20 February 2002Geant4 Users' Workhsop, SLAC1 Low-Energy Electromagnetic Processes in P. Nieminen...

20 February 2002 Geant4 Users' Workhsop, SLAC 1

Low-Energy Electromagnetic Processes in

P. Nieminen (ESA-ESTEC)

http://www.ge.infn.it/geant4/lowE/


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

Low-Energy e.m. applications

Mineralogical surveys of Solar System bodies

Spacecraft internal charging analyses

Dark matter search,Fundamental physics

Radiation effects analysis in X-and -ray astrophysical observatories

Radiotherapy, brachytherapy

Neutrino physics

Antimatter experiments

High EnergyPhysics


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 (-rays) 1 keV- Multiple scattering 1 keV

Geant4 low-energy models 250 eV


X-Ray Surveys of Solar System Bodies

Induced X-ray line emission:indicator of target composition(~100 m surface layer)

Cosmic rays,jovian electrons

Geant3.21

ITS3.0, EGS4

Geant4

Solar X-rays, e, p

Courtesy SOHO EIT

C, N, O line emissions included


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.


Compton scattering Photoelectric effect Rayleigh effect Pair production Bremsstrahlung Ionisation Atomic relaxation Polarised processes

…in preparation:

Auger effect Positrons

Processes included:

New physics


OOAD

Rigorous adoption of OO methods

openness to extension and evolution

Extensive use of design patterns

Booch methodology

Technology as a support to physics


Calculation of total cross sections

12

1221

/log

/loglog/logloglog

EE

EEEEE

where E1 and E2 are respectively the lower andhigher energy for which data (1 and 2) is available.

iii nE

1

Mean free path for a given process at energy E, withni the atomic density of the ith element contributingto the material composition


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.

Compton scattering

Rayleigh effect

Angular distribution: (E,)=[1+cos2F2(q), where F(q) is the energy-dependent form factor obtained from EPDL97.


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

Gamma conversion

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.


PhotonsPhotons


Electron bremsstrahlung

s

T

eV

T

Ts

MAX

MAX

C

dtdt

d

dtdt

d

TT

1.0

s

T

eV

T

eVs

MAX

C

dtdt

d

dtdt

dt

Tdx

dE

1.0

1.0

Continuous energy loss

Gamma ray production

T

tx

x

xF

dt

d ,

275.01 xxxF

F(x) obtained from EEDL. At high energies:

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)


Electron ionisation

The -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 -ray are considered

The resulting atomic relaxation treated as follow-on separate process


Electron ionisation

s

T

eV

T

Ts

MAX

MAX

C

dtdt

d

dtdt

d

TT

1.0

s

T

eV

T

eVs

MAX

C

dtdt

d

dtdt

dt

Tdx

dE

1.0

1.0

s

s

BT

Btx

x

xPC

dt

d

,2

Continuous energy loss

-electron production

x

Ag

xx

xxggxxP

1

1

111

22

2/12 g

Value of coefficient A for each element is obtained from fit to EEDL data for energies available in the database

Bs is the binding energy of sub-shell s


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


Domain decomposition leads to a design open to

physics extensions

Atomic relaxationAtomic relaxation


Photon attenuation coefficient

Comparison with NIST data

Standard Standard electromagnetic package

and Low EnergyLow Energy extensions0.01 0.1 1 10

0.01

0.1

1

10

100

1000

Geant4 LowEn NIST

/ (

cm 2

/g) i

n iro

n

Photon Energy (MeV)

Fe

0.01 0.1 1 10-16

-14

-12

-10

-8

-6

-4

-2

0

2

4

6

8

10

12

14

16

Delta = (NIST-G4EMStand) / NIST

Delta = (NIST-G4LowEn) / NIST

Del

ta (

%)

Photon Energy (MeV)

water water


Courtesy LIP and IPOFG-CROC (Coimbra delegation of the Portuguese Oncology Institute)

6 MV photon beamSiemens KD2

Thorax sliceCT image


Polarised Compton Scattering

2

0

020

220 cos42

h

h

h

h

h

hr

4

1

d

d

The Klein-Nishina cross section:

Where,h0 : energy of incident photon

h : energy of the scattered photon

: angle between the two polarization vectors

y

O z

x

h

h A

C


Angular distribution of scattered radiation composed of two components: ’

and ’with respect to AOC plane

’

’

CO

Ah

’

x

22

0

020

220 cossin2

h

h

h

h

h

hr

2

1

d

d distribution obtained with the class


Test of the distribution:

a) Low energy b) High energy

Low energy: ho << mc2 => h ho => =1 => a = 0

the distribution reduces to the Thompson distribution

=> the probability that the two polarization vectors are perpendicular is zero.

The distribution function is: where

and = h / h0.

High energy: small => h ho => 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.

2cos1

baba

P 4,21

ba


ResultsScalar product between the two polarization vectors for three different energies.

Upper histograms: Low polar angle

Lower histograms: High polar angle

100 keV 10 MeV1 MeVThese distributions are in agreement with the limits obtained previously.


Hadron and ion processesVariety of models, depending on energy range, particle type and charge

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

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

Positive charged hadronsPositive charged hadrons

Positive charged ionsPositive charged ions

Negative charged hadronsNegative charged hadrons

Scaling:

0.01 < < 0.05 parameterisations, Bragg peak

based on Ziegler and ICRU reviews

< 0.01: Free Electron Gas Model

Parameterisation of available experimental data Quantum Harmonic Oscillator Model

Effective charge model Nuclear stopping power

Model original to Geant4 Negative charged ions: required, foreseen

ion

ppppionion m

mTTTSZTS ,2

26Geant4 Users' Workhsop, SLAC20 February 2002

HERMES X-Ray Spectrometer on

Mercury Planetary Orbiter

PIXE from solar proton events


Algorithms encapsulated in

objects

Physics models handled through abstract classes

Interchangeable and transparent access to data sets

Hadrons and ionsHadrons and ions Open to extension and evolution

Transparency of physics, clearly exposed to users


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


Proton energy loss in H2O

Ziegler and ICRU parameterisations


Application examples

Five advanced examplesadvanced examples developed by the LowE EM WG released as part of the Geant4 Toolkit (support process)

Extensive collaboration with Analysis Tools groups

Brachytherapy Underground physics & radiation background X-ray fluorescence and PIXE

X-ray telescope -ray telescope

Full scale applications showing physics guidelines and advanced interactive facilities in real-life set-ups

GaAs linesFe lines

fluorescence


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


Useful links

http://www.ge.infn.it/geant4/lowE/ http://www.llnl.gov/cullen1/ http://www.icru.org/pubs.htm








http://www.llnl.gov/cullen1/





http://www.icru.org/pubs.htm




20 February 2002Geant4 Users' Workhsop, SLAC1 Low-Energy Electromagnetic Processes in P. Nieminen...

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