Stopping Power, Bragg Curve and Range
The stopping power depends on the type and energy of the particle and on the properties of the material it passes. Since the production of an ion pair (usually a positive ion and a (negative) electron) requires a fixed amount of energy (for example, 33.97 eV in dry air), the density of ionisation along the path is proportional to the stopping power of the material.
Both electrons and positive ions lose energy while passing through matter. Positive ions are considered in most cases below.
'Stopping power' is treated as a property of the material, while 'energy loss per unit path length' describes what happens to the particle. However, numerical value and units are identical for both quantities; they are usually written with a minus sign in front:
where E means energy, and x is the path length. The minus sign makes S positive.
The stopping power and hence, the density of ionization, usually increases toward the end of range and reaches a maximum, the Bragg peak, shortly before the energy drops to zero. The curve that describes this is called the Bragg curve. This is of great practical importance for radiation therapy.
The equation above defines the linear stopping power which may be expressed in units like MeV/mm or similar. If a substance is compared in gaseous and solid form, then the linear stopping powers of the two states are very different just because of the different density. One therefore often divides S(E) by the density of the material to obtain the mass stopping power which may be expressed in units like MeV/(mg/cm2) or similar. The mass stopping power then depends only very little on the density of the material.
The picture shows how the stopping power of 5.49 MeV alpha particles increases while the particle traverses air, until it reaches the maximum. This particular energy corresponds to that of the alpha particle radiation from naturally radioactive gas radon (222Rn) which is present in the air in minute amounts wherever the ground contains granite.
The mean range can be calculated by integrating the reciprocal stopping power over energy:
where
- E0 is the initial kinetic energy of the particle
- R is the "continuous slowing down approximation (CSDA)" range and
- dE/dx is the total linear stopping power.
The deposited energy can be obtained by integrating the stopping power over the entire path length of the ion while it moves in the material.
Read more about this topic: Stopping Power (particle Radiation)
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