Can a Single Photon Carry All the Momentum in Electron-Positron Annihilation?

[melonhead]

Hi,

I understand that momentum before and after annihilation must be conserved. However, why isn't it possible to have a net momentum not equal to zero before hand, (ex. an electron and a positron traveling head on, but at different velocities) and then just have a single photon travel in the direction of that net momentum after annihilation?

Any insight would be greatly appreciated. We just barely touched on annihilation in class, and this was bugging me.

Thanks

 

[Khashishi]

You need to conserve energy also. Since photons have no rest mass, a photon's energy and momentum are proportional. An electron and positron have a large ratio of energy to momentum than a single photon can possibly have.

 

[melonhead]

So my question now is how would I go about proving that a single photon can't have a large enough E/p ratio?

What I was trying to do is show that the ratio for the electron-positron pair will never equal to the ratio for a single photon.

E/p of a photon is c, correct?

To calculate the Energy of the electron positron pair, do you simply use 2(mc^2+(1/2)mv^2)?

Is the momentum p=mvsin(theta) for each of the particles?

How does relativity factor into all of this?

 

[willem2]

In the center of mass frame, the electron and positron have no net momentum, so the resulting photon(s) will have no net momentum either.

 

[melonhead]

What exactly is the centre of mass frame? Is the net momentum in the centre of mass frame equal to 0 in every annihilation reaction?