development of micro-pattern gaseous detectors – gem - LMU

10 Chapter 1 Interactions of Charged Heavy Particle and Photons in Matter
• The matter’s atomic number Z, atomic weight A and density ρ, the Avogadro number NA, it’s
ionization potential I and the maximum energy transfer Tmax.
The additional terms in the brackets refer to corrections, firstly the density effect δ which describes
the screening of the incident particle’s electric field by the charge density of the atomic electrons.
It can be neglected for gases under normal pressure thus it is important for dense absorbers. The
second corrections C is due to the movement of the electrons in the shells .
The energy loss decreases like 1/β 2 in the low momentum range and reaches a minimum near
βγ ≈ 4. Comparing the minima of different absorbers one observes a decreasing energy loss at the
ionization minimum with increasing atomic number of the absorber. These characteristics are mainly
due to the Z/A term in Eq. 1.9 and is shown in Fig. 1.3.
Figure 1.3: Mean energy loss rate in liquid
hydrogen, gaseous helium, carbon, aluminium,
iron, tin and lead. [PDG 10]
Figure 1.4: Energy deposit measurements
of different incident particle in a Time Projection
Chamber (TPC) filled with Ar : CH4
in ratio 80 : 20 at 8.5 atm pressure [PDG 10]
Relativistic particle with βγ ≈ 4 are called minimum-ionizing particle (MIP). Their energy loss
corresponds to the mentioned minimum. The logarithmic term in Eq. (1.9) provides an increasing
energy loss for values of βγ ≈ 5...100. Large energy transfer per interaction is responsible for a large
fraction of the rise in this energy range. These electrons, detached from the atom by large energy
transfers, are called δ- electrons or knock-on electrons. The logarithmic or relativistic rise is followed
by a constant plateau for βγ ≈ 500...1000, induced by the density effect. For incident particle with
higher momentum (βγ ≫ 1000) the formula of Bethe-Bloch receives further corrections caused by
radiation losses since Eq. 1.9 holds only for energy losses due to ionization and excitation.
If the incident heavy charged particle is not traveling through a pure medium but a mixture of absorber
materials or chemical compounds, the average energy loss per length can be approximated by Bragg’s
additivity for the energy loss which is also named the stopping power in this context [Thwa 83]. Thus
the average mass stopping power is: