In an elastic scattering process the incident particle imparts energy to the stationary target. The energy ?E
Question:
In an elastic scattering process the incident particle imparts energy to the stationary target. The energy ?E lost by the incident particle appears as recoil kinetic energy of the target. In the notation of Problem 11.23, m3 = m1 and m4 = m2, while ?E = T4 = E4?- m4.
(a) Show that AE can be expressed in the following different ways,
where Q2 = ?(p1 ? p3)2 = (p1 ? ?3)2 ? (?1 ? E3)2 is the Lorentz invariant momentum transfer (squared).
(b) Show that for charged particles other than electrons incident on stationary electrons (m1 >> m2) the maximum energy loss is approximately
?Emax ? 2?2?2me
where ? and ft are characteristic of the incident particle and ? 1/me). Give this result a simple interpretation by considering the relevant collision in the rest frame of the incident particle and then transforming back to the laboratory.
(c) For electron-electron collisions, show that the maximum energy transfer is
?E(e)max = (? ? 1),me
Step by Step Answer:
a The diagrams appropriate to this problem are shown for Jackson problem 1123 m 1 is the incident pa...View the full answer
