Transcript Seminario Geant4 INFN

Atomic Relaxation Models
A. Mantero, B. Mascialino, Maria Grazia Pia
INFN Genova, Italy
P. Nieminen
ESA/ESTEC
Monte Carlo 2005
Chattanooga, 18-21 April 2005
http://www.ge.infn.it/geant4/lowE/index.html
Maria Grazia Pia, INFN Genova
Geant4 Low Energy Electromagnetic Physics
Geant4 provides a specialised package to handle electromagnetic
interactions down to low energy
“Low” means up to 100 GeV
Electrons and
photons
Models based on Livermore
Library (EEDL, EPDL)
down to 250 eV
(lower in principle)
Penelope re-engineering
down to 100 eV
Positive charged
hadrons and ions
Bethe-Bloch
high energy
Ziegler/ICRU
Parameterisations
~ MeV region
Free electron gas
low energy
(down to ~ionisation potential)
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Negative charged
hadrons
Quantum Harmonic
Oscillator
low energy
(< 1 keV)
+ same as positive
hadrons
Photon transmission, 1mm Pb
shell effects
Vision
Precise process modeling
– Cross sections, angular distributions
Charge dependence
– Relevant at low energies
Take into account the atomic structure of matter
– Detailed description of atoms (shells)
Secondary effects after the primary process
– De-excitation of the atom after the creation of a vacancy
Atomic Relaxation
X-ray fluorescence
Auger electron emission
PIXE (Particle Induced X-ray Emission)
following the creation of a vacancy by photoelectric effect, Compton effect and ionisation
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Use case: fluorescence emission
Cosmic rays,
jovian electrons
Original motivation from astrophysics requirements
X-Ray Surveys of Asteroids and Moons
Solar X-rays, e, p
Geant3.21
ITS3.0, EGS4
Courtesy SOHO EIT
Induced X-ray line emission:
indicator of target composition
(~100 mm surface layer)
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Geant4
C, N, O line emissions included
Wide field ofCourtesy
applications
beyond& astrophysics
ESA Space Environment
Effects Analysis Section
Design
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Used by processes
Implementation
Two steps:
Identification of the atomic shell where a vacancy is created by a
primary process (photoelectric, Compton, ionisation), based on
the calculation of cross sections at the shell level
– Cross section modeling and calculation specific to each process
Generation of the de-excitation chain and its products
– Common package, used by all vacancy-creating processes
– Also used by Geant4 hadronic package, at the end of the nuclear de-excitation
chain (e.g. radioactive decay)
Maria Grazia Pia, INFN Genova
X-ray fluorescence and Auger effect
Calculation of shell cross sections
– Based on Livermore (EPDL) Library for photoelectric effect
– Based on Livermore (EEDL) Library for electron ionisation
– Based on Penelope model for Compton scattering
Detailed atom description and calculation of the energy of
generated photons/electrons
– Based on Livermore EADL Library
– Production threshold as in all other Geant4 processes, no photon/electrons
generated and local energy deposit if the transition predicts a particle
below threshold
Maria Grazia Pia, INFN Genova
Test process
Unit, integration and system tests
Test Plan
Test Guidelines
Test Automation Architecture
Test Cases
Test Data
Test Results
Verification of direct physics results against established references
Comparison of simulation results to experimental data from test beams
– Pure materials
– Complex composite materials
Quantitative comparison of simulation/experimental distributions with
rigorous statistical methods
– Parametric and non-parametric analysis
Maria Grazia Pia, INFN Genova
Verification: X-ray fluorescence
Comparison of monocromatic photon lines generated by Geant4 Atomic
Relaxation w.r.t. reference tables (NIST)
Transitions (Fe)
K transition
K transition
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Transition
Probability
Energy (eV)
K L2
1.01391 -1
6349.85
K L3
1.98621 -1
6362.71
K M2
1.22111 -2
7015.36
K M3
2.40042 -2
7016.95
L2 M1
4.03768 -3
632.540
L2 M4
1.40199 -3
720.640
L3 M1
3.75953 -3
619.680
L3 M5
1.28521 -3
707.950
Verification: Auger effect
Auger electron lines from
various materials w.r.t.
published experimental results
428.75, 429.75 eV
(430 unresolved)
366.25 eV (367)
436.75, 437.75 eV
(437 unresolved)
Precision: 0.74 % ± 0.07
Cu
Auger
spectrum
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Test beam at Bessy - 1
Advanced Concepts and Science Payloads
A. Owens, A. Peacock
Pure material samples:
• Cu
• Si
• Fe
• Al
• Ti
• Stainless steel
Monocromatic photon beam
HpGe detector
detector
67 mm
40 mm
45°
beam
40 mm
material samples
Maria Grazia Pia, INFN Genova
Comparison with experimental data
Photon energy
Experimental data
Simulation
Parametric analysis:
fit to a gaussian
% difference of photon energies
Compare experimental and
simulated distributions
Detector effects!
(resolution, efficiency)
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Precision better than 1%
Test beam at Bessy - 2
Advanced Concepts and Science Payloads
A. Owens, A. Peacock
Complex geological materials
Hawaiian basalt
Icelandic basalt
Anorthosite
Dolerite
Gabbro
Hematite
FCM beamline
Si reference
GaAs
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Si
XRF chamber
Comparison with experimental data
Fluorescence spectrum of Icelandic Basalt
8.3 keV beam
Effects of detector response function
+ presence of trace elements
Pearson correlation analysis:
r>0.93
p<0.0001
Counts
Anderson Darling test
Beam Energy
4.9
6.5
8.2
9.5
Energy (keV)
A2
0.04
0.01
0.21
0.41
Ac (95%) = 0.752
Experimental and simulated X-ray spectra are
statistically compatible at 95% C.L.
Maria Grazia Pia, INFN Genova
PIXE
Calculation of cross sections for shell ionisation induced by
protons or ions
Two models available in Geant4:
– Theoretical model by Grizsinsky – intrinsically inadequate
– Data-driven model, based on evaluated data library by Paul & Sacher
(compilation of experimental data complemented by calculations from
EPCSSR model by Brandt & Lapicki)
Generation of X-ray spectrum based on EADL
– Uses the common de-excitation package
Maria Grazia Pia, INFN Genova
PIXE – Cross section model
Fit to Paul & Sacher data library; results of the fit are used to predict the
value of a cross section at a given proton energy
– allow extrapolations to lower/higher E than data compilation
First iteration, Geant4 6.2 (June 2004)
–
–
–
–
The best fit is with three parametric functions for different groups of elements
6 ≤ Z ≤ 25
26 ≤ Z ≤ 65
66 ≤ Z ≤ 99
Second iteration, Geant4 7.0 (December 2004)
– Refined grouping of elements and parametric
functions, to improve the model at low energies
Maria Grazia Pia, INFN Genova
Next: protons, L shell
ions, K shell
Quality of the PIXE model
How good is the regression model adopted w.r.t. the data library?
Goodness of model verified with analysis of residuals and of
regression deviation
Regression deviation
Residual deviation
– Multiple regression index R2
– ANOVA
– Fisher’s test
Total deviation
Test
statistics
Results (from a set of elements covering the periodic table)
– 1st version (Geant4 6.2): average R2 99.8
– 2nd version (Geant4 7.0): average R2 improved to 99.9 at low energies
– p-value from test on the F statistics < 0.001 in all cases
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Fisher
distribution
Bepi Colombo
Mission to Mercury
Study of the elemental composition
of Mercury by means of
X-ray fluorescence and PIXE
Insight into the formation of the
Solar System
(discrimination among various models)
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Summary
Geant4 provides precise models for detailed processes at the
level of atomic substructure (shells)
X-ray fluorescence, Auger electron emission and PIXE are
accurately simulated
Rigorous test process and quantitative statistical analysis for
software and physics validation
Beware: intrinsic precision of physics modeling and comparison
with test beam results are two different aspects
– both must be verified
Thanks to ESA for the support and collaboration to development
and physics validation
Maria Grazia Pia, INFN Genova