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first of all: Geant4 9.4 is a very old version and the processes that you are using (G4LowEnergyPhotoElectric and G4LowEnergyCompton) are no longer maintained or developed. So, I would suggest to update to a more recent version of Geant4 (10.3, but also the last patch 9.6, if you don't want to migrate the code to Geant4 10) and to use the new models G4LivermorePhotoElectricModel and G4LivermoreComptonModel instead of G4LowEnergyPhotoElectric and G4LowEnergyCompton.
And the total kinetic energy of the secondary particles (Esecondary) will less than the kinetic energy of the primary photon. The sum of the Edeposit and Esecondary will equal to the kinetic energy of the primary photon.
yes, correct. The energy conservation is enforced by the process, so the sum of the secondaries plus the local energy deposit is always matching the total available energy from the primary photon.
1, What does the energy deposit of that step do? Can the deposit energy make the crystal to fluoresce?
the localEnergyDeposit should be taken into account when you consider the response of the NaI as a detector. Basically, localEnergyDeposit is the sum of the energies of all "very-low-energy" secondaries that are not produced as independent tracks but just absorbed in the production point. So, if you want to get a reasonable spectrum from your NaI, you have to include the localEdep. Of course, this will produce scintillation. In principle you can have more secondaries produced (and less localEnergyDeposit) by decreasing the value of the production cut for gammas and electrons. You can have a look here
for more details
2, Why the distribution of Edeposit is like that? For the low energy compton process, why the deposit energy will more than 30keV?
I cannot comment on the old G4LowEnergyCompton model. I think you should give a try with the more recent version/model and check if you find the same results.