.
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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