Non collinearity of gammas in e+-e- annihilation

Physics Processes, Models and Cross Sections
21

I attach the paper.

non_collinearity.pdf (387.0 KB)

Fig. 3 shows the energy distribution, centred in 511 keV, with a spread of 2.68 keV FWHM. They claim that the distribution of the deviation from 180 deg of the angle between the two gammas comes from Eq. 6, and should be a gaussian centred in 0 with a sigma of 0.54 degrees.
I attach the plot of the energy of my gammas, which appear to be exactly 511 keV, with no spread (so, different from Fig. 3) and also the plot of the angle between the gammas (different from a gaussian with 0.54 degrees FWHM, too).

energy
energy2064×1404 94.1 KB

angle
angle2014×1430 175 KB

22

Yes, you are right ! I wanted to write " do NOT include such effects "

23

Hi

I did not see this back in 2022. But non-collinearity can be activated, e.g:

  G4Material* water_mat = nist->FindOrBuildMaterial("G4_WATER");
  water_mat->GetIonisation()->SetMeanEnergyPerIonPair(5*eV);

Here is an extract from a forthcoming paper:

Towards the end of its range, at low energies, a positron captures an electron from the outer shell of the surrounding material and forms positronium, a bound state of electron and positron, a neutral atom about half the size of a normal atom. It will have a substantial kinetic energy from both the remaining energy of the positron and the energy of the electron within the targeted atom. It quickly cascades down to a ground state, either the 1s para-positronium, or the 3s ortho-positronium. In normal materials, the life times are long enough for this small atom to thermalise to some extent. In any case, when it decays, it has some motion that leads to an acollinearty of the para-positronium decay into two gammas.

The {\tt G4AllisonPositronAtRestModel} assumes a Maxwell-Boltzmann distribution for the velocity of this motion. The mean energy is material dependent and is chosen to fit experimental observation. PET systems observe a non-collinearity of, typically, 0.5 degrees FWHM, which corresponds to a Maxwell-Boltzmann mean energy of about 5 eV. This must be set for each relevant material, e.g:
\begin{verbatim}
G4Material* water = nist->FindOrBuildMaterial(“G4_WATER”);
water->GetIonisation()->SetMeanEnergyPerIonPair(5*eV);
\end{verbatim}