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Ion transport simulation using
Geant4 hadronic physics
Koi, Tatsumi
SLAC
And Geant4 Hadronic Working Group
CHEP04 Sep. 27th 2004 at
Interlaken, Switzerland
• Cross sections
– NN total reaction formulae
• Reactions
– BinaryCascade
– QGS Glauber
• Validation
• Conclusions
CHEP04 Sep. 27th 2004 at
Interlaken, Switzerland
Cross Sections
GetCrossSection()
G4HadronicProcess
GetMicroscopicCrossSection()
PostStepDoIt()
Models
ApplyYoursel()
Cross Sections
• Many cross section formulae for NN
collisions are included in Geant4
– Tripathi, Shen, Kox and Sihver
• These are empirical and parameterized
formulae with theoretical insights.
• G4GeneralSpaceNNCrossSection was
prepared to assist users in selecting the
appropriate cross section formula.
CHEP04 Sep. 27th 2004 at
Interlaken, Switzerland
References to NN Cross Section
Formulae implemented in Geant4
• Tripathi Formula
•
•
•
•
– NASA Technical Paper TP-3621 (1997)
Tripathi Light System
– NASA Technical Paper TP-209726 (1999)
Kox Formula
– Phys. Rev. C 35 1678 (1987)
Shen Formula
– Nuclear Physics. A 49 1130 (1989)
Sihver Formula
– Phys. Rev. C 47 1225 (1993)
CHEP04 Sep. 27th 2004 at
Interlaken, Switzerland
Inelastic Cross Section
C12 on C12
CHEP04 Sep. 27th 2004 at
Interlaken, Switzerland
Models
• Binary Cascade
• QGS Glauber
CHEP04 Sep. 27th 2004 at
Interlaken, Switzerland
Binary Cascade ~Model Principals~
• In Binary Cascade, each participating nucleon is seen as
a Gaussian wave packet, (like QMD)
4
2
2
x, qi , pi , t L exp
2 ip i t x
L
x
q
t
i
3
• Total wave function of the nucleus is assumed to be
•
•
direct product of these. (no anti-symmetrization)
This wave form have same structure as the classical
Hamilton equations and can be solved numerically.
The Hamiltonian is calculated using simple time
independent optical potential. (unlike QMD)
CHEP04 Sep. 27th 2004 at
Interlaken, Switzerland
Binary Cascade ~nuclear model ~
• 3 dimensional model of the nucleus is
•
constructed from A and Z.
Nucleon distribution follows
– A>16 Woods-Saxon model
– Light nuclei harmonic-oscillator shell model
• Nucleon momenta are sampled from 0 to Fermi
•
momentum and sum of these momenta is set to
0.
time-invariant scalar optical potential is used.
CHEP04 Sep. 27th 2004 at
Interlaken, Switzerland
Binary Cascade
~Light Ion Reactions~
• Two nuclei are prepared according to this model
•
•
•
•
(previous page).
The lighter nucleus is selected to be projectile.
Nucleons in the projectile are entered with position and
momenta into the initial collision state.
Until first collision of each nucleon, its Fermi motion is
neglected in tracking.
Fermi motion and the nuclear field are taken into
account in collision probabilities and final states of the
collisions.
CHEP04 Sep. 27th 2004 at
Interlaken, Switzerland
Validation results
Neutrons from 290MeV/n C12 on Copper
CHEP04 Sep. 27th 2004 at
Interlaken, Switzerland
Validation results
Pions from 1.05 A GeV/c C on Be, C, Cu and Pb
CHEP04 Sep. 27th 2004 at
Interlaken, Switzerland
Validation results
Neutrons from 290MeV/n C12 on Carbon
CHEP04 Sep. 27th 2004 at
Interlaken, Switzerland
Dual parton or quark gluon string
model – hadron hadron scattering
• In the approach based on the topological expansion, the
•
Pomeranchuk pole is described by graphs of the
cylindrical type, while the secondary Reggeons are
described by planar graphs
The planar case involves annihilation of valence quarks
of the colliding hadrons, and a qq-bar string.
CHEP04 Sep. 27th 2004 at
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• In the cylindrical (Pomeron) case, the
•
colliding hadrons simply exchange one or
several gluons, resulting in color coupling
between the valence quarks of the hadrons.
They are connected by quark gluon strings.
Breaking the strings leads to the appearance
of white hadrons.
CHEP04 Sep. 27th 2004 at
Interlaken, Switzerland
Multiple Pomeron
exchange
• The parameters of the Pomeron trajectory
•
•
•
cannot at present be calculated, but are taken
from fits to experimental data.
Kaydalov D 1 P 0.07, and 'P 0.25(GeV / C ) 2
For the supercritical Pomeron, D>0, multiPomeron exchange becomes important, since
the contribution to the total cross-section grows
approximately like s / s0 nD
(Ter-Martyrosian, Phys.Lett.44B,377,1973)
CHEP04 Sep. 27th 2004 at
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n-pomeron exchange contributions to charged
multiplicities (Ter-Martirosyan, PLB44, 377, 1973).
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Hadron nucleus collisions
• With respect to hadron hadron collisions, hadron
nuclear collisions offer the additional twist of
multiple participating target nucleons.
CHEP04 Sep. 27th 2004 at
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Ion-ion reaction cross-sections.
• Ion-ion reactions simply add additional primary
•
nucleon lines to the diagrams.
The amplitudes calculated can be integrated to
obtain reaction cross-sections for ion-ion
collisions at high energies
– From O(5A GeV) to O(10A TeV)
– Realistic distributions for nuclear densities
– Predictions within experimental errors.
CHEP04 Sep. 27th 2004 at
Interlaken, Switzerland
Preliminary results of cross section
predictions by QGS-Glauber
Difference in Pb
comes form mainly
EM dissociation effect
4.2 GeV/n C ions
158A GeV Pb ions
CHEP04 Sep. 27th 2004 at
Interlaken, Switzerland
Summary of Cross Section and models
for N-N Inelastic Interaction in Geant4
Tripathi & TripathiLightSystem ~10 GeV/A
Cross Section
Kox & Shen ~10 GeV/A
~100 MeV/A Sihver
100 MeV
1 GeV
Binary Cascade Light Ions
Reaction model
10 GeV
~10 GeV/A
~5 GeV/A QGS - Glauber
CHEP04 Sep. 27th 2004 at
Interlaken, Switzerland
Energy
Other Ion related processes already
implemented in Geant4
•
•
•
•
Ionization Energy Loss
Multiple Scattering
EM Dissociation
Abrasion-Ablation Model
– Macroscopic model for nuclear-nuclear interaction
All these processes work together for
Ion transportation in Geant4
CHEP04 Sep. 27th 2004 at
Interlaken, Switzerland
The people involved
J. P. Wellisch (CERN)
G. Folger (CERN)
B. Trieu (CERN)
P. Truscott (ESA)
I. Corneliu (INFN)
CHEP04 Sep. 27th 2004 at
Interlaken, Switzerland
Conclusions
• Now Geant4 has abundant processes for
Ion interactions with matter.
• Without any extra modules, users may
simulate ion transportation in the complex
and realistic geometries of Geant4.
• Validation has begun and the first results
show reasonable agreement with data.
This work continues.
CHEP04 Sep. 27th 2004 at
Interlaken, Switzerland
Validation results
Neutrons from 290MeV/n C12 on Carbon
CHEP04 Sep. 27th 2004 at
Interlaken, Switzerland
Validation results
Neutrons from 400MeV/n C12 on Carbon
CHEP04 Sep. 27th 2004 at
Interlaken, Switzerland
Validation results
Neutrons from 400MeV/n C12 on Copper
CHEP04 Sep. 27th 2004 at
Interlaken, Switzerland
Validation results
Neutrons from 400MeV/n Ne20 on Carbon
CHEP04 Sep. 27th 2004 at
Interlaken, Switzerland
Validation results
Neutrons from 400MeV/n Ne20 on Copper
CHEP04 Sep. 27th 2004 at
Interlaken, Switzerland
Validation results
Neutrons from 400MeV/n Ne20 on Lead
CHEP04 Sep. 27th 2004 at
Interlaken, Switzerland
Validation results
Neutrons from 600MeV/n Ne20 on Carbon
CHEP04 Sep. 27th 2004 at
Interlaken, Switzerland
Validation results
Neutrons from 600MeV/n Ne20 on Copper
CHEP04 Sep. 27th 2004 at
Interlaken, Switzerland
Validation results
Neutrons from 600MeV/n Ne20 on Lead
CHEP04 Sep. 27th 2004 at
Interlaken, Switzerland
Validation results
Neutrons from 600MeV/n Ar40 on Lead
CHEP04 Sep. 27th 2004 at
Interlaken, Switzerland