Why can't photons reverse annihilate ?

[Darkmisc]

Why can't photons "reverse annihilate"?

If electron-positron pairs annihilate to product gamma radiation, why can't gamma photons spontaneously become a electron-positron pair?

 

[M Quack]

They can. You need two photons for conservation of momentum, but one can come from the electric field near a nucleus.

The process is called pair production.

 

[Darkmisc]

Why does another photon or nuclei have to be involved?

Can't the photon's energy and momentum be converted into the mass, kinetic energy and momentum of the electron-positron pair in free space?

 

[Jonathan Scott]

If electron-positron pairs annihilate to product gamma radiation, why can't gamma photons spontaneously become a electron-positron pair?

A pair of gamma photons can produce an electron-positron pair if they have high enough energy and meet in the right way. Look up "two-photon physics" or "gamma-gamma physics" for more details.

A positron and an electron are mutually attractive so the probability of annihilation is high. It is much more difficult to get gamma photons to collide in a such a way that the center of mass energy is sufficient to produce an electron-positron pair.

 

[Jonathan Scott]

Why does another photon or nuclei have to be involved?

Can't the photon's energy and momentum be converted into the mass, kinetic energy and momentum of the electron-positron pair in free space?

No, it's not possible to satisfy energy and momentum conservation laws in that case.

 

[M Quack]

Look at the center-of-mass system. Here you have two photons with the same energy (and therefore momentum) heading towards each other, to total momentum is zero. They convert into a particle and antiparticle pair, which head away from each other with the same speed. They have the same mass, therefore again the total momentum is zero. Momentum is conserved. Energy conservation is easy, you take the energy of the photons, subtract the rest energy of the new particles, what is left is the kinetic energy. Each new particle gets 50% of that.

With a single photon you cannot find a solution that satisfies energy and momentum conservation.

The process actually is very efficient for photons with >1.022 GeV energy. Then the second photon can have close to zero energy, which is the case for virtual photons in a static electric field. For such high-energy gamma rays, pair production is the dominant absorption mechanism.