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Geant4 Physics Reference Manual |
The energy loss processes are very similar for e+/e- , 
and
charged hadrons , so it is quite natural to have a common description for them
and we have chosen this way.
The G4eEnergyLoss class computes the continuous energy loss
of electrons/positrons.
The continuous energy loss is calculated as
a sum of the contribution of the different processes.
At present there are two processes
contributing to the continuous energy loss , they are:
the ionisation process (class G4eIonisation ) and the bremsstrahlung process (class G4eBremsstrahlung).
The class G4eIonisation calculates the contribution due to ionisation and it simulates the 'discrete' part of the ionisation , the Moller and Bhabha scattering or delta ray production by e+/e-.
The class G4eBremsstrahlung computes the energy loss contribution due to soft bremsstrahlung and it simulates the 'discrete' or hard bremsstrahlung. The formulae used to compute the continuous energy loss are the same than those in GEANT3, but the two programs are not the same. The main difference between GEANT3 and GEANT4 is that while in GEANT3 the continuous energy loss, delta ray production and bremsstrahlung are three independent processes , in GEANT4 these processes are closely connected, they form a unified scheme.
The G4eEnergyLoss class constructs dE/dx and range tables for every material. First the dE/dx tables are costructed and filled , the energy loss class simply summes up of the contributions computed by the ionisation and bremsstrahlung processes. After this step G4eEnergyLoss creates range tables of e+/e- for every material and computes the inverse of these range tables as well. All the tables are constructed at the beginning of the GEANT4 run , at initialisation time. Later, during the simulation the energy loss process performs two tasks : it imposes a limit on the stepsize of the particle and computes the energy loss after a step travelled by the particle.
The continuous energy loss imposes a limit on the stepsize.
The reason of this is the
energy dependence of the cross sections. It is generally assumed in MC programs that
the cross sections of the particles are approximately constant during a step , i.e.
the step size should be so small that the relative difference of the cross sections
at the beginning of the step and at the end should be small enough.In principle one
has to use very small steps in order to have an accurate simulation , but the computing
time increases if the stepsize decreases. As a good compromise the stepsize is
limited here by the requirement that the stopping range of the particle can
decrease by not more than 20 % during the step. This condition works fine for
a particle of kinetic energy
> 0.5 MeV - 1. MeV , but for low energy it
gives very short step sizes.
To cure this problem a lower limitation on the stepsize is also introduced.
The choice of this lower limit is quite natural , the stepsize can not be
smaller than the cut in range parameter of the program. The stepsize
limit varies smoothly with decreasing energy from the value given by the
condition
to the lowest possible value
cut in range .
It is worthwile to mention , that the lower limit used here is much more
natural and physical , than the one is used in GEANT3 at the automatic
calculation of the tracking parameters.
The computation of the mean energy loss after a given step is done
by using the range and inverse range tables. The mean loss 
can be written as
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(3.1) |
where T0 is the kinetic energy, r0 the range at the beginning of the step step, the function fT(r) is the inverse of the range table (i.e. it gives the kinetic energy of the particle for a range value of r) . After the mean energy loss has been calculated the process computes the actual energy loss , i.e. the loss with fluctuation. The fluctuation is computed from a fluctuation model , from the model GLANDZ of the GEANT3 code [GEANT3] , [La95] .
The energy loss of muons is computed by the class G4MuEnergyLoss. The scheme of the computation is the same as in the case of e+/e-, the only difference is that now there are three processes contributing to the total continuous energy loss , these are
the ionisation process (class G4MuIonisation),
the bremsstrahlung process (class G4MuBremsstrahlung) and
the direct pair production of muons (class G4MuPairProduction).
The G4MuIonisation class computes the contribution to the continuous energy
loss due to ionisation and simulates the corresponding 'discrete' process,
the knock-on electron or 
-ray production by muons.
The G4MuBremsstrahlung class calculates the continuous loss due to the soft bremsstrahlung and simulates the 'discrete', hard bremsstrahlung.
The G4MuPairProduction class gives the contribution to the continuous energy loss due to sub-cutoff e+/e- pairs and performs the simulation of the pair production.
The continuous energy loss of the charged hadrons are calculated by the class G4hEnergyLoss . The algorithm is the same than in the case of e+/e- energy loss. Here there is only one process , the ionisation (class G4hIonisation) which contributes to the continuous energy loss .
The G4hIonisation class computes the continuous energy loss and simulates
the -ray producion by hadrons.
In the case of energy loss of the hadrons two dE/dx , range and inverse range tables are constructed only , these are the tables for proton and antiproton . The energy loss for othe charged hadrons are computed from these tables at the scaled kinetic energy Tscaled
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(3.2) |
where T is the kinetic energy of the particle, Mproton and Mparticle are the masses of the proton and particle, respectively.
There is an important constraint for this process: the cut in range must be the same for all the charged hadrons . This condition is meaningful physically and it makes possible to use the proton/antiproton tables only when computing the energy loss.