The interaction of photons with the matter.

The behavior
of photons in matter is
completely different from that
of charged particles. In
particular, the photon’s lack of
an electric charge makes
impossible the many inelastic
collision with atomic electrons
so characteristic of charged
particles. For this kind of
radiation the most important
mechanism of interaction are:
a) Photoelectric
effect
b) Compton
and Rayleigh scattering
c) Pair
production
As
consequence of such kind of
interactions a photon that
interacts with the target is
completely removed from the
incident beam, in other words a
beam of photons that cross a
medium is not degraded in energy
but only attenuated in
intensity. Moreover, due to the
smallest cross section of all
this kind of reactions,x‑ray or γray are
many times more penetrating than
charged particles. The
attenuation of the incident beam
is exponential with the
thickness of the absorbing
medium and can be expressed by
the following relation:
I(x)= I_{0} exp
(xμ_{l})
where μ_{l} is
the linear attenuation
coefficient, I_{0} is
the incident beam intensity and x the
thickness. The linear
attenuation coefficient is
related to the cumulative cross
section by the relation:
μ_{l
=}η_{A }σ_{tot}
where η_{A} is
the number of atoms per unit of
mass and σ_{tot} is
the total cross section. The
total or cumulative cross
section σ_{tot} is
the sum of all the cross
sections of the interactions
mentioned above. A plot of this
quantity is shown in Figure 1.6
where the different components
have been highlighted.
In
photoelectric absorption, a
photon disappears being absorbed
by an atomic electron. The
process results in ionization by
subsequent ejection of the
electron from the atom. The
energy of the liberated electron
is the difference between the
photon energy and the energy
needed to extract the electron
from the atom i.e. the binding
energy of the electron. The
recoil momentum is absorbed by
the nucleus to which the ejected
electron was bound. If the
resulting photoelectron has
sufficiently enough of kinetic
energy, it may be a source of a
secondary ionization occurring
along its trajectory, and in the
case of the semiconductor
material, it may create further
eh pairs. If the electron does
not leave the detector the
deposited energy corresponds to
the energy possessed by the
incident photon. This feature of
the photoelectric effect allows
calibrating the gain of the
detector chained with its
readout system if the energy
required to create a single eh
pair is known. The range R of
the electron having the kinetic
energy E is of the order of some
micrometers, as given by the
follow equation:
R[um] = 40.8 10^{^(3)
x }
( E[keV] )^{^1.5}
Thus the cloud of generated charge is confined close to the photon absorption point. The clear image may be smeared by escape photons, which can leave the detector volume leading to less amount of energy deposited. These photons are actually the fluorescence photons emitted by deexciting atoms. Photons of fluorescence radiation are emitted by atoms after the ejection of a deep shell (K, L) electron. The incident photon creates a vacancy in the shell, thus leaving an atom in an excited state. Then, the vacancy can be filled by an outer orbital electron, giving rise to the emission of the characteristic Xrays photons of the fluorescence radiation. The missing energy, which is conveyed by the escape photons leads to, so called escape peaks in the measured energy spectrum. Photon interaction coefficient for photoelectric absorption depends strongly on the atomic number of the absorbing material. The relevant cross section increases roughly as Z^{^3}. For silicon, the photoelectric effect is a dominant process for photon energies below 100 keV.
Figure 1
Cross sections of photons in
Carbon (a) and Lead (b) in
barns/atom; 1barn=10^{24 }cm^{2}.
The Compton
scattering, instead of
photoelectric effect, involves
the free electrons. In matter of
course, the electrons are bound
to an atom; however, if the
photon energy is high with
respect to the binding energy,
this latter energy can be
ignored and the electrons can be
treated as essentially free.
When Compton scattering occurs,
the electron is scattered away
in conjunction with a new photon
that have a lower energy than
the incoming one. In Rayleigh
scattering the photon interact
with the whole atom and the only
effect of this interaction is a
deflection of the incoming
photon; it does not participate
to the absorption and for most
purposes can be neglected.
At very high
energy another effect starts to
be relevant: the pair
production. In this process the
photon interacts with an
electron or a nucleus producing
a positronelectron pair. In
order to produce the pair the
photon must have at least an
energy of 1.022 MeV. In
Figure 1, with k_{nuc} and
k_{e},
are shown the two components of
the pair production cross
section, respectively for the
interaction with nuclei or
electrons. Another possible
interaction, but usually
negligible compared to the
previous ones is the
Photonuclear reaction, in this
case the photon interact
directly with the nucleus. The
related cross section is shown
in Figure 1 in dotted line (σ_{g.d.r.}).
The above cross section in
barns/atom (1barn = 10^{24 }cm^{2},
approximately the section of an
uranium nucleus) expresses the
probability of an interaction. A
more suitable quantity, often
used to characterize the
absorption of a photon shower,
is the mass attenuation
coefficient. The mass
attenuation coefficient is
defined as:
μ_{m}=η_{A }σ_{tot/ρ}
where ρ is the density of the material. Figure 2 shows the mass attenuation coefficient of the silicon with the indication of its different components.
Figure 2
Mass attenuation coefficient of
the silicon and its components.
References

YungSu Tsai, Pair production and bremsstrahlung of charged leptons, Reviews of Modern Physics, vol. 46, no. 815, 1974

M.Bronshtein, B.S. Fraiman, “Determination of the Path Lengths of Slow Secondary Electrons”, Sov. Phys. Solid State, Vol.3, (1961), pp.11881197.

R. Wunstorf, Systematische Untersuchungen zur Strahlenresistenz von SiliziumDetektoren fur die Verwendung in HochenergiephysikExperimenten, PhD Thesis, Universitat Hamburg, Germany (1992)
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