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Thank you for your help first.
After reading your answer, yet, there are some points thar I still can not quite understand.
1) Is the multiple scattering the only one process of which the geometrical step length does not equal the true step length among Geant4 physics?
2) Do the multiple scattering and transportation both calculate the geometry limits? I can not see the reason that the multiple scattering should do this, beacause the multiple scattering also give the step length, you can compare it with other ordinary process, then take the shortest one, consequently there is no need to handle it specially.
3) ...Compton process limit is 1.2 mm and it is known that minimal distance to a geometry boundary is above 10 cm, there is no need o perform precise geometry computations... How do these ordinary processes know the distance to a boundary? Are there member functions of these G4 physical process to calculate it? I read the "Geant4 User's Guide for Application Developers (version-4.9.1)", it says "The geometry navigator calculates "Safety", the distance to the next volume boundary." on page 135. What is the geometry navigator? Is it the same as transportation or just a member function of all G4 processes, so that all processes including transportation and multiple scattering are able to calculate the geometry limit?
4) ...then it is mandatory first define the step of a particle before any other computation... What does define mean? I think that the role of transportation is to move the particle to the endpoint of the current step based on the minimum step length(including direction??), velocity(including direction) and position of the beginpoint of the current step. Therefore, one can carry out the transportation lastly after computing the particle change due to all other processes unless the transportation can not access the information of the beginpoint of the step after particle change.
5) ...For charged particles it is mandatory to apply multiple scattering as a next process... Does it mean that other ordinary processes need to compute their respective particle change based on the "true step length" given by multiple scattering process?
I hope these questions won't inconvenience you.