Compton Scattering

Background

The Compton Effect (1922) demonstrates that massless photons possess momentum as well as quantized energy. Photon momentum and energy can be transferred to a stationary electron of mass m in an inelastic collision. Special relativity and quantum mechanics are essential to explain the change in frequency (equivalently wavelength) of the scattered photon and the motion of the electron.

Compton scattering is derived using conservation of energy and momentum, where the energy and momentum of a photon of frequency ν are taken as hν and hν/c, respectively. The rest energy of the electron is mc2 and it is assumed to have zero momentum prior to its interaction with the photon

To observe the effect, photons with energies comparable to the electron rest energy mc2 are required. The needed high energy photons are found in the gamma-ray portion of the electromagnetic spectrum. A variety of radioactive isotopes spontaneously emit the appropriate gamma-rays and are used in this experiment. Because their energy is so high, it is difficult to detect gamma-rays directly. Indirect detection is used here through a process called scintillation. A scintillator is a special material – in this case a sodium iodide (NaI) crystal – that converts high-energy photons such as gamma-rays into visible photons that can be detected. The NaI scintillation crystal is directly attached to a photo-multiplier tube (PMT) that is sensitive enough to resolve very few visible photons. Detected photons appear as voltage pulses at the output of the PMT. The height of the voltage pulse is directly proportional to the energy of the gamma-ray that created it.

A multi-channel analyzer (MCA) measures the distribution of the PMT voltage pulses. By mapping the height of each pulse into a corresponding bin (x-axis on its display), the MCA produces a spectrum of the gamma-ray photons that strike the scintillator. The combination of scintillation, PMT, and MCA forms a gamma-ray spectrometer. There are many possible interactions that occur when gamma-rays collide with a scintillator, but the two most relevant for this experiment are photo-electric absorption and Compton scattering. In photo-electric absorption, a gamma-ray liberates a bound electron from the scintillator crystal. This highly energetic electron travels through the NaI giving up its kinetic energy in collisions with other atoms along the path. These excitations relax back to the ground state by emitting visible photons. The more kinetic energy the electron possesses, the further it travels, the more photons are emitted, and the larger the voltage pulse at the output of the PMT. Although many visible photons are emitted, each voltage pulse corresponds to a single gamma-ray event. The gamma-rays irradiate the scintillator at a low enough rate that they can be individually distinguished. It is important to understand that the PMT cannot detect gamma-ray photons. It only detects visible photons that result from the dissipation of kinetic energy of fast moving electrons in the scintillator.