Implementation of a new G4VDiscreteProcess - energy dependence of the cross section along step

Hello everyone,
I want to implement in Geant4 a new process that describes the annihilation of a positron with an electron to an invisible final state, through a s-channel diagram:

e+ e- -> A’ -> CHI CHI

where CHI is the (invisible) final state particle and A’ is the intermediate (virtual) particle. I know the cross section for this process, including the finite A’ width.

If this process is implemented as a G4VDiscreteProcess, the method GetMeanFreePath would be used to return the mean free path. This is computed from the total cross section, using the positron energy at the end of the previous step.

I am unsure about how the energy loss across the step due to ionization and Bremmstrahlung can be handled here: due to resonant process, the annihilation cross section depends significantly on the positron energy, and the positron looses energy along the step due to the aforementioned continuous processes.

Is there a possible way to handle this? I noticed that in the physics manual ( there is a reference to this problem, but the processes that are presented as an example ( G4eIonisation , G4hIonisation , G4eBremsstrahlung) are all of the type G4VEnergyLossProcess, and thus not directly applicable to this case.

Maybe it is not appropriate to implement this process using a new class inheriting from G4VDiscreteProcess class?



if it is electromagnetic process inheriting of G4VEmProcess, then the integral approach is applied automatically.