Physics and Engineering of Radiation Detection

2.4. Interaction of Heavy Charged Particles with Matter 121

E.2 RangeofProtons........................

There have been several theoretical and experimental studies of variation of range
of protons with energy in several materials (see, for example (36; 9; 58; 45)). These
studies have lead to the development of empirical relations specific for the material
under investigation and within the energy range used in the experiment. Fortu-
nately the number of such studies is so high that, together with some theoretical
computations, several large databases of the proton range values are now available.
Let us have a look at the proton range relations for air and aluminum. In air the
range of protons having energyEpcan be computed from (61)

Rairp [m]=

[

Ep

9. 3

] 1. 8

forEp< 200 MeV, (2.4.26)

while for aluminum, one can use the relation (8)

RAlp[mgcm−^2 ]=

⎧

⎪⎨

⎪⎩

3. 837 E^1 p.^5874 for 1. 13 MeV < Ep≤ 2. 677 MeV

2. 837 E^2 p

0 .68+logEp for 2.^677 MeV≤Ep≤^18 MeV.

(2.4.27)

These two relations have been plotted in Fig.2.4.8. The reader should note that
equation 2.4.27 gives range inmg/cm^2 and therefore the value must be divided by
the density of aluminum to obtain the range in dimensions of length.

Energy(MeV)

024681012141618

Range (Al(mm), air(cm))

0

50

100

150

200

250

300

350

Aluminum

Air

Figure 2.4.8: Range of protons in air

(dashed line) and in aluminum (solid

line) as computed from equations 2.4.26

and 2.4.27. For aluminum the equa-

tion has been divided by its density

2. 7 gcm−^3 to yield range in dimension

of length.