Tensors and Relativity: Chapter 2

Example 2.2

Example 2.2

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Consider a collision between a photon with frequency tex2html_wrap_inline1394 moving in the x direction, with an electron of rest mass tex2html_wrap_inline1470 initially at rest [ see Figure 2.3 ].

figure531
Figure 2.3: Diagram illustrating Compton scattering.

Before the collision, the four- momenta of the photon and electron are

eqnarray1107

After the collision we have

eqnarray1109

where tex2html_wrap_inline1402 is the photon's frequency after the collision, v is the speed of the electron and tex2html_wrap_inline1476 , tex2html_wrap_inline1478 are shown in Figure 2.3.

Conservation of four- momentum gives

equation1115

Rearranging and squaring we get

eqnarray1117

Using tex2html_wrap_inline1480 and tex2html_wrap_inline1482 we obtain

equation1119

which gives the Compton scattering formula 

equation1123