Low Energy Electromagnetic Physics http://www.ge.infn.it/geant4/lowE Maria Grazia Pia INFN Genova on behalf of Geant4 Low Energy Electromagnetic Working Group Monte Carlo 2005 Chattanooga, 18-21 April 2005

From deep underground to galaxies XMM Boulby mine Dark matter searches Courtesy of NASA/CXC/SAO Bepi Colombo From deep underground to galaxies From crystals to human beings Brachytherapy Radiotherapy Radiobiology

Low Energy Electromagnetic Physics A set of processes extending the coverage of electromagnetic interactions in Geant4 down to “low” energy 250/100 eV (in principle even below this limit) for electrons and photons down to approximately the ionisation potential of the interacting material for hadrons and ions Processes based on detailed models shell structure of the atom precise angular distributions Specialised models depending on particle type data-driven models based on the Livermore Libraries for e- and photons analytical models for e+, e- and photons (reengineering Penelope into Geant4) parameterised models for hadrons and ions (Ziegler 1977/1985/2000, ICRU49) original model for negative hadrons

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 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

Posted on the WG web site User requirements Various methodologies adopted to capture URs User Requirements Elicitation through interviews and surveys useful to ensure that UR are complete and there is wide agreement Joint workshops with user groups Use cases Analysis of existing Monte Carlo codes Study of past and current experiments Direct requests from users to WG coordinators Posted on the WG web site

Technology as a support to physics OOAD Technology as a support to physics Rigorous adoption of OO methods openness to extension and evolution

Testing Integrated with development (not “something to do at the end”) Suite of unit tests (at least 1 per class) Cluster testing 3 integration/system tests Suite of physics tests (in progress with publications) Regression testing Testing process Testing requirements Testing procedures etc. Physics validation XP practice “write a test before writing the code” recommended to WG developers!

Photons and electrons: processes based on the Livermore library Based on evaluated data libraries from LLNL: EADL (Evaluated Atomic Data Library) EEDL (Evaluated Electrons Data Library) EPDL97 (Evaluated Photons Data Library) especially formatted for Geant4 distribution (courtesy of D. Cullen, LLNL) Validity range: 250 eV - 100 GeV The processes can be used down to 100 eV, with degraded accuracy In principle the validity range of the data libraries extends down to ~10 eV Elements Z=1 to Z=100 Atomic relaxation: Z > 5 (transition data available in EADL)

Calculation of cross sections Interpolation from the data libraries: E1 and E2 are the lower and higher energy for which data (s1 and s2) are available Mean free path for a process, at energy E: ni = atomic density of the ith element contributing to the material composition

Photons

Compton scattering Rayleigh scattering Klein-Nishina cross section: Energy distribution of the scattered photon according to the Klein-Nishina formula, multiplied by scattering function F(q) from EPDL97 The effect of scattering function becomes significant at low energies suppresses forward scattering Angular distribution also based on EPDL97 Rayleigh scattering Angular distribution: F(E,q)=[1+cos2(q)]F2(q) where F(q) is the energy-dependent form factor obtained from EPDL97

Photoelectric effect g conversion Cross section Final state generation Integrated cross section (over the shells) from EPDL + interpolation Shell from which the electron is emitted selected according to EPDL Final state generation Direction of emitted electron = direction of incident photon Improved angular distribution in preparation Deexcitation via the atomic relaxation sub-process Initial vacancy + following chain of vacancies created g conversion Pair and triplet production cross sections The secondary e- and e+ energies are sampled using Bethe-Heitler cross sections with Coulomb correction e- and e+ assumed to have symmetric angular distribution Energy and polar angle sampled w.r.t. the incoming photon using Tsai differential cross section

Scattered Photon Polarization Polarisation Cross section: x Scattered Photon Polarization 250 eV -100 GeV x f hn  A hn0  Polar angle  Azimuthal angle  Polarization vector q Low Energy Polarised Compton O a z C y 10 MeV small  large  100 keV 1 MeV More details: talk on Geant4 Low Energy Electromagnetic Physics Other polarised processes under development

Electron Bremsstrahlung Parameterisation of EEDL data 16 parameters for each atom At high energy the parameterisation reproduces the Bethe-Heitler formula Precision is ~ 1.5 % Plans Systematic verification over Z and energy

Bremsstrahlung Angular Distributions Three LowE generators available in GEANT4: G4ModifiedTsai, G4Generator2BS and G4Generator2BN G4Generator2BN allows a correct treatment at low energies (< 500 keV)

Electron ionisation Parameterisation based on 5 parameters for each shell Precision of parametrisation is better then 5% for 50 % of shells, less accurate for the remaining shells Work in progress to improve the parameterisation and the performance

Processes à la Penelope The whole physics content of the Penelope Monte Carlo code has been re-engineered into Geant4 (except for multiple scattering) processes for photons: release 5.2, for electrons: release 6.0 Physics models by F. Salvat et al. Power of the OO technology: extending the software system is easy all processes obey to the same abstract interfaces using new implementations in application code is simple Profit of Geant4 advanced geometry modeling, interactive facilities etc. same physics as original Penelope

Hadrons and ions Variety of models, depending on energy range particle type charge Composition of models across the energy range, with different approaches analytical based on data reviews + parameterisations Specialised models for fluctuations Open to extension and evolution

Algorithms encapsulated in objects Physics models handled through abstract classes Hadrons and ions Interchangeable and transparent access to data sets Transparency of physics, clearly exposed to users

Hadron and ion processes Variety of models, depending on energy range, particle type and charge Positive charged hadrons Density correction for high energy Shell correction term for intermediate energy Spin dependent term Barkas and Bloch terms Chemical effect for compound materials Nuclear stopping power Bethe-Bloch model of energy loss, E > 2 MeV 5 parameterisation models, E < 2 MeV based on Ziegler and ICRU reviews 3 models of energy loss fluctuations Positive charged ions Effective charge model Nuclear stopping power Scaling: 0.01 < b < 0.05 parameterisations, Bragg peak based on Ziegler and ICRU reviews b < 0.01: Free Electron Gas Model Negative charged hadrons Parameterisation of available experimental data Quantum Harmonic Oscillator Model Model original to Geant4 Negative charged ions: required, foreseen

Some results: protons Stopping power Ziegler and ICRU models Z dependence for various energies Ziegler and ICRU models Some results: protons Ziegler and ICRU, Fe Ziegler and ICRU, Si Nuclear stopping power Straggling Bragg peak (with hadronic interactions)

Positive charged ions Effective charge model Nuclear stopping power Scaling: 0.01 < b < 0.05 parameterisations, Bragg peak based on Ziegler and ICRU reviews b < 0.01: Free Electron Gas Model Effective charge model Nuclear stopping power Deuterons

Models for antiprotons  > 0.5 Bethe-Bloch formula 0.01 <  < 0.5 Quantum harmonic oscillator model  < 0.01 Free electron gas model Proton G4 Antiproton Antiproton from Arista et. al Antiproton exp. data Proton G4 Antiproton Antiproton from Arista et. al Antiproton exp. data

Atomic relaxation See next talk

Geant4 validation vs. NIST database All Geant4 physics models of electrons, photons, protons and a compared to NIST database Photoelectric, Compton, Rayleigh, Pair Production cross-sections Photon attenuation coefficients Electron, proton, a stopping power and range Comparison of Geant4 Standard and Low Energy Electromagnetic packages against NIST reference data document the respective strengths of Geant4 electromagnetic models Quantitative comparison Statistical goodness-of-fit tests See talk by B. Mascialino on Wednesday

Electrons: dE/dx Ionisation energy loss in various materials Compared to Sandia database More systematic verification planned Also Fe, Ur

The problem of validation: finding reliable data Note: Geant4 validation at low energy is not always easy experimental data often exhibit large differences! Backscattering low energies - Au

Applications A small sample in the next slides various talks at this conference concerning Geant4 Low Energy Electromagnetic applications Many valuable contributions to the validation of LowE physics from users all over the world excellent relationship with our user community

LINAC for IMRT Kolmogorov-Smirnov Test: p-value=1 M.Piergentili, INFN Genova

Interstitial brachytherapy Leipzig applicator Dosimetry Superficial brachytherapy Dosimetry Interstitial brachytherapy Bebig Isoseed I-125 source Dosimetry Endocavitary brachytherapy MicroSelectron-HDR source

Hadrontherapy beam line at INFN-LNS, Catania G.A.P. Cirrone, G. Cuttone, INFN LNS

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)

Shielding in Interplanetary Space Missions Aurora Programme Fe - 52 Si - 28 O - 16 C - 12 p GCR (all ion components) a ESA REMSIM Project Dose in astronaut resulting from Galactic Cosmic Rays

Conclusions New physics domain in HEP simulation Wide interest in the user community A wealth of physics models A rigorous approach to software engineering Significant results from an extensive validation programme A variety of applications in diverse domains