443a3751e477d732c8d1b4bf8acc7fb81201 (1) - Phys 452 Winter 2011 Karine Chesnel Compton Scattering 1 Experiment In the early 20th century research

443a3751e477d732c8d1b4bf8acc7fb81201 (1) - Phys 452...

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Phys 452- Winter 2011 Karine Chesnel Compton Scattering 1. Experiment In the early 20th century, research into the interaction of X-rays with matter was an emerging field. It was observed that when a beam of X-rays is directed at an atom, an electron is ejected and the light is scattered through an angle θ , as illustrated below. Classical electromagnetism predicts that the wavelength of scattered rays should be equal to the initial wavelength; however, experiments showed that the wavelength of the scattered rays is actually greater than the initial wavelength. In 1923, Compton published a paper in the Physical Review explaining the phenomenon: A quantum theory of the scattering of X-rays by light elements (Phys. Rev. 21, 483 (1923)). Experimental measurements were also included in that paper, to support the theory. The Compton effect is essentially an inelastic scattering process between photons and electrons in the matter. This effect could not be explained by the classical theory of Thomson’s scattering – which basically describes an elastic scattering process. In the Compton effect, the inelastic scattering of photons in matter results in a decrease in energy (increase in wavelength) of an X-ray or gamma ray photon. Part of the energy of the X/gamma ray is transferred to a scattering electron, which recoils and is ejected from its atom, and the rest of the energy is taken by the scattered, "degraded" photon. 2. Classical theory of the phenomenon In the classical view, Compton scattering can be simply described as a collision process between photons carrying the light and electrons in the matter. Invoking the particle – wave duality, the incident light is assimilated to a single photon of initial energy E ϖ = and initial momentum p k = arrowrightnosp arrowrightnosp . After the “collision”, the photon is in a final state, with energy ' ' E ϖ = and final momentum ' ' p k = arrowrightnosp arrowrightnosp . The initial and final wave vectors k arrowrightnosp and ' k arrowrightnosp define the scattering plane, and the collision process can be reduced to a two- dimensional problem in that plane. The electron, initially at rest, acquires a final
momentum f p arrowrightnosp and a final kinetic energy f E . By applying the conservation laws from Newtonian mechanics, one can obtain these relationships: Conservation of momentum: ' f p k k + = arrowrightnosp arrowrightnosp arrowrightnosp ℏ ℏ [1] Conservation of energy: ' f E ϖ ϖ + = ℏ ℏ [2] Using the De Broglie relationship 2 / kc c ϖ π λ = = [3]

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