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 \page ExampleTestEm15 Example TestEm15
 
 How to compute and plot the final state of:
  - Multiple Scattering
  - Gamma Conversion
 
 considered as an isolated processes, see PHYSICS.
 
 For Multiple Scattering, the method is exposed below.
 
 For Gamma Conversion, when G4BetheHeitler5DModel Model is used,
 see \ref ExampleTestEm15_GC for Histograms and UI commands description.
 
 ## GEOMETRY DEFINITION
 
   It is a single box representing a 'semi infinite' homogeneous medium.
   Two parameters define the geometry:
   - the material of the box,
   - the (full) size of the box.
 
   The default geometry (100 m of water) is constructed in
   DetectorConstruction, but the above parameters can be changed
   interactively via the commands defined in DetectorMessenger.
 
 ## PHYSICS LIST
 
   The physics list contains the standard electromagnetic processes.
   In order not to introduce 'articicial' constraints on the step size,
   there is no limitation from the maximum energy lost per step.
 
 ## AN EVENT: THE PRIMARY GENERATOR
 
   The primary kinematic consists of a single particle starting at the edge
   of the box. The type of the particle and its energy are set in
   PrimaryGeneratorAction (1 MeV electron), and can be changed via the G4
   build-in commands of G4ParticleGun class (see the macros provided with
   this example).
 
 ## PHYSICS
 
    All discrete processes are inactivated (see provided macros),
    so that Multiple Scattering or Gamma Conversion is 'forced' to
    determine the first step of the primary particle.
    The step size and the final state are computed  and plotted.
    Then the event is immediately killed.
 
  __Multiple Scattering:__
 
   The result is compared with the 'input' data, i.e. with the cross sections stored in the PhysicsTables and used by Geant4.
 
   The stepMax command provides an additionnal control of the step size of
   the multiple scattering.
 
 
 ## HISTOGRAMS
 
   The test contains 16 built-in 1D histograms, which are managed by the
   HistoManager class and its Messenger. The histos can be individually
   activated with the command :
 ```
 /analysis/h1/set id nbBins  valMin valMax unit
 ```
   where unit is the desired unit for the histo (MeV or keV, etc..)
   (see the macros xxxx.mac).
 
    - 1 :  Multiple Scattering. True step length
    - 2 :  Multiple Scattering. Geom step length
    - 3 :  Multiple Scattering. Ratio geomSl/trueSl
    - 4 :  Multiple Scattering. Lateral displacement: radius
    - 5 :  Multiple Scattering. Lateral displac: psi_space
    - 6 :  Multiple Scattering. Angular distrib: theta_plane
    - 7 :  Multiple Scattering. Phi-position angle
    - 8 :  Multiple Scattering. Phi-direction angle
    - 9 :  Multiple Scattering. Correlation: cos(phiPos-phiDir)
 
    - 10 : Gamma Conversion. Open Angle * Egamma
    - 11 : Gamma Conversion. Log10(P recoil)
    - 12 : Gamma Conversion. Phi P recoil angle
    - 13 : Gamma Conversion. Phi P plus angle
    - 14 : Gamma Conversion. 2 * cos(phiplus + phiminus) Asymmetry
    - 15 : Gamma Conversion. E plus / E gamma
    - 16 : Gamma Conversion. Phi of Gamma Polarization
 
 
    The histograms are managed by the HistoManager class and its Messenger.
    The histos can be individually activated with the command :
 ```
 /analysis/h1/set id nbBins  valMin valMax unit
 ```
    where unit is the desired unit for the histo (MeV or keV, deg or mrad, etc..)
 
    One can control the name of the histograms file with the command:
 ```
 /analysis/setFileName  name  (default testem15)
 ```
 
    It is possible to choose the format of the histogram file : root (default),
    hdf5, xml, csv, by changing the default file type in HistoManager.cc
 
    It is also possible to print selected histograms on an ascii file:
 ```
 /analysis/h1/setAscii id
 ```
    All selected histos will be written on a file name.ascii (default testem15)
 
 ## VISUALIZATION
 
    The Visualization Manager is set in the main().
    The initialisation of the drawing is done via the commands
    /vis/... in the macro vis.mac. To get visualisation:
 ```
 > /control/execute vis.mac
 ```
 
    The detector has a default view which is a longitudinal view of the
    box.
 
    The tracks are drawn at the end of event, and erased at the end of run.
 
 ## HOW TO START ?
 
   - Execute TestEm15 in 'batch' mode from macro files:
 ```
 % ./TestEm15   compt.mac
 ```
 
   - Execute TestEm15 in 'interactive mode' with visualization:
 ```
 % ./TestEm15
 Idle> control/execute vis.mac
 ....
 Idle> type your commands
 ....
 Idle> exit
 ```
 
 ## - MACROS
 
  The examples of macros for Multiple Scattering:
   - electron.mac
   - muon.mac
   - proton.mac
 
  The example of Gamma Conversion macro:
   - gamma.mac - gamma to e+ e-
 
 \subpage ExampleTestEm15_GC
 
 \page ExampleTestEm15_GC Example TestEm15 - Gamma Conversion
 
 ## Gamma Conversion macros:
   - gamma.mac - tests of the 5D gamma -> e+ e- conversion model G4BetheHeitler5DModel
 
 All discrete processes are inactivated (see macro),
 so Gamma Conversion is 'forced'.
 
 ## HISTOGRAMS for gamma conversion
 
   - 10 : Open Angle (rad)* E gamma (MeV).
 
 The most probable value of the e+ e- pair opening angle multiplied by the
 photon energy is 1.6 rad*MeV and 338 rad*MeV in case mu+ mu- pair.
 See: Olsen, Phys. Rev. 131 (1963) 406.
 See also: Fig. 7 of arXiv:1802.08253 and Fig. 6 arXiv:1910.12501.
 
   - 11 :  Log10 ( recoil momentum).
 
 The distribution of the  recoil momentum is described by
 Jost, Phys. Rev. 80 (1950) 189 (no form factor).
 See also Fig. 2 of Astroparticle Physics 88 (2017) 60.
 
   - 12 :  Phi recoil.
 
   - 13 :  Phi positron.
 
   For linearly polarized incident photons, the distributions should show
   a sinusoidal shape with period 180°, for non polarized incident photons,
   the distribution of azimuthal angles should be flat.
 
   - 14 : Asymmetry 2 * cos(phi_+ + phi_-).
 
 For a photon propagating along x, polarized along y,
 the average value of ( 2.0 * cos(phi_+ + phi_-) ),
 provides a measurement of the polarization asymmetry, A.
 Eq. (12) of Nucl. Instrum. Meth. A 729 (2013) 765
 The azimuthal angle of the event defined as the bisector angle
 of the azimuthal angles of the positron and of the electron,
 (phi_+ + phi_-)/2,
 provides the optimal measurement of the asymmetry
 Astroparticle Physics 88 (2017) 30.
 
 For high-energy photons (E >> 20 MeV), the asymptotic expression for A
 can be used for comparison.
 Boldyshev, Yad. Fiz. 14 (1971) 1027, Sov.J.Nucl.Phys. 14 (1972) 576.
 See also eq. (13) of arXiv:1802.08253
 Example : A ~ 0.17 at 100 GeV.
 
   - 15 : E plus / E gamma.
 
 x_+ = E plus / E gamma has a more-or-less flat spectrum that extends
 almost from 0. to 1.
 See Fig. 16 page 261 of "The Quantum Theory of Radiation", W. Heitler,
 3rd edition, 1954.
 
   - 16 : Phi of Gamma Polarization.
 
 The phi of polarization vector after transformation into reference system
  defined by gamma direction (z) , gamma polarization (x).
 
 ## UI COMMANDS
 
 There are two commands to control G4BetheHeitler5DModel:
 
 ```
 /process/gconv/conversionType itype
 /process/gconv/onIsolated bool
 ```
 
 The command:
 ```
 /process/gconv/conversionType
 ```
 
 Allow to force conversion on nuclear or electron
 The parameter values:
  - 0 - (default) both triplet and nuclear conversion in proportion triplet/nuclear 1/Z
  - 1 - force nuclear conversion
  - 2 - force triplet
 
 The command:
 ```
 /process/gconv/onIsolated
 ```
 
 Allow simulate conversion on isolated particles without screening
 The perimeter values:
  - false - (default) atomic electron screening
  - true - conversion on isolated particles

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