page_title: Bethe formula
section_title: The mean excitation potential
hierarchical_section_title: Bethe formula / The mean excitation potential
caption_attribution_description: Mean Excitation Potential used in Bethe formula
context_page_description: The Bethe formula describes the mean energy loss per distance travelled of swift charged particles traversing matter. For electrons the energy loss is slightly different due to their small mass and their indistinguishability, and since they suffer much larger losses by Bremsstrahlung, terms must be added to account for this. Fast charged particles moving through matter interact with the electrons of atoms in the material. The interaction excites or ionizes the atoms, leading to an energy loss of the traveling particle.
  The non-relativistic version was found by Hans Bethe in 1930; the relativistic version was found by him in 1932. The most probable energy loss differs from the mean energy loss and is described by the Landau-Vavilov distribution.
  The Bethe formula is sometimes called "Bethe-Bloch formula", but this is misleading.
context_section_description: In the Bethe theory, the material is completely described by a single number, the mean excitation potential I. In 1933 Felix Bloch showed that the mean ionization potential of atoms is approximately given by
  where Z is the atomic number of the atoms of the material. If this approximation  is introduced into formula (1) above, one obtains an expression which is often called Bethe-Bloch formula. But since we have now accurate tables of I as a function of Z (see below), the use of such a table will yield better results than the use of formula (3).
  The figure shows normalized values of I, taken from a table. The peaks and valleys in this figure lead to corresponding valleys and peaks in the stopping power. These are called "Z₂-oscillations" or "Z₂-structure" (where Z₂ = Z means the atomic number of the target).
caption: The mean excitation potential I of atoms, versus atomic number Z, in eV, divided by Z
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