This preview shows page 1. Sign up to view the full content.
Unformatted text preview: 41. The diﬀerence between the electronphoton scattering process in this problem and the one studied in
the text (the Compton shift, see Eq. 3911) is that the electron is in motion relative with speed v to the
laboratory frame. To utilize the result in Eq. 3911, shift to a new reference frame in which the electron
is at rest before the scattering. Denote the quantities measured in this new frame with a prime ( ), and
apply Eq. 3911 to yield
h
2h
∆ λ = λ − λ0 =
(1 − cos π ) =
,
me c
me c
where we note that φ = π (since the photon is scattered back in the direction of incidence). Now, from
the Doppler shift formula (Eq. 3825) the frequency f0 of the photon prior to the scattering in the new
reference frame satisﬁes
c
1+β
= f0
f0 =
,
λ0
1−β
where β = v/c. Also, as we switch back from the new reference frame to the original one after the
scattering
c
1−β
1−β
=
.
f =f
1+β
λ
1+β
We solve the two Dopplershift equations above for λ and λ0 and substitute the results into the Compton
shift formula for ∆λ :
1 1−β
1 1−β
2h
.
−
=
∆λ =
f 1+β
f0 1 + β
me c2
Some simple algebra then leads to
−1 E = hf = hf0 2h
1+
me c2 1+β
1−β . ...
View
Full
Document
 Fall '08
 SPRUNGER
 Physics, Photon

Click to edit the document details