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An electron of energy Ee and a photon of energy Ev collide in a scattering event. The photon is scattered in the forward direction, to travel at an angle theta from the horizontal. Assume the electron and photon both remain in the x-y plane after the scattering event.

i) Draw a diagram showing the photon and electron after the scattering. Defi ne and include appropriate angles on the diagram.

ii) Give expressions for the energy and 3-momentum of the photon before and after scattering, in terms of the photon frequency and relevant angles. Similarly, give expressions for the electron energy and 3-momentum before and after the collision, in terms of gamma, beta and me and relevant angles. De fine all symbols used.

iii) Starting from (and stating) physical principles, show that the final photon energy E vfinal and the initial photon and electron energies E vinitial, E einitial are related by:

E einitialE vinitial=E vinitialE vfinal(1-sin(theta)) + E einitialE vfinal(1-(Beta)ecos(theta)) where (Beta)ec is the intial velocity of the electron.

Clearly explain all steps in your derivation.

iv) If the photon was scattered with (Theta) = 0 to travel horizontally (according to the diagram
above), starting from equation 1 show that the fi nal scattered photon energy can be written as:

E vfinal = 2(Gamma)2E vinitial

Define Gamma in your answer, and describe any approximations used.

If the initial photon had wavelength Lambda = 500nm and the initial electron energy was E einitial = 500 MeV, what is the wavelength of a forward scattered photon?

Please answer part i-iii, thank you!

An electron of energy Ee and a photon of energy E, collide in a scattering event. The photon is scattered in the forward direction, to travel at an angle 0 from the horizontal. Assume the electron and photon both remain in the x-y plane after the scattering event. Scattering collision electron Photon i) Draw a diagram showing the photon and electron after the scattering. Define and include appropriate angles on the diagram. ii) Give expressions for the energy and 3-momentum of the photon before and after scattering, in terms of the photon frequency and relevant angles. Similarly, give expressions for the electron energy and 3-momentum before and after the collision, in terms of terms of y, B, me and relevant angles. Define all symbols used. iii) Starting from (and stating) physical principles, show that the final photon energy Einal and the initial photon and electron energies Einitial Einitial are related by Einitial Finitial Einitial Efinal (1 - sin 0) + Emitial Efinal (1 – Be cos 0) (1) where B.c is the initial velocity of the electron. Clearly explain all steps in your derivation. (hint: you may wish to review lecture 7.) iv) If the photon was scattered with 0 = 0 to travel horizontally (according to the diagram above), starting from equation 1 show that the final scattered photon energy can be written as Enal = 2,2Einitial (define y in your answer, and describe any approximations used) v) If the initial photon had wavelength A = 500 nm and the initial electron energy was Emitial 500 MeV, what is the wavelength of a forward scattered photon?
Transcribed Image Text:An electron of energy Ee and a photon of energy E, collide in a scattering event. The photon is scattered in the forward direction, to travel at an angle 0 from the horizontal. Assume the electron and photon both remain in the x-y plane after the scattering event. Scattering collision electron Photon i) Draw a diagram showing the photon and electron after the scattering. Define and include appropriate angles on the diagram. ii) Give expressions for the energy and 3-momentum of the photon before and after scattering, in terms of the photon frequency and relevant angles. Similarly, give expressions for the electron energy and 3-momentum before and after the collision, in terms of terms of y, B, me and relevant angles. Define all symbols used. iii) Starting from (and stating) physical principles, show that the final photon energy Einal and the initial photon and electron energies Einitial Einitial are related by Einitial Finitial Einitial Efinal (1 - sin 0) + Emitial Efinal (1 – Be cos 0) (1) where B.c is the initial velocity of the electron. Clearly explain all steps in your derivation. (hint: you may wish to review lecture 7.) iv) If the photon was scattered with 0 = 0 to travel horizontally (according to the diagram above), starting from equation 1 show that the final scattered photon energy can be written as Enal = 2,2Einitial (define y in your answer, and describe any approximations used) v) If the initial photon had wavelength A = 500 nm and the initial electron energy was Emitial 500 MeV, what is the wavelength of a forward scattered photon?
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