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4.5 Absorption of particles and dosimetry
4.5.1 Range and stopping power of ions in various materials
When a fast ion passes through matter, it loses energy
principally by scattering electrons within the matter it passes through and,
more importantly at low energies, by scattering from the nuclei of the
atoms.
The mean range of an ion is defined as the mean
thickness of material, which is usually expressed in terms of mass per unit
area, traversed before it comes to rest. The stopping power (S)
of a material for an ion is defined as the rate of change of the energy
(−dE/dT) with material thickness (T) and is
dependent on the energy E of the ion.
For very thin absorbers, the energy loss of an ion is
approximately ST. For thick absorbers, the energy loss ΔE
is better obtained from the range tables as follows. Let R0
be the mean range of an ion of energy E0 in a given absorber
material. After passing through an absorber of thickness T, it emerges
as an ion with a mean range (R0 − T) and a
corresponding energy E1, from which the energy lost in
passing through the absorber is seen to be ΔE =
E0 − E1.
Statistical fluctuations in the processes of energy loss
result in a distribution about the mean energy loss in passing through the
absorber and also about the mean range. For light ions, the fractional
variation about the mean range is of the order of 10% for low energies, falling to a few
per cent at high energies. The fractional variation in energy loss is at least
a few per cent and can be 40%
for very thin absorbers and high energies. A more detailed treatment of energy
loss variations for thick absorbers is given by Tschalär (1968).
The stopping power goes through a maximum at an energy
of about 0.1 MeV/amu for protons to about 5 MeV/amu for uranium ions, depending
also on the atomic number of the absorber. This maximum is evident in the table
of stopping power in air of protons and alpha particles as a function of
distance from end of range.
The proton range and stopping powers were derived from
Janni (1982), which tabulates values for 92 elements and 63 compounds. For
α-particles, the data
were based on Ziegler (1980), where ranges and stopping powers in 92 elements
are plotted.
For pi-mesons and muons, the data in the tables were
derived from Janni's proton tables by using the following scaling relations.
For particles of charge ze, mass M and energy E, the
stopping power, S, for a given material is given by
|
|
[S(E)]M,ze =
z2[S(EMp/M)]proton |
|
where Mp is the proton mass. Similarly, their range is
given by:
|
|
[R(E)]M,ze =
M/(Mpz2)[R(EMp/M)]proton |
|
These formulae are based on the assumption that the rate of energy loss
for a particle of a given charge in a given medium depends only on its
velocity, and are generally accepted as accurate for z  2, and
above 1 MeV/amu. They can be used to extend the above tables to other isotopes
of hydrogen and helium and to other light elementary particles.
The range/energy functions have a power law relationship varying
approximately between R
 E1/2 and E5/3 below and
above the stopping power maximum, respectively. Interpolation in energy should
therefore be made by interpolating logarithms of the range against logarithms
of energy.
References
J. F. Janni (1982) Atomic Data and Nuclear Data Tables,
27, Nos 2–5.
C. Tschalär (1968) Nuclear Instruments
and Methods, 64, 237.
J. F. Ziegler (ed.) (1980) The Stopping
and Ranges of Ions in Matter, Vols 5 and 6, Pergamon Press, New
York.
Stopping power (keV/mm) as a function of distance
from end of range in air
|
Distance (mm) |
50 |
30 |
20 |
15 |
10 |
7 |
5 |
3 |
2 |
1.5 |
1.0 |
0.5 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
α . . . . . |
81 |
105 |
126 |
146 |
179 |
214 |
254 |
252 |
201 |
168 |
123 |
72 |
|
p . . . . . |
20 |
24 |
29 |
33 |
39 |
47 |
55 |
70 |
82 |
91 |
95 |
77 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Ranges of light ions
|
Energy (MeV) |
Range/(kg m−2) for protons
in: |
| |
H |
C |
Al |
Ti |
Cu |
Ag |
Pb |
U |
Water |
Air |
Multiplier |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
0.005 |
0.37 |
1.76 |
2.15 |
2.76 |
3.14 |
3.38 |
4.87 |
4.75 |
1.32 |
1.79 |
10 −4 |
|
0.01 |
0.62 |
3.02 |
3.84 |
5.19 |
6.00 |
6.23 |
9.24 |
8.65 |
2.30 |
3.10 |
10 −4 |
|
0.05 |
0.19 |
0.94 |
1.32 |
1.96 |
2.51 |
2.58 |
4.04 |
3.61 |
0.71 |
0.97 |
10 −3 |
|
0.10 |
0.32 |
1.61 |
2.41 |
3.36 |
4.66 |
4.93 |
7.32 |
6.82 |
1.22 |
1.65 |
10 −3 |
|
0.5 |
0.27 |
0.96 |
1.50 |
1.76 |
2.44 |
2.84 |
4.02 |
4.05 |
0.80 |
1.01 |
10 −2 |
|
1.0 |
0.88 |
2.75 |
3.93 |
4.76 |
6.02 |
7.26 |
10.3 |
10.6 |
2.40 |
2.95 |
10 −2 |
|
2.0 |
2.94 |
8.44 |
11.4 |
13.5 |
16.3 |
20.3 |
28.4 |
29.2 |
7.60 |
9.20 |
10 −2 |
|
5.0 |
1.52 |
4.02 |
5.13 |
5.99 |
6.87 |
8.39 |
11.3 |
11.8 |
3.68 |
4.36 |
10 −1 |
|
10.0 |
5.40 |
13.6 |
16.8 |
19.4 |
21.7 |
25.8 |
33.9 |
35.6 |
12.5 |
14.6 |
10 −1 |
|
20.0 |
1.93 |
4.71 |
5.68 |
6.45 |
7.08 |
8.23 |
10.6 |
11.1 |
4.31 |
5.02 |
100 |
|
50.0 |
10.4 |
24.6 |
29.0 |
32.4 |
35.0 |
39.7 |
49.5 |
51.5 |
22.5 |
26.0 |
100 |
|
100 |
3.66 |
8.54 |
9.90 |
11.0 |
11.7 |
13.2 |
16.1 |
16.8 |
7.79 |
8.97 |
101 |
|
200 |
12.5 |
28.7 |
33.0 |
36.4 |
38.6 |
42.9 |
51.8 |
53.7 |
26.2 |
30.0 |
101 |
|
500 |
5.69 |
13.0 |
14.7 |
16.1 |
17.0 |
18.7 |
22.3 |
23.1 |
11.8 |
13.5 |
102 |
|
1000 |
1.59 |
3.60 |
4.08 |
4.45 |
4.67 |
5.12 |
6.05 |
6.25 |
3.28 |
3.74 |
103 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Energy (MeV) |
Range/(kg m−2) for alphas
in: |
| |
H |
C |
Al |
Ti |
Cu |
Ag |
Pb |
U |
Water |
Air |
Multiplier |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
0.01 |
9.0 |
18.8 |
35.1 |
35.7 |
47.4 |
47.1 |
56.6 |
61.0 |
16.9 |
28.8 |
10 −5 |
|
0.05 |
3.0 |
6.6 |
10.9 |
13.6 |
20.6 |
20.9 |
27.2 |
28.6 |
5.95 |
9.57 |
10 −4 |
|
0.10 |
4.3 |
11.1 |
16.7 |
22.1 |
34.9 |
36.6 |
47.5 |
49.5 |
10.0 |
15.7 |
10 −4 |
|
0.5 |
1.12 |
3.6 |
4.9 |
6.6 |
9.2 |
12.0 |
17.0 |
15.8 |
3.24 |
3.92 |
10 −3 |
|
1.0 |
1.71 |
5.95 |
8.77 |
10.8 |
17.9 |
19.4 |
28.3 |
27.6 |
4.95 |
6.53 |
10 −3 |
|
2.0 |
3.40 |
12.3 |
17.8 |
20.2 |
32.0 |
36.4 |
52.7 |
54.9 |
10.3 |
12.8 |
10 −3 |
|
5.0 |
1.28 |
4.23 |
5.85 |
6.75 |
9.08 |
10.9 |
15.5 |
16.5 |
3.68 |
4.35 |
10 −2 |
|
10.0 |
4.35 |
12.4 |
16.3 |
19.5 |
23.6 |
28.9 |
42.3 |
43.8 |
11.3 |
12.7 |
10 −2 |
|
20.0 |
1.51 |
3.97 |
4.97 |
6.00 |
6.84 |
83.9 |
11.7 |
12.3 |
3.73 |
4.14 |
10 −1 |
|
50.0 |
0.80 |
2.03 |
2.37 |
2.85 |
3.15 |
3.79 |
5.00 |
5.22 |
1.86 |
2.17 |
100 |
|
100 |
2.90 |
7.18 |
8.10 |
9.60 |
10.6 |
12.4 |
15.7 |
16.7 |
6.45 |
7.48 |
100 |
|
200 |
1.03 |
2.58 |
2.80 |
3.25 |
3.61 |
4.11 |
5.00 |
5.23 |
2.25 |
2.60 |
101 |
|
500 |
5.42 |
13.3 |
14.2 |
16.3 |
17.9 |
19.5 |
23.9 |
24.7 |
11.6 |
13.3 |
101 |
|
1000 |
1.83 |
4.28 |
4.64 |
5.40 |
5.70 |
5.99 |
7.55 |
7.85 |
3.83 |
4.39 |
102 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Energy (MeV) |
Range/(kg m−2) for pions
in: |
| |
H |
C |
Al |
Ti |
Cu |
Ag |
Pb |
U |
Water |
Air |
Multiplier |
| |
|
|
|
|
|
|
|
|
|
|
|
|
1.0 |
3.88 |
10.0 |
12.6 |
14.7 |
16.6 |
20.1 |
26.7 |
28.0 |
9.19 |
10.8 |
10 −2 |
|
2.0 |
1.38 |
3.43 |
4.20 |
4.81 |
5.33 |
6.28 |
8.15 |
8.57 |
3.15 |
3.67 |
10 −1 |
|
5.0 |
7.45 |
17.9 |
21.2 |
23.9 |
26.0 |
29.8 |
37.5 |
39.2 |
16.4 |
18.9 |
10 −1 |
|
10.0 |
2.65 |
6.24 |
7.29 |
8.13 |
8.73 |
9.86 |
12.2 |
12.7 |
5.70 |
6.57 |
100 |
|
20.0 |
9.22 |
21.4 |
24.7 |
27.4 |
29.1 |
32.5 |
39.6 |
41.1 |
19.5 |
22.5 |
100 |
|
50.0 |
4.46 |
10.2 |
11.7 |
12.8 |
13.5 |
15.0 |
17.9 |
18.5 |
9.30 |
10.7 |
101 |
|
100 |
13.3 |
30.2 |
34.3 |
37.5 |
39.5 |
43.4 |
51.5 |
53.3 |
27.5 |
31.5 |
101 |
|
200 |
3.55 |
7.98 |
9.03 |
9.84 |
10.3 |
11.3 |
13.3 |
13.7 |
7.28 |
8.29 |
102 |
|
500 |
10.8 |
24.1 |
27.3 |
29.6 |
30.8 |
33.7 |
39.2 |
40.5 |
22.1 |
25.0 |
102 |
|
1000 |
22.6 |
50.2 |
57.0 |
61.8 |
64.0 |
69.7 |
80.3 |
82.8 |
46.4 |
51.7 |
102 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Energy (MeV) |
Range/(kg m−2) for muons
in: |
| |
H |
C |
Al |
Ti |
Cu |
Ag |
Pb |
U |
Water |
Air |
Multiplier |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1.0 |
4.89 |
12.4 |
15.4 |
17.8 |
20.0 |
23.9 |
31.5 |
33.1 |
11.4 |
13.4 |
10 −2 |
|
2.0 |
1.74 |
4.28 |
5.19 |
5.90 |
6.50 |
7.58 |
9.76 |
10.2 |
3.92 |
4.57 |
10 −1 |
|
5.0 |
9.44 |
22.5 |
26.5 |
29.7 |
32.1 |
36.5 |
45.7 |
47.7 |
20.6 |
23.7 |
10 −1 |
|
10.0 |
3.32 |
7.78 |
9.05 |
10.1 |
10.8 |
12.1 |
14.8 |
15.4 |
7.10 |
8.18 |
100 |
|
20.0 |
11.4 |
26.4 |
30.3 |
33.5 |
35.5 |
39.5 |
47.9 |
49.6 |
24.0 |
27.6 |
100 |
|
50.0 |
5.32 |
12.1 |
13.8 |
15.2 |
16.0 |
17.6 |
21.0 |
21.8 |
11.1 |
12.7 |
101 |
|
100 |
15.2 |
34.3 |
38.9 |
42.5 |
44.6 |
48.9 |
57.9 |
59.8 |
31.3 |
35.7 |
101 |
|
200 |
3.85 |
8.63 |
9.76 |
10.6 |
11.1 |
12.1 |
14.3 |
14.7 |
7.88 |
8.95 |
102 |
|
500 |
11.1 |
24.8 |
28.1 |
30.4 |
31.6 |
34.5 |
40.0 |
41.2 |
22.8 |
25.6 |
102 |
|
1000 |
22.7 |
50.2 |
57.0 |
61.8 |
63.9 |
69.5 |
79.8 |
82.2 |
46.6 |
51.5 |
102 |
|
|
|
|
|
|
|
|
|
|
|
|
|
Stopping powers of light ions
|
Energy (MeV) |
Stopping power/(MeV kg−1m2)
for protons in: |
| |
H |
C |
Al |
Ti |
Cu |
Ag |
Pb |
U |
Water |
Air |
Multiplier |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
0.005 |
17.1 |
2.71 |
1.73 |
0.991 |
0.700 |
0.647 |
0.287 |
0.373 |
3.80 |
2.56 |
101 |
|
0.01 |
22.0 |
4.01 |
2.54 |
1.41 |
1.03 |
0.967 |
0.401 |
0.543 |
5.13 |
3.67 |
101 |
|
0.05 |
38.9 |
7.14 |
4.48 |
2.98 |
1.91 |
1.72 |
0.963 |
1.08 |
9.72 |
7.07 |
101 |
|
0.10 |
34.1 |
7.34 |
4.31 |
3.50 |
2.16 |
1.86 |
1.23 |
1.23 |
9.53 |
7.18 |
101 |
|
0.5 |
11.0 |
3.64 |
2.51 |
2.08 |
1.65 |
1.33 |
0.893 |
0.863 |
4.15 |
3.40 |
101 |
|
1.0 |
66.3 |
22.9 |
17.2 |
14.1 |
11.8 |
9.28 |
6.39 |
6.15 |
25.4 |
21.0 |
100 |
|
2.0 |
38.5 |
14.3 |
11.0 |
9.35 |
8.03 |
6.38 |
4.54 |
4.33 |
15.5 |
13.0 |
100 |
|
5.0 |
18.1 |
7.14 |
5.74 |
4.96 |
4.42 |
3.67 |
2.74 |
2.60 |
7.78 |
6.63 |
100 |
|
10.0 |
10.1 |
4.13 |
3.40 |
2.98 |
2.71 |
2.31 |
1.77 |
1.68 |
4.50 |
3.87 |
100 |
|
20.0 |
5.64 |
2.35 |
1.98 |
1.76 |
1.62 |
1.41 |
1.11 |
1.06 |
2.57 |
2.22 |
100 |
|
50.0 |
26.3 |
11.2 |
9.66 |
8.68 |
8.10 |
7.19 |
5.80 |
5.57 |
12.3 |
10.7 |
10 −1 |
|
100 |
15.2 |
6.58 |
5.72 |
5.17 |
4.86 |
4.36 |
3.57 |
3.44 |
7.22 |
6.29 |
10 −1 |
|
200 |
9.28 |
4.06 |
3.55 |
3.23 |
3.05 |
2.76 |
2.29 |
2.20 |
4.45 |
3.89 |
10 −1 |
|
500 |
5.60 |
2.48 |
2.19 |
2.00 |
1.90 |
1.73 |
1.45 |
1.40 |
2.72 |
2.38 |
10 −1 |
|
1000 |
4.48 |
2.00 |
1.77 |
1.62 |
1.55 |
1.41 |
1.20 |
1.16 |
2.19 |
1.93 |
10 −1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Energy (MeV) |
Stopping power/(MeV kg−1
m2) for alphas in: |
| |
H |
C |
Al |
Ti |
Cu |
Ag |
Pb |
U |
Water |
Air |
Multiplier |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
0.01 |
12.7 |
5.67 |
2.63 |
2.09 |
1.13 |
1.06 |
0.64 |
0.54 |
5.00 |
3.48 |
101 |
|
0.05 |
28.1 |
9.8 |
6.41 |
4.40 |
2.35 |
2.17 |
1.40 |
1.31 |
10.5 |
7.4 |
101 |
|
0.10 |
41.9 |
12.5 |
9.04 |
8.35 |
3.31 |
2.99 |
1.97 |
1.93 |
16.3 |
10.4 |
101 |
|
0.50 |
80.6 |
19.1 |
13.0 |
11.0 |
6.51 |
5.75 |
3.81 |
4.20 |
25.1 |
19.7 |
101 |
|
1.0 |
71.1 |
18.1 |
12.3 |
10.6 |
7.06 |
6.25 |
4.01 |
4.45 |
22.2 |
19.2 |
101 |
|
2.0 |
46.1 |
13.6 |
9.87 |
8.28 |
6.28 |
5.29 |
3.49 |
3.57 |
16.0 |
13.9 |
101 |
|
5.0 |
22.6 |
7.72 |
6.05 |
5.08 |
4.28 |
3.43 |
2.40 |
2.27 |
8.81 |
7.62 |
101 |
|
10.0 |
13.0 |
4.79 |
3.79 |
3.21 |
2.81 |
2.28 |
1.61 |
1.54 |
5.27 |
4.69 |
101 |
|
20.0 |
7.41 |
2.85 |
2.28 |
1.92 |
1.71 |
1.42 |
1.10 |
0.99 |
3.11 |
2.81 |
101 |
|
50.0 |
33.8 |
13.6 |
11.4 |
10.0 |
9.19 |
7.87 |
6.10 |
5.82 |
15.0 |
13.4 |
100 |
|
100 |
18.8 |
7.77 |
6.61 |
5.90 |
5.46 |
4.75 |
3.81 |
3.62 |
8.59 |
7.62 |
100 |
|
200 |
10.5 |
4.45 |
3.82 |
3.45 |
3.21 |
2.87 |
2.29 |
2.25 |
4.92 |
4.36 |
100 |
|
500 |
5.13 |
2.18 |
1.91 |
1.76 |
1.63 |
1.48 |
1.23 |
1.19 |
2.45 |
2.14 |
100 |
|
1000 |
3.22 |
1.41 |
1.23 |
1.12 |
1.06 |
0.96 |
0.80 |
0.78 |
1.55 |
1.38 |
100 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Energy (MeV) |
Stopping power/(MeV kg−1
m2) for pions in: |
| |
H |
C |
Al |
Ti |
Cu |
Ag |
Pb |
U |
Water |
Air |
Multiplier |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1.0 |
14.1 |
5.66 |
4.61 |
4.00 |
3.61 |
3.03 |
2.29 |
2.17 |
6.17 |
5.28 |
100 |
|
2.0 |
7.88 |
3.25 |
2.71 |
2.39 |
2.18 |
1.88 |
1.46 |
1.38 |
3.55 |
3.06 |
100 |
|
5.0 |
36.5 |
15.5 |
13.2 |
11.8 |
10.9 |
9.63 |
7.70 |
7.37 |
16.9 |
14.7 |
10 −1 |
|
10.0 |
20.7 |
8.91 |
7.69 |
6.93 |
6.50 |
5.79 |
4.70 |
4.52 |
9.76 |
8.64 |
10 −1 |
|
20.0 |
12.2 |
5.33 |
4.63 |
4.20 |
3.96 |
3.56 |
2.93 |
2.82 |
5.83 |
5.08 |
10 −1 |
|
50.0 |
6.80 |
2.99 |
2.63 |
2.40 |
2.28 |
2.06 |
1.72 |
1.66 |
3.28 |
2.87 |
10 −1 |
|
100 |
5.00 |
2.22 |
1.96 |
1.80 |
1.71 |
1.56 |
1.31 |
1.27 |
2.44 |
2.14 |
10 −1 |
|
200 |
4.26 |
1.91 |
1.69 |
1.55 |
1.49 |
1.36 |
1.16 |
1.12 |
2.08 |
1.84 |
10 −1 |
|
500 |
4.12 |
1.87 |
1.64 |
1.51 |
1.47 |
1.34 |
1.16 |
1.13 |
2.02 |
1.81 |
10 −1 |
|
1000 |
4.34 |
1.96 |
1.72 |
1.59 |
1.54 |
1.42 |
1.25 |
1.21 |
2.09 |
1.93 |
10 −1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Energy (MeV) |
Stopping power/(MeV kg−1
m2) for muons in: |
| |
H |
C |
Al |
Ti |
Cu |
Ag |
Pb |
U |
Water |
Air |
Multiplier |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
1.0 |
11.2 |
4.54 |
3.73 |
3.26 |
2.95 |
2.51 |
1.92 |
1.81 |
4.94 |
4.24 |
100 |
|
2.0 |
6.23 |
2.59 |
2.18 |
1.93 |
1.77 |
1.54 |
1.21 |
1.15 |
2.83 |
2.44 |
100 |
|
5.0 |
28.9 |
12.3 |
10.6 |
9.48 |
8.85 |
7.83 |
6.30 |
6.04 |
13.5 |
11.7 |
10 −1 |
|
10.0 |
16.7 |
7.19 |
6.24 |
5.63 |
5.29 |
4.74 |
3.87 |
3.72 |
7.88 |
6.86 |
10 −1 |
|
20.0 |
10.0 |
4.38 |
3.83 |
3.48 |
3.29 |
2.97 |
2.46 |
2.37 |
4.81 |
4.20 |
10 −1 |
|
50.0 |
5.90 |
2.60 |
2.30 |
2.10 |
1.99 |
1.81 |
1.52 |
1.47 |
2.86 |
2.50 |
10 −1 |
|
100 |
4.61 |
2.05 |
1.81 |
1.66 |
1.59 |
1.45 |
1.23 |
1.18 |
2.25 |
1.98 |
10 −1 |
|
200 |
4.14 |
1.86 |
1.64 |
1.51 |
1.46 |
1.33 |
1.14 |
1.10 |
2.03 |
1.80 |
10 −1 |
|
500 |
4.19 |
1.90 |
1.67 |
1.54 |
1.49 |
1.37 |
1.19 |
1.16 |
2.04 |
1.85 |
10 −1 |
|
1000 |
4.47 |
2.01 |
1.76 |
1.63 |
1.58 |
1.47 |
1.29 |
1.26 |
2.13 |
2.00 |
10 −1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
For heavy ions, the range data were derived from the
semi-empirical calculations in U. Littmark and J. F. Ziegler (1980) The
Range and Energy Loss of Particles in Matter, Vol. 6, ed. J. F. Ziegler,
Pergamon Press, where ranges of ions from protons to uranium in all elemental
substrates are plotted graphically from 0.2 MeV/amu up to 1000 MeV. The authors
account for shell effects in the atomic number of the substrate by scaling to
detailed α-particle stopping
powers in which those effects are experimentally observed.
Where the tables extend beyond the range of Littmark and
Ziegler, extrapolation is made using, as a guide, L. C. Northcliffe and R. F.
Schilling (1970) Nuclear Data Tables, Vol. 7A, Nos 3–4, where
calculated ranges and stopping powers for 103 species in 24 materials are
tabulated. These tables do not include atomic shell effects in the substrate
and thus were used only to provide the shape of the range curves in the
extrapolation region.
There are limited experimental data, mainly for the
lighter heavy ions, in a few substrates; agreement with the curves is generally
within 10%, which is comparable with scatter in the data. There is little, if
any, experimental data for heavier ions at the higher energies.
Ranges of heavy ions
|
Energy per mass unit |
Ranges of heavy ions |
|
MeV/amu
|
Range/(kg m−2
×10−2) for
42He ions in: |
|
C |
Al |
Ti |
Ge |
Ag |
Au |
U |
|
|
|
|
|
|
|
|
|
|
0.0125 . . . . . . |
0.084 |
0.120 |
0.150 |
0.25 |
0.30 |
0.58 |
0.47 |
|
0.050 . . . . . . |
0.20 |
0.28 |
0.36 |
0.56 |
0.68 |
1.20 |
1.05 |
|
0.200 . . . . . . |
0.50 |
0.72 |
0.85 |
1.35 |
1.60 |
2.55 |
2.35 |
|
0.800 . . . . . . |
2.20 |
3.10 |
3.46 |
5.2 |
6.0 |
9.4 |
9.3 |
|
3.20 . . . . . . |
18.4 |
24.5 |
28.7 |
35.2 |
42.2 |
58.5 |
61.5 |
|
12.00 . . . . . . |
189 |
233 |
262 |
305 |
357 |
459 |
490 |
|
|
|
|
|
|
|
|
|
|
MeV/amu
|
Range/(kg
m−2 ×10−2)
for 126C ions in:
|
|
C |
Al |
Ti |
Ge |
Ag |
Au |
U |
|
|
|
|
|
|
|
|
|
|
0.0125 . . . . . . |
0.065 |
0.096 |
0.11 |
0.19 |
0.24 |
0.35 |
0.36 |
|
0.050 . . . . . . |
0.17 |
0.25 |
0.27 |
0.47 |
0.58 |
0.82 |
0.80 |
|
0.200 . . . . . . |
0.52 |
0.73 |
0.90 |
1.15 |
1.32 |
1.90 |
1.80 |
|
0.800 . . . . . . |
1.48 |
2.10 |
2.35 |
3.55 |
3.95 |
6.25 |
6.15 |
|
3.20 . . . . . . |
8.3 |
10.8 |
12.9 |
16.0 |
19.2 |
27.0 |
28.1 |
|
12.00 . . . . . . |
65.5 |
81.0 |
91.2 |
109 |
128 |
163 |
179 |
|
|
|
|
|
|
|
|
|
|
|
|
|
MeV/amu |
Range/(kg m−2 × 10
−2) for 2713Al ions
in: |
|
C |
Al |
Ti |
Ge |
Ag |
Au |
U |
|
|
|
|
|
|
|
|
|
|
0.0125 . . . . . . |
0.087 |
0.12 |
0.15 |
0.21 |
0.24 |
0.36 |
0.34 |
|
0.050 . . . . . . |
0.24 |
0.34 |
0.41 |
0.62 |
0.64 |
1.00 |
0.99 |
|
0.200 . . . . . . |
0.59 |
0.85 |
0.94 |
1.47 |
1.58 |
2.40 |
2.28 |
|
0.800 . . . . . . |
1.53 |
2.17 |
2.43 |
3.65 |
4.02 |
6.27 |
6.12 |
|
3.20 . . . . . . |
6.33 |
8.2 |
9.51 |
12.2 |
14.5 |
20.5 |
21.0 |
|
12.00 . . . . . . |
38.3 |
48.0 |
54.1 |
66.0 |
72.2 |
97.0 |
104 |
|
|
|
|
|
|
|
|
|
|
|
|
|
MeV/amu |
Range/(kg m−2 ×
10−2) for 4018Ar ions
in: |
|
C |
Al |
Ti |
Ge |
Ag |
Au |
U |
|
|
|
|
|
|
|
|
|
|
0.0125 . . . . . . |
0.090 |
0.11 |
0.13 |
0.21 |
0.26 |
0.39 |
0.38 |
|
0.050 . . . . . . |
0.28 |
0.33 |
0.43 |
0.63 |
0.73 |
1.18 |
1.05 |
|
0.200 . . . . . . |
0.67 |
0.97 |
1.08 |
1.68 |
1.83 |
2.76 |
2.63 |
|
0.800 . . . . . . |
1.68 |
2.40 |
2.65 |
4.05 |
4.40 |
7.0 |
6.80 |
|
3.20 . . . . . . |
5.99 |
8.0 |
9.20 |
12.0 |
14.3 |
20.5 |
21.0 |
|
12.00 . . . . . . |
34.6 |
42.0 |
47.0 |
55.0 |
62.8 |
83.0 |
89.5 |
|
|
|
|
|
|
|
|
|
|
|
|
|
MeV/amu |
Range/(kg m−2 ×
10−2) for 5828Ni ions
in: |
|
C |
Al |
Ti |
Ge |
Ag |
Au |
U |
|
|
|
|
|
|
|
|
|
|
0.0125 . . . . . . |
0.11 |
0.15 |
0.14 |
0.23 |
0.25 |
0.41 |
0.39 |
|
0.050 . . . . . . |
0.36 |
0.46 |
0.49 |
0.78 |
0.84 |
1.32 |
1.25 |
|
0.200 . . . . . . |
0.88 |
1.15 |
1.38 |
2.10 |
2.27 |
3.35 |
3.22 |
|
0.800 . . . . . . |
1.80 |
2.71 |
3.05 |
4.55 |
5.05 |
7.65 |
7.50 |
|
3.20 . . . . . . |
5.6 |
7.6 |
8.8 |
11.6 |
13.2 |
19.3 |
19.9 |
|
12.00 . . . . . . |
27.2 |
31.5 |
36.5 |
43.5 |
49.0 |
65.5 |
70.5 |
|
|
|
|
|
|
|
|
|
|
|
|
|
MeV/amu |
Range/(kg m−2 ×
10−2) for 7432Ge ions
in: |
|
C |
Al |
Ti |
Ge |
Ag |
Au |
U |
|
|
|
|
|
|
|
|
|
|
0.0125 . . . . . . |
0.13 |
0.16 |
0.15 |
0.25 |
0.28 |
0.42 |
0.38 |
|
0.050 . . . . . . |
0.43 |
0.54 |
0.56 |
0.88 |
0.96 |
1.38 |
1.35 |
|
0.200 . . . . . . |
1.02 |
1.43 |
1.57 |
2.39 |
2.57 |
3.79 |
3.65 |
|
0.800 . . . . . . |
2.18 |
3.08 |
3.44 |
5.09 |
5.65 |
8.6 |
8.4 |
|
3.20 . . . . . . |
6.15 |
8.3 |
9.7 |
12.7 |
14.8 |
21.2 |
21.7 |
|
12.00 . . . . . . |
27.2 |
33.5 |
38.3 |
46.5 |
53.5 |
69.8 |
74.5 |
|
|
|
|
|
|
|
|
|
|
|
|
|
MeV/amu |
Range/(kg m−2 ×
10−2) for 9040Zr ions
in: |
|
C |
Al |
Ti |
Ge |
Ag |
Au |
U |
|
|
|
|
|
|
|
|
|
|
0.0125 . . . . . . |
0.11 |
0.14 |
0.15 |
0.21 |
0.23 |
0.36 |
0.35 |
|
0.050 . . . . . . |
0.36 |
0.49 |
0.53 |
0.79 |
0.87 |
1.31 |
1.24 |
|
0.200 . . . . . . |
0.93 |
1.32 |
1.46 |
2.23 |
2.42 |
3.63 |
3.52 |
|
0.800 . . . . . . |
2.16 |
3.07 |
3.40 |
5.10 |
5.64 |
8.75 |
8.65 |
|
3.20 . . . . . . |
6.1 |
8.1 |
9.5 |
12.5 |
14.5 |
20.8 |
21.6 |
|
12.00 . . . . . . |
25.0 |
30.5 |
36.0 |
41.5 |
49.8 |
63.0 |
67.5 |
|
|
|
|
|
|
|
|
|
|
|
|
|
MeV/amu |
Range/(kg m−2 ×
10−2) for 10747Ag ions
in: |
|
C |
Al |
Ti |
Ge |
Ag |
Au |
U |
|
|
|
|
|
|
|
|
|
|
0.0125 . . . . . . |
0.12 |
0.16 |
0.15 |
0.24 |
0.27 |
0.38 |
0.38 |
|
0.050 . . . . . . |
0.42 |
0.55 |
0.60 |
0.91 |
1.00 |
1.47 |
1.55 |
|
0.200 . . . . . . |
1.12 |
1.56 |
1.73 |
2.60 |
2.82 |
4.17 |
4.04 |
|
0.800 . . . . . . |
2.44 |
3.56 |
3.86 |
5.75 |
6.37 |
9.70 |
9.60 |
|
3.20 . . . . . . |
6.18 |
8.30 |
9.70 |
12.7 |
14.8 |
21.4 |
20.3 |
|
12.00 . . . . . . |
26.0 |
31.8 |
33.8 |
41.9 |
49.1 |
65.0 |
69.5 |
|
|
|
|
|
|
|
|
|
|
|
|
|
MeV/amu |
Range/(kg m−2 ×
10−2) for 15363Eu ions
in: |
|
C |
Al |
Ti |
Ge |
Ag |
Au |
U |
|
|
|
|
|
|
|
|
|
|
0.0125 . . . . . . |
0.13 |
0.16 |
0.16 |
0.24 |
0.26 |
0.36 |
0.34 |
|
0.050 . . . . . . |
0.45 |
0.60 |
0.65 |
0.96 |
1.00 |
1.52 |
1.45 |
|
0.200 . . . . . . |
1.23 |
1.72 |
1.92 |
2.86 |
3.11 |
4.66 |
4.49 |
|
0.800 . . . . . . |
2.81 |
3.94 |
4.39 |
6.55 |
7.20 |
11.1 |
11.0 |
|
3.20 . . . . . . |
7.25 |
9.68 |
11.2 |
14.8 |
17.1 |
24.7 |
25.5 |
|
12.00 . . . . . . |
25.8 |
33.1 |
35.4 |
43.7 |
51.9 |
67.2 |
72.5 |
|
|
|
|
|
|
|
|
|
| |
|
|
MeV/amu |
Range/(kg m−2 ×
10−2) for 18173Ta ions
in: |
|
C |
Al |
Ti |
Ge |
Ag |
Au |
U |
|
|
|
|
|
|
|
|
|
|
0.0125 . . . . . . |
0.14 |
0.18 |
0.17 |
0.28 |
0.28 |
0.37 |
0.36 |
|
0.050 . . . . . . |
0.53 |
0.68 |
0.70 |
1.13 |
1.12 |
1.65 |
1.59 |
|
0.200 . . . . . . |
1.42 |
1.96 |
2.16 |
3.43 |
3.54 |
5.17 |
5.12 |
|
0.800 . . . . . . |
3.26 |
4.51 |
5.02 |
7.32 |
8.08 |
12.3 |
12.2 |
|
3.20 . . . . . . |
7.81 |
10.4 |
12.0 |
15.8 |
18.4 |
26.5 |
27.3 |
|
12.00 . . . . . . |
26.0 |
32.0 |
36.9 |
43.2 |
53.1 |
69.0 |
75.2 |
|
|
|
|
|
|
|
|
|
|
|
|
|
MeV/amu |
Range/(kg m−2 ×
10−2) for 19779Au ions
in: |
|
C |
Al |
Ti |
Ge |
Ag |
Au |
U |
|
|
|
|
|
|
|
|
|
|
0.0125 . . . . . . |
0.15 |
0.19 |
0.20 |
0.27 |
0.29 |
0.38 |
0.36 |
|
0.050 . . . . . . |
0.54 |
0.72 |
0.79 |
1.09 |
1.18 |
1.67 |
1.64 |
|
0.200 . . . . . . |
1.47 |
2.16 |
2.39 |
3.47 |
3.76 |
5.53 |
5.40 |
|
0.800 . . . . . . |
3.37 |
4.67 |
5.20 |
7.62 |
8.34 |
12.7 |
12.8 |
|
3.20 . . . . . . |
8.15 |
10.8 |
12.4 |
16.3 |
19.0 |
27.4 |
28.3 |
|
12.00 . . . . . . |
27.0 |
33.2 |
36.5 |
45.4 |
53.4 |
70.3 |
76.0 |
|
|
|
|
|
|
|
|
|
|
|
|
|
MeV/amu |
Range/(kg m−2 ×
10−2) for 23892U ions
in: |
|
C |
Al |
Ti |
Ge |
Ag |
Au |
U |
|
|
|
|
|
|
|
|
|
|
0.0125 . . . . . . |
0.16 |
0.19 |
0.20 |
0.27 |
0.29 |
0.36 |
0.35 |
|
0.050 . . . . . . |
0.60 |
0.75 |
0.80 |
1.12 |
1.21 |
1.66 |
1.65 |
|
0.200 . . . . . . |
1.68 |
2.28 |
2.53 |
3.64 |
3.97 |
5.73 |
5.67 |
|
0.800 . . . . . . |
3.67 |
5.10 |
5.68 |
8.27 |
9.11 |
13.7 |
13.7 |
|
3.20 . . . . . . |
8.65 |
11.4 |
13.3 |
17.5 |
20.2 |
29.0 |
29.9 |
|
12.00 . . . . . . |
27.3 |
33.5 |
36.6 |
46.3 |
53.9 |
70.8 |
76.5 |
|
|
|
|
|
|
|
|
|
J. Asher
|
