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15.7: The differential cross section is
 . In
calculating the transverse impulse, write the transverse force as
 , and take the derivative outside the
longitudinal integral.
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PROBLEM SET 7
Due Friday, March 26, 1999
Reading: Jackson, Chap. 15
Problems: Jackson, 15.4, 15.9; LD10, LD11
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15.7: The differential cross section is
. In
calculating the transverse impulse, write the transverse force as
, and take the derivative outside the
longitudinal integral.
|
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LD10:Calculations of this sort lead to the statement
that the change in
the electromagnetic field of a relativistic particle is radiated away in any
sudden transition. Think about how this calculation is connected to the
calculation of bresstrahlung in a hard scattering. The result in any of these
cases, given the fact that the field of the particle is predominantly
transverse to its direction of motion, is a burst of radiation in a narrow
cone with angular width  relative to its
inital and final directions.
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LD11: It is important to add the fields coherently. You may drop
the nonresonant term obtained after integration over t'. Show how the
result is to be transformed to the laboratory frame, that is, give the
transformations for the frequency and angles, and discuss their implications
for this problem.
It was shown only recently that this method can be used to derive the expressions 14.67 and 14.71 in Jackson used to treat synchrotron radiation by considering Thomson scattering in a sequence of instantaneous rest frames for the accelerated particle, with the fields added coherently in the laboratory frame. See R. Lieu and W.I. Axford, Astrophysical J. 447, 302 (1995), 416 700 (1993). |
Send comments or questions to: ldurand@theory2.physics.wisc.edu
© 1997, Loyal Durand