alialhulu
12-01-2010, 08:02 PM
Compton scattering:
Compton scattering was first discovered and studied by Compton in 1923. During an scattering experiment he found out that the wavelength of the scattered light was different from that of the incident light. He successfully explained this phenomenon by considering light to consist of quantized wave packets or photons.[ physics and engineering of radiation detection pag 87]
Compton scattering (Figure) is a direct interaction of the gamma-ray with an electron, transferring part of the gamma-ray energy. The energy imparted to the recoil electron is given by the following equation:
file:///C:/DOCUME%7E1/ALI/LOCALS%7E1/Temp/msohtml1/01/clip_image002.gif
Figure () The mechanism of Compton scattering
file:///C:/DOCUME%7E1/ALI/LOCALS%7E1/Temp/msohtml1/01/clip_image004.gif
……….()
………()
Putting different values of into this equation shows how the energy absorbed varies with the scattering angle. Thus, with = 0, i.e. scattering directly forward from the interaction point, Ee is found to be 0 and no energy is transferred to the detector. At the other extreme when the gamma-ray is backscattered and = 180, the term within brackets in the equation above is still less than 1
and so only a proportion of the gamma-ray energy will
file:///C:/DOCUME%7E1/ALI/LOCALS%7E1/Temp/msohtml1/01/clip_image006.gif
Figure ( ) Energy transferred to absorber by Compton scattering related to scattering angle
be transferred to the recoil electron. At intermediate scattering angles, the amount of energy transferred to the electron must be between those two extremes. (Figure )is a schematic diagram showing this relationship.) The
inescapable conclusion is that, at all scattering angles, less than 100% of the gamma-ray energy is absorbed within the detector.
Simplistically, I have assumed that the gamma-ray interacts with a free electron. In fact, it is much more likely that the electron will be bound to an atom and the binding energy of the electron ought to be taken into account. Most interactions will involve outer, less tightly bound, electrons and in many cases the binding energy will be insignificant compared to the energy of the gamma-ray (a few eV) compared to hundreds of keV). Taking binding energy into account alters the shape of the Compton response function to some extent, making the sharp point at the maximum recoil energy become more rounded and the edge corresponding to 180 backscatter acquires a slope. This is indicated by the dotted curve in Figure ( ). The Compton scattering absorption cross-section, often given the symbol , is related to the atomic number of the material and the energy of the gamma-ray:
file:///C:/DOCUME%7E1/ALI/LOCALS%7E1/Temp/msohtml1/01/clip_image008.gif
………. ( )
An energy function of 1/E رمز has been suggested as appropriate. Using an analogous relationship to that of Equation ( ), we can calculate a Compton scattering coefficient, µCS. If we also take into account the fact that over a large part of the Periodic Table the ratio A/Z is reasonably constant with a value near to 2 we can show that:
file:///C:/DOCUME%7E1/ALI/LOCALS%7E1/Temp/msohtml1/01/clip_image010.gif …………….. ( )
the implication being that the probability of Compton scattering at a given gamma-ray energy is almost independent of atomic number but depends strongly on the density of the material. Moreover, there is little variation of the mass attenuation coefficient, µCS/P with atomic number, again at a particular energy – a fact which ameliorates the difficulties of making a correction for self-absorption of gamma-rays within samples of unknown composition . [Practical Gamma-ray Spectrometry pag 28]
Compton scattering was first discovered and studied by Compton in 1923. During an scattering experiment he found out that the wavelength of the scattered light was different from that of the incident light. He successfully explained this phenomenon by considering light to consist of quantized wave packets or photons.[ physics and engineering of radiation detection pag 87]
Compton scattering (Figure) is a direct interaction of the gamma-ray with an electron, transferring part of the gamma-ray energy. The energy imparted to the recoil electron is given by the following equation:
file:///C:/DOCUME%7E1/ALI/LOCALS%7E1/Temp/msohtml1/01/clip_image002.gif
Figure () The mechanism of Compton scattering
file:///C:/DOCUME%7E1/ALI/LOCALS%7E1/Temp/msohtml1/01/clip_image004.gif
……….()
………()
Putting different values of into this equation shows how the energy absorbed varies with the scattering angle. Thus, with = 0, i.e. scattering directly forward from the interaction point, Ee is found to be 0 and no energy is transferred to the detector. At the other extreme when the gamma-ray is backscattered and = 180, the term within brackets in the equation above is still less than 1
and so only a proportion of the gamma-ray energy will
file:///C:/DOCUME%7E1/ALI/LOCALS%7E1/Temp/msohtml1/01/clip_image006.gif
Figure ( ) Energy transferred to absorber by Compton scattering related to scattering angle
be transferred to the recoil electron. At intermediate scattering angles, the amount of energy transferred to the electron must be between those two extremes. (Figure )is a schematic diagram showing this relationship.) The
inescapable conclusion is that, at all scattering angles, less than 100% of the gamma-ray energy is absorbed within the detector.
Simplistically, I have assumed that the gamma-ray interacts with a free electron. In fact, it is much more likely that the electron will be bound to an atom and the binding energy of the electron ought to be taken into account. Most interactions will involve outer, less tightly bound, electrons and in many cases the binding energy will be insignificant compared to the energy of the gamma-ray (a few eV) compared to hundreds of keV). Taking binding energy into account alters the shape of the Compton response function to some extent, making the sharp point at the maximum recoil energy become more rounded and the edge corresponding to 180 backscatter acquires a slope. This is indicated by the dotted curve in Figure ( ). The Compton scattering absorption cross-section, often given the symbol , is related to the atomic number of the material and the energy of the gamma-ray:
file:///C:/DOCUME%7E1/ALI/LOCALS%7E1/Temp/msohtml1/01/clip_image008.gif
………. ( )
An energy function of 1/E رمز has been suggested as appropriate. Using an analogous relationship to that of Equation ( ), we can calculate a Compton scattering coefficient, µCS. If we also take into account the fact that over a large part of the Periodic Table the ratio A/Z is reasonably constant with a value near to 2 we can show that:
file:///C:/DOCUME%7E1/ALI/LOCALS%7E1/Temp/msohtml1/01/clip_image010.gif …………….. ( )
the implication being that the probability of Compton scattering at a given gamma-ray energy is almost independent of atomic number but depends strongly on the density of the material. Moreover, there is little variation of the mass attenuation coefficient, µCS/P with atomic number, again at a particular energy – a fact which ameliorates the difficulties of making a correction for self-absorption of gamma-rays within samples of unknown composition . [Practical Gamma-ray Spectrometry pag 28]