differential cross-sections have been obtained
by fitting proper analytical formulae to numerical results of Feng et al.
[10]. The photon angular distribution, fully correlated with the photon
energy sampled from the Seltzer-Berger distributions. is obtained sampling
the emission angle from the double differential formula reported by
Koch and Motz [11].
- Positron annihilation: at rest and & in flight, according to Heitler.
- at rest: account for mutual polarization of the two photons
- Compton scattering
inclusion of binding effects through use of inelastic Hartree-Fock
form factors or full Compton profile treatment, using detailed
momentum distributions for each atomic shell [27] (Doppler shift comes
out automatically)
- Photon cross sections: The photon cross-sections used in FLUKA are taken from
the EPDL97 evaluated library [12], with the exception of Compton, which is
computed from the free electron one according to the corrections explained
above.
- Pair production
angular and energy distributions are described in full detail and correlated.
Much care has been devoted to the low photon energy range.
LPM effect.
- Coherent (Rayleigh) scattering: algorithm using EPDL97 elastic atomic
form factors.
- Photon polarization in Compton, Rayleigh and photoelectric effects.
- Photonuclear cross sections: total cross sections as follow.
* Giant Resonance: tabulation from fits to experimental data when possible,
otherwise parameterization
* Quasi-deuteron: analytical formula (Levinger's model [28], with the value
of the Levinger constant as recommended by Tavares et al. [29] and a
Pauli-blocking function according to Chadwick et al. [30].
* Delta resonance: fit to available experimental data
* High-energy region: weighted sum of (gamma,n) and (gamma,p) cross
sections, plus a shadowing factor.
The interaction dynamics in all cases is handled via the FLUKA hadronic
models (evaporation, PEANUT, Vector Meson Dominance).
- Electromagnetic dissociation of ions
- Heavy charged particle bremsstrahlung: treated as a continuous energy loss
and deposition or as discrete processes depending on user choice
- Heavy charged particle pair production: continuous or explicit treatment on
user request
- Heavy ion direct particle pair production
- Leading particle biasing improved and extended to all EMF particles
- Negative muon capture: mu- at rest + atom --> excited muonic atom -->
X-rays + g.s. muonic atom -> muon capture by nuclei
Competition between mu decay and mu capture (Goulard-Primakoff formula)
- Muon photonuclear interactions, with or without transport of the produced
secondaries. The cross section is factorized (following Bezrukov-Bugaev) in
virtual photon production and photon-nucleus reaction. Nuclear screening is
taken into account. Only Virtual Meson Interactions are modeled, following
the FLUKA meson-nucleon interaction models.
- Actual muon decay distribution
- pion/muon polarized decays
- Deexcitation gamma generation
- Cerenkov photon production and full transport of optical photons, including
reflection/refraction and absorption (with user provided optical properties)
- Scintillation photon production (with user provided production properties)
- Explicit capture photon generation for Xenon isotopes, for 113-Cd, 10-B
and for 40-Ar and 36-Ar
- Ability to define different materials for dE/dx and nuclear interactions.
Region-by-region (and voxel-by-voxel) density correction factors for dE/dx
and other processes
- Photomuon production (Bethe-Heitler)
- Individual primary ionization events for both close and distant
collisions implemented on request (with user provided infos)
- Complete databases for gamma and beta radiations generated out of the data
collected from NNDC.
- Online evolution of radioactive isotopes and remnant doses calculations for
arbitrary irradiation profiles and cooling times
- Beta +/- spectra including Coulomb and screening corrections.
- Gamma and beta radioactive decays
References
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scattering model for charged particle transport",
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Proc. 2nd Workshop on Simulating Accelerator Radiation Environments
(SARE 2), CERN, Geneva, Switzerland 9-11 Oct. 1995.Ed. G.R. Stevenson, CERN
Report TIS-RP/97-05 (1997), p. 158
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[17] F. Bloch, "Bremsvermoegen von Atomen mit mehreren Elektronen",
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