development of micro-pattern gaseous detectors – gem - LMU

42 Chapter 4 Energy Resolution and Pulse Height Analysis
180
160
140
120
100
80
60
40
20
55Fe Pulse Height
dE
| = 0.1771
E Kα
Cu anode seg
preamp: Canberra
cm
kV
Edrift
= 1.25
cm
kV
Etrans1,2
= Eind
= 2.00
Δ Ugem3=
330 V
Δ Ugem2=
330 V
Δ Ugem1=
330 V
data_gem_0221_pulseheight_fit
Entries 19368
Mean 340
RMS 145.3
χ 2 / ndf 980.2 / 550
p0 272 ± 0.6
p1 50 ± 0.0
p2 8 ± 0.0
p3 20.03 ± 0.50
p4 194.5 ± 1.8
p5 66.53 ± 1.78
K α norm 139.4 ± 1.7
K α mean 414.8 ± 0.8
K α σ 31.2 ± 0.6
p9 22.36 ± 2.44
p10 482.7 ± 2.6
p11 25 ± 0.2
muon
Mn K
Mn Kα
Mn K
α esc.
0
0 100 200 300 400 500 600 700 800
voltage [0.244mV]
Figure 4.3: 55 Fe pulse height spectrum as taken with Canberra2004 preamplifier. All peaks are resolved. An
energy resolution of dE/E = 17.7% for Kα is observed.
for all tested setups.
dE
= 0.20 ± 0.03 (4.3)
E FWHM
The statistical limit gives a lower limit for the resolution. The relative mean error of a Poisson
distribution is given by [Leo 94]:
σ
µ = 1
√ µ
with the mean µ and the standard deviation σ. Considering the fact that the energy of a single Kα
photon can be identified with an ionization of µ = N = 223 molecules of the filling gas, one receives
theoretically a lower limit for the relative resolution at FWHM:
dE
E
FWHM
= 2.35 ·
1
õ
= 2.35 ·
1
√N
= 2.35 ·
β
(4.4)
1
√ 223 = 0.1576 . (4.5)
The factor 2.35 corresponds to the former presented relation of the standard deviation of a Gaussian
distribution and the full width at half maximum. Inclusion of the Fano factor F [Fano 47] leads to:
σ 2 corr = F · µ . (4.6)
where F characterizes the detecting gas as a function of all possible processes of particle in the
medium, i.e. including photon excitation [Leo 94]. In the case of pure Argon the Fano factor has a
value of [Hash 84]:
F = 0.23 . (4.7)