Range (particle radiation)

The range of charged particle radiation in a material is the path length that the radiation particles cover until their kinetic energy is completely consumed (more precisely: down to thermal energy ). The energy is gradually consumed in many individual collision processes that lead, for example, to excitation or ionization of the atoms or molecules hit. The range depends on the material, the type of radiation and the radiation energy. It is the integral of the reciprocal braking power over the particle energy from the incident energy to zero; it clearly ends at the point where the Bragg curve falls to zero.

Especially with heavy particles (ions), less so with electrons , the energy loss per unit of path length reaches a maximum shortly before the end of the path, the so-called Bragg peak . This effect is of great practical importance in radiation therapy .

The energy release through impacts is a stochastic process: the number of impacts per unit of travel as well as the loss of energy and change of direction through the impact are somewhat random. This means that particles with the same input energy have slightly different ranges. The particle also does not travel in a straight path, but performs "zigzag" movements. If one neglects the stochastic energy output and assumes continuous, one obtains the so-called CSDA-range (CSDA = continuous slowing down approximation ; range (English) = range).

Electrons of higher energy lose energy not only through impact but also through the generation of bremsstrahlung . The bremsstrahlung then also reaches the region beyond the range of the electrons.

Unlike particle radiation, photons ( x-rays , gamma rays ) are only attenuated exponentially and gradually. Instead of a range, there is a half-value thickness here .

Range and braking power

The CSDA range can be calculated using the braking power , which indicates the loss of kinetic energy of the projectile particle when traversing a medium: ${\ displaystyle S (E) = - {\ frac {\ mathrm {d} E} {\ mathrm {d} x}}}$ ${\ displaystyle E}$

{\ displaystyle \ textstyle {R} _ {\ mathrm {CSDA}} (E_ {0}) = \ int \ limits _ {E_ {0}} ^ {0} {\ frac {1} {S (E)} } \ mathrm {d} E = \ int \ limits _ {E_ {0}} ^ {0} - {\ frac {\ mathrm {d} x} {\ mathrm {d} E}} \ mathrm {d} E .}

Since the Bethe formula of the braking power only includes the charge and not the mass of the projectile, there is an approximately simple relationship between the range of an ion with charge , number of nucleons and kinetic energy per nucleon with the range of a proton: ${\ displaystyle Z}$ ${\ displaystyle A}$ ${\ displaystyle E / O}$ ${\ displaystyle R_ {p ^ {+}}}$

{\ displaystyle R (E) = {\ frac {A} {Z ^ {2}}} R_ {p +} (E / O).}

Measurement techniques

The range of a given radiation in a material can be determined by "trial and error" by placing foils, plates, etc. of the material between the radiation source and a suitable particle detector and observing at which minimum layer thickness no more particles are registered.

Conversely, if the relationship between the initial energy of the particle and the range is known, conclusions can be drawn about the energy from the range found. This technique used to be used to measure alpha-ray energies by determining the range in air .

Examples

The range of alpha radiation from natural radioactive substances is a few centimeters in air. A sheet of paper completely stops this radiation. In contrast, the range of beta radiation in air is in many cases a few meters and the range of high-energy muons in rock can be several kilometers.

literature

Berend J. Smit, Hans Breuer: Proton Therapy and Radiosurgery . Springer, Berlin 1999, ISBN 3-540-64100-9 .
K. Bethge, G. Walter, B. Wiedemann: Nuclear Physics. 3. Edition. Springer, Berlin 2007, ISBN 978-3-540-74566-2 , p. 127.

Individual evidence

^ W. Schlegel, J. Bille (Ed.): Medical Physics 2. Medical radiation physics. Springer, Berlin / Heidelberg / New York 2002, ISBN 3-540-65254-X , pp. 55-64.