Low Energy Electromagnetic Physics

1. Low Energy Electromagnetic Physics Maria Grazia Pia INFN Genova Maria.Grazia.Pia@cern.ch on behalf of the Low Energy Electromagnetic Working Group Geant4 Workshop Helsinki, 30-31 October 2003 http://www.ge.infn.it/geant4/training/

2. Part 1 Overview Software process OOAD Physics Electrons and photons Hadrons and ions Atomic relaxation Polarisation Part 2 How to use LowE processes Examples Some experimental applications Outlook Plan of the tutorial

3. What is • A package in the Geant4 electromagnetic package • geant4/source/processes/electromagnetic/lowenergy/ • A set of processes extending the coverage of electromagnetic interactions in Geant4 down to “low” energy • 250 eV (in principle even below this limit)/100 eVfor electrons and photons • down to the approximately the ionisation potential of the interacting material for hadrons and ions • A set of processes based on detailed models • shell structure of the atom • precise angular distributions • Complementary to the “standard” electromagnetic package • will learn more on domains of application in the second lecture

4. Compton scattering Rayleigh scattering Photoelectric effect Pair production Bremsstrahlung Ionisation Polarised Compton + atomic relaxation fluorescence Auger effect following processes leaving a vacancy in an atom In progress More precise angular distributions (Rayleigh, photoelectric, Bremsstrahlung etc.) Polarised g conversion, photoelectric Development plan Driven by user requirements Schedule compatible with available resources Overview of physics • in two “flavours” of models: • based on theLivermore Library • à laPenelope

5. Compton scattering Rayleigh scattering Photoelectric effect Pair production Bremsstrahlung Ionisation Polarised Compton + atomic relaxation fluorescence Auger effect following photoelectric effect and ionisation In progress Polarised g conversion, photoelectric More precise angular distributions (Rayleigh, photoelectric, Bremsstrahlung etc.) Foreseen New models, based on different physics approaches Processes for positrons Development plan Driven by user requirements Schedule compatible with available resources Overview of physics

6. Software Process • A rigorous approach to software engineering • in support of a better quality of the software • especially relevant in the physics domain of Geant4-LowE EM • several mission-critical applications (space, medical…) • Public URD • Full traceability through UR/OOD/implementation/test • Testing suite and testing process • Public documentation of procedures • Defect analysis and prevention • etc.… Spiral approach A life-cycle model that is both iterative and incremental Collaboration-wide Geant4 software process, tailored to the WG projects current status Huge effort invested into SPI

7. 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

8. LowE e/g processes based on Livermore Library

9. Photons and electrons different approach w.r.t. Geant4 standard e.m. package • 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)

10. Data Management Cross sections, final state Intelligent data: know how to handle themselves through algorithm objects e.g.: interpolation algorithms encapsulated in objects (to let them vary and be interchangeable) Composite pattern to treat different physical entities (e.g. whole atom and atom with shell structure) transparently

11. 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

12. Photons

13. Compton scattering • Energy distribution of the scattered photon according to the Klein-Nishina formula, multiplied by scattering functions F(q) from EPDL97 data library • The effect of scattering function becomes significant at low energies • suppresses forward scattering • Angular distribution of the scattered photon and the recoil electron also based on EPDL97 Klein-Nishina cross section:

14. Rayleigh scattering • Angular distribution: F(E,q)=[1+cos2(q)]F2(q) • where F(q) is the energy-dependent form factor obtained from EPDL97 • Improved angular distribution to be available in next Geant4 release, December 2002

15. Photoelectric effect • Cross section • Integrated cross section (over the shells) from EPDL + interpolation • Shell from which the electron is emitted selected according to the detailed cross sections of the EPDL library • Final state generation • Direction of emitted electron = direction of incident photon • Deexcitation via the atomic relaxation sub-process • Initial vacancy + following chain of vacancies created

16. g conversion • 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 • Azimuthal angle generated isotropically • Choice of which particle in the pair is e- or e+ is made randomly

17. LowE Fe NIST-XCOM G4 Standard standard G4 LowE Photons: mass attenuation coefficient Tests by IST - Natl. Inst. for Cancer Research, Genova (F. Foppiano et al.) LowE accuracy ~ 1% 2N-L=13.1 – =20 - p=0.87 Comparison against NIST data LowE accuracy ~ 1% 2N-S=23.2 – =15 - p=0.08

18. Photons, evidence of shell effects Photon transmission, 1 mm Pb Photon transmission, 1 mm Al

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

20. Polarisation theory 500 million events simulation Polarisation of a non-polarised photon beam, simulation and theory Ratio between intensity with perpendicular and parallel polarisation vector w.r.t. scattering plane, linearly polarised photons

21. 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

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

23. Electron ionisation • New parameterisations of EEDL data library recently released • precision is now better than 5 % for ~ 50% of the shells, poorer for the 50% left • Plans • Systematic verification over shell, Z and energy • Need Test & Analysis Project for automated verification (all shells, 99 elements!)

24. NIST-ESTAR G4 Standard G4 LowE Electrons: range Range in various simple and composite materials Compared to NIST database Al

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

26. Electrons, transmitted 20 keV electrons, 0.32 and 1.04 mm Al

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

28. LowE e/g processes based on Penelope models

29. 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. • analytical approach • 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

30. LowE hadron/ion processes

31. 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

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

33. Stopping power Z dependence for various energies Ziegler and ICRU models Ziegler and ICRU, Fe Ziegler and ICRU, Si Straggling Nuclear stopping power Positive charged hadrons • Bethe-Bloch model of energy loss, E > 2 MeV • 5 parameterisation models, E < 2 MeV • based on Ziegler (1977,1985,2000) and ICRU reviews • 3 models of energy loss fluctuations • Density correction for high energy • Shell correction term for intermediate energy • Spin dependent term • Barkas and Bloch terms • Chemical effect for compounds • Nuclear stopping power • PIXE included(preliminary)

34. Bragg peak (with hadronic interactions) The precision of the stopping power simulation for protons in the energy from 1 keV to 10 GeV is of the order of a few per cent

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

36. Deuterons Positive charged ions • 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

37. Atomic relaxation

38. X-ray fluorescence spectrum in Iceand basalt (EIN=6.5 keV) Counts Fe lines GaAs lines Scattered photons Energy (keV) Fluorescence Experimental validation: test beam data, in collaboration with ESA Advanced Concepts Division Microscopic validation: against reference data Spectrum from a Mars-simulant rock sample Anderson-Darling Ac (95%) =0.752

39. Auger effect New implementation, validation in progress Auger electron emission from various materials Sn, 3 keV photon beam, electron lines w.r.t. published experimental results

40. Contribution from users • Many valuable contributions to the validation of LowE physics from users all over the world • excellent relationship with our user community • User comparisons with data usually involve the effect of several physics processes of the LowE package • sometimes combining LowE + Standard e.m. processes • A small sample in the next slides • no time to show all!

41. 15x15 cm2 Differences Differences 10x10 cm2 10x10 cm2 15x15 cm2 Homogeneous Phantom P. Rodrigues, A. Trindade, L.Peralta, J. Varela, LIP • Simulation of photon beams produced by a Siemens Mevatron KD2 clinical linear accelerator • Phase-space distributions interface with GEANT4 • Validation againstexperimental data: depth dose and profile curves LIP – Lisbon

42. Dose Calculations with 12C P. Rodrigues, A. Trindade, L.Peralta, J. Varela, LIP • Bragg peak localization calculated with GEANT4 (stopping powers from ICRU49 and Ziegler85) and GEANT3 in a water phantom • Comparison with GSI data preliminary

43. Uranium irradiated by electron beam Jean-Francois Carrier, Louis Archambault, Rene Roy and Luc Beaulieu Service de radio-oncologie, Hotel-Dieu de Quebec, Quebec, Canada Departement de physique, Universite Laval, Quebec, Canada The following results will be published soon. They are part of a general Geant4 low energy validation project. Fig 1. Depth-dose curve for a semi-infinite uranium slab irradiated by a 0.5 MeV broad parallel electron beam 1Chibani O and Li X A, Med. Phys. 29 (5), May 2002

44. Ions Independent validation at Univ. of Linz (H. Paul et al.) Geant4-LowE reproduces the right side of the distribution precisely, but about 10-20% discrepancy is observed at lower energies

45. The future… • In progress • More precise angular distributions (Rayleigh, photoelectric, Bremsstrahlung etc.) • Foreseen • Penelope processes for electrons (December 2003 release) • Processes for positrons (Penelope, December 2003 release) • Performance optimisation (later time scale) • Polarised g conversion, photoelectric • Development plan • Driven by user requirements • Schedule compatible with available resources

46. Compton scattering Rayleigh scattering Photoelectric effect Pair production Bremsstrahlung Ionisation Polarised Compton + atomic relaxation fluorescence Auger effect following photoelectric effect and ionisation The following code is required in your PhysicsList.cc [All code has been lifted from the relevant advanced examples] Low Energy Em Physics Implementation:

47. brachytherapy • Low energy electromagnetic processes for precise calculation of dose distribution // gamma #include "G4LowEnergyRayleigh.hh" #include "G4LowEnergyPhotoElectric.hh" #include "G4LowEnergyCompton.hh" #include "G4LowEnergyGammaConversion.hh" // e- #include "G4LowEnergyIonisation.hh" #include "G4LowEnergyBremsstrahlung.hh" // e+ #include "G4eIonisation.hh" #include "G4eBremsstrahlung.hh" #include "G4eplusAnnihilation.hh"

48. Brachytherapy Implementation void BrachyPhysicsList::ConstructEM() { theParticleIterator->reset(); while( (*theParticleIterator)() ){ G4ParticleDefinition* particle = theParticleIterator->value(); G4ProcessManager* pmanager = particle->GetProcessManager(); G4String particleName = particle->GetParticleName(); //processes lowePhot = new G4LowEnergyPhotoElectric("LowEnPhotoElec"); loweIon = new G4LowEnergyIonisation("LowEnergyIoni"); loweBrem = new G4LowEnergyBremsstrahlung("LowEnBrem"); if (particleName == "gamma") { //gamma pmanager->AddDiscreteProcess(new G4LowEnergyRayleigh); pmanager->AddDiscreteProcess(lowePhot); pmanager->AddDiscreteProcess(new G4LowEnergyCompton); pmanager->AddDiscreteProcess(new G4LowEnergyGammaConversion); } else if (particleName == "e-") { //electron pmanager->AddProcess(new G4MultipleScattering, -1, 1,1); pmanager->AddProcess(loweIon, -1, 2,2); pmanager->AddProcess(loweBrem, -1,-1,3); } else if (particleName == "e+") { //positron pmanager->AddProcess(new G4MultipleScattering, -1, 1,1); pmanager->AddProcess(new G4eIonisation, -1, 2,2); pmanager->AddProcess(new G4eBremsstrahlung, -1,-1,3); pmanager->AddProcess(new G4eplusAnnihilation, 0,-1,4); } } }

49. sample detector beam Fe lines GaAs lines Scattered photons X-ray fluorescence • Physics: Low Energy processes, atomic relaxation #include "G4LowEnergyCompton.hh" #include "G4LowEnergyGammaConversion.hh" #include "G4LowEnergyPhotoElectric.hh" #include "G4LowEnergyRayleigh.hh" // e+ #include "G4MultipleScattering.hh" #include "G4eIonisation.hh" #include "G4eBremsstrahlung.hh" #include "G4eplusAnnihilation.hh" #include "G4LowEnergyIonisation.hh" #include "G4LowEnergyBremsstrahlung.hh" #include "G4hLowEnergyIonisation.hh"

50. Process Registration X-rayFluo else if (particleName == "proton") { //proton pmanager->AddProcess(new G4MultipleScattering,-1,1,1); pmanager->AddProcess(new G4hLowEnergyIonisation,-1, 2,2); } else if ( particleName == "alpha" ) { pmanager->AddProcess(new G4MultipleScattering,-1,1,1); G4hLowEnergyIonisation* iIon = new G4hLowEnergyIonisation() ; pmanager->AddProcess(iIon,-1,2,2); } } } void XrayFluoPhysicsList::ConstructEM() { theParticleIterator->reset(); while( (*theParticleIterator)() ){ G4ParticleDefinition* particle = theParticleIterator->value(); G4ProcessManager* pmanager = particle->GetProcessManager(); G4String particleName = particle->GetParticleName(); if (particleName == "gamma") { // gamma pmanager->AddDiscreteProcess(new G4LowEnergyCompton); LePeprocess = new G4LowEnergyPhotoElectric(); //LePeprocess->ActivateAuger(false); //LePeprocess->SetCutForLowEnSecPhotons(10000 * keV); //LePeprocess->SetCutForLowEnSecElectrons(10000 * keV); pmanager->AddDiscreteProcess(LePeprocess); pmanager->AddDiscreteProcess(new G4LowEnergyRayleigh); } else if (particleName == "e-") { //electron pmanager->AddProcess(new G4MultipleScattering,-1, 1,1); LeIoprocess = new G4LowEnergyIonisation(); //LeIoprocess->ActivateAuger(false); //LeIoprocess->SetCutForLowEnSecPhotons(10000 keV); //LeIoprocess->SetCutForLowEnSecElectrons(10000 keV); pmanager->AddProcess(LeIoprocess, -1, 2, 2); LeBrprocess = new G4LowEnergyBremsstrahlung(); pmanager->AddProcess(LeBrprocess, -1, -1, 3); } else if (particleName == "e+") { //positron pmanager->AddProcess(new G4MultipleScattering,-1, 1,1); pmanager->AddProcess(new G4eIonisation, -1, 2,2); pmanager->AddProcess(new G4eBremsstrahlung, -1,-1,3); pmanager->AddProcess(new G4eplusAnnihilation, 0,-1,4); }