2 The Interaction of Radiation with Matter
25
Table 2.2 Integral properties of collision cross sections for Si calculated with Bethe-Fano (B-F)
and FVP algorithms
M 0 [μm −1 ]
M 1 [eV/μm]
p /x [eV/μm]
βγ
B-F
FVP
B-F
FVP
B-F
FVP
0.316
30.325
32.780
2443.72
2465.31
1677.93
1722.92
0.398
21.150
22.781
1731.66
1745.57
1104.90
1135.68
0.501
15.066
16.177
1250.93
1260.18
744.60
765.95
0.631
11.056
11.840
928.70
935.08
520.73
536.51
0.794
8.433
9.010
716.37
720.98
381.51
394.03
1.000
6.729
7.175
578.29
581.79
294.54
304.89
1.259
5.632
5.996
490.84
493.65
240.34
249.25
1.585
4.932
5.245
437.34
439.72
207.15
215.02
1.995
4.492
4.771
406.59
408.70
187.39
194.60
2.512
4.218
4.476
390.95
392.89
176.30
183.06
3.162
4.051
4.296
385.29
387.12
170.70
177.16
3.981
3.952
4.189
386.12
387.89
168.59
174.81
5.012
3.895
4.127
391.08
392.80
168.54
174.63
6.310
3.865
4.094
398.54
400.24
169.62
175.60
7.943
3.849
4.076
407.39
409.07
171.19
177.10
10.000
3.842
4.068
416.91
418.58
172.80
178.66
12.589
3.839
4.064
426.63
428.29
174.26
180.06
15.849
3.839
4.063
436.30
437.96
175.45
181.24
19.953
3.839
4.063
445.79
447.44
176.36
182.14
25.119
3.840
4.063
455.03
456.68
177.04
182.79
31.623
3.840
4.064
463.97
465.63
177.53
183.28
39.811
3.841
4.064
472.61
474.27
177.86
183.61
50.119
3.842
4.065
480.93
482.58
178.09
183.83
63.096
3.842
4.065
488.90
490.55
178.22
183.95
79.433
3.842
4.065
496.52
498.17
178.32
184.06
100.000
3.842
4.066
503.77
505.42
178.38
184.10
125.893
3.843
4.066
510.66
512.31
178.43
184.15
158.489
3.843
4.066
517.20
518.84
178.44
184.17
199.526
3.843
4.066
523.40
525.05
178.47
184.18
251.189
3.843
4.066
529.29
530.94
178.48
184.18
316.228
3.843
4.066
534.91
536.56
178.48
184.21
398.107
3.843
4.066
540.28
541.92
178.48
184.22
501.187
3.843
4.066
545.43
547.08
178.48
184.22
630.958
3.843
4.066
550.40
552.05
178.48
184.22
794.329
3.843
4.066
555.21
556.86
178.48
184.22
1000.000
3.843
4.066
559.89
561.54
178.48
184.22
The third column shows the most probable value p of the energy loss spectrum divided by the
track length x, for x = 8 μm. The minimum values for M 0 are at βγ ∼ 18, for M 1 at βγ ∼ 3.2,
for p at βγ ∼ 5. The relativistic rise for M 0 is 0.1%, for M 1 it is 45%, for p it is 6%
25
Table 2.2 Integral properties of collision cross sections for Si calculated with Bethe-Fano (B-F)
and FVP algorithms
M 0 [μm −1 ]
M 1 [eV/μm]
p /x [eV/μm]
βγ
B-F
FVP
B-F
FVP
B-F
FVP
0.316
30.325
32.780
2443.72
2465.31
1677.93
1722.92
0.398
21.150
22.781
1731.66
1745.57
1104.90
1135.68
0.501
15.066
16.177
1250.93
1260.18
744.60
765.95
0.631
11.056
11.840
928.70
935.08
520.73
536.51
0.794
8.433
9.010
716.37
720.98
381.51
394.03
1.000
6.729
7.175
578.29
581.79
294.54
304.89
1.259
5.632
5.996
490.84
493.65
240.34
249.25
1.585
4.932
5.245
437.34
439.72
207.15
215.02
1.995
4.492
4.771
406.59
408.70
187.39
194.60
2.512
4.218
4.476
390.95
392.89
176.30
183.06
3.162
4.051
4.296
385.29
387.12
170.70
177.16
3.981
3.952
4.189
386.12
387.89
168.59
174.81
5.012
3.895
4.127
391.08
392.80
168.54
174.63
6.310
3.865
4.094
398.54
400.24
169.62
175.60
7.943
3.849
4.076
407.39
409.07
171.19
177.10
10.000
3.842
4.068
416.91
418.58
172.80
178.66
12.589
3.839
4.064
426.63
428.29
174.26
180.06
15.849
3.839
4.063
436.30
437.96
175.45
181.24
19.953
3.839
4.063
445.79
447.44
176.36
182.14
25.119
3.840
4.063
455.03
456.68
177.04
182.79
31.623
3.840
4.064
463.97
465.63
177.53
183.28
39.811
3.841
4.064
472.61
474.27
177.86
183.61
50.119
3.842
4.065
480.93
482.58
178.09
183.83
63.096
3.842
4.065
488.90
490.55
178.22
183.95
79.433
3.842
4.065
496.52
498.17
178.32
184.06
100.000
3.842
4.066
503.77
505.42
178.38
184.10
125.893
3.843
4.066
510.66
512.31
178.43
184.15
158.489
3.843
4.066
517.20
518.84
178.44
184.17
199.526
3.843
4.066
523.40
525.05
178.47
184.18
251.189
3.843
4.066
529.29
530.94
178.48
184.18
316.228
3.843
4.066
534.91
536.56
178.48
184.21
398.107
3.843
4.066
540.28
541.92
178.48
184.22
501.187
3.843
4.066
545.43
547.08
178.48
184.22
630.958
3.843
4.066
550.40
552.05
178.48
184.22
794.329
3.843
4.066
555.21
556.86
178.48
184.22
1000.000
3.843
4.066
559.89
561.54
178.48
184.22
The third column shows the most probable value p of the energy loss spectrum divided by the
track length x, for x = 8 μm. The minimum values for M 0 are at βγ ∼ 18, for M 1 at βγ ∼ 3.2,
for p at βγ ∼ 5. The relativistic rise for M 0 is 0.1%, for M 1 it is 45%, for p it is 6%