Stopping power of charged particles in matter So I have this diagram of how the stopping power of muons changes with energy:

Depending on energy different equations are used to describe the stopping power variation. Now, currently I'm reading about external radiation therapy with charged particles (especially protons). And my teacher have stated that the stopping power of a proton can pretty much be described by the Bethe equation, since it holds for the ranges of energies that proton therapy uses (The diagram is probably a bit different for protons than for muons). And yes, that does make some sense I think. My question is then: The particles, it being tissue or any other type of matter, will eventually stop, i.e. having no energy at all. So in turn, wouldn't that mean that you would have to include Anderson-Ziegler, Lindhard-Scharff corrections in order to get the correct stopping power, or am I missing something (Assuming the diagram looks just a bit like the one above). Again, I've been told the Bethe equation is "good enough" for proton therapy in patients, so I am not sure if it also holds if I were to fire at an iron target or something.
Thanks in advance.
 A: During proton therapy, most of the damage is actually done in the last few mm before the beam stops - at the point called the Bragg Peak
Yes, the penetration distance is largely determined by the energy above a few MeV; as the particle slows down, it starts to dump more energy per unit length. Quoting from "The physics of protons for patient treatment" (Wroe, Slater and Slater):

Protons and
  other heavy charged particles come close to fulfilling this objective: they deposit most of their energy
  in a high-dose peak (known as the Bragg peak) at the end of their track (Fig. 1). This peak is created
  through an exponential increase in stopping power towards the end of the protons’ track. Hence, as a
  heavy charged particle (such as a proton) slows down, the amount of energy it deposits per unit length
  covered increases exponentially, creating a high-dose peak (2). The depth of this peak in a given
  material (such as a patient) depends on its initial energy; varying this energy allows the high-dose
  region to be placed at any depth. 

And figure 1 from the paper:

