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Precision validation of Geant4 electromagnetic physics Katsuya Amako, Susanna Guatelli, Vladimir Ivanchenko, Michel Maire, Barbara Mascialino, Koichi Murakami, Petteri Nieminen, Luciano Pandola, Sandra Parlati, Andreas Pfeiffer, Maria Grazia Pia, Michela Piergentili, Takashi Sasaki, Lazslo Urban Monte Carlo 2005 Topical Meeting Chattanooga, April 2005

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Introduction authoritative reference datacritical issue fundamentalreliability The validation of Geant4 physics models with respect to authoritative reference data is a critical issue, fundamental to establish the reliability of Geant4-based simulations. is an object-oriented toolkit for the simulation of the passage of particles through matter It offers an ample set of complementary and alternative physics models for both electromagnetic and hadronic interactions, based on: theory experimental data parameterisations

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Aim of the project Validation of Geant4 electromagnetic models against established references (ICRU - NIST), with the purpose of to evaluate their accuracy and to document their respective strengths Simulation of physics quantities in the same experimental set-up as reference data Rigorous quantitative statistical comparison PHYSICAL TEST GOODNESS-OF-FIT TESTING Quantitative statistical analysis - Evaluation of Geant4 physics models 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

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Alternative and complementary models are provided in the various packages 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 Geant4 includes a number of packages to handle the e.m. interactions of electrons and positrons, gamma, X-ray and optical photons, muons, charged hadrons, ions 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 Geant4 Electromagnetic Package Standard Package LowEnergy Package Muon Package Optical photon Package specialised according to - the particle type managed, - the energy range of processes covered. Geant4 Electromagnetic Physics models

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PhotonPhoton Mass Attenuation Coefficient PhotonPhoton Partial Interaction Coefficient (mass attenuation coefficients with only one process activated) ElectronElectron CSDA range and Stopping Power (no multiple scattering, no energy fluctuations) ProtonProton CSDA range and Stopping Power (no multiple scattering, no energy fluctuations) AlphaAlpha CSDA range and Stopping Power (no multiple scattering, no energy fluctuations) Physics quantities under study Elements: Be, Al, Si, Fe, Ge, Ag, Cs, Au, Pb, U + water Energy range: 1 keV – 100 GeV photon 10 keV – 1 GeV electron 1 keV – 10 GeV proton 1 keV – 1 GeV alpha Testing activity has been automatised (INFN Gran Sasso Laboratory and KEK) Ionisation potentials of the selected materials were modified w.r.t. the default values in Geant4, and were set as in the NIST database.

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- The simulation results were produced with Geant4 version The Geant4 test process verifies that the accuracy of the physics models will not deteriorate in future versions of the toolkit with respect to the results presented here. - Results obtained can be considered as an objective guidance to select the Geant4 electromagnetic models most appropriate to any specific simulation application. Simulation results

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Statistical analysis The statistical analysis has been performed by means of a Goodness-of-Fit Statistical Toolkit, specialised in the comparison of data distributions The two alternative hypothesis under test are the following: H 0 : Geant4 simulations = NIST data H 1 : Geant4 simulations ≠ NIST data GoF test ( χ 2 test) Distance between Geant4 simulations and NIST reference data Test result (p-value) GoF Toolkit at least 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 p < 0.05: Geant4 simulations and NIST data differ significantly p > 0.05: Geant4 simulations and NIST data do not differ significantly

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Test of Geant4 photon processes

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Photon mass attenuation coefficient Physics models under test: Geant4 Standard Geant4 Low Energy – EPDL Geant4 Low Energy – Penelope Reference data: NIST - XCOM Mass attenuation coefficient in Fe 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 with reference data p-value stability study H 0 REJECTION AREA Experimental set-up Monochromatic photon beam (I o ) Transmitted photons (I) 1 keV – 100 GeV

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Compton interaction coefficient Physics models under test: Geant4 Standard Geant4 Low Energy – EPDL Geant4 Low Energy – Penelope Reference data: NIST - XCOM The three Geant4 models reproduce Compton scattering cross sections with high accuracy The Geant4 LowE – EPDL model exhibits the best overall agreement with reference data Geant4 LowE Penelope Geant4 Standard Geant4 LowE EPDL NIST - XCOM Compton interaction coefficient in Ag p-value stability study H 0 REJECTION AREA 1 keV – 100 GeV

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Photoelectric interaction coefficient Physics models under test: Geant4 Standard Geant4 Low Energy – EPDL Geant4 Low Energy – Penelope Reference data: NIST - XCOM The three Geant4 models reproduce photoelectric cross sections with high accuracy The two Geant4 LowE models exhibit the best agreement Geant4 LowE Penelope Geant4 Standard Geant4 LowE EPDL NIST - XCOM Geant4 LowE Penelope Geant4 Standard Geant4 LowE EPDL NIST - XCOM Photoelectric interaction coefficient in Ge H 0 REJECTION AREA p-value stability study 1 keV – 100 GeV

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Pair production interaction coefficient Physics models under test: Geant4 Standard Geant4 Low Energy – EPDL Geant4 Low Energy – Penelope Reference data: NIST - XCOM The three Geant4 models reproduce pair production cross sections with high accuracy Geant4 LowE Penelope Geant4 Standard Geant4 LowE EPDL NIST - XCOM Pair production interaction coefficient in Au p-value stability study H 0 REJECTION AREA p-value (pair production interaction coefficient test) 1 keV – 100 GeV

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Rayleigh interaction coefficient Physics models under test: Geant4 Low Energy – EPDL Geant4 Low Energy – Penelope Reference data: NIST - XCOM The Geant4 Low Energy models seem to be in disagreement with the reference data for some materials Geant4 LowE Penelope Geant4 LowE EPDL NIST - XCOM Rayleigh interaction coefficient in Be Be0.991 Al0.32<0.05 Si0.77<0.05 Fe1<0.05 Ge< Ag Cs<0.05 Au<0.05 Pb<0.05 U EPDL XCOM Penelope XCOM 1 keV – 100 GeV

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Rayleigh interaction coefficient Zaidi H., 2000, Comparative evaluation of photon cross section libraries for materials of interest in PET Monte Carlo simulation IEEE Transaction on Nuclear Science The disagreement is evident between 1 keV and 1 MeV photon energies. For what concerns the Geant4 Low Energy EPDL model, the effect observed derives from an intrinsic inconsistency between Rayleigh cross section data in NIST-XCOM and the cross sections of EPDL97, on which the model is based. Differences between EPDL97 and NIST- XCOM have already been highlighted in a paper by Zaidi, which recommends the Livermore photon and electron data libraries as the most up-to-date and accurate databases available for Monte Carlo modeling. EPDL 97 NIST Rayleigh interaction coefficient in Au

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Test of Geant4 electron processes

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Electron Stopping Power centre Experimental set-up Physics models under test: Geant4 Standard Geant4 Low Energy – Livermore Geant4 Low Energy – Penelope Reference data: NIST ESTAR - ICRU 37 The comparison test exhibited that all the Geant4 physics models are in excellent agreement with the NIST- ESTAR reference data. The test has not pointed out any particular difference among the three sets of models. p-value stability study H 0 REJECTION AREA Geant4 LowE Penelope Geant4 Standard Geant4 LowE Livermore NIST - ESTAR Electrons are generated with random direction at the center of the box and stop inside the box 10 keV – 1 GeV CSDA : particle range without energy loss fluctuations and multiple scattering Maximum step allowed in tracking particles was set about1/10 of the expected range value, to ensure the accuracy of the calculation

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Electron CSDA Range CSDA : particle range without energy loss fluctuations and multiple scattering Physics models under test: Geant4 Standard Geant4 Low Energy – Livermore Geant4 Low Energy – Penelope Reference data: NIST ESTAR - ICRU 37 The three Geant4 models are equivalent Geant4 LowE Penelope Geant4 Standard Geant4 LowE Livermore NIST - ESTAR CSDA range in U p-value stability study H 0 REJECTION AREA 10 keV – 1 GeV

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Test of Geant4 proton and alpha processes

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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 NIST PSTAR – ICRU 49 Standard Standard Low Energy – ICRU 49 Low Energy – ICRU 49 Low Energy – Ziegler 85 Low Energy – Ziegler 85 Low Energy – Ziegler 2000 Low Energy – Ziegler 2000 Geant4 models under test: Reference data: Protons Alpha particles Standard Standard Low Energy – ICRU 49 Low Energy – ICRU 49 Low Energy – Ziegler 77 Low Energy – Ziegler 77 Geant4 models under test: NIST ASTAR – ICRU 49 Reference data:

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Proton processes Proton processes Stopping power in Al Geant4 LowE Ziegler 1985 Geant4 LowE Ziegler 2000 Geant4 Standard Geant4 LowE ICRU 49 NIST - PSTAR + H 0 REJECTION AREA Stopping power: p-value stability study H 0 REJECTION AREA CSDA range: p-value stability study 1 keV – 10 GeV

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Alpha particles processes H 0 REJECTION AREA Stopping power: p-value stability studyCSDA range in Si Geant4 LowE Ziegler 1977 Geant4 Standard Geant4 LowE ICRU 49 NIST - ASTAR The complex physics modeling of ion interactions in the low energy range is addressed by the Geant4 Low Energy package and it represented one of the main motivations for the developing of this package. 1 keV – 1 GeV

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Conclusions Systematic validationSystematic validation of Geant4 electromagnetic models against ICRU protocols and NIST reference data rigorousquantitativeValidation based on a rigorous, quantitative statistical analysis of test results All Geant4 electromagnetic models are found in good agreement with the reference data Quantitative statistical analysis documents the respective strengths of the Geant4 models in detail, for each of the physics distributions considered in the NIST reference. The quantitative documentation presented provides an objective guidance to select the Geant4 electromagnetic models most appropriate to any specific simulation application.

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systematic validationGeant4 electromagnetic physics models This work is a part of a wider project for the systematic validation of Geant4 electromagnetic physics models, covering also other particles types, physics processes and energy ranges outside the scope of the NIST reference data.

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