1. Low-Energy Electromagnetic Processes in
P. Nieminen (ESA-ESTEC)
20 February 2002
Geant4 Users' Workhsop, SLAC

2. Geant4 Users' Workhsop, SLAC
Contents
Introduction
Electron and photon low-energy electromagnetic processes in Geant4
Hadron and ion low-energy electromagnetic processes in Geant4
Conclusions
20 February 2002
Geant4 Users' Workhsop, SLAC

3. Low-Energy e.m. applications
Dark matter search,
Fundamental physics
High Energy
Physics
Radiotherapy,
brachytherapy
Neutrino physics
Low-Energy e.m. applications
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 processes Energy cut-offs
Geant keV
EGS4, ITS 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 models 250 eV
20 February 2002
Geant4 Users' Workhsop, SLAC

5. Geant4 Users' Workhsop, SLAC
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
20 February 2002
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.
20 February 2002
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7. Geant4 Users' Workhsop, SLAC
Processes included:
…in preparation:
Compton scattering
Photoelectric effect
Rayleigh effect
Pair production
Bremsstrahlung
Ionisation
Atomic relaxation
Polarised processes
Auger effect
Positrons
New physics
20 February 2002
Geant4 Users' Workhsop, SLAC

8. Technology as a support to physics
OOAD
Technology as a support to physics
Rigorous adoption of OO methods
 openness to extension and evolution
Extensive use of design patterns
Booch methodology
20 February 2002
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
20 February 2002
Geant4 Users' Workhsop, SLAC

10. Geant4 Users' Workhsop, SLAC
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.
20 February 2002
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11. Geant4 Users' Workhsop, SLAC
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.
20 February 2002
Geant4 Users' Workhsop, SLAC

12. Geant4 Users' Workhsop, SLAC
Photons
20 February 2002
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13. Electron bremsstrahlung
F(x) obtained from EEDL. At high energies:
Continuous energy loss
Direction of the outgoing electron the same 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
20 February 2002
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14. Geant4 Users' Workhsop, SLAC
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
20 February 2002
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
20 February 2002
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16. Geant4 Users' Workhsop, SLAC
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
20 February 2002
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17. Atomic relaxation
Domain decomposition leads to a design open to physics extensions
20 February 2002
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18. Geant4 Users' Workhsop, SLAC
20 February 2002
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19. Geant4 Users' Workhsop, SLAC
water
water
Photon attenuation coefficient
Comparison with NIST data
Standard electromagnetic package
and Low Energy extensions Fe
20 February 2002
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20. Geant4 Users' Workhsop, SLAC
Thorax slice
CT image
6 MV photon beam
Siemens KD2
Courtesy LIP and IPOFG-CROC (Coimbra delegation of the Portuguese Oncology Institute)
20 February 2002
Geant4 Users' Workhsop, SLAC

21. Polarised Compton Scatteringy O z x q a f hn
hn0  A C
The Klein-Nishina cross section:
Where,
h0 : energy of incident photon
h : energy of the scattered photon
 : angle between the two polarization vectors
20 February 2002
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22. Geant4 Users' Workhsop, SLAC
Angular distribution of scattered radiation composed of two components: e’|| and e’^ with respect to AOC plane
e’^
e’|| C O e A hn e’ x b Q
 distribution obtained with the class
20 February 2002
Geant4 Users' Workhsop, SLAC

23. Geant4 Users' Workhsop, SLAC
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.
20 February 2002
Geant4 Users' Workhsop, SLAC

24. Geant4 Users' Workhsop, SLAC
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.
20 February 2002
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
20 February 2002
Geant4 Users' Workhsop, SLAC

26. Geant4 Users' Workhsop, SLAC
HERMES X-Ray Spectrometer on Mercury Planetary Orbiter
PIXE from solar proton events
20 February 2002
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
20 February 2002
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
20 February 2002
Geant4 Users' Workhsop, SLAC

29. Proton energy loss in H2O Ziegler and ICRU parameterisations
20 February 2002
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30. Geant4 Users' Workhsop, SLAC
Application examples
Five advanced 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
GaAs lines
Fe lines
fluorescence
Full scale applications showing physics guidelines and advanced interactive facilities in real-life set-ups
Extensive collaboration with
Analysis Tools groups
20 February 2002
Geant4 Users' Workhsop, SLAC

31. Geant4 Users' Workhsop, SLAC
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 physics developments and refinements are underway
20 February 2002
Geant4 Users' Workhsop, SLAC

32. Geant4 Users' Workhsop, SLAC
Useful links
20 February 2002
Geant4 Users' Workhsop, SLAC