Physics and Engineering of Radiation Detection

2.4. Interaction of Heavy Charged Particles with Matter 117

Residual Energy (MeV)

St

opp

ing

P

ower

(re

la

ti

ve

)

102

103

104

10 8 6 4 2 0

Figure 2.4.5: Plot of equation 2.4.18

forα-particles having initial energy of

10 MeVpassing through a material hav-

ing an ionization potential of 100eV.

This variation of stopping power with re-

spect to residual energy of the particles

is generally known as Bragg curve.

respect to range as well and get the same Bragg curve. In fact, it is much easier to
draw the Bragg curve in this way because most of the empirical relations between
range and energy of particles can be used to derive very simple relations between
stopping power and range. We will see how this is done shortly, but before that let
us have a look at a couple of very important phenomena related to energy loss and
range.

2.4.D EnergyStraggling

The stopping power equations presented above do not contain information about
the statistical variations in the energy lost by the incident particles. In fact, due to
this statistical effect, a mono-energetic beam of incident particles gets a finite width
in its energy distribution as it travels through the medium. The effect is known
asenergy stragglingand can be represented by a Gaussian distribution for thick
absorbers.

N(E)dE=

N

απ^1 /^2

e−(E−

E ̄)^2 /α^2

(2.4.19)

Hereαis known as thestraggling parameterIt can be computed from

α^2 =4πq^2 e^4 Nx 0

[

1+

kI

mv^2

ln

(

2 mv^2

I

)]

,

wherek≈ 4 /3isaconstant,Iis the ionization potential of the medium,qis the
electrical charge of the ion (in units of unit electrical charge) having massmand
velocityv,eis the unit electronic charge, andx 0 is the thickness of the medium.
At lower absorber thicknesses, the energy straggling distribution becomes skewed
and develops a tail at higher energies. For very thin absorbers it is best represented
by a Landau distribution (31; 37). We will look at this distribution in the section on