Interaction of Radiation With Matter: Dhruba Gupta
Interaction of Radiation With Matter: Dhruba Gupta
Interaction of Radiation With Matter: Dhruba Gupta
with Matter
Dhruba Gupta
Department of Physics
Bose Institute, Kolkata
Based on transfer of part or all of radiation energy to the detector mass where it
is converted into some other form more accessible to human perception
Ionization detectors
First electrical devices developed for radiation detection. Direct collection of
the ionization electrons and ions produced in a gas by passing radiation, form
an electric current signal
Semiconductor Detectors
Basic reactions which occur when radiation encounters matter and the
effects produced by these processes
Primarily interact with matter through Coulomb forces with the orbital electrons
within the absorber atoms. Entering the medium, the charged particle
immediately interacts simultaneously with many electrons. In any one such
encounter, the electron feels an impulse from the Coulomb force as the
particle passes its vicinity.
Interactions of the particles with nuclei occur rarely (not significant in the
detector response). Typically σinel ~ 10-16 cm2 >> σnucl scatt ~ 10-24 cm2 (barn)
dominant energy loss due to atomic electron collisions
The maximum energy that can be transferred to the electron of mass m from a
charged particle of mass M with kinetic energy E in a single collision is
4E(m/M), or about 1/500 of its energy for a proton. At any given time, the
particle is interacting with many electrons, so the net effect is to decrease
its velocity continuously until the particle is stopped.
Because their number per macroscopic path length is generally large, the
fluctuations in the total energy loss are small and one can meaningfully
work with the average energy loss per unit path length : stopping power
dE/dx and the range of the penetrating particles (distance beyond which no
particle will penetrate).
e.g 10 MeV proton already loses all of its energy in 0.25 mm of Copper
Stopping Power
The quantum mechanical calculation of stopping power S
Bethe-Bloch formula : basic expression used for energy loss calculations.
dE 4πe 4 z 2 ⎡ 2mv 2 ⎛ v2 ⎞ v2 ⎤
− = 2
NZ ⎢ln − ln⎜⎜1 − 2 ⎟⎟ − 2 ⎥
dx mv ⎣ I ⎝ c ⎠ c ⎦
The material with higher NZ will be a better absorber (higher stopping power)
→ lead is used as a very effective absorber.
Limitations : valid as long as velocity of incoming particle remains large
compared with orbital electron velocities in the absorbing material. At
very low velocity (E/A < 1 MeV) the positively charged particle tends to
pick up electrons which effectively reduces its charge (Zeff < Z), and finally
it becomes a neutral atom. Reducing effective charge reduces the electronic
energy loss. At these energies nuclear stopping power dominates.
Bethe-Bloch formula as
function of kinetic energy
for different particles
Non-relativistic energies : dE/dx dominated by the over all 1/β 2 factor and
decreases with increasing velocity. At v ~ 0.96c (particles minimum ionizing).
(dE/dx)min almost same for particles of same charge. Beyond this point, the
term 1/β 2 almost constant and dE/dx rises again due to the log term.
For energies below minimum ionizing value, each particle exhibits a distinct
dE/dx curve – particle identification
Very low energy region (not shown) : Bethe-Bloch formula breaks down.
dE/dx reaches a maximum and drops sharply (particle picks up electrons)
Copper
Density correction : Electric field of the particle tends to polarize atoms along
its path, shielding electrons (far from the particle path) from full electric
field intensity. Collisions with these outer lying electrons contribute less to
energy loss. Important at high energy (effect depends on material density).
Particle loses most of its energy near the end of its path
This fact is utilized in medical applications of radiation where high
radiation dose delivered to deeply embedded malignant growths with
minimum destruction to overlaying tissue.
Proton therapy
Proton therapy uses a beam of protons to irradiate diseased
tissue, most often in the treatment of cancer. The dose delivered
to tissue is maximum just over the last few millimeters of the
particle’s range : Bragg peak
Advantage
Irradiation of Skin exposure at the entrance point is higher, but tissues on the
nasopharyngeal opposite side of the body than the tumor receive no radiation.
carcinoma
Protons of different energies with Bragg peaks at different depths are applied to
treat the entire tumor- blue lines. The total radiation dosage of the protons is
called the Spread-Out Bragg Peak (SOBP) - red line.
Range of charged particles
Depends on material type, particle
type and its energy. Range of charged
particles of a given energy is thus a
fairly unique quantity in a specific
absorber material.
The basic mechanism of collision loss is also valid for electrons/positrons, the
Bethe-Bloch formula must be modified due to
The Coulomb forces that constitute the major mechanism of energy loss for
both electrons and HCP are present for positive or negative charge on the
particle. Whether the interaction involves a repulsive or attractive force
between the incident particle and orbital electron, the impulse and energy
transfer for particles of equal mass are about the same.
For positrons the annihilation radiation is generated at the end of the track.
Because these 0.511 MeV photons are very penetrating compared with the
range of the positron, they can lead to the deposition of energy far from the
original positron track.
For electrons/positrons energy loss through electromagnetic radiation arising
from scattering in the electric field of a nucleus (bremsstrahlung) also
becomes important. These can emanate from any position along the track.
⎛ dE ⎞ NEZ (Z + 1) e 4 ⎛ 2E 4 ⎞
−⎜ ⎟ = 2 4 ⎜ 4 ln 2
− ⎟
⎝ dx ⎠r 137 m c ⎝ mc 3⎠
dE ⎛ dE ⎞ ⎛ dE ⎞
The total stopping power : =⎜ ⎟ + ⎜ ⎟
dx ⎝ dx ⎠ c ⎝ dx ⎠ r
collisional radiative
∞Z ∞ Z2
(dE/dx )r ≅
EZ
The ratio of the specific energy losses is :
(dE/dx )c 700
where E is in MeV. Clearly for electrons with very high energy,
radiative processes are more significant than ionization and excitation
specially in absorber materials of high atomic number.
Bremsstrahlung
E ~ MeV : a relatively small factor
E ~ 10 MeV : radiation loss ~ collision loss
E ~ 100 GeV, electrons and positrons only particles in which radiation
contributes substantially to the energy loss. The emission probability
~ 1/m2. Radiation loss by muons (m = 106 MeV) is thus some 40,000
times smaller than electrons.
Cerenkov radiation
Cerenkov radiation arises when a charged particle
in a material medium moves faster than the speed
of light in that same medium (βc = vparticle > c/n,
n – index of refraction, c – speed of light in
vacuum). An electromagnetic shock wave similar
to a sonic shock wave is generated. The coherent
wavefront formed is conical in shape and is
emitted at a well-defined angle cosθ = 1/βn
w.r.t the trajectory of the particle.
The energy loss increases with β, however even at relativistic energies the
energy loss is small compared to collision loss.
All these processes lead to the partial or complete transfer of the γ-ray photon energy
to electron energy. Each of the interaction processes removes the γ-ray photon
from the incident direction either by absorption or by scattering away. The
probability that the γ-ray photon is removed from the beam is called linear
attenuation coefficient µ and is given by I(x) =Ioe-µx
µ = Nσ , N: no. density of atoms, σ : total interaction cross section
7/2
r Z ⎡m c ⎤ sin 2 θ cos 2 ϕ
2 5 2
dσ
=4 2 e 4 ⎢ e ⎥
dΩ (137) ⎣ hω ⎦ ⎡ v ⎤
4
1
⎢⎣ c− cos θ ⎥⎦
At energies above the highest electron BE of the atom (K shell), the cross
section is relatively small but increases rapidly as the K-shell energy is
approached. Just after this point, the cross section drops drastically
(discontinuous jump) since the K-electrons are no longer available for the
photoelectric effect (K absorption edge). Below this energy, the cross
section rises once again and dips as the L, M levels etc are passed (L-
absorption edges, M-absorption edge). The effect is more pronounced in
the high-Z material.
Compton scattering :
Because all angles are possible, the energy transfer vary from zero to a large
fraction of the γ-ray energy.
e─ Recoil electron
Incident photon
φ hν’ = hν /[1+α(1-cosθ)]
hν θ cotφ = (1+α) tan(θ /2)
where α= hν /mc2
Scattered photon
hν’
α 2 (1 − cos θ )2
2
dσ 2⎡ 1 ⎤ ⎡1 + cos 2 θ ⎤ ⎡ ⎤
= Zro ⎢ 1 +
dΩ ⎣1 + α (1 − cos θ ) ⎥ ⎢
⎦ ⎣ 2
⎥⎢
⎦⎣ (
1 + cos 2
θ )
[1 + α (1 − cos θ )]⎥
⎦
Neutrons do not carry electric charge, so they can not interact in matter by
means of Coulomb force. Principal means of interaction is through the
strong force with nuclei of the absorbing material (for which it must come
within ~ 10-13 cm of the nucleus). Since matter is mostly empty space, the
neutron is observed to be a very penetrating particle traveling many
centimeters of matter without any interaction.
i(t) i(t)
tc
∫ i(t)dt = Q
0
t=tc t→
The circuit normally used is of the following form:
Detector C R V(t)
Time required for signal pulse to reach its maximum value depends on tc
the intrinsic charge collection time of the detector. It can not be changed
by any external circuit. But the decay time of the pulse is determined by
the time constant t of the circuit.
Also the amplitude of the pulse Vmax = Q / C. Thus since the capacitance
is normally fixed, the amplitude of the signal pulse is directly proportional
to the corresponding charge generated within the detector.