Atomic Relaxation Models

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Atomic Relaxation Models

• A. Mantero, B. Mascialino, Maria Grazia Pia
• INFN Genova, Italy

Monte Carlo 2005 Chattanooga, 18-21 April 2005
http//www.ge.infn.it/geant4/lowE/index.html
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Geant4 Low Energy Electromagnetic Physics

• Geant4 provides a specialised package to handle
  electromagnetic interactions down to low energy
• Low means up to 100 GeV

Negative charged hadrons
Positive charged hadrons and ions
Electrons and photons
Bethe-Bloch
Models based on Livermore Library (EEDL, EPDL)
Quantum Harmonic Oscillator
high energy
Ziegler/ICRU Parameterisations
low energy (lt 1 keV)
down to 250 eV (lower in principle)
MeV region
Penelope re-engineering
same as positive hadrons
Free electron gas
down to 100 eV
low energy (down to ionisation potential)
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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

• X-ray fluorescence
• Auger electron emission
• PIXE (Particle Induced X-ray Emission)

Atomic Relaxation
following the creation of a vacancy by
photoelectric effect, Compton effect and
ionisation
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The process in a nutshell

• Rigorous software process
• Iterative and incremental model
• Based on the Unified Process bidimensional,
  static dynamic dimension
• Use case driven, architecture centric
• Continuous software improvement process
• User Requirements Document
• Updated with regular contacts with users
• Analysis and design
• Design validated against use cases
• Unit, package integration, system tests physics
  validation
• We do a lot but we would like to do more
• Limited by availability of resources for core
  testing
• Rigorous quantitative tests, applying statistical
  methods
• Peer design and code reviews
• We would like to do more main problem
  geographical spread overwork
• Close collaboration with users

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Use case fluorescence emission
Original motivation from astrophysics requirements
Cosmic rays, jovian electrons
X-Ray Surveys of Asteroids and Moons
Solar X-rays, e, p
Geant3.21
ITS3.0, EGS4
Courtesy SOHO EIT
Geant4
Induced X-ray line emission indicator of target
composition (100 mm surface layer)
C, N, O line emissions included
Wide field of applications beyond astrophysics
Courtesy ESA Space Environment Effects Analysis
Section
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Design
Used by processes
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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)

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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

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Test process
Test Plan Test Guidelines Test Automation
Architecture Test Cases Test Data Test Results

• Unit, integration and system tests
• 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

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Verification X-ray fluorescence
Comparison of monocromatic photon lines generated
by Geant4 Atomic Relaxation w.r.t. reference
tables (NIST)
Transitions (Fe)
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
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Verification Auger effect
Auger electron lines from various materials
w.r.t. published experimental results
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
Monocromatic photon beam
HpGe detector
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Comparison with experimental data
Photon energy
Experimental data Simulation
Parametric analysis fit to a gaussian Compare
experimental and simulated distributions Detector
effects! (resolution, efficiency)
difference of photon energies
Precision better than 1
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Test beam at Bessy - 2
Advanced Concepts and Science Payloads
A. Owens, A. Peacock
Complex geological materials
Hawaiian basalt Icelandic basalt Anorthosite Doler
ite Gabbro Hematite
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Comparison with experimental data
Pearson correlation analysis rgt0.93
plt0.0001
Effects of detector response function presence
of trace elements
Experimental and simulated X-ray spectra are
statistically compatible at 95 C.L.
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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

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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

Next protons, L shell ions, K shell
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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
• Multiple regression index R2
• ANOVA
• Fishers test
• 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 lt 0.001 in
  all cases

Test statistics
Fisher distribution
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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

Dont worry it is not just for space
science (also used at LHC!)