Unit 4: Interaction of Nuclear Radiation with Matter & Particle Accelerators

1. Cerenkov Radiation

Cerenkov radiation is the electromagnetic radiation emitted when a charged particle (like an electron) passes through a dielectric medium at a speed greater than the phase velocity of light in that medium.

This phenomenon is analogous to a "sonic boom" produced by a supersonic aircraft. When the particle travels faster than light in the medium, it creates a coherent shock wave of light, typically appearing as a blue glow in water-cooled nuclear reactors.

Condition: v > c / n
where v is the particle velocity, c is the speed of light in vacuum, and n is the refractive index of the medium.

2. Gamma Ray Interaction through Matter

Gamma rays are high-energy photons and interact with matter primarily through three distinct processes depending on their energy:

A. Photoelectric Effect

Occurs primarily at low energies (below 0.5 MeV). A gamma-ray photon is completely absorbed by a bound electron of an atom. The electron is then ejected with kinetic energy:

Where B.E. is the binding energy of the electron. This effect is dominant for materials with a high atomic number (Z).

B. Compton Scattering

Occurs at medium energies (0.5 MeV to 5 MeV). The photon collides with a "free" or weakly bound electron, transferring part of its energy and being scattered at an angle.

Compton Shift: Δλ = (h / m_e*c) * (1 - cos θ)

C. Pair Production

Occurs at high energies (above 1.022 MeV). In the vicinity of a nucleus, the gamma photon is converted into an electron-positron pair.

3. Mossbauer Effect

The Mossbauer effect is the recoil-free emission and absorption of gamma-ray photons in solids.

Normally, when a nucleus emits a gamma photon, it recoils to conserve momentum, which shifts the energy of the photon slightly. In a crystal lattice, the recoil momentum can be absorbed by the entire crystal rather than a single atom. Since the crystal mass is huge, the recoil energy loss is negligible, allowing for extremely high-precision spectroscopy.

4. Detectors for Nuclear Radiations

Detectors convert the ionization or excitation produced by radiation into an electrical signal.

5. Particle Accelerators: Cyclotron & Betatron

Accelerators are used to provide charged particles with high kinetic energy to penetrate target nuclei.

Cyclotron

Uses a constant magnetic field to bend particles in a circular path and a high-frequency alternating electric field between two "D" shaped electrodes (Dees) to accelerate them.

Resonance Condition: The frequency of the applied AC must match the cyclotron frequency of the particle: f = qB / (2πm).

Limitation: At very high speeds, the mass increases relativistically, causing the particle to go out of step with the AC frequency.

Betatron

Used specifically for accelerating electrons to high energies using magnetic induction. A changing magnetic flux through a circular orbit induces an electromotive force (EMF) that accelerates the electrons.