Simple fun with polarizers!

I’ve had a set of small polarized films sitting in my office for months. The other day, I finally broke them out and, after some fiddling, it occurred to me that there are plenty of simple experiments that one can do with them!

One of the fun forays is showing the effects of stress-induced birefringence, one of my favorites, as you might recall, or recall again.

I’ve mentioned that I did a postdoc at TRIUMF (the Tri-Universities Meson Facility/Factory) but it occurs to me I have never explained the physics I did while I was there.

There is information to be gained and physics to be learned (or confirmed) if one can accurately and precisely analyze what is happening in the decay of nuclei, specifically the \(\beta\)+ decay of nuclei, in which a proton changes into a neutron and emits a positron and a neutrino. If one could gather the information about the emitted particles, one could investigate the decay and look to confirm the standard model or investigate if there are deviations from it.

Oner method of analyzing a decay would be to measure the energy (or momentum) of the emitted particles, in order to reconstruct the mechanics of the decay. The parent nucleus is typically embedded in some sample, a solid or liquid, and you’d like to measure the emitted positrons and neutrinos. The daughter nucleus will still be embedded in your sample material, so measuring it is difficult at best, since it probably won’t have enough energy to be ejected and hit a detector, and you don’t know where it was (or how much it was moving, though thermal energy is small) anyway. Also, the positron’s path can be distorted in leaving the sample.

But those are minor inconveniences, because neutrinos are really, really, really hard to detect. Billions of them from the sun pass through every square centimeter of the earth’s surface each second, and we can detect only a few at a time in large pools of detectors. But this is science, and smart people think about hard problems and try to find ways to do things that are difficult.

If you want to reconstruct a decay without the neutrino, you must gather the information about the other particles, and apply conservation of energy and momentum. In essence, neutrino spectrometry is like finding the shape of something by looking at its shadow.

OK, but how do you hold a sample of radioactive nuclei in a way that allows you to detect both the positron and the recoiling daughter? This is where the magneto-optical trap (MOT) enters the picture. Atoms confined in a MOT are a gas, but localized to a small volume, of order a mm in diameter, and at temperatures of order a milliKelvin, suspended in space in a vacuum system. Better still, the resonant interactions with the photons that trap the atoms are specific to the element (and isotope) you are trapping. This means that once an atom has decayed, the daughter atom is no longer trapped, and is free to move and be detected.

This was the plan that was implemented in the TRINAT (TRIumf Neutral Atom Trap) group. Two different investigations were started, each using an isotope of Potassium. I’ve mentioned some difficulties in trapping radioactive atoms, where the laser frequencies are unknown, and the aha! moment when you get them trapped; another issue was the short half-lives: we trapped an isomer of K-38 and also K-37, both of which have half-lives of around a second, which presents a significant challenge — your samples are quickly decaying away while you get them loaded into the trap. But rather than go into technical details I’m going to talk a little about the physics (not a lot, because this is nuclear stuff, and I’m an atomic physics person)

K-38m has a nuclear spin of 0, and it decays into Ar-38, which also has a nuclear spin of 0. (one atomic physics note, here — a zero-spin nucleus has no hyperfine structure, so it really is a two-level system and trapping it is easy in the scheme of things). Having no spin in both the parent and daughter means that the spin-1/2 emitted positron and neutrino must take away a net zero angular momentum. In the standard model*, neutrinos are left-handed (spin vector is opposite the momentum vector) and the positron is right-handed, so if we look at the case where the positron, neutrino and daughter have only momentum along a straight line, we have two possibilities: the positron and neutrino either go in the same direction, taking almost all the energy and the daughter recoiling in the opposite direction, or the positron and neutrino go in opposite directions, splitting the momentum to some extent, and leaving the daughter with a much smaller momentum. By detecting the coincidences and time-of-flight of the positron and daughter with detectors on opposite sides of the vacuum chamber, you can tell the two cases apart. If the standard model is correct, you will only get a co-moving positron and neutrino (so the spins cancel), i.e. a large recoil. But if there is new physics (a scalar Boson), you will see the particles going in opposite directions, with a larger time-of-flight owing to the lower momentum.
(Here’s the paper for that experiment, and the ArXiv version)

Another test you can do is if you can polarize the atoms so that the atomic and nuclear spins align, which can be done via optical pumping into the maximum angular momentum state. You can measure angular correlation of the recoil daughter and the polarization vector, and see if there is any deviation from the angular correlation predicted by the standard model. This was being worked on when I left; I was involved in proving we could trap the radioactive K-37, but the system to spin-polarize the nuclei belonged to another postdoc, and was still in progress when I left, but it looks like they completed the experiment and then moved on to do it more precisely in Rb-80

*I have absolutely no idea how the subsequently-identified neutrino oscillations come into play here, though I think they don’t

Bootleg Einstein/Far Side title reference.

How Einstein’s most famous equation affects you

But there’s a far more common and even mundane application of Einstein’s most famous equation: every single nuclear and chemical reaction, ever.

Even though the mass difference is small, it’s still there.

Also, a reminder, that the effect a mass increase for a nuclear excited state has been measured

Unlike some projects that I kvetch about where “design” is merely art, and nobody has run the numbers, here’s a project that can actually work.

Body-heat powered flashlight takes teen to Google Science Fair

Makosinski did some calculations to see if the amount of energy produced by warmth from a person’s hand was theoretically sufficient to power an LED bright enough to use in a flashlight, and she found it was more than enough.

Boom! That’s how you do it!

It’s not going to work (or work well) in hot weather because it needs a temperature difference, but it’s great for cooler climes and times.