94
H. J. Hilke and W. Riegler
The probability distribution f(l)dl for a free flight pass l between two ionizing
collisions—i.e. the probability of no ionization in l and one in dl-is an exponential,
f(l)dl = (dl/λ) exp (−l/λ) ,
(4.4)
i.e. short distances are favoured.
An electron ejected in a primary collision on atom A may have enough energy to
ionize one or more other atoms. Thus clusters of two or more electrons are formed
by secondary ionization. These clusters are mostly rather localized, as the ejection
energy is usually low and results in a short range. High ejection energies for socalled δ-electrons are rare, their average number per cm is approximately inversely
proportional to energy:
P (E > E 0 ) − y/
β
2 E 0
/cm,
(4.5)
with E 0 in keV, and y = 0.114 for Ar, and y = 0.064 for Ne [20]; β= particle
velocity/speed of light in vacuum. Thus, in Ar, for β~1 and E 0 = 10 keV,
P = 0.011/cm, i.e., on average one collision with E > 10 keV will occur on a
track length of 90 cm. The range of a 10 keV electron is about 1.4 mm. The range
decreases very rapidly with decreasing energy and is only about 30 μm for a 1 keV
electron.
It tums out that, although the majority of the ‘clusters’ consist of a single electron,
clusters of size >1 contribute significantly to the mean total number n T of electrons
produced per cm, so that n T is significantly larger than n p , the mean number of
primary clusters per cm. Table 4.1 gives experimental values for some of the
common detector gases. In Ar at NTP one finds on average n p = 26 and n T = 100
electrons/cm for a minimum ionizing particle, where n T depends on the volume
around the track taken into account. The most probable value for the total ionization
is n mp = 42 electrons/cm. The big difference between n T and n mp is an indication
of the long tail of the distribution.
Table 4.1 Properties of gases at 20
◦ C, 1 atm
Gas
n p
n T
w [eV]
E I [eV]
E x [eV]
p [mg/cm 3 ]
He
4.8
7.8
45
24.5
19.8
0.166
Ne
13
50
30
21.6
16.7
0.84
Ar
25
100
26
15.7
11.6
1.66
Xe
41
312
22
12.1
8.4
5.50
CH 4
37
54
30
12.6
8.8
0.67
CO 2
35
100
34
13.8
7.0
1.84
i-butane
90
220
26
10.6
6.5
2.49
CF 4
63
120
54
16.0
10.0
3.78
n p , n T mean primary and total number of electron-ion pairs per cm; w: average energy dissipated
per ion pair; E I , E x : lowest ionization and excitation energy [21]
H. J. Hilke and W. Riegler
The probability distribution f(l)dl for a free flight pass l between two ionizing
collisions—i.e. the probability of no ionization in l and one in dl-is an exponential,
f(l)dl = (dl/λ) exp (−l/λ) ,
(4.4)
i.e. short distances are favoured.
An electron ejected in a primary collision on atom A may have enough energy to
ionize one or more other atoms. Thus clusters of two or more electrons are formed
by secondary ionization. These clusters are mostly rather localized, as the ejection
energy is usually low and results in a short range. High ejection energies for socalled δ-electrons are rare, their average number per cm is approximately inversely
proportional to energy:
P (E > E 0 ) − y/
β
2 E 0
/cm,
(4.5)
with E 0 in keV, and y = 0.114 for Ar, and y = 0.064 for Ne [20]; β= particle
velocity/speed of light in vacuum. Thus, in Ar, for β~1 and E 0 = 10 keV,
P = 0.011/cm, i.e., on average one collision with E > 10 keV will occur on a
track length of 90 cm. The range of a 10 keV electron is about 1.4 mm. The range
decreases very rapidly with decreasing energy and is only about 30 μm for a 1 keV
electron.
It tums out that, although the majority of the ‘clusters’ consist of a single electron,
clusters of size >1 contribute significantly to the mean total number n T of electrons
produced per cm, so that n T is significantly larger than n p , the mean number of
primary clusters per cm. Table 4.1 gives experimental values for some of the
common detector gases. In Ar at NTP one finds on average n p = 26 and n T = 100
electrons/cm for a minimum ionizing particle, where n T depends on the volume
around the track taken into account. The most probable value for the total ionization
is n mp = 42 electrons/cm. The big difference between n T and n mp is an indication
of the long tail of the distribution.
Table 4.1 Properties of gases at 20
◦ C, 1 atm
Gas
n p
n T
w [eV]
E I [eV]
E x [eV]
p [mg/cm 3 ]
He
4.8
7.8
45
24.5
19.8
0.166
Ne
13
50
30
21.6
16.7
0.84
Ar
25
100
26
15.7
11.6
1.66
Xe
41
312
22
12.1
8.4
5.50
CH 4
37
54
30
12.6
8.8
0.67
CO 2
35
100
34
13.8
7.0
1.84
i-butane
90
220
26
10.6
6.5
2.49
CF 4
63
120
54
16.0
10.0
3.78
n p , n T mean primary and total number of electron-ion pairs per cm; w: average energy dissipated
per ion pair; E I , E x : lowest ionization and excitation energy [21]