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

Introduction 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: experimental data theory parameterisations 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.

Quantitative statistical analysis 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 Quantitative statistical analysis PHYSICAL TEST GOODNESS-OF-FIT TESTING - 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

Geant4 Electromagnetic Physics models It handles electrons and positrons, gamma, X-ray and optical photons, muons, charged hadrons, ions Geant4 Electromagnetic Physics models Standard Package Geant4 Electromagnetic Package LowEnergy Package 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 Muon Package specialised according to - the particle type managed, - the energy range of processes covered. Optical photon Package 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

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

Simulation results - The simulation results were produced with Geant4 version 6.2. 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.

and NIST reference data 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: 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) 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

Test of Geant4 photon processes

Photon mass attenuation coefficient Physics models under test: Geant4 Standard Geant4 Low Energy – EPDL Geant4 Low Energy – Penelope Reference data: NIST - XCOM Experimental set-up Monochromatic photon beam (Io) Transmitted photons (I) 1 keV – 100 GeV Mass attenuation coefficient in Fe Geant4 LowE Penelope Geant4 Standard Geant4 LowE EPDL NIST - XCOM p-value stability study H0 REJECTION AREA The three Geant4 models reproduce total attenuation coefficients with high accuracy The two Geant4 LowE models exhibit the best agreement with reference data

Compton interaction coefficient 1 keV – 100 GeV 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 H0 REJECTION AREA

Photoelectric interaction coefficient 1 keV – 100 GeV 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 Photoelectric interaction coefficient in Ge H0 REJECTION AREA p-value stability study

Pair production interaction coefficient 1 keV – 100 GeV 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 H0 REJECTION AREA p-value (pair production interaction coefficient test)

Rayleigh interaction coefficient 1 keV – 100 GeV 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 EPDL XCOM Penelope XCOM Rayleigh interaction coefficient in Be Be 0.99 1 Al 0.32 <0.05 Si 0.77 Fe Ge 0.39 Ag 0.36 0.08 Cs Au Pb U Geant4 LowE Penelope Geant4 LowE EPDL NIST - XCOM

Rayleigh interaction coefficient 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. EPDL 97 NIST Rayleigh interaction coefficient in Au 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. 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

Test of Geant4 electron processes

Electron Stopping Power 10 keV – 1 GeV Physics models under test: Geant4 Standard Geant4 Low Energy – Livermore Geant4 Low Energy – Penelope Reference data: NIST ESTAR - ICRU 37 Experimental set-up Electrons are generated with random direction at the center of the box and stop inside the box centre CSDA: particle range without energy loss fluctuations and multiple scattering p-value stability study H0 REJECTION AREA Maximum step allowed in tracking particles was set about1/10 of the expected range value, to ensure the accuracy of the calculation 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. Geant4 LowE Penelope Geant4 Standard Geant4 LowE Livermore NIST - ESTAR

The three Geant4 models are equivalent Electron CSDA Range 10 keV – 1 GeV Physics models under test: Geant4 Standard Geant4 Low Energy – Livermore Geant4 Low Energy – Penelope Reference data: NIST ESTAR - ICRU 37 CSDA: particle range without energy loss fluctuations and multiple scattering The three Geant4 models are equivalent Geant4 LowE Penelope Geant4 Standard Geant4 LowE Livermore NIST - ESTAR CSDA range in U p-value stability study H0 REJECTION AREA

Test of Geant4 proton and alpha processes

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

Proton processes Stopping power: p-value stability study Stopping power in Al Geant4 LowE Ziegler 1985 Geant4 LowE Ziegler 2000 Geant4 Standard Geant4 LowE ICRU 49 NIST - PSTAR + H0 REJECTION AREA Stopping power: p-value stability study CSDA range: p-value stability study 1 keV – 10 GeV

Alpha particles processes 1 keV – 1 GeV CSDA range in Si Geant4 LowE Ziegler 1977 Geant4 Standard Geant4 LowE ICRU 49 NIST - ASTAR H0 REJECTION AREA Stopping power: p-value stability study 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.

Conclusions Systematic validation of Geant4 electromagnetic models against ICRU protocols and NIST reference data Validation 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.

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.