Creating a positron and a electron with a photon

[Frank Einstein]

Homework Statement

Hi everybody. I have to demostrate that a photon, no matter it's energy, will never be able to create a positron and an electron on it's own.

Homework Equations

E=Sqrt(m^2+p^2) as long as c=1
Conservation of energy Ei=Ef; initial energy is equal to final energy.
Conservation of momentum Pi=Pf; initial momentum is equal to final momentum

The Attempt at a Solution

This violates the conservation of momentum because if we go to the centre of mass, the photon will have momentum E; but in the same system, the total final momentum will be zero.
Is this enough to demostrate that the desintegration of a photon on its own in two particles is impossible?[/B]


Thanks for reading

 

[mfb]

Should be fine if you add that a photon with energy E and 0 momentum does not exist.
Alternatively, find a frame where the photon energy is too low.

 

[Frank Einstein]

Should be fine if you add that a photon with energy E and 0 momentum does not exist.
Alternatively, find a frame where the photon energy is too low.

Thanks for the anwser.

I am also trying to demostrate that if we introduce a heavy atomic core, this will be possible, but the energy of the nucleus will be almost zero. All I can think of is that the core has the same momentum that the photon had before the colision; and since the mass of the core is huge compared with the energy of the photon, the energy of the core will be almost is mass; but I am not very sure if I can say that the electron and positron are created at rest.

 

[mfb]

but I am not very sure if I can say that the electron and positron are created at rest.

They don't have to, but they can. Usually their combined momentum points (roughly) in the same direction as the photon momentum, so the momentum transfer to the nucleus is even smaller than the photon momentum.

 

[Frank Einstein]

Then I can solve the exercice properly. Thanks.