Low-Energy Electromagnetic Processes in

1. Low-Energy Electromagnetic Processes in P. Nieminen (ESA-ESTEC) http://www.ge.infn.it/geant4/lowE/ Geant4 Users' Workhsop, SLAC

2. Contents • Introduction • Electron and photon low-energy electromagnetic processes in Geant4 • Hadron and ion low-energy electromagnetic processes in Geant4 • Conclusions Geant4 Users' Workhsop, SLAC

3. Dark matter search, Fundamental physics High Energy Physics Radiotherapy, brachytherapy Low-Energy e.m. applications Neutrino physics Spacecraft internal charging analyses Radiation effects analysis in X-and g-ray astrophysical observatories Mineralogical surveys of Solar System bodies Antimatter experiments

4. Electron and photon processesEnergy cut-offs • Geant3.21 10 keV • EGS4, ITS3.0 1 keV • Geant4 “standard models” - Photoelectric effect 10 keV - Compton effect 10 keV - Bremsstrahlung 1 keV - Ionisation (d-rays) 1 keV - Multiple scattering 1 keV • Geant4 low-energy models250 eV Geant4 Users' Workhsop, SLAC

5. Cosmic rays, jovian electrons X-Ray Surveys of Solar System Bodies Solar X-rays, e, p Geant3.21 ITS3.0, EGS4 Courtesy SOHO EIT Geant4 Induced X-ray line emission: indicator of target composition (~100 mm surface layer) C, N, O line emissions included Geant4 Users' Workhsop, SLAC

6. Features of electron and photon models • Validity range from 250 eV to 100 GeV • Elements Z=1 to 100 • Data bases: - EADL (Evaluated Atomic Data Library), - EEDL (Evaluated Electrons Data Library), - EPDL97 (Evaluated Photons Data Library) from LLNL, courtesy Dr. Red Cullen. A version of libraries especially formatted for use with Geant4 available from Geant4 distribution source. Geant4 Users' Workhsop, SLAC

7. …in preparation: Processes included: • Compton scattering • Photoelectric effect • Rayleigh effect • Pair production • Bremsstrahlung • Ionisation • Atomic relaxation • Polarised processes • Auger effect • Positrons New physics Geant4 Users' Workhsop, SLAC

8. OOAD Technology as a support to physics • Rigorous adoption of OO methods •  openness to extension and evolution • Extensive use of design patterns • Booch methodology Geant4 Users' Workhsop, SLAC

9. Calculation of total cross sections where E1 and E2 are respectively the lower and higher energy for which data (s1 and s2) is available. Mean free path for a given process at energy E, with ni the atomic density of the ith element contributing to the material composition Geant4 Users' Workhsop, SLAC

10. Compton scattering • Energy distribution of the scattered photon according to 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. Rayleigh effect • Angular distribution: F(E,q)=[1+cos2(q)]F2(q), where F(q) is the energy-dependent form factor obtained from EPDL97. Geant4 Users' Workhsop, SLAC

11. Gamma conversion • The secondary e- and e+ energies 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 Photoelectric effect • Subshell from which the electron is emitted selected according to the cross sections of the sub-shells. De-excitation via isotropic fluorescence photons; transition probabilities from EADL. Geant4 Users' Workhsop, SLAC

12. Photons Geant4 Users' Workhsop, SLAC

13. Electron bremsstrahlung F(x) obtained from EEDL. At high energies: Continuous energy loss Direction of the outgoing electron thesame as that of the incoming one; angular distribution of emitted photons generated according to a simplified formula based on the Tsai cross section (expected to become isotropic in the low-E limit) Gamma ray production Geant4 Users' Workhsop, SLAC

14. Electron ionisation • The d-electron production threshold Tc is used to separate the continuous and discrete parts of the process • Partial sub-shell cross sections ss obtained by interpolation of the evaluated cross section data in the EEDL library • Interaction leaves the atom in an excited state; sampling for excitation is done both for continuous and discrete parts of the process • Both the energy and the angle of emission of the scattered electron and the d-ray are considered • The resulting atomic relaxation treated as follow-on separate process Geant4 Users' Workhsop, SLAC

15. Electron ionisation Bs is the binding energy of sub-shell s Continuous energy loss Value of coefficient A for each element is obtained from fit to EEDL data for energies available in the database d-electron production Geant4 Users' Workhsop, SLAC

16. Atomic relaxation • EADL data used to calculate the complete radiative and non-radiative spectrum of X-rays and electrons emitted • Auger effect and Coster-Kronig effect under development; fluorescent transitions implemented • Transition probabilities explicitly included for Z=6 to 100 • K, L, M, N, and some O sub-shells considered. Transition probabilities for sub-shells O, P, and Q negligible (<0.1%) and smaller than the precision with which they are known • For Z=1 to 5, a local energy deposit corresponding to the binding energy B of an electron in the ionised sub-shell simulated. • For O, P, and Q sub-shells a photon emitted with energy B Geant4 Users' Workhsop, SLAC

17. Atomic relaxation Domain decomposition leads to a design open to physics extensions Geant4 Users' Workhsop, SLAC

18. Geant4 Users' Workhsop, SLAC

19. water water Photon attenuation coefficient Comparison with NIST data Standard electromagnetic package and Low Energy extensions Fe Geant4 Users' Workhsop, SLAC

20. Thorax slice CT image 6 MV photon beam Siemens KD2 Courtesy LIP and IPOFG-CROC (Coimbra delegation of the Portuguese Oncology Institute) Geant4 Users' Workhsop, SLAC

21. x x f hn  A hn0 q a z O C y Polarised Compton Scattering The Klein-Nishina cross section: Where, h0: energy of incident photon h: energy of the scattered photon  : angle between the two polarization vectors Geant4 Users' Workhsop, SLAC

22. e’|| x e’ b Q x A hn e’^ x e O C Angular distribution of scattered radiation composed of two components: e’|| and e’^with respect to AOC plane  distribution obtained with the class Geant4 Users' Workhsop, SLAC

23. Test of the distribution: a) Low energy b) High energy The distribution function is: where and  = h / h0. Low energy: ho << mc2 => hho =>  =1 => a = 0 the distribution reduces to the Thompson distribution => the probability that the two polarization vectors are perpendicular is zero. High energy: small  => hho => equal to low energy high : it is possible to demonstrate that b/(a+b) ->0, so in this case the distribution tend to be isotropic. Geant4 Users' Workhsop, SLAC

24. Results Scalar product between the two polarization vectors for three different energies. Upper histograms: Low polar angle  Lower histograms:High polar angle  100 keV 1 MeV 10 MeV These distributions are in agreement with the limits obtained previously. Geant4 Users' Workhsop, SLAC

25. 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 • PIXE included • 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 • Model original to Geant4 • Negative charged ions: required, foreseen • Parameterisation of available experimental data • Quantum Harmonic Oscillator Model Geant4 Users' Workhsop, SLAC

26. HERMESX-Ray Spectrometer onMercury Planetary Orbiter PIXE from solar proton events Geant4 Users' Workhsop, SLAC

27. Hadrons and ions Open to extension and evolution Physics models handled through abstract classes Algorithms encapsulated in objects Transparency of physics, clearly exposed to users Geant4 Users' Workhsop, SLAC Interchangeable and transparent access to data sets

28. Hadron and ion low-energy e.m. extensions Low energy hadrons and ions models based on Ziegler and ICRU data and parameterisations Barkas effect: models for antiprotons Geant4 Users' Workhsop, SLAC

29. Proton energy loss in H2OZiegler and ICRU parameterisations Geant4 Users' Workhsop, SLAC

30. fluorescence GaAs lines Fe lines Applicationexamples • Fiveadvanced examples developed by the LowE EM WG released as part of the Geant4 Toolkit (support process) • X-ray telescope • g-ray telescope • Brachytherapy • Underground physics & radiation background • X-ray fluorescence and PIXE Full scale applications showing physics guidelines and advanced interactive facilitiesin real-life set-ups Extensive collaboration with Analysis Tools groups Geant4 Users' Workhsop, SLAC

31. Conclusions • A set of models has been developed to extend the Geant4 coverage of electromagnetic interactions of photons and electrons down to 250 eV, and of hadrons down to < 1 keV • Rigorous software process applied • Wide user community in astrophysics, space applications, medical field, HEP, in the U.S., Europe, and elsewhere • Modularity of Geant4 enables easy extensions and implementation of new models • Further low-energy electromagnetic physicsdevelopments and refinements are underway Geant4 Users' Workhsop, SLAC

32. Useful links • http://www.ge.infn.it/geant4/lowE/ • http://www.llnl.gov/cullen1/ • http://www.icru.org/pubs.htm Geant4 Users' Workhsop, SLAC