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### Electromagnetic physicsvalidation

Katsuya Amako,Susanna Guatelli, Vladimir Ivanchenko, Michel Maire, Barbara Mascialino, Koichi Murakami, Sandra Parlati, Andreas Pfeiffer, Maria Grazia Pia, Takashi Sasaki, Lazslo Urban

IEEE - NSS

Rome, October 2004

- Evaluation of Geant4 physics goodness

- How the various Geant4 models behave in the same experimental condition
- - Systematic data analysis allows to improve the physics models and guarantees the reliability

Scope

Aim of the project- Validation of Geant4 electromagnetic models against established references (ICRU - NIST)
- Simulation of physics quantities in the same experimental set-up as reference data
- Rigorous quantitative statistical comparison

Quantitative statistical analysis

PHYSICAL TEST

GOODNESS-OF-FIT

TESTING

Alternative models for the same physics process

High energy models

fundamental for LHC experiments, cosmic ray experiments etc.

Low energy models

fundamental for space and medical applications, neutrino experiments, antimatter spectroscopy etc.

two “flavours” of models:

model based on Livermore libraries

à la Penelope

multiple scattering

bremsstrahlung

ionisation

annihilation

photoelectric effect

Compton scattering

Rayleigh effect

gamma conversion

e+e- pair production

synchrotron radiation

transition radiation

Cherenkov

refraction

reflection

absorption

scintillation

fluorescence

Auger

It handles electrons and positrons, gamma, X-ray and optical photons, muons, charged hadrons, ions

Geant4 Electromagnetic Physics modelsStandard Package

Geant4

Electromagnetic

Package

LowEnergy Package

Muon Package

Optical photon Package

Physics quantities under study

- Photon Attenuation Coefficient
- Photon Cross Sections(attenuation coefficients with only one process activated)
- ElectronCSDA range and Stopping Power

(no multiple scattering, no energy fluctuations)

- ProtonCSDA range and Stopping Power

(no multiple scattering, no energy fluctuations)

- AlphaCSDA range and Stopping Power

(no multiple scattering, no energy fluctuations)

Elements: Be, Al, Si, Fe, Ge, Ag, Cs, Au, Pb, U

+ water

Energy range: 1 keV – 10 GeV

Testing activity has been automatised (INFN Gran Sasso Laboratory and KEK)

p < 0.05: Geant4 simulations and NIST data

differ significantly

p > 0.05: Geant4 simulations and NIST data

do not differ significantly

The p-value represents the probability that the test statistics has a value at least as extreme as that observed, assuming the null hypothesis is true

0 ≤ p ≤ 1

Statistical analysis- The statistical analysis has been performed by means of a Goodness-of-Fit Statistical Toolkit
- The two hypothesis under study are the following:
- H0: Geant4 simulations = NIST data
- H1: Geant4 simulations ≠ NIST data

Distance between

Geant4 simulations

and NIST reference data

GoF

Toolkit

GoF test

(χ2 test)

Test result

(p-value)

- Geant4 Standard
- Geant4 Low Energy – EPDL
- Geant4 Low Energy – Penelope

- Reference data:
- NIST - XCOM

p-value stability study

Transmitted

photons (I)

Photon

beam (Io)

p-value

H0 ACCEPTANCE AREA

H0 REJECTION AREA

Z

Photon attenuation coefficientExperimental

set-up

Geant4 LowE Penelope

Geant4 Standard

Geant4 LowE EPDL

NIST - XCOM

- The three Geant4 models reproduce total attenuation coefficients with high accuracy
- The two Geant4 LowE models exhibit the best agreement

- Geant4 Standard
- Geant4 Low Energy – EPDL
- Geant4 Low Energy – Penelope

- Reference data:
- NIST - XCOM

p-value

H0 REJECTION AREA

Z

Photoelectric cross section- The three Geant4 models reproduce photoelectric cross sections with high accuracy
- The two Geant4 LowE models exhibit the best agreement

p-value stability study

Geant4 LowE Penelope

Geant4 Standard

Geant4 LowE EPDL

NIST - XCOM

Geant4 LowE Penelope

Geant4 Standard

Geant4 LowE EPDL

Compton scattering cross section

- Physics models under test:
- Geant4 Standard
- Geant4 Low Energy – EPDL
- Geant4 Low Energy – Penelope

- Reference data:
- NIST - XCOM

p-value stability study

Geant4 LowE Penelope

Geant4 Standard

Geant4 LowE EPDL

p-value

H0 REJECTION AREA

Z

- The three Geant4 models reproduce Compton scattering cross sections with high accuracy
- The Geant4 LowE – EPDL model exhibits the best agreement

Geant4 LowE Penelope

Geant4 Standard

Geant4 LowE EPDL

NIST - XCOM

- Physics models under test:
- Geant4 Standard
- Geant4 Low Energy – EPDL
- Geant4 Low Energy – Penelope

- Reference data:
- NIST - XCOM

p-value

H0 REJECTION AREA

- The three Geant4 models reproduce pair production cross sections with high accuracy
- The Geant4 LowE – EPDL model exhibits the best agreement

p-value stability study

Geant4 LowE Penelope

Geant4 Standard

Geant4 LowE EPDL

Geant4 LowE Penelope

Geant4 Standard

Geant4 LowE EPDL

NIST - XCOM

Z

- Geant4 Standard
- Geant4 Low Energy – EPDL
- Geant4 Low Energy – Penelope

- Reference data:
- NIST - XCOM

Geant4 Penelope

Geant4 LowE EPDL

p-value

H0 REJECTION AREA

Rayleigh scattering cross section

The Geant4 models seem to be in disagreement with the reference data

p-value stability study

Geant4 Penelope

Geant4 LowE EPDL

NIST - XCOM

Z

Rayleigh scattering cross section

- The NIST database and the EPDL97 evaluated data library give Rayleigh cross section data in disagreement for E < 1 MeV
- EPDL97 is the most up-to- date, complete and consistent data library available at the moment (Zaidi, 2000).

NIST

EPDL 97

* Zaidi H., 2000, Comparative evaluation of photon cross section libraries for materials of interest in PET Monte Carlo simulation IEEE Transaction on Nuclear Science 47 2722-35

- Physics models under test:
- Geant4 Standard
- Geant4 Low Energy – Livermore
- Geant4 Low Energy – Penelope

- Reference data:
- NIST ESTAR - ICRU 37

Experimental

set-up

centre

p-value stability study

Geant4 LowE Penelope

Geant4 Standard

Geant4 LowE EEDL

NIST - XCOM

p-value

Geant4 LowE Penelope

Geant4 Standard

Geant4 LowE EEDL

The three Geant4 models are equivalent

H0 REJECTION AREA

Z

- Geant4 Standard
- Geant4 Low Energy – Livermore
- Geant4 Low Energy – Penelope

- Reference data:
- NIST ESTAR - ICRU 37

p-value

H0 REJECTION AREA

Electron CSDA Range

CSDA range: particle range without energy

loss fluctuations and multiple scattering

p-value stability study

Geant4 LowE Penelope

Geant4 Standard

Geant4 LowE EEDL

NIST - XCOM

Geant4 LowE Penelope

Geant4 Standard

Geant4 LowE EEDL

The three Geant4 models are equivalent

Z

Alpha particles

- Geant4 models under test:

- Geant4 models under test:

- Standard
- Low Energy – ICRU 49
- Low Energy – Ziegler 85
- Low Energy – Ziegler 2000

- Standard
- Low Energy – ICRU 49
- Low Energy – Ziegler 77

- Reference data:

- Reference data:

NIST PSTAR – ICRU 49

NIST ASTAR – ICRU 49

Protons and alpha particles

- Comparison of Geant4 models with respect to ICRU 49 protocol
- Geant4 LowE Package has ICRU 49 parameterisations as one of its models verification, not validation
- The Ziegler parameterisations are as authoritative as the ICRU 49 reference
- comparison rather than validation

Proton stopping power

Proton CSDA range

Geant4 LowE ICRU

Geant4 Standard

Geant4 LowE Ziegler 85

Geant4 LOWe Ziegler 2000

NIST PSTAR - ICRU 49

p>0.05

Geant4 LowE ICRU

Geant4 Standard

Geant4 LowE Ziegler 85

Geant4 LOWe Ziegler 2000

NIST PSTAR - ICRU 49

Geant4 LowE ICRU

Geant4 Standard

Geant4 LowE Ziegler 85

Geant4 LOWe Ziegler 2000

NIST PSTAR - ICRU 49

p>0.05

Similar results for alpha particles

Conclusions

- Systematic validationof Geant4 electromagnetic models against ICRU protocols and NIST reference data
- Validation based on arigorous, quantitative statistical analysis of test results
- All Geant4 electromagnetic models are in agreement with the reference data
- The Geant4 Low Energy Package is the most accurate with respect to the ICRU protocol
- More results: http://www.ge.infn.it/geant4/analysis/book
- Future: extend the validation test to other physics quantities

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