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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. Geant4 Low Energy Electromagnetic Physics.

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Atomic relaxation models

Atomic Relaxation Models

A. Mantero, B. Mascialino, Maria Grazia Pia

INFN Genova, Italy

P. Nieminen


Monte Carlo 2005

Chattanooga, 18-21 April 2005

Geant4 low energy electromagnetic physics
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


Models based on Livermore Library (EEDL, EPDL)

Quantum Harmonic Oscillator

high energy

Ziegler/ICRU Parameterisations

low energy (< 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)


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)

Photon transmission, 1mm Pb

shell effects


Atomic Relaxation

following the creation of a vacancy by photoelectric effect, Compton effect and ionisation

Use case fluorescence emission
Use case: fluorescence emission

Original motivation from astrophysics requirements

Cosmic rays,

jovian electrons

X-Ray Surveys ofAsteroids and Moons

Solar X-rays, e, p


ITS3.0, EGS4

Courtesy SOHO EIT


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


Used by processes


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)

X ray fluorescence and auger effect
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

Test process

Test Plan

Test Guidelines

Test Automation Architecture

Test Cases

Test Data

Test Results

Test process

  • 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

Verification x ray fluorescence

K transition

K transition

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

Verification auger effect

428.75, 429.75 eV (430 unresolved)

366.25 eV (367)

436.75, 437.75 eV (437 unresolved)

Verification: Auger effect

Auger electron lines from various materials w.r.t. published experimental results

Precision: 0.74 % ± 0.07

Cu Auger spectrum

Test beam at bessy 1

Pure material samples:

  • Cu

  • Fe

  • Al

  • Si

  • Ti

  • Stainless steel

Test beam at Bessy - 1

Advanced Concepts and Science Payloads

A. Owens, A. Peacock

Monocromatic photon beam

HpGe detector

Comparison with experimental data
Comparison with experimental data

Photon energy

Experimental data


Parametric analysis:

fit to a gaussian

Compare experimental and simulated distributions

Detector effects!

(resolution, efficiency)

% difference of photon energies

Precision better than 1%

Test beam at bessy 2


FCM beamline

Si reference

XRF chamber


Test beam at Bessy - 2

Advanced Concepts and Science Payloads

A. Owens, A. Peacock

Complex geological materials

Hawaiian basalt

Icelandic basalt





Comparison with experimental data1

Anderson Darling test






Beam Energy





Fluorescence spectrum of Icelandic Basalt

8.3 keV beam

Ac (95%) = 0.752


Energy (keV)

Comparison with experimental data

Pearson correlation analysis:

r>0.93 p<0.0001

Effects of detector response function + presence of trace elements

Experimental and simulated X-ray spectra are statistically compatibleat 95% C.L.


  • 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

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

PIXE – Cross section model

Next: protons, L shell

ions, K shell

Quality of the pixe model

Regression deviation used to predict the value of a cross section at a given proton energy

Residual deviation

Total deviation

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

    • Fisher’s 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 < 0.001 in all cases

Test statistics

Fisher distribution

Bepi colombo mission to mercury
Bepi Colombo Mission to Mercury used to predict the value of a cross section at a given proton energy

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)

Summary used to predict the value of a cross section at a given proton energy

  • 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