Low-Energy Electromagnetic Processes in
P. Nieminen (ESA-ESTEC)
http://www.ge.infn.it/geant4/lowE/
20 February 2002
Geant4 Users' Workhsop, SLAC
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Contents
1. Introduction
2. Electron and photon low-energy
electromagnetic processes in Geant4
3. Hadron and ion low-energy
electromagnetic processes in Geant4
4. Conclusions
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Dark matter search,
Fundamental physics
High Energy
Physics
Radiotherapy,
brachytherapy
Neutrino physics
Radiation effects analysis in X-and
g-ray astrophysical observatories
Low-Energy e.m.
applications
Mineralogical surveys of
Solar System bodies
Spacecraft internal
charging analyses
Antimatter
experiments
Electron and photon processes
Energy cut-offs
 Geant3.21
 EGS4, ITS3.0
 Geant4 “standard models”
- Photoelectric effect
- Compton effect
- Bremsstrahlung
- Ionisation (d-rays)
- Multiple scattering
 Geant4 low-energy models
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10 keV
1 keV
10 keV
10 keV
1 keV
1 keV
1 keV
250 eV
4
Cosmic rays,
jovian electrons
X-Ray Surveys of Solar
System Bodies
Solar X-rays, e, p
Geant3.21
ITS3.0, EGS4
Courtesy SOHO EIT
Induced X-ray line emission:
indicator of target composition
(~100 mm surface layer)
20 February 2002
Geant4
C, N, O line emissions included
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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.
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Processes included:
…in preparation:








 Auger effect
 Positrons
Compton scattering
Photoelectric effect
Rayleigh effect
Pair production
Bremsstrahlung
Ionisation
Atomic relaxation
Polarised processes
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New physics
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OOAD
Technology as a support to physics
Rigorous adoption of OO methods
 openness to extension and evolution
Extensive use of design patterns
Booch methodology
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Calculation of total cross sections
log  1 log E2 / E   log  2 log E / E1 
log  E  
log E2 / E1 
where E1 and E2 are respectively the lower and
higher energy for which data (1 and 2) is available.

1
  i  E   ni
i
Mean free path for a given process at energy E, with
ni the atomic density of the ith element contributing
to the material composition
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Compton scattering
 Energy distribution of the scattered photon according to KleinNishina 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.
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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.
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Photons
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Electron bremsstrahlung
TC

d 

t
dt


dt 
dE
0.1 eV
    s T  TMAX

dx
d
s 

dt



dt
0
.
1
eV


Continuous energy loss
TMAX

d 

dt

dt


TC
 T      s T  TMAX

d 
s 
dt 


dt 
0.1 eV

d F x 
t

, x
dt
x
T
F(x) obtained from EEDL. At
high energies:
F x   1  x  0.75x 2
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
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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 s 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
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Electron ionisation
TC

d 

t
dt


dt 
dE
0.1 eV
    s T  TMAX

dx
d
s 

dt



dt
0
.
1
eV


t  Bs
d
P x 
C 2 , x
dt
T  Bs
x
Bs is the binding energy of sub-shell s
x2  1
 A
Px   1  gx  1  g x 
 g

1 x 1 x
 x
2
Continuous energy loss
TMAX

d 

dt

dt


TC
 T      s T  TMAX

d 
s 
dt 


dt 
0.1 eV

g  2g  1 / g 2
Value of coefficient A for each element is
obtained from fit to EEDL data for
energies available in the database
d-electron production
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Atomic relaxation
 EADL data used to calculate the complete radiative and nonradiative 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
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Atomic relaxation
Domain decomposition
leads to a design open to
physics extensions
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Delta = (NIST-G4EMStand) / NIST
Delta = (NIST-G4LowEn) / NIST
16
14
12
water
10
water
8
6
Delta (%)
4
2
0
-2
-4
-6
-8
-10
-12
-14
-16
0.01
m /r (cm 2 /g) in iron
100
10
Photon attenuation coefficient
Comparison with NIST data
Fe
10
1
Photon Energy (MeV)
Geant4 LowEn
NIST
1000
0.1
1
0.1
0.01
0.01
0.1
Photon Energy (MeV)
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1
10
Standard electromagnetic package
and Low Energy extensions
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Thorax slice
CT image
6 MV photon beam
Siemens KD2
Courtesy LIP and IPOFG-CROC (Coimbra delegation of the
Portuguese Oncology Institute)
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Polarised Compton Scattering
x
The Klein-Nishina cross section:
d 1 2 h2  h0 h
2 
 r0 2 

 2  4 cos 
d 4 h0  h h0

x
h0
Where,
h0 : energy of incident photon
h : energy of the scattered photon
 : angle between the two
y
polarization vectors
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
O
h
q
a
f
A
z
C
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Angular distribution of scattered radiation composed of two
components: ’|| and ’^ with respect to AOC plane
’||
x

’ b
x
h
O

x
’^ A
C
d 1 2 h2  h0 h
2
2 
 r0


2
sin
q
cos
f
2 
d 2 h0  h h0

20 February 2002
f distribution obtained
with the class
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Test of the distribution:
a) Low energy b) High energy
The distribution function is: P  
and m = h / h0.
Low energy: ho << mc2

1
a  b cos 2 
ab
=> h  ho
=>
m =1

where a  m 
=>
1
m
2,b  4
a=0
the distribution reduces to the Thompson distribution
=> the probability that the two polarization vectors are perpendicular
is zero.
High energy:
small q => h  ho => equal to low energy
high q: it is possible to demonstrate that b/(a+b) ->0, so
in this case the distribution tend to be isotropic.
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Results
Scalar product between the two polarization vectors for three different energies.
Upper histograms: Low polar angle q
Lower histograms: High polar angle q
100 keV
1 MeV
10 MeV
These distributions are in agreement with the limits obtained previously.
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Hadron and ion processes
Variety of models, depending on energy range, particle type and charge
Positive charged hadrons
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
Scaling:
2
S ion T   Z ion
S p T p , T p  T
mp
mion
- 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
- Effective charge model
- Nuclear stopping power
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
20 February 2002
- Model original to Geant4
- Negative charged ions: required, foreseen
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HERMES X-Ray Spectrometer on
Mercury Planetary Orbiter
PIXE from solar
proton events
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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
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Interchangeable
and transparent access
to data
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Hadron and ion low-energy e.m. extensions
Low energy hadrons and ions models based on Ziegler and
ICRU data and parameterisations
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Barkas effect:
models for antiprotons
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Proton energy
loss in H2O
Ziegler and ICRU
parameterisations
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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

fluorescence
Full scale applications showing
physics guidelines and advanced
interactive facilities in real-life set-ups
Fe lines
GaAs lines
Extensive collaboration with
Analysis Tools groups
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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
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Useful links
 http://www.ge.infn.it/geant4/lowE/
 http://www.llnl.gov/cullen1/
 http://www.icru.org/pubs.htm
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