Remove extra sampling of asymmetry in photopairproduction secondary energy calculation

[Jean1995]

I noticed that in PhotoPairProductionInterpolant::CalculateEnergy, there is a step where we "randomize" how we distribute the energy between the electron and positron.

However, for this parametrization, rho (or in literature rather known as x, the ratio of the electron and photon energy) is already between [0, 1). This means we don't need to randomize the distribution.

This is probably a remnant from other classes, where rho is just sampled between [0, 1) due to the symmetry of the function. However, this is not implemented for PhotoPairProduction (although it could be implemented).

Therefore, we don't need 5, but 4 random numbers here.

[sudojan]

So the questions are,

• is the distribution symmetric in rho?
• if the above is the case, is the distribution, we need to sample from, also much easier when just considering the range between 0 and 0.5? (which is e.g. the case for the PairProduction induced by muons, where it greatly improves the accuracy).
• is the increase in accuracy worth it to draw an additional random number?

But for now, you are right, it does not make sense to draw this additional random number.

[Jean1995]

• is the distribution symmetric in rho?

While the KochMotz parametrization is completely symmetric in rho, the parametrization of Tsai surprisingly isn't. It is for E >> m_e, but otherwise, there is an asymmetry. It appears when transforming the differential cross section from dsigma/dp (with p the absolute electron momentum) to dsigma/dx.

I have to think a bit more about why this is happening.

I would open a new issue about the idea of sampling rho between 0 and 0.5.