Transcript Stopping Power

Stopping Power

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The linear stopping power S for charged
particles in a given absorber is simply
defined as the differential energy loss for
that particle within the material divided by
the corresponding differential path length:
 S = – dE / dx ………………………. (1.3)
The value of – dE / dx along a particle track
is also called specific energy loss or rate of
energy loss. For particles with a given charge
state, S increases as the particle velocity is
decreased
Stopping Time
The time required to stop a charged particle in an absorber
can be deduced from its range and average velocity. For
nonrelativistic particles of mass m and kinetic energy E, the
velocity is,
2E
 v  2E  c 2E  3 10 m / s 
... (1.6)

8
m
2
mc
931Mev / am u/ m A
Where mA is the particle mass in atomic mass units and E is
particle energy in MeV. If we assume that the average particle
1 mc
velocity as it slow down is v = Kv, where v =
c 2E
 and evaluated at initial energy, then the stopping time T can
be calculated from the range R as

2

R R
 T 
v Kc
m c2
R
931Mev / am u mA

2 E K (3  108 m / s)
2
E
…(1.7)
Energy Loss in Thin Absorbers
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For thin absorbers or detectors that are
penetrated by a given charged particle, the
energy deposited within the absorber can be
calculated from
∆E = (- dE/dx)avg. t ……………(1.8)
Where t is the absorber thickness and (dE/dx)avg is the average linear stopping power.
If the energy loss is small, the stopping
power does not change much and it can be
approximated to its value at the incident
particle energy.
INTERACTIONS OF PHOTONS
WITH MATTER
Photons, also called X-rays or rays are electromagnetic
radiation, are considered as particles that travel with the
speed of light c and they have zero rest mass and charge.
 There is no clear destination between X-rays and γ–rays.
The term X-rays is applied generally to photons with E <
1 MeV. Gammas are the photons with E > 1 MeV. X-rays
are generally produced by atomic transitions such as
excitation and ionizations. Gamma rays are emitted in
nuclear transitions. Photons are also produced in
bremsstrahlung, by accelerating or decelerating charged
particles. X-rays and γ-rays emitted by atoms and nuclei
are monoenergetic; bremsstrahlung has a continuous
energy spectrum.
 There are several possible interactions of photons, but
the three most important ones are: the photoelectric
effect, Compton scattering and pair production.

A) The Photoelectric Effect
The energy of the gammaray photon is completely
transferred to an orbital
electron which is ejected
from its atom (figure 1.2).
The gamma-ray no longer
exists after the collision.
The ejected electron then
causes ionization until it
loses its energy, and is
captured by an atom. The
photoelectric effect is
more likely to occur when
the photon energy is low,
i.e. below 0.5 MeV and the
absorber is a heavy
material

B) Compton Scattering
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Higher energy photons may lose
only part of their energy to the
atomic electron which is again
ejected from its atom (figure 1.3).
This electron goes on to create
ionization. The remaining energy is
taken up by another photon of
reduced energy which is scattered
in a new direction. The new
photon will either be absorbed by
a photoelectric effect, or if the
energy is still high by further
Compton scattering.
Compton scattering occurs in all
materials and predominantly with
photons of medium energy, i.e.
about 0.5 to 3.5 MeV.
C) Pair Production

Gamma-ray photons with energy
greater than 1.02 MeV may interact
with a nucleus to form an electronpositron pair. This amount of energy
is just sufficient to provide the rest
masses of the electron and
positron (0.51 MeV each). Excess
energy will be carried away equally
by these two particles which
produce ionization as they travel in
the material. The positron is
eventually
captured
by
an
electron and annihilation of the two
particles occurs. This results in the
release of two photons each of 0.51
MeV known as annihilation radiation.
These two photons then lose energy
by Compton scattering or the
photoelectric
effect.
Pair
production is illustrated in Figure 1.4
D) Coherent scattering

In addition to Compton scattering, another type
of scattering can occur in which the gamma-ray
photon interacts coherently with all the electrons
of an absorber atom. This coherent scattering or
Raleigh scattering process neither excites nor
ionizes the atom, and the gamma-ray photon
retains its original energy after the scattering
event. Because virtually no energy is transferred,
this process is often neglected in basic discussions
of gamma-ray interactions. However, the direction
of the photon is changed in coherent scattering.
The probability of coherent scattering is
significant only for low photon energies (typically
below a few hundred keV for common materials)
and is most prominent high-Z absorbers.
Gamma-ray attenuation
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If monoenergetic gamma-rays are collimated into a narrow beam and
allowed to strike a detector after passing through an absorber of
variable thickness, the result should be simple exponential attenuation
of the gamma rays. Each of the interaction processes removes the
gamma-rays photon from the beam either by absorption or by
scattering away from the detector direction and can be characterized
by a fixed probability of occurrence per unit path length in the
absorber. The sum of these probabilities is simply the probability per
unit path length that the gamma-ray photon is removed from the
beam.
µ = Ί (photoelectric) + σ (Compton) + ĸ (pair)
[1.3]
And is called the linear attenuation coefficient. The number of
transmitted photons I is then given in terms of the number without
an absorber I0 as
I
 e  t
I0
The gamma-ray photon can also be characterized by their mean free
path λ, defined as the average distance traveled in the absorber before
an interaction takes place.
Directly ionizing and indirectly
ionizing radiations

Ionizing radiations can be divided into two major groups, the
first consists of charged particles such as electrons, protons,
alpha particles and heavy ions, which have sufficient energy to
cause ionization on collision and do so by coulomb
interactions with electrons in the absorbing material. Such
radiations are directly ionizing. This situation may be
contrasted with indirectly ionizing radiations, which are
uncharged. Incident photons (X-rays and γ-rays) release
secondary electrons, while incident neutrons release
secondary charged recoil nuclei, which in turn produce most
of the excitations and ionizations in the absorber. The major
difference between the interactions of directly ionizing and
indirectly ionizing radiations is that the latter experience
relatively few collisions, each involving a large energy loss,
whereas the former undergo a very large number of
interactions, with little loss of energy each time. Indeed,
charged particles are often considered to lose energy and so
slow down in a continuous manner.
NEUTRONS (BASIC
CONCEPTS)