Initial Lab Frame 4-momentum components

Initial Lab Frame 4-momentum components

Figure 1: Definition of variables in the Lab Frame

Begining with the assumption that the incoming electron, p₁, has momentum of 11000 MeV in the positive z direction.

[math]\displaystyle{ \vec p_{1(z)}\equiv \vec p_{1}=11000 MeV \widehat {z} }[/math]

We can also assume the Moller electron, p₂, is initially at rest

[math]\displaystyle{ \vec p_{2}\equiv 0 }[/math]

This gives the total energy in this frame as

[math]\displaystyle{ E\equiv E_1+E_2 }[/math]

where,

[math]\displaystyle{ E\equiv \sqrt{p^2+m^2} }[/math]

This gives,

[math]\displaystyle{ E\equiv \sqrt{(p_{1})^2+(m_{1})^2}+m_{2} }[/math]

[math]\displaystyle{ \Longrightarrow E\equiv \sqrt{(11000 MeV)^2+(.511 MeV)^2}+.511MeV\approx 11000.511 MeV }[/math]