Bremsstrahlung and Cherenkov radiation

Bremsstrahlung and Cherenkov radiation


Bremsstrahlung is a German word that means ‘ to break or deceleration radiation’. When high-speed electrons whose energy is of the order of X-rays strike a metal target, they encounter with the due orbital electrons of the atoms. And get slowed down or decelerated due to the electrostatic repulsion or completely stopped. The energy lost by the electrons in the process either absorbed by the atom or converted to another form of energy.

When the energy of the bombarding electron is high enough that the emitted radiation is in the X-rays region of the electromagnetic spectrum, these traditions are called bremsstrahlung radiation. It is characterized by the continuous distribution of X-rays energy which becomes more intense and shifts towards higher frequencies when the energy of the bombarding electrons is increased as shown in fig.

Bremsstrahlung and Cherenkov radiation

The energy lost due to bremsstrahlung is more important for electrons than for heavy particles because electrons are more violently accelerated in comparison of heavy particles when passing near the nuclei of the target atoms.

The greater the energy of the bombarding electrons and the greater the atomic number of the target atoms, the more rapid is its energy loss. The energy loss pre-unit length due to Bremsstrahlung radiation is directly proportional to the square of the atomic number of the matter and also directly proportional to the kinetic energy of the incident particles.

{-dE/dx}rad αZ²₁E

Thus the energy loss due to Bremsstrahlung for small values of incident energy is very small. The radiation loss increases with the increase of kinetic energy of the incident particles. Radiation loss depends on the Z² ₁, whereas energy loss due to ionization depends on the Z₁. At higher energies, however, the radiation loss is, therefore, more prominent due to heavy material.

Cherenkov Radiation

According to the special theory of relativity, the velocity of electrons cannot exceed the velocity of light c in the vacuum. But if an electron or any other charged particles move in a substance of refractive index n, then its velocity v may exceed the phase velocity of the light c/n in the given medium. In this case, a cone of electromagnetic radiation is emitted by the moving electron that is called Cerenkov radiation.

Cerenkov radiation is similar to the Mach sonic shock wave produced when the bodies travel at velocities greater than the phase velocity of elastic waves in the medium. Cerenkov radiation is contained within a cone whose envelope makes an angle θ with the direction of the motion of electrons. Thus

cosθ = c/nv+h/2mvλ{1-1/n²}
Where λ is the wavelength of the moving electrons.
Radiation is possible under the condition v>c/n. Cerenkov radiation is visible as a bluish glow when an intense beam of particles is in involved. Such type of glow was first observed in the nuclear reactor.

Gamma Ray Interaction With Matter

Gamma rays are electromagnetic waves and emitted in the form of photons and move with the velocity of light. Their rest mass is zero and charge is also zero. When α or β are particles are emitted from the radioactive nuclei, they go to the excited state. The excited nuclei return to the ground state by emitting γ- rays. This γ- rays are not deflected by electric and magnetic fields.

These are highly penetrating and hence their energy during the collisions with atoms, whereas each photon of γ- rays are removed individually from its beam by the absorber as a single event. The event may be an actual absorption process or scattering of the photon from the beam.

Law of absorption of γ – rays

Suppose a beam of γ – rays of intensity I₀ is incident on a slab of thickness x. The intensity of γ – rays decreases with the thickness of the slab. The change in intensity of the beam as it passes through the slab is proportional to (i) the thickness of the slab or depth of penetration and (ii) the intensity of the incident beam.

Thus in passing through a small thickness dx the change in intensity
dI = -μI dx. ………(1)
Where μ is a constant of proportionality. It is called linear absorption coefficients. For equation (1),
dI/I = -μdx
Integrating it,
loge I = μx + C
Where C is a constant of integration. At x = 0, I = I₀, the initial intensity of γ – rays
C = loge I₀
loge I = -μx + loge I₀
I = I₀e -μx. ………(2)

Thus the intensity of γ – rays decreases exponentially with the thickness of the slab. This is called the law of absorption of γ – rays in the matter. This relation can be put in different from also. If B be the number of photons crossing a unit area in a unit time i.e, flux and hv is the energy of the photon, then
I = Bhv
Using this relation in equation (2),
B = B₀e -μx. ……….(3)

(1) Linear absorption coefficient

If x= μ⁻ ¹, then

I = I₀/e = 0.37 I₀

The linear absorption coefficient μ is defined as the reciprocal of the thickness of the slab which reduced the intensity of the of the γ-rays to 37% of its initial intensity.

Then dimension of μ is (length)⁻¹ and its unit are metre⁻¹.

(2) Mass absorption coefficient

It is defined as the ratio of the linear absorption coefficient μ and the density ρ of the material of the slab i.e.

Mass absorption coefficient μm =μ/ ρ

(3) The half-depth of penetration

The half-depth of penetration is defined as the thek thickness of the slab which reduces the intensity of the γ-rays to half of its initial value.

Putting I = I₀/2 and x = x₁/₂ in equation (2),

I₀/2 = I₀ e⁻μx₁/₂

∴ X₁/₂ = 0.693/μ

(4) Radiation length

Radiation length is defined as the reciprocal of the linear absorption coefficient and is defined as the depth of penetration in the material of the slab which reduces the intensity of the γ-rays to 37% f is original value.


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