# Unlimited Barns

We know Dark Matter exists. What we don’t know is what it is made of. And what that tells you immediately is that if Dark Matter interacts with us, it will only do so very rarely – otherwise we would have found it long time ago.

To quantify exactly how rarely, physicists use a quantity called the cross-section. If we leave quantum mechanics aside for a moment, the cross-section would be the size of a particle. For example, a pool billiard ball has a radius of a little over an inch. We would attribute to it cross-section of pi times one inch squared, that’s about 3 square inch or, hey, it’s science here, about 20 cm2.

If we go to the largest atoms we know, uranium for example, their nuclei have a radius of about 8 femtometers, that’s 8×10-13cm. Thus, their cross section is about 2×10-24cm2. Clearly, square centimetres are not a convenient unit for nuclear physics. So when physicists at Purdue University were working on the Manhattan project in the 1940s, they were looking for a convenient measure to describe the size of the uranium nucleus. Convenient, and also secretive. With Purdue University being in a pretty rural area back then (it still is in some sense), they called the uranium nucleus “big as a barn”, and so, to this day, the unit barn is defined as being equal to 10-24cm2.

Aerial view of the Purdue Campus, 1940, directly adjacent to fields and farms. Image courtesy Purdue University Libraries, Archives and Special Collections from http://earchives.lib.purdue.edu.

Clearly, if you randomly hit the white ball in a game of pool billiard with your queue, it is more likely to hit a coloured ball the bigger these are. In other words, the probability of a scattering to occur grows with the cross-section of the particles that scatter. In the mind-set of quantum mechanics, this concept is generalized: the cross-section is used to indicate the probability of particles scattering with each other.

For example, the probability for a thermal neutron to interact with a helium-3 nucleus, kicking it to its excited level, is 0.00005 barn. The probability for the same neutron to instead react with the helium-3 nucleus and kick out a proton from it is much higher, 5330 barn. Clearly, picturing the cross-section as a geometrical size of the particles can be misleading in these cases. Even so, the barn unit really is convenient in nuclear physics.

As science progressed, particles were discovered that are much less likely to interact with us. If we hit a hydrogen nucleus (a proton) with another proton, the cross-section is about 40 millibarn, or 4×10-26cm2. That’s still nuclear physics. But a typical neutrino coming from the sun will have a cross-section of only 10-41cm2, that’s 10 atto-barn, to hit the proton. At this stage, we enter an area of particle physics where even the nuclear physicist’s unit barn becomes somewhat useless again.

Dark Matter particles interact even less with us. We have searched for Dark Matter particles that would interact with us as “often” as neutrinos do, but with no success. Our current detectors have a sensitivity to detect Dark Matter particles if they interact as rarely as with a cross-section of only 2×10-45cm2. If you’re curious to see how that looks in our research publications, that is available online free to read and shown in the last figure of the paper.

What we are working on is to push this sensitivity further, within the next few years, by another factor of 1000 or so to fully cover the cross-section range where we would expect the cross-section of Dark Matter to be. This requires larger detectors and some clever ideas of how to build and operate them, which is what keeps us busy for the time being. So, back to work.