4

I know that in particle annihilation, for momentum to be conserved, we have to create a minimum of 2 photons moving in the opposite direction.

According to Wikipedia:

Pair production often refers specifically to a photon creating an electron-positron pair near a nucleus.

My question is not why are 2 photons released during the annihilation of positron and electron, I know that 2 photons are released because there is a need to converse momentum. My question is: why does only one gamma-ray is needed to produce 2 particles, 1 positron and 1 electron?

CountDOOKU
  • 856

2 Answers2

2

Annihilation produces two photons, because momentum is a vector quantity, and it needs to be conserved. The only way to do that in the case of annihilation is to have two photons exiting in opposite direction, making the sum of their momenta vectors add up to 0 (in the center of mass frame).

For instance pair creation/annihilation can occur inside an electric field (say, close to a nucleus), or inside a magnetic field, in which case one-photon processes are fully allowed, and quadri-momentum conservation is made possible by the presence of the nucleus and/or the magnetic field.

Why during annihilation of an electron and positron 2 gamma rays are produced instead of 1?

Now in the case of pair production, the only way to do that with one photon is to have a nucleus in the vicinity, where the nucleus will take the recoil, meaning that the nucleus' momentum vector and the photon's momentum vector will add up to 0 (in the center of mass frame). Thus, momentum is always conserved.

Deschele Schilder
  • 1
Árpád Szendrei
  • 28,452
  • Why a nucleus is needed? Doesn't it suffice that the produced pair carries away the (four) momentum of the photon? – Deschele Schilder Sep 08 '20 at 09:24
  • @DescheleSchilder not in the center of mass frame. In the center of mass frame, the four momentum of the produced pair is 0. That is impossible with a single photon. Thus, the nucleus gets a recoil, and the nucleus and photon sum four momentum is 0 in the center of mass frame, momentum is conserved even in that frame. – Árpád Szendrei Sep 08 '20 at 15:31
0

The words "near a nucleus" are critical here. The electric field around a nucleus is the source of a second (virtual) photon, which is needed to conserve energy and momentum. When there truly is only one photon around (i.e. in a vacuum), pair-production cannot occur.

probably_someone
  • 35,459
  • please write some lines on virtual photons also. – crabNebula Aug 29 '20 at 08:49
  • If there is only one photon around in a vacuum, why can't an electron-positron pair be produced? -1 – Deschele Schilder Sep 08 '20 at 09:16
  • @DescheleSchilder it is not the vacuum itself. In vacuum, near a black hole for example, where there is a very strong gravitational field, pair production is possible. Or, near a magnetar, where there is a very strong EM field around, it is possible too. If the field has very strong energy, the pair production can occur. But in vacuum, without any stress-energy (not mass), that would create a strong field, pair production has very little probability. Now momentum needs to be conserved too in the center of mass frame. – Árpád Szendrei Sep 08 '20 at 15:36
  • In these cases you named there is not a single real photon around. Only virtual force particles related to gravitation.and the e.m. field. I thought we are talking only about real partcl]es. – Deschele Schilder Sep 08 '20 at 16:23