“Gentlemen, start your envelopes”

At a high level, the name of the game in building dark matter detectors is to find cleverer ways of measuring progressively smaller energy deposits. Nowadays that means things in the eV scale, which even a decade ago would have been unheard of.

So with that in mind, I was at a talk recently about “novel” diamond detectors. It was super interesting and there seems to be a lot of work going on in that direction. Diamond as a particle detector medium is not a particularly new concept though, with prototypes demonstrated in the 1970s. The idea was shelved, since Silicon and Germanium were much more attractive semiconductors, only to start reappearing now that some technical challenges have been solved and its upsides might prove to be useful.

The reason I’m being vague in explaining what exactly those upsides and downsides are though is that the whole thing is moot because of one *huge* problem – something it seems nobody bothered to work out until my advisor, sitting in the audience, pointed it out by a quick back of the envelope calculation.

You see, diamond is made out of Carbon of which there are 3 naturally occurring isotopes. In any given sample of Carbon, you’ll have roughly 99% Carbon-12 and 1% Carbon-13. Carbon-14 is technically not 0 and is present at the level of 1 part-per-trillion, a number that at first pass you assume behaves like 0. That is a deadly assumption. 14C is actually unstable and decays (via beta-decay, i.e. spits out an electron of max ~150 keV) with a half-life of 5730 years (which also seems unimaginably long). The question you, as a hard nosed experimentalist, should ask is: will my super super sensitive diamond detector be affected by this source of background radiation? Let’s work that out in 3 lines.

If I have 1g of Carbon (~ 6E23 /12 atoms thanks to Avogadro) with 1 p.p.t 14C then I have:

5E22 * 1E-12 = 5E10 atoms/gram of 14C.

Now the activity (decay rate) of 14C (by the law of radioactive decay):

ln(2) / 5730 years = ~4E-12 decays/atom/second

Which means that your detector will see:

5E10 * 4E-12 = ~0.2 decays/second/gram (!!)

Your state of the art ultra sensitive device will have a dump of energy ~10000x its threshold about once every few seconds. And this was just for a gram – imagine scaling that up to any reasonable size or exposure.

Say you wanted to get this background rate down to currently planned next generation device levels of < 10 event/kg/day (that’s a pretty malleable number but we’re talking about numbers in this ballpark). You would need to improve your isotopic purity of 14C by over 6 orders of magnitude down to 1E-18 before you’d be in the running. Currently the best hope you have for quick purification seems to get you 1E-14 but even that doesn’t seem to be in large enough quantities to begin to construct detector crystals out of. So you’d have to sink an enormous amount of  R&D time and money to get more than this 2 orders of magnitude (which is still like 8 decays/hour/gram!) – we’re talking about millions of dollars cumulatively over many many years before you can begin to talk about competing at the current state of the art limits. And this just 14C. You’ll of course have Tritium, Radon, trace Uranium and Thorium and whatever junk is lying around all adding to this (often in significant quantities too).

I want to stress that this isn’t to disparage the these kinds of novel ideas – diamond detectors are super cool – but just to reinforce the point that this stuff is very hard! Also, one of the strongest skills an experimentalist can have is a sense of intuition and the ability to work something out / estimate things ultra-quickly. In my experience, the best physicists possess the ability  (one that I certainly don’t have) of being able to reason through something in an ad-hoc manner and get to the crux of the issue without wasting time in drawn out computations. So to loop back to my title, have those envelopes at the ready – you never know when you have to scribble something on the back of them in a flash during someone else’s talk!


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