Physics and Engineering of Radiation Detection

2.4. Interaction of Heavy Charged Particles with Matter 107

θ

0 20 40 60 80 100120140 160180

N (relative)

10 -8

10 -7

10 -6

10 -5

10 -4

10 -3

10 -2

10 -1

1

Figure 2.4.2: Angular dependence of

the relative number of particles de-

flected through Rutherford scattering.

Z 1

b=rsinφ Z^2

b

θ

φ

r

Target Nucleus

Figure 2.4.3: Rutherford scattering of a particle with

chargeeZ 1 by nucleus having chargeeZ 2 .Thecross

section of the process depends strongly the impact

parameterb.

The above formula has been developed through quantum mechanical considerations.
However if the incident particle can be considered non-relativistic (such asv<<
c) then classical mechanics can also be employed to derive a simpler from of the
Rutherford formula given by

dσ

dΩ

=

[

ZiZte^2

16 π 0 T

] 2

1

sin^4 (θ/2)

. (2.4.3)

whereTis the kinetic energy of the incident particle. The reader should readily
realize that the angular dependence of differential cross section is the same in both