maria grazia pia, infn genova precision electromagnetic physics in geant4: the atomic relaxation...

Maria Grazia Pia, INFN Genova

Precision Electromagnetic Physics in Geant4: Precision Electromagnetic Physics in Geant4:

thethe Atomic Relaxation Models Atomic Relaxation Models

A. Mantero, B. Mascialino, Maria Grazia Pia, S. Saliceti

INFN Genova, Italy

http://www.ge.infn.it/geant4/lowE/index.html

CHEP, Interlaken, 27-30 September 2004


Geant4 Low Energy Electromagnetic PhysicsGeant4 Low Energy Electromagnetic PhysicsGeant4 provides a specialised package to handle electromagnetic interactions down to low energy

“Low” means up to 100 GeV

Electrons and Electrons and photonsphotons

Electrons and Electrons and photonsphotons

Positive charged Positive charged hadrons and ionshadrons and ionsPositive charged Positive charged hadrons and ionshadrons and ions

Negative charged Negative charged hadronshadrons

Negative charged Negative charged hadronshadrons

Models based on Livermore Library (EEDL, EPDL)

Penelope re-engineering

down to 250 eV (lower in principle)

down to 100 eV

Bethe-Bloch

Ziegler/ICRU Parameterisations

Free electron gas

Quantum Harmonic Oscillator

+ same as positive hadrons

~ MeV region

low energy (down to ~ionisation potential)

high energy

low energy (< 1 keV)


VisionPrecise 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 vacancyDe-excitation of the atom after the creation of a vacancy

X-ray fluorescence

Auger electron emission

PIXE (Particle Induced X-ray Emission)

Photon transmission, 1m Pb

shell effects

Atomic RelaxationAtomic Relaxation

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


The process in a nutshellRigorous 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 resourcesavailability 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

Maria Grazia Pia, INFN Genova Courtesy ESA Space Environment & Effects Analysis Section

X-Ray Surveys of Asteroids and Moons

Induced X-ray line emission:indicator of target composition(~100 m surface layer)

Cosmic rays,jovian electrons

Geant3.21

ITS3.0, EGS4

Geant4

Solar X-rays, e, p

Courtesy SOHO EIT

C, N, O line emissions included

Use case: fluorescence emission

Original motivation from astrophysics requirements

Wide field of applications beyond astrophysics


DesignUsed 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 sectionscross sections at the shell level

– Cross section modeling and calculation specific to each process

Generation of the de-excitation chain and its productsproducts– 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

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

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

Test PlanTest Guidelines Test Automation ArchitectureTest CasesTest DataTest Results


Verification: X-ray fluorescence

Transition Probability Energy (eV)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

K transition

K transition

Transitions (Transitions (FeFe))

Comparison of monocromatic photon lines generated by Geant4 Atomic Relaxation w.r.t. reference tables (NIST)


Verification: Auger effect

Auger electron lines from various materials w.r.t.

published experimental results366.25 eV (367)

428.75, 429.75 eV (430 unresolved)

436.75, 437.75 eV (437 unresolved)

Precision: 0.74 % ± 0.07

Cu Auger

spectrum


Test beam at Bessy - 1

Monocromatic photon beamHpGe detector

• Cu• Fe• Al

• Si• Ti• Stainless steel

Pure material samples:

Advanced Concepts and Science PayloadsA. Owens, A. Peacock


Comparison with experimental data

Parametric analysis:fit to a gaussian

Compare experimental and simulated distributions

Detector effects!(resolution, efficiency)

Photon energy

Experimental dataSimulation

Precision better than 1%

% difference of photon energies


Test beam at Bessy - 2Advanced Concepts and Science Payloads

A. Owens, A. Peacock

SiSi

GaAsGaAs

FCM beamlineFCM beamline

Si referenceSi reference

XRF chamberXRF chamber

Complex geological materials

Hawaiian basaltIcelandic basalt

AnorthositeDoleriteGabbro

Hematite


Comparison with experimental data

Experimental and simulated X-ray spectra are statistically compatiblestatistically compatible at 95% C.L. 95% C.L.

Ac (95%) = 0.752

Anderson Darling testBeam Energy

4.96.58.29.5

A20.040.010.210.41

Fluorescence spectrum of Icelandic Basalt8.3 keV beam

Counts

Energy (keV)

Effects of detector response function + presence of trace elements

Pearson correlation analysis:r>0.93 p<0.0001


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


PIXE – Cross section modelFit 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


Quality of the PIXE modelHow 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

Residual deviation

Total deviation

Regression deviation

Test statistics

Fisher distribution


Bepi Colombo Bepi Colombo Mission to MercuryMission 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)


SummaryGeant4 provides precise models for detailed processes at the level of atomic substructure (shells)

X-ray fluorescenceX-ray fluorescence, Auger electronAuger electron emission and PIXEPIXE are accurately simulated

Rigorous test process and quantitative statistical analysisquantitative statistical analysis for software and physics validation

Beware: intrinsic precision of physics modeling and comparison intrinsic precision of physics modeling and comparison with test beam results are two different aspectswith test beam results are two different aspects

– both must be verified

Thanks to ESA for the support and collaboration to development and physics validation

Don’t worry… it is not just for space science(also used at LHC!)(also used at LHC!)

maria grazia pia, infn genova precision electromagnetic physics in geant4: the atomic relaxation...

Documents

maria grazia pia

infn genova design

infn genova verification

infn genova test process

infn genova test beam

infn genova xray fluorescence

infn genova implementation

saliceti infn genova