Pair Production and gamma ray

[DiracPool]

Pair Production questions:

1) When a gamma ray photon pair produces an electron and a positron, do the two particles always have the opposite spin? That is, one always has +1/2(h-bar) spin and the other has -1/2(h-bar) spin?

2) Other than charge and spin, what are some other notable properties of the two particles that "cleave" in a symmetric way in order to preserve conservation laws?

3) Is it true that pair production cannot happen in "empty space" but rather has to happen in a solid or at least near a nucleus in order to maintain the conservation of momentum? What does this mean for "vacuum" models of empty space that posit pair production events going on constantly in universe everywhere and all the time?

 

[jtbell]

What does this mean for "vacuum" models of empty space that posit pair production events going on constantly in universe everywhere and all the time?

Those are pairs of virtual particles. Virtual particles do not generally have the same mass ($\sqrt{E^2 - (pc)^2}$) as the corresponding real particles. In physicist jargon, they are "off the mass shell." Energy and momentum are always conserved, at each vertex of a Feynman diagram.

 

[snorkack]

Pair Production questions:

1) When a gamma ray photon pair produces an electron and a positron, do the two particles always have the opposite spin? That is, one always has +1/2(h-bar) spin and the other has -1/2(h-bar) spin?

I think yes. Because only electron and positron with opposite spins can produce pair or any other even number of photons. Electron and positron with same spin can only produce three or bigger odd number of photons, so an odd number of photons would be needed to create electron and positron with same spin.

3) Is it true that pair production cannot happen in "empty space" but rather has to happen in a solid or at least near a nucleus in order to maintain the conservation of momentum?

Yes, if pair from one photon is concerned. Two or more photons from different directions meeting in empty space can also produce pairs.

 

[alw34]

http://hyperphysics.phy-astr.gsu.edu/hbase/particles/parint.html
Particle Interactions and Conservation Laws

 

[nikkkom]

1) When a gamma ray photon pair produces an electron and a positron, do the two particles always have the opposite spin? That is, one always has +1/2(h-bar) spin and the other has -1/2(h-bar) spin?

I think they should have the same spin. Photon is a spin-1 particle. Electron/positron pair with opposite spins would have zero total angular momentum, thus such production violates conservation of angular momentum.

 

[mfb]

There are at least two photons involved in the production.
In addition, orbital angular momentum is possible (just not very frequent).

 

[DiracPool]

Thanks for everyone's replies. However, I'm not sure if we've reached consensus on what actually happens here. Here are some outstanding questions I have:

I think they should have the same spin. Photon is a spin-1 particle. Electron/positron pair with opposite spins would have zero total angular momentum, thus such production violates conservation of angular momentum.

That argument does make sense. The photon is a spin-1 particle. However, as a spin 1 particle it has three spin states, correct? +1, 0, -1. Therefore, couldn't one argue that the pair production could produce two + half spin particles for the spin 1 condition, two - half spin particles for the spin (-1) condition, and then opposite (sign) spins for the spin 0 condition? Or is this not how this works?

There are at least two photons involved in the production.
In addition, orbital angular momentum is possible (just not very frequent).

So does that mean that a singe gamma ray photon with an energy greater than 2x(.511 MeV) cannot pair produce and electron and a positron? For the two photons needed to produce the pair production, is one a positive energy photon and the other a negative energy photon? Or are they both positive energy photons?

Relating back to nikkom's conservation of angular momentum argument, how do the spins of the pair produced particles add up if we are dealing with more than one photon?

 

[vanhees71]

Photons have spin 1 but are also massless particles, and massless particles do not have $2s+1$ but only two polarization states (for $s \geq 1/2$). A usual single-particle basis to construct the Fock space are momentum-helicity eigenstates. Helicity $h \in \{-s,+s \}$ is the projection of the angular momentum of the particle to the direction of its momentum. The reason is quite deep in the representation theory of the Poincare group. For a detailed treatment, see my QFT manuscript

http://fias.uni-frankfurt.de/~hees/publ/lect.pdf

You get the correct angular momentum/polarization by applying the Feynman rules of the process under consideration. The most simple one is the tree level of the process $\gamma +A = A+\mathrm{e}^+ + \mathrm{e}^-$. In textbooks like Landau&Lifshitz vol. 4 you usually find the calculation for the unpolarized cross section.

 

[DiracPool]

A usual single-particle basis to construct the Fock space are momentum-helicity eigenstates. Helicity h∈{−s,+s}h \in \{-s,+s \} is the projection of the angular momentum of the particle to the direction of its momentum. The reason is quite deep in the representation theory of the Poincare group.

Thank you for the response, vanhees, but I was hoping for a more B-level explanation. I guess I mistakenly thought there would be a relatively straightforward answer to the question.

From: https://en.wikipedia.org/wiki/Pair_production

"In order for pair production to occur, the incoming energy of the interaction must be above a threshold in order to create the pair – at least the total rest mass energy of the two particles – and that the situation allows both energy and momentum to be conserved. However, all other conserved quantum numbers (angular momentum, electric charge, lepton number) of the produced particles must sum to zero – thus the created particles shall have opposite values of each other. For instance, if one particle has electric charge of +1 the other must have electric charge of −1, or if one particle has strangeness of +1 then another one must have strangeness of −1."

When I read this, I thought they simply forgot to add something like, "if one particle has a positive 1/2 spin, then the other particle must have a negative 1/2 spin." I thought the discussion of spin was conspicuously missing here. From what I gather from this thread, however, is that it was probably left out because the answer is not so straightforward. It actually seems pretty complicated.

 

[snorkack]

So does that mean that a singe gamma ray photon with an energy greater than 2x(.511 MeV) cannot pair produce and electron and a positron?

Not in free space.
Because free space is, well, free space. You can always choose a frame of reference where the gamma ray photon is Doppler redshifted to less than 1022 keV. And then the photon cannot produce a pair. In fact, nothing whatsoever can happen to a lone photon in free space save propagation.
Another question is if the photon collides with a massive particle. Then, yes, a lone photon plus the massive particle can form a pair plus the same massive particle.

For the two photons needed to produce the pair production, is one a positive energy photon and the other a negative energy photon? Or are they both positive energy photons?

Both positive energy.

 

[nikkkom]

So does that mean that a singe gamma ray photon with an energy greater than 2x(.511 MeV) cannot pair produce and electron and a positron?

This can't be done so that both momentum and energy are conserved. Photon is moving at c, but electron+positron can't do that. To pair-produce, photon needs something to absorb some of the excess energy.

 

[vanhees71]

Thank you for the response, vanhees, but I was hoping for a more B-level explanation. I guess I mistakenly thought there would be a relatively straightforward answer to the question.

From: https://en.wikipedia.org/wiki/Pair_production

"In order for pair production to occur, the incoming energy of the interaction must be above a threshold in order to create the pair – at least the total rest mass energy of the two particles – and that the situation allows both energy and momentum to be conserved. However, all other conserved quantum numbers (angular momentum, electric charge, lepton number) of the produced particles must sum to zero – thus the created particles shall have opposite values of each other. For instance, if one particle has electric charge of +1 the other must have electric charge of −1, or if one particle has strangeness of +1 then another one must have strangeness of −1."

When I read this, I thought they simply forgot to add something like, "if one particle has a positive 1/2 spin, then the other particle must have a negative 1/2 spin." I thought the discussion of spin was conspicuously missing here. From what I gather from this thread, however, is that it was probably left out because the answer is not so straightforward. It actually seems pretty complicated.

I thought, everything was answered except this question concerning the polarization states of photons, and the issue with the spins/polarizations is not so simple (at least, I've not a simple straight-forward answer). The most simple way to sort it out, is to do a concrete perturbative calculation in terms of Feynman diagrams.