TestEm15 : 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 :

  10    # Open Angle (rad)* E gamma (MeV)
The most probable value of the pair opening angle multiplied by the
photon energy is 1.6 rad*MeV.
Olsen, Phys. Rev. 131 (1963) 406. See also Fig. 7 of arXiv:1802.08253

  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 

 14    # Asymmetry 2 * cos(phi_+ + phi_-)
For a photon propagating along x, polarized along y, the average value of 
 2 * 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).