Nuclear Interaction Models
in FLUKA
Francesco CERUTTI, CERN
GANIL, March 19th, 2010
Outline
•  FLUKA
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hN
hA
(pre-)Equilibrium de-excitation
residue decay and buildup
•  AA
- high energies (DPMJET)
▫ LHC 208Pb beam fragmentation
- intermediate energies (RQMD)
▫ space radiation protection
▫ hadrontherapy
- low energies (BME)
•  planned developments
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FLUKA [1]
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Hadron-nucleus interactions
Nucleus-Nucleus interactions
Electron interactions
Photon interactions
Muon interactions (inc. photonuclear)
Neutrino interactions
Decay
Low energy neutrons
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Ionization
Multiple scattering
Combinatorial geometry
Voxel geometry
Magnetic field
Analogue or biased
On-line buildup and evolution of
induced radioactivity and dose
User-friendly GUI thanks to Flair
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FLUKA [2]
Main authors:
A. Fassò, A. Ferrari, J. Ranft, P.R. Sala
Contributing authors: G.Battistoni, F.Cerutti, T.Empl, M.V.Garzelli, M.Lantz,
A.Mairani, V.Patera, S.Roesler, G.Smirnov, F.Sommerer, V.Vlachoudis
http://www.fluka.org
>2000 users
Developed and maintained under an INFN-CERN agreement
Copyright 1989-2010 CERN and INFN
user support through [email protected]
9 beginner courses held up to now (2 per year since 2007)
The FLUKA collaborations includes also members from HIT, UH, SLAC ...
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Hadron—nucleon (hN)
p-p and p-n cross section
FLUKA and data
total
elastic
Particle production interactions:
two kinds of models
Those based on “resonance”
production and decays,
cover the energy range up to 3–5 GeV
Those based on quark/parton string
models, provide reliable results up to
several tens of TeV
Elastic, charge exchange and strangeness exchange reactions:
• Available phase-shift analysis and/or fits of experimental differential data
• At high energies, standard eikonal approximations are used
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Inelastic hN interaction benchmark
π+ + p → π+ + X (6 & 22 GeV/c) π+ + p → Ch+/Ch- + X (250 GeV/c)
6 GeV/c
22 GeV/c
Connected points: FLUKA
Symbols with errors : DATA
M.E. Law et. Al, LBL80 (1972)
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Overview
[even three from BME]
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Hadron—nucleus (hA)
P
E
A
N
U
T
Target nucleus description (density, Fermi motion, etc)
t (s)
Glauber-Gribov cascade with formation zone
10-23
Generalized IntraNuclear cascade
10-22
Preequilibrium stage
with current exciton configuration and excitation energy
(all non-nucleons emitted/decayed + all nucleons below 30-100 MeV)
Evaporation/Fragmentation/Fission model
γ de-excitation
10-20
10-16
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GINC
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Primary and secondary particles moving in the nuclear medium
Target nucleons motion and nuclear well according to the Fermi gas model
Interaction probability
σfree + Fermi motion × ρ(r) + exceptions (ex. π)
Glauber cascade at higher energies
Classical trajectories (+) nuclear mean potential (resonant for π)
Curvature from nuclear potential → refraction and reflection
Interactions are incoherent and uncorrelated
Interactions in projectile-target nucleon CMS → Lorentz boosts
Multibody absorption for π, µ-, KQuantum effects (Pauli, formation zone, correlations…)
Exact conservation of energy, momenta and all additive quantum numbers,
including nuclear recoil
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Effect of Glauber and formation zone
Rapidity distribution of charged particles
produced in 250 GeV π+ collisions
on Au
Yes Glau
Yes FZ
No Glau
No FZ
Yes Glau
No FZ
No Glau
Yes FZ
data from Agababyan et al., ZPC50, 361 (1991)
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Inelastic hA interaction benchmark
HARP experiment 12.9 GeV/c p on Al
Double differential π+ production
for p C interactions at 158 GeV/c
π+ production
at different angles
as measured by NA49 (symbols)
and predicted by FLUKA (histograms)
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Equilibrium particle emission
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Evaporation: Weisskopf-Ewing approach
  ~600 possible emitted particles/states (A<25) with an extended evaporation/
fragmentation formalism
  Full level density formula with level density parameter A,Z and excitation
dependent
  Inverse cross section with proper sub-barrier
  Analytic solution for the emission widths (neglecting the level density
dependence on U, taken into account by rejection)
  Emission energies from the width expression with no approximation
Fission: past, improved version of the Atchison algorithm, now
  Γfis based of first principles, full competition with evaporation
  Improved mass and charge widths
  Myers and Swiatecki fission barriers, with exc. en. dependent level density
enhancement at saddle point
Fermi Break-up for A<18 nuclei
  ~ 50000 combinations included with up to 6 ejectiles
γ de-excitation: statistical + rotational + tabulated levels
In ALL reaction steps, from first interaction to last γ :
Exact energy conservation
including binding energy and recoil of residual nucleus
Evaporation/fission benchmark [1]
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Quasi-elastic products
Spallation products
Deep spallation products
  Fission products
  Fragmentation products
  Evaporation products
1 A GeV 208Pb + p reactions Nucl. Phys. A 686 (2001) 481-524
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Evaporation/fission benchmark [2]
1 A GeV 208Pb + p reactions Nucl. Phys. A 686 (2001) 481-524
The deep spallation region is
intimately related to
heavy fragment emission!
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Pre-equilibrium [1]
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The normal (“naïve”) conditions for considering a system equilibrated
enough to transition to equilibrium is (n = number of excitons, g=single
particle level density, E*=excitation energy):
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Veselski (NPA705, 193, (2002)), analyzing heavy ion reactions has
proposed that the probability of pre-equilibrium emission for a given
reaction stage is evaluated randomly for n<neq, according to (a=level
density parameter, σ in the range 0.2-0.4):
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Pre-equilibrium [2]
1 A GeV 208Pb + p reactions Nucl. Phys. A 686 (2001) 481-524
… and to Pre-eq.
termination conditions!!
Mass distributions at pre-equilibrium termination: when pre-equilibrium is
pushed too far, too much excitation energy is spent in the emission of particles
at energies which are better dealt with by evaporation. Heavy fragment
evaporation suffers as well
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On-line evolution and buildup of induced activity [1]
  Custom irradiation/cooling down profiles defined by the user of
(almost) unlimited complexity
  … residuals produced during the “prompt” part either by “high” energy
models, or by “low” energy neutrons processed online
  … time evolution of induced radioactivity calculated analytically
Results available for activities: 2D and 3D spatial distributions, and
full inventories/activities at each buildup/cooling time
Limitations
- No “automatic” update of the target composition → Φσ << 1, ok for most accelerator
applications, not for reactors
- Isomers: models not yet able to predict the ground state/metastable level(s) split.
Rough assumptions are used
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On-line evolution and buildup of induced activity [2]
Results available for energy deposition (dose, decay heat),
particle fluences (including dose equivalent folding conversion
coefficients online) etc, including 2D and 3D distributions
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Residual dose rate benchmark (at CERF)
Dose rate as function of cooling time
for different distances between sample and detector
Radiat. Prot. Dosim. 116 (2005) 12-15
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Residual dose rate benchmark (at nTOF)
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Heavy ion interactions
E > 5 GeV/n
Dual Parton Model (DPM)
DPMJET-III (original code by R.Engel, J.Ranft and S.Roesler,
FLUKA-implemenation by T.Empl et al.)
0.1 GeV/n < E < 5 GeV/n
Relativistic Quantum Molecular Dynamics Model (RQMD)
RQMD-2.4 (original code by H.Sorge et al.,
FLUKA-implementation by A.Ferrari et al.)
E < 0.1 GeV/n
Boltzmann Master Equation (BME) theory
BME (original code by E.Gadioli et al.,
FLUKA-implementation by F.Cerutti et al.)
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DPMJET – The original code
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DPMJET – Main steps of a high energy interaction
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DPMJET – Intranuclear cascade and fragmentation
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DPMJET – Comparison to data [1]
Pseudorapidity distribution of charged hadrons
produced in minimum bias d-Au and p-p collisions at a c.m. energy of 200GeV/A.
Exp. data: BRAHMS- and PHOBOS-Collaborations
J.Ranft, in Proceedings of the Hadronic Shower Simulation Workshop, CP896, Batavia, Illinois (USA), 6-8 September 2006
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DPMJET – Comparison to data [2]
Pseudorapidity distribution of charged hadrons
produced in Au-Au collisions at a c.m. energy of 130GeV/A (left) and 200GeV/A (right)
for different ranges of centralities
Exp. data: PHOBOS-Collaboration
J.Ranft, in Proceedings of the Hadronic Shower Simulation Workshop, CP896, Batavia, Illinois (USA), 6-8 September 2006
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DPMJET – Interface to FLUKA
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High energy AA benchmark
Fragment charge cross sections for 158GeV/n Pb ions on various targets
FLUKA: yellow histograms
em dissociation: purple histograms
Exp. data:
NPA662, 207 (2000)
NPA707, 513 (2002) blue circles
C. Scheidenberger et al.
PRC70, 014902 (2004) red squares
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Application: Ion fragmentation at LHC
LHC will also run 208Pb beams at 2760 GeV/c per nucleon
Pb ion interactions with collimators will be a source of extra hazards relative to
proton beams
Fragments generated in interactions
with collimators etc. will travel
possibly for long distances in the
machine
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208Pb ions @ 2760 A GeV/c on Carbon [1]
Fragment production cross section as a function of R
(== Ratio of fragment magnetic rigidity vs. projectile magnetic rigidity
for Lead interactions on Carbon as calculated with FLUKA)
d, α
207Pb
3H
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208Pb ions @ 2760 A GeV/c on Carbon [2]
“nominal” values, i.e. with
fragment momentum/A=projectile momentum/A
“real” values, taking into account
the momentum spread at interaction
Note the importance of light fragments
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208Pb ions @ 2760 A GeV/c on Tungsten [1]
Fragment production cross section as a function of R
(== Ratio of fragment magnetic rigidity vs. projectile magnetic rigidity
for Lead interactions on Tungsten as calculated with FLUKA)
σ  four times larger
than on C
207Pb
E.M. dissociation
enhances projectile-like
production
d, α
3H
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208Pb ions @ 2760 A GeV/c on Tungsten [2]
“nominal” values, i.e. with
fragment momentum/A=projectile momentum/A
“real” values, taking into account
the momentum spread at interaction
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RQMD - References
interface to a suitably modified RQMD model
RQMD-2.4 (H. Sorge, 1998) was successfully applied
to relativistic A-A particle production over a wide energy range
[H. Sorge, Phys. Rev. C 52, 3291 (1995);
H. Sorge, H. Stöcker, and W. Greiner, Ann. Phys. 192, 266 (1989)
and Nucl. Phys. A 498, 567c (1989)]
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RQMD – The original code
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RQMD – The interfaced code
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Intermediate energy AA benchmark [1]
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Intermediate energy AA benchmark [2]
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Intermediate energy AA benchmark [3]
Isotopic distributions of fragmentation products
fission products excluded
like in the experimental
analysis
exp. data (stars) from J. Benlliure, P. Armbruster et al., Eur. Phys. J A 2, 193 (1998)
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Intermediate energy AA benchmark [4]
Acta Astronautica 63 (2008) 865 – 877
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Intermediate energy AA benchmark [4bis]
exp. data from http://fragserver.lbl.gov/main.html
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Application: Space radiation protection
Solar Energetic Particles
integrated flux: ∼7 109 (nucleon/cm2), E > 1 MeV/n
voxel phantom
open space doses
after 1 g/cm2 Al, to Skin
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Intermediate energy AA benchmark [5]
400 MeV/n
12C
in water: He energy-angle spectra at 28.8 cm
The simulated data assume perfect energy resolution: accounting for the experimental
ToF resolution will further improve the comparison
Preliminary exp. data courtesy of E. Haettner (Diploma thesis),
D.Schardt, GSI, and S.Brons, K.Parodi, HIT.
Simulations: A.Mairani PhD thesis
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Application: Hadrontherapy [1]
270 and 330 MeV/n
12C in water
dose delivered…
F. Sommerer et al Phys. Med. Biol. 51 2006
260 MeV/n
12C in PMMA
F. Sommerer et al Phys. Med. Biol. 54 2009
…and induced β+ activity
from 10 to 20 min
after irradiation end
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Application: Hadrontherapy [2]
Clival Chordoma, 0.96 GyE / field, ΔT1 ~ 26 min, ΔT2 ~ 16 min
[mGy]
@ MGH
[mGy]
dose delivered…
K. Parodi et al, IJROBP 2007
[Bq/ml]
[Bq/ml]
…and induced β+ activity
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BME - References
interface to a Monte Carlo code
founded on the BME theory (E. Gadioli et al.)
[M. Cavinato et al., Nucl. Phys. A 679, 753 (2001),
M. Cavinato et al., Phys. Lett. B 382, 1 (1996)]
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BME – The interfaced code
two different reaction paths have been adopted:
1. COMPLETE FUSION
2. PERIPHERAL COLLISION
PCF=σCF/σR
P = 1 - PCF
pre-equilibrium
according to the BME theory
work in progress
three body mechanism
pickup/stripping (for asymmetric systems at low b)
inelastic scattering (at high b)
FLUKA evaporation
1. In order to get the multiplicities of the pre-equilibrium particles and their double differential
spectra, the BME theory is applied to a few representative systems at different bombarding energies
and the results are parameterized.
2. The complete fusion cross section decreases with increasing bombarding energy. We integrate the
nuclear densities of the projectile and the target over their overlapping region, as a function of the
impact parameter, and obtain a preferentially excited “middle source” and two fragments (projectileand target-like). The kinematics is suggested by break-up studies.
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BME – The database for the pre-equilibrium emissions
16O
+ 6Li, 8Li, 8B,
12C
+ 8Li, 8B,
10B, 12C, 14N, 16O, 19F, 20Ne, 24Mg, 27Al, 56Fe, 197Au
12C, 27Al, 40Ca
@ 12, 30, 50, 70, 100 MeV/n
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BME – Theoretical framework
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BME – Theoretical framework [1]
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BME – Theoretical framework [2]
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BME – Peripheral collisions
i. selection of the impact parameter b
ii. kinematics determination
θPL , θTL chosen according to [dσ/dΩ]cm ~ exp(-kθcm)
θMS momentum conservation
pPL , pTL chosen according to a given energy loss distribution
pMS momentum conservation
φPL free
φTL , φMS same reaction plane
work in progress
iii. excitation energy sharing
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BME – (differential) reaction cross-section
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BME – reaction cross-section benchmark
Eur. Phys. J. A 25, 413 (2005)
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Low energy AA benchmark [1]
Double differential neutron spectra @ 100 MeV/n
work in progress
12C+12C
12C+27Al
Exp. Data (points): T.Kurosawa, N.Nakao, T.Nakamura et al., Nucl. Sci. Eng. 132,30-57(1999)
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Low energy AA benchmark [2]
Fragment Production in 12C+12C @ 86 MeV/n
work in progress
Exp. Data (points): H. Ryde, Physica Scripta T5, 114-117 (1983)
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(near) Future
•  deuteron interactions (break-up)
•  development of BME peripheral collision mechanisms
(quasi elastic break-up)
•  RQMD interface to pre-equilibrium
•  angular momentum tracking -> improving photofission
•  ...
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Equilibrium particle emission [2]
From statistical considerations and the detailed balance principle,
the probabilities for emitting a particle of mass mj, spin Sjħ and energy E,
or of fissioning are given by:
(i, f for initial/final state, Fiss for fission saddle point)
Probability per unit time of
emitting a particle j with energy E
Probability per unit time of
fissioning
•  ρ’s: nuclear level densities
•  U’s: excitation energies
•  Vj’s: possible Coulomb barrier
for emitting a particle type j
•  BFiss: fission barrier
•  Qj’s: reaction Q for emitting a
particle type j
•  σinv: cross section for the inverse
process
•  Δ’s: pairing energies
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DPMJET – The Gribov-Glauber formalism
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DPMJET – Comparison to data
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