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Maria Grazia Pia, INFN Genova Precision Electromagnetic Physics in Geant4: the Atomic Relaxation Models A. Mantero, B. Mascialino, Maria Grazia Pia, S. Saliceti INFN Genova, Italy CHEP, Interlaken, September 2004

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Maria Grazia Pia, INFN Genova Geant4 Low Energy Electromagnetic Physics Geant4 provides a specialised package to handle electromagnetic interactions down to low energy Low means up to 100 GeV Electrons and photons Positive charged hadrons and ions Negative charged hadrons 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)

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Maria Grazia Pia, INFN Genova Vision 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, 1 m Pb shell effects Atomic Relaxation following the creation of a vacancy by photoelectric effect, Compton effect and ionisation

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Maria Grazia Pia, INFN Genova The process in a nutshell Rigorous 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 availability of resources –Limited by availability 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

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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

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Maria Grazia Pia, INFN Genova Design Used by processes

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Maria Grazia Pia, INFN Genova Implementation Two steps: cross sections 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 products 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)

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Maria Grazia Pia, INFN Genova 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

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Maria Grazia Pia, INFN Genova 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 Plan Test Guidelines Test Automation Architecture Test Cases Test Data Test Results

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Maria Grazia Pia, INFN Genova Verification: X-ray fluorescence Transition Probability Energy (eV) K L K L K M K M L2 M L2 M L3 M L3 M K transition Transitions (Fe) Comparison of monocromatic photon lines generated by Geant4 Atomic Relaxation w.r.t. reference tables (NIST)

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Maria Grazia Pia, INFN Genova Verification: Auger effect Auger electron lines from various materials w.r.t. published experimental results eV (367) , eV (430 unresolved) , eV (437 unresolved) Precision: 0.74 % ± 0.07 Cu Auger spectrum

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Maria Grazia Pia, INFN Genova Test beam at Bessy - 1 Monocromatic photon beam HpGe detector Cu Fe Al Si Ti Stainless steel Pure material samples: Advanced Concepts and Science Payloads A. Owens, A. Peacock

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Maria Grazia Pia, INFN Genova Comparison with experimental data Parametric analysis: fit to a gaussian Compare experimental and simulated distributions Detector effects! (resolution, efficiency) Photon energy Experimental data Simulation Precision better than 1% % difference of photon energies

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Maria Grazia Pia, INFN Genova Test beam at Bessy - 2 Advanced Concepts and Science Payloads A. Owens, A. Peacock Si GaAs FCM beamline Si reference XRF chamber Complex geological materials Hawaiian basalt Icelandic basalt Anorthosite Dolerite Gabbro Hematite

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Maria Grazia Pia, INFN Genova Comparison with experimental data statistically compatible 95% C.L. Experimental and simulated X-ray spectra are statistically compatible at 95% C.L. Ac (95%) = Anderson Darling test Beam Energy A Fluorescence spectrum of Icelandic Basalt 8.3 keV beam Counts Energy (keV) Effects of detector response function + presence of trace elements Pearson correlation analysis: r>0.93 p<0.0001

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Maria Grazia Pia, INFN Genova 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

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Maria Grazia Pia, INFN Genova 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 Next: protons, L shell ions, K shell

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Maria Grazia Pia, INFN Genova 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 R 2 –ANOVA –Fishers test Results (from a set of elements covering the periodic table) –1 st version (Geant4 6.2): average R –2 nd version (Geant4 7.0): average R 2 improved to 99.9 at low energies –p-value from test on the F statistics < in all cases Residual deviation Total deviation Regression deviation Test statistics Fisher distribution

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Maria Grazia Pia, INFN Genova Bepi Colombo Mission 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)

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Maria Grazia Pia, INFN Genova Summary Geant4 provides precise models for detailed processes at the level of atomic substructure (shells) X-ray fluorescenceAuger electronPIXE X-ray fluorescence, Auger electron emission and PIXE are accurately simulated quantitative statistical analysis Rigorous test process and quantitative statistical analysis for software and physics validation intrinsic precision of physics modeling and comparison with test beam results are two different aspects 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 Dont worry… it is not just for space science (also used at LHC!)

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