development of micro-pattern gaseous detectors – gem - LMU

4.3. Cosmic Muon Spectrum 47
to zero. Nevertheless, the fit function used in Fig. 4.9 suits the measurements in a good manner,
confirmed by a χ 2 /nd f = 1.41.
Figure 4.10: Energy loss distribution function for MIP βγ = 3.6 in an 1.2 cm thin Argon layer. The function
corresponding to the solid line includes fluctuations. The original Landau distribution is indicated by the dotted
line [Bich 06].
A
statement
of quality for the presented data can be given by approximating the average energy loss
dE of the shown distribution and comparing it with theoretical values. The 55Fe measurements
dx
presented in Ch. 4.1 suits for transforming the FADC scale into meaningful energy units. Since the
Kα line and the Kα escape peak represent energies of 5.90 keV and 2.68 keV respectively, (see Ch.
1.1.2), one derives a scaling factor by taking a data set with corresponding operation parameters.
This is done via the measurement presented in Fig. 4.2. From table 4.1 one derives a linear relation
between the two energies with 10% deviation. This results in a scaling factor of 9.4 eV/channel.
Thus the mean value of 118.2 of the distribution in Fig. 4.9 is equivalent to a mean energy loss of:
eV
mean × scalingfactor = 118.2 channel × 9.4
channel =
dE 1111 eV
≈ (4.9)
dx 4mm
On the other hand, the mean energy loss is related to the average energy 〈Wi〉 required for the production
of primary electron-ion-pair and their total number 〈nt〉 as explained in Ch. 1.1.2. Including
the theoretical values of 〈nt〉 = 97 per cm and 〈Wi〉 = 26.50 eV for Ar/CO2 at a ratio of 93/7 one
derives a mean energy loss of:
dE
dx
= 〈Wi〉 · 〈nt〉 = 26.50 eV · 97
· 0.4 cm = 1028 eV (4.10)
cm
in 4 mm drift. The experimental results are consistent with the theoretical estimated mean energy loss
within 8% deviation.