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Date: 21-8-2016
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Inverse Compton Scattering
The HERA electron storage ring at Hamburg, Germany contains circulating electrons with an energy of 27 GeV. Photons of wavelength 514 nm from an argon-ion laser are directed so as to collide head-on with the stored electrons. Calculate the maximum scattered photon energy.
SOLUTION
Write the energy and momentum conservation laws in 4-notation, where we use units in which c = 1:
(1)
where pγ, pe, and are the 4-momenta of the photon and electron before and after the collision, respectively. After subtracting from both sides of (1) and squaring, we obtain
(2)
Here we used and pμγ pγ μ = 0. We may rewrite (2) in the form
(3)
Introducing the angle θ between the direction of the incident and scattered photons, we have
(4)
From (4)
(5)
The maximum energy in (5) corresponds to the minimum of the denominator which yields cos θ = -1, θ = π (backscattering). Therefore
(6)
Using the fact that me << εe (pe ≈ εe) and expanding the denominator, we can rewrite (6) in the form
(7)
We may now substitute values into (7): εγ = hc/λ = 2.42 eV, me = 0.51 MeV, and εe ≈ pe = 27 GeV, so
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