Overview of Geant4 Physics

2nd Finnish Geant4 Workshop

6-7 June 2005

Dennis Wright (SLAC)

Outline

Introduction

Physics Processes in General

Production Thresholds

Specific Processes

Electromagnetic

Optical

Decay

Physics Lists

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Physics in Geant4

Geant4 is a toolkit

physics approach is atomistic as opposed to integral

-> many particles and many interactions available for use

with a few exceptions, Geant4 physics interactions are not coupled

Very flexible way to build a physics environment

user can pick and choose only the particles and physics of interest

But, user must have a good understanding of the physics required

omission of particles or physics could cause errors or poor simulation

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Physics Provided by Geant4

EM physics

“standard” processes valid from ~ 1 keV to ~ PeV

“low-energy” valid from 250 eV to ~ PeV

optical photons

Weak physics

decay of subatomic particles

radioactive decay of nuclei

Hadronic physics

pure hadronic processes valid from 0 to ~100 TeV

e-,nuclear valid from 10 MeV to ~TeV

Parameterized or “fast simulation” physics

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Physics Processes (1)

Geant4 physics (interactions, decays, transportation, etc.) occurs through processes

A process does two things:

decides when and where an interaction will occur

method: GetPhysicalInteractionLength()

relies on cross sections

generates the final state (changes momentum, generates secondaries, etc)

method: DoIt()

relies on a model or implementation

The physics of a process may be:

well-located in space -> PostStep

not well-located in space -> AlongStep

well-located in time -> AtRest

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Physics Processes (2)

Gamma

Electron

Compton

scattering

Pair

production

Multiple

scattering

Ionization

Brems-

strahlung

A particle will do nothing unless a process is

assigned to it

If more than one process is assigned to a particle,

they compete to see which one occurs

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Example Event with Standard EM Processes Turned On

50 MeV e- entering LAr-Pb calorimeter

Processes used:

bremsstrahlung

ionization

multiple scattering

positron annihilation

pair production

Compton scattering

1

EM Physics:
Propagation of Charged Particles

Three essential topics:

Energy loss – what processes cause charged particles to lose energy in matter?

Secondary production threshold – when energy is lost, does Geant4 generate “real” secondaries (electrons, photons) or “virtual” ones?

Multiple scattering – how does Geant4 handle the potentially large number of Coulomb scatterings along a path?

These three topics are coupled:

multiple scattering requires energy loss

energy loss requires a knowledge of the secondary production threshold

These issues do not apply to purely hadronic interactions or to photon-induced reactions

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Threshold for Secondary Production (1)

A simulation must impose an energy cut below which secondaries are not produced

avoid infrared divergence

save CPU time used to track low energy particles

But, such a cut may cause imprecise stopping location and deposition of energy

Particle dependence

range of 10 keV  in Si is a few cm

range of 10 keV e- in Si is a few microns

Inhomogeneous materials

Pb-scintillator sandwich: if cut OK for Pb, energy deposited in sensitive scintillator may be wrong

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Threshold for Secondary Production (2)

Solution: impose a cut in range

Given a single range cut, Geant4 calculates for all materials the corresponding energy at which production of secondaries stops

During tracking:

Incident particle loses energy by generation of secondaries (energy loss is discrete)

Real secondaries are produced only if they can travel beyond their minimum calculated range in the material

If incident particle no longer has enough energy to produce such a secondary, energy loss is treated as continuous (virtual secondaries)

Incident particle is then tracked down to zero energy using continuous energy loss.

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Production Threshold vs. Energy Cut

Cut = 2 MeV

Cut = 450 keV

Production range =1.5 mm

500 MeV p in

LAr-Pb sampling

calorimeter

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Multiple Coulomb Scattering (1)

Geant4 adopts a “condensed model” of multiple scattering:

Sum over repeated elastic scatterings from nuclei over step length L

Cumulative effect:

net deflection Q

net spatial displacement D

true path length T

Many simulation packages use Moliere theory to sample angles:

Gaussian for small angles

Rutherford for larger angles

1

L

D

Q

T

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Multiple Coulomb Scattering (2)

But Moliere scattering:

is only accurate for small angles

is not good for very low E

is not good for very low Z or high Z

does not calculate spatial displacement (D)

Geant4 uses Lewis theory instead

based on full transport theory of charged particles

model functions are used to sample angular and spatial distributions

model parameters are determined by comparison to data

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Multiple Coulomb Scattering (3)

Physics processes determine a particle's path length

Multiple scattering conserves the “physical” path length, but the effective path length is shorter

Geant4 transportation process uses the effective path length to see if track hits volumes

-> multiple scattering process is always applied next to last (after all other physics processes but before transportation)

a

physical

effective

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Energy Loss

1

dE/dxtotal = dE/dxbrems + dE/dxioniz

integrate [dE/dxtotal ]-1 to get range

at initialization time total energy loss tables are built which require both bremsstrahlung and ionization to be instantiated

calculation of energy loss tables depends on secondary production threshold

ionization

production

threshold

range

path length

brems-

strahlung

energy loss

multiple scattering

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Geant4 Offers Three Categories of Electromagnetic Processes

Standard

optimized for high energy physics (250 eV – 1 PeV)

atomic shell structure is parameterized, binding energies ignored for most processes

Low Energy

developed for use in medical and space physics (250 eV – 100 GeV)

more detailed treatment of shell structure and binding energies (taken from data libraries)

Penelope

developed for coupled transport of e-, e+ and g (200 eV – 1 GeV)

most detailed model

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Ionization (1)

Ejection of atomic electrons is the primary means of energy loss for most charged particles

above the secondary production threshold: explicit emission of e-

below threshold: soft e- emission treated as continuous energy loss with fluctuations

Low Energy processes available:

G4PenelopeIonisation (for e+, e- only)

G4LowEnergyIonisation (for e- only)

G4hLowEnergyIonisation (for charged hadrons, ions)

e+, e- treated differently from heavier particles

small mass requires different formula

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Ionization (2)

electrons

above production threshold: secondaries produced by Moller scattering

below threshold: Berger-Seltzer formula used to get mean energy loss

positrons

above threshold: secondaries produced by Bhabha scattering

below threshold: Berger-Seltzer formula for mean energy loss

hadrons, ions

above threshold (spin ½) : ds/dT a [ 1 – b2T/Tmax + T2/2E2 ] /b2T2

below threshold (protons):

6 MeV and above: truncated Bethe-Bloch for mean energy loss

0.5 MeV – 6 MeV Barkas, Bloch effects

parameterized energy loss for 1 keV < T < 2 MeV (Bragg peak region)

nuclear stopping power (ions)

effective charge (ions)

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Energy Loss Fluctuations

Berger-Seltzer (e+,e-) and Bethe-Bloch (hadrons) used to get mean energy loss

But a small number of collisions with large energy transfers introduce fluctuations in energy loss

Typically, Landau theory is used to simulate fluctuations

but this assumes the full instead of truncated Bethe-Bloch formula

In Geant4 fluctuations are

Gaussian in thick materials (parametrized screening for low energies)

simulated by a “two-level” atom model in thin materials

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Bremsstrahlung (1)

Deceleration of charged particle in Coulomb field of an atom

real photon is produced

dominant process for e+, e- above 20 MeV in most materials

not important for heavier particles until ~200 GeV

Low Energy processes available:

G4PenelopeBremsstrahlung (e+, e- only)

G4LowEnergyBremsstrahlung (e- only)

g

e-

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Bremsstrahlung (2)

particles above production threshold: g secondaries produced

energy spectrum from EEDL functions

below threshold:

energy loss from EEDL total and differential cross sections

Three choices for g angular distribution:

G4ModifiedTsai : good above 500 keV

G4Generator2BS: good sampling efficiency

G4Generator2BN: good for 1 keV < E < 100 keV

Effects included:

brems from atomic electrons

screening by atomic electrons

Coulomb corrections to Born approximation

differences between e+, e- (Penelope)

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Atomic Relaxation

What happens in Geant4 to ionized atoms left behind after some process?

G4AtomicDeexcitation:

included as part of low energy ionization process

allows user to turn on:

fluorescence – x-ray generated as electron de-excites

vacant shell randomly sampled according to tabulated transition probabilities

Auger process – electron ejected as another electron de-excites

same as fluorescence except two shells must be chosen

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Pair Production

Conversion of photon into e+ e- pair

in Coulomb field of nucleus

in field of atomic electron

Closely related to bremsstrahlung

same set of corrections apply

Low energy processes available:

G4PenelopeGammaConversion

G4LowEnergyGammaConversion

g

e-

e+

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Compton Scattering

Scattering of g from an atomic electron

each atomic electron acts as an independent scatterer -> process is incoherent

described by Klein-Nishina formula

Low Energy Processes Available

G4LowEnergyCompton

shell structure taken into account with scattering function S(k,k')

G4LowEnergyPolarizedCompton

simulates polarization of incoming and outgoing photons

G4PenelopeCompton

atomic binding, shell structure

Doppler broadening

pz distribution of electrons in subshells

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Rayleigh Scattering

Coherent scattering of g from atom

Rayleigh formula: ds/dW a ½ (1 + cos2q)F2(q,Z)

Atomic form factor F read from tables

Low Energy Processes available:

G4LowEnergyRayleigh

G4PenelopeRayleigh (more detailed, takes longer to initialize)

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Photo-electric Effect

Ejection of atomic electron by incident photon

emitted electron has same direction as incident photon

electron shell selected according to tabulated cross sections

Ee = Eg – BEshell

Low Energy Processes Available:

G4LowEnergyPhotoElectric

G4PenelopePhotoElectric

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Cerenkov Radiation

Standard EM process: G4Cerenkov (no low energy version)

Photons emitted when incident charged particle has v > c/n

Energy distribution:

f(E) = 1 – 1/ [ n2(E) b2 ]

Emission angle: cosq = 1/bn

at x-ray energies n(E) ~ 1 -> no x-ray Cerenkov radiation

Number of photons produced roughly proportional to particle path length in material

emitted along the step

optical photons generated

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Scintillation

Standard EM process: G4Scintillation (no low energy version)

Charged particle deposits energy in a material

photons/length: dN/dx a dE/dx

proportionality constant can be changed by user to match measured scintillation yield

optical photons emitted uniformly along step

User must assign scintillation process to particle, and scintillation properties to material

photon emission spectrum

ratio of fast to slow time components

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Optical Photons (1)

Technically, should belong to electromagnetic category, but:

optical photon wavelength is >> atomic spacing

treated as waves -> no smooth transition between optical and gamma particle classes

Optical photons are produced by the following Geant4 processes:

G4Cerenkov

G4Scintillation

G4TransitionRadiation

Warning: these processes generate optical photons without energy conservation

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Optical Photons (2)

Optical photons undergo:

refraction and reflection at medium boundaries

bulk absorption

Rayleigh scattering

wavelength shifting

Geant4 keeps track of polarization

but not overall phase -> no interference

Optical properties can be specified in G4Material

reflectivity, transmission efficiency, dielectric constants, surface properties

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Optical Photons (3)

Geant4 demands particle-like behavior for tracking:

thus, no “splitting”

event with both refraction and reflection must be simulated by at least two events

q

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The Decay Process

Should be applied to all unstable, long-lived particles

Different from other physical processes:

mean free path for most processes: l = Nrs /A

for decay: l = gbct

1 process for all eligible particles

decay process retrieves BR and decay modes from decay table stored in each particle type

Decay modes for heavy flavor particles not included in Geant4

leave that to the event generators

decay process can invoke decay handler from the generator

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Available Decay Modes

Phase space:

2-body e.g. p0 -> gg , L -> p p-

3-body e.g. K0L -> p0 p+ p-

many body

Dalitz: P0 -> g l+ l-

Muon decay

V – A, no radiative corrections, mono-energetic neutrinos

Leptonic tau decay

like muon decay

Semi-leptonic K decay: K -> p l n

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Physics Lists (1)

This is where the user defines all the physics to be used in his simulation

First step: derive a class (e.g. MyPhysicsList) from the G4VUserPhysicsList base class

Next, implement the methods:

ConstructParticle() - define all necessary particles

ConstructProcess() - assign physics processes to each particle

SetCuts() - set the range cuts for secondary production

Register the physics list with the run manager in the main program

runManager -> SetUserInitialization(new MyPhysicsList);

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Physics List (ConstructParticle)

void MyPhysicsList::ConstructParticle()

{

G4Electron::ElectronDefinition();

G4Positron::PositronDefinition();

G4Gamma::GammaDefinition();

G4MuonPlus::MuonPlusDefinition();

G4MuonMinus::MuonMinusDefinition();

G4NeutrinoE::NeutrinoEDefinition();

G4AntiNeutrinoE::AntiNeutrinoEDefinition();

G4NeutrinoMu::NeutrinoMuDefinition();

G4AntiNeutrinoMu::AntiNeutrinoMuDefinition();

}

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Physics List
(SetCuts and ConstructProcess)

void MyPhysicsList::SetCuts()

{

defaultCutValue = 1.0*mm;

SetCutsWithDefault();

}

void MyPhysicsList::ConstructProcess()

{

AddTransportation(); //Provided by Geant4

ConstructEM(); //Not provided by Geant4

ConstructDecay(); // “ “ “ “

}

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Physics List (ConstructEM) (1)

void MyPhysicsList::ConstructEM()

{

theParticleIterator -> Reset();

while( (*theParticleIterator)() ) {

G4ParticleDefinition* particle = theParticleIterator -> Value();

G4ProcessManager* pm = particle -> GetProcessManager();

G4String particleName = particle -> GetParticleName();

if (particleName == “gamma”) {

pm -> AddDiscreteProcess(new G4ComptonScattering);

pm -> AddDiscreteProcess(new G4GammaConversion);

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PhysicsList (ConstructEM) (2)

} else if (particleName == “e-”) {

pm -> AddProcess(new G4MultipleScattering, -1, 1, 1);

pm -> AddProcess(new G4eIonisation, -1, 2, 2);

pm -> AddProcess(new G4eBremsstrahlung, -1, 3, 3);

These are “compound” processes: both discrete and continuous.

Integers indicate the order in which the process is applied

first column: process is AtRest

second column: process is AlongStep

third column: process is PostStep

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More Physics Lists

For a complete EM physics list see novice example N03

best way to start

modify it according to your needs

A physics list for a realistic application can become cumbersome

consider deriving from G4VModularPhysicsList

has RegisterPhysics method which allows writing “sub” physics lists (muon physics, ion physics, etc.)

Or completely avoid writing a physics list !

both electromagnetic and hadronic physics lists are included with the Geant4 distribution ( see geant4/physics_lists )

physics lists are application specific – decide which is best

then link to your application

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Application Specific Physics Lists

Pre-packaged physics lists documented at

Geant4 home page -> site index -> physics lists -> hadronic

Applications covered:

Medical

Dosimetry

Shielding penetration

Low background (underground dark matter searches, double beta decay)

Cosmic ray air showers

intermediate energy physics

high energy physics

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Summary

Physics processes decide where an interaction will occur and what will happen in the interaction

Secondary particle thresholds are determined by a minimum range for the secondary. Thresholds set the boundary between virtual and real particle emission in some EM processes.

Geant4 provides many electromagnetic processes which are especially accurate at low energies.

Optical and decay processes are also available

Physics lists are where the user builds particles, processes and sets the range for secondary production thresholds

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The GEANT4 toolkit and its application to the simulation of ast

2005-05-06T16:13:47