PHY6040 Particle Detectors Dr C N Booth

   Interaction of a Charged Particle with Matter

Most particle detectors make use of the effect charged particles have on the matter they traverse.  The interaction of charged particles with matter is covered in considerable detail in the lecture handouts, PostScript versions of which can be seen here and here, while PDF versions can be seen here and here. The aim of this summary is not to reproduce the mathematics but to give a brief overview of the physical principles involved in calculating both how much energy a particle loses as it passes through matter and where that energy goes. The result of the calculation, for particles heavier than an electron, is known as the Bethe Bloch equation:


where   is the mean energy loss in passing through thickness Δx,
,
  me is the mass of the electron,
Z and A are the atomic number and mass of the medium being traversed,
z is the charge (in units of electronic charge) of the projectile particle,
β and γ are the usual relativistic parameters,
ρ is the density of the medium,
I0 is its mean ionisation energy,
ε is the shell correction  and
δ is the density effect.

(For an alternative formulation and description, with different notation, see the BriefBook.)

The energy loss therefore only depends on the incoming particle's velocity, and not directly on its mass, as is shown in the figure below.


Energy loss in argon, as a function of particle mass and momentum;  the vertical scale gives the relative increase above the minimum of ionisation.
(With apologies for the poor quality of the figure!)

The energy loss therefore shows four regions:

  1. a rapid decrease proportional to 1/β2 at lower velocities (mostly off the left of this plot);

  2.  
  3. a minimum at E ~ 3 Mc2 (i.e. γ ~ 3);

  4.  
  5. a slow logarithmic "relativistic rise", proportional to ln(γ)

  6.  
  7. a plateau as ionisation is limited by the density effect.
Note that the changes in energy loss for γ above the minimum are very much less than those in the low velocity region.  For this reason, any particle with γ above 3 is often known as a minimum ionising particle, or mip.


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