Difference between revisions of "Compton Scattering"
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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 | 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. | 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. | ||
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| + | Although multiple visible photons are produced by a single-gamma ray, the detected photon count can vary even though the gamma-ray photon energy does not change. This results in a statistical (Gaussian) distribution in the spectrometer bins. The spectrometer does not display a δ-function, but a broad peak having a width that reflects this distribution. | ||
| + | |||
| + | The primary difference between Compton scattering and photo-electric absorption is in the amount of energy transferred. In the photo-electric interaction, an electron is ionized with kinetic energy almost identical to the gamma-ray. In Compton scattering, there is a continuum of energies that can be exchanged, ranging from 0 to 100% of the incident gamma-ray energy. This arises from the angle-dependence in Equation (1). Energy is partitioned between the electron that is struck and | ||
| + | the scattered photon. The maximum energy an electron can acquire in Compton scattering occurs at θ = 180◦ , in which it directly recoils from a head-on collision. This produces the minimum possible scattered photon energy: | ||
Revision as of 22:32, 3 February 2020
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.
Although multiple visible photons are produced by a single-gamma ray, the detected photon count can vary even though the gamma-ray photon energy does not change. This results in a statistical (Gaussian) distribution in the spectrometer bins. The spectrometer does not display a δ-function, but a broad peak having a width that reflects this distribution.
The primary difference between Compton scattering and photo-electric absorption is in the amount of energy transferred. In the photo-electric interaction, an electron is ionized with kinetic energy almost identical to the gamma-ray. In Compton scattering, there is a continuum of energies that can be exchanged, ranging from 0 to 100% of the incident gamma-ray energy. This arises from the angle-dependence in Equation (1). Energy is partitioned between the electron that is struck and the scattered photon. The maximum energy an electron can acquire in Compton scattering occurs at θ = 180◦ , in which it directly recoils from a head-on collision. This produces the minimum possible scattered photon energy:
