Stopping power (particle radiation)

The stopping power (English: Stopping Power ) of a material is the kinetic energy lost a charged particle per unit of path length on penetration into the material, for example, measured in MeV / cm ( see figure). The energy is consumed in a variety of collision processes. The stopping power depends of the instantaneous particle energy from, as well as of material and particle type.

Stopping power, the Bragg peak and range

All electrically charged particles lose energy while passing through matter. In the following special positive ions are considered. The term braking capacity describes the situation, so to speak, from the standpoint of the braking of the material, while the energy loss per path length is related to the particle. In terms of unit and value, both variables are identical. The energy loss per unit of path length is usually written with a negative sign:

Where E is the energy and x is the path length mean. As a result of the minus sign S is a positive quantity. Most of the energy loss per unit path rises during the path traveled by the particle to. The curve describing this is called Bragg curve (named after William Henry Bragg ). Shortly before the end of the path of the energy loss per unit path passes through a maximum, the Bragg peak, and then drops abruptly to (almost) zero. This is of great practical importance in the radiotherapy.

The above equation describes the linear stopping power, which is measured, for example, in MeV / mm. Dividing the linear stopping power by the density of the material, the result is the mass stopping power, which is measured in, for example MeV / ( mg/cm2 ). The mass stopping power is independent of the material density.

The picture shows how the stopping power of air - and thus the ionization density - increases for alpha particles along the path until it reaches the maximum. 5:49 MeV is the energy of alpha particles from the natural radon gas ( radon -222 ), which is found everywhere where there is granite in the ground.

The path that the particles in matter until their energy drops to zero, ie reach. The range depends on the particle type, the initial energy and material. One can calculate the range by integrating the reciprocal stopping power over the energy ( from the initial energy to zero):

The third picture shows the energy deposition of a proton beam of 250 MeV in water ( orange curve ); the curve has a very sharp Bragg peak. The blue curve shows the total energy deposition for several consecutive proton irradiations with varying energies. Such proton beams used for radiotherapy of extensive tumors, as this takes place, most of the energy deposition and thus the damage in the tumor itself.

The figure shows, for comparison, the absorption of a high energy photon beam. This curve is completely different (essentially an exponential decrease ), since the photon does not gradually release energy through many shocks, but mostly in a single ionization process loses all his energy (see also radiation). The absorption of a photon beam is not described by the stopping power, but by an absorption coefficient.

English expressions Stopping Power and Bragg peak are very common in German.

Electronic and nuclear stopping power

Under electronic stopping power is defined as the deceleration by inelastic collisions between the fast ion and the electrons of the medium traversed. These surges can cause both the electrons of the medium and the electrons of the ion excitation and ionization.

With an accuracy of a few percent can be the electronic stopping power above an energy of several hundred keV theoretically calculate, for example, by the Bethe formula. For lower energies, the calculation becomes more difficult.

Graphical representations of the measured values ​​of the electronic stopping power for many ions in many different substances have been documented. The accuracy of different tables to the stopping power was by means of statistical methods, among others investigated by H. Paul.

Under the nuclear stopping power is understood to elastic collisions between the ion and the atoms of the material (the term " nuclear" here has nothing to do with nuclear forces, so do nuclear forces ). If one knows the shape of the repulsive potential between ion and atom, one can calculate the nuclear stopping power. In the picture for protons in aluminum shown above, the nuclear contribution is negligible everywhere except at the lowest energy. With increasing mass of the ion but grows the nuclear contribution. Shown here in the figure to the right of the nuclear entry is larger than the electronic at low energy.

At not too high energies, the stopping power is therefore the sum of two quantities: . There are several semi- empirical models to calculate the stopping power. The model of Ziegler, Biersack and Littmark was originally described in a book. The latest version of the program is very much used today.

Lattice guiding effect ( channeling )

Deviations from the usual stopping power occur in monocrystalline solids. At not too low energies the regular arrangement of the lattice atoms leads here to a change of the impact probabilities then depend strongly on the direction of incidence of the particles relative to the orientation of the crystal.

References

Pictures of Stopping power (particle radiation)

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