## April 30, 2010

I was at a gathering of physics teachers earlier this week and the teaching of modern physics at the high school level came up a few times during the meeting.  It was really cool to see that there are high school physics teachers who are able to cover topics like the photoelectric effect, Compton scattering, and of course, the meaning of E=mc2.

In conversation with a few teachers the topic of antimatter came up.  I've always been fascinated with the existence of antimatter (thank you, Star Trek) and the means of producing antimatter.

One of the ways of producing antimatter is through a process called pair production.  The pair production process is the transformation of a photon into a positron (the antimatter complement to the electron) and an electron.  The positron has the mass of an electron, but has a positive charge. The production of a positron-electron pair from a photon requires a minimum energy of 1.022 MeV be involved in the reaction.  The mass of the electron and positron are each 0.511 MeV/c2. So if all the of the energy carried by a photon is converted into the mass of the two particles, the required energy is just 2mc2, where m is the mass of the electron (remember the positron has the same mass).  If the energy involved in the pair production process is just at that threshold energy, then the electron and positron would be produced at rest.

Scientists (and especially physicists) love conservation relationships.  The pair production process conserves charge, since the photon is not charged and the electron-positron pair is oppositely charged. Energy is conserved as I was discussing above.  The real issue with pair production is the conservation of momentum.

I don't want to get into the math of the momentum conservation right now. But, if you think about our hypothetic case where the pair are produced at rest, there is a problem which should be obvious: before the production the photon had momentum, but if the pair is produced at rest, then they have no momentum.  This is BAD, since momentum conservation is a fundamental principle of physics.

The teachers and I were standing around talking about pair production and the conservation of momentum when one of the teachers said that he explained to his class that two photons were required to  produces an electron-positron pair.  The collision of two photons with opposing momenta satisfies the momentum conservation law.  Then another teach piped up and said that he had read a paper saying that in face FIVE photons were required.  I tried to explain that I was under the impression that the typical observation of pair production was done in the presence of a heavy nucleus which would account for the momentum conservation.

None of the teachers really seemed to believe my explanation and they probably didn't think that I was going to be swayed by their reasonings, either.  The next day I flipped through some textbooks to see if I could make sense of what we were talking about.   I only found the type of pair production that I was familiar with, and the question of photon-photon (or multi-photon) interactions was never brought up in any of the books I had with me.

So I went to google and did some digging.

The first thing I found was an astrophysics book which discussed photon-photon interaction leading to pair production. The relevant part of the text is on pages 127-8 of that book.  It turns out that photon-photon collisions leading to pair production provide a means of screening high energy gamma rays in some cosmic environments. (Gould & Schreder PRL 1966)

But I had to figure out if the five photon interaction claimed by the other teacher had any basis in reality. What I found was a paper by Burke et. al. in PRL from 1997. (If you aren't reading this from a place where you can see the full text of the article, I apologize.)  I haven't fully digested this article, but the relevant quote says:

"...the multiphoton Breit-Wheeler reaction

becomes accessible for n ≥ 4 laser photons of wavelength 527 nm colliding with a photon of energy 29 GeV."
Whoa!  That's cool!  The point of that article was to show that while in cosmic sources, two photon collisions can produce electron-positron pairs, it has not been observed in a lab.  But, using one high energy photon and four (or more) photons from a laser, the pair production can be done in the lab.

What I learned was that all three of us standing around were right in what we each understood, but that our individual understanding of the topic was incomplete.  I'm so glad that I went and had that discussion with the teachers!

(The prediction of the existence of antimatter was a surprising result of the unification of Einstein's relativity theory with the burgeoning field of quantum mechanics in the earth 20th century.  This prediction was made by Dirac, a brilliant and eccentric theoretical physicist.  There was a book recently published on Dirac which I have not had a chance to read, but I'm linking to below.)