What Is An Inverse Femtobarn? Barns: Area Units

What’s an inverse femtobarn? The definition of an inverse femtobarn is a little complicated, and physicists don’t often bring this term up. However, the inverse femtobarn is easy to explain, has some interesting history, and some comical related terms too. The inverse femtobarn is a unit of measurement, just like a meter or a second, but while those measure length and time, the concept that the inverse femtobarn measures is a little more abstract.

Specifically, it’s the effectiveness of a particle collider– such as the Large Hadron Collider (LHC) at CERN in Europe, or the Tevatron at Fermilab in Illinois. But just telling you that doesn’t provide the full explanation. So let’s start at the beginning…

World War II: The Los Alamos Countryside

We all know how World War II was ended- in a spectacular and frightening display of engineering known as the atomic bomb. The theories behind this bomb were frantically pieced together at a specially built laboratory in Los Alamos, NM. Of course, this research was extremely confidential, and in this era of cloaks and daggers and secrets on microfilm, precautions needed to be taken so the Axis powers wouldn’t steal this weapon for themselves.

nuclear-weapons-test-67557_1280

A nuclear weapons test.

Scientists at this time were experimenting with uranium atom collisions. While the nucleus of an atom is very small, each element’s atom is a different size since it’s made up of more or less protons and neutrons. The nucleus of a uranium atom, compared to other elements, is gigantic. And you’ve surely heard of the phrase “it’s as big as the broad side of a barn!” We do not know the identity of the specific scientist who managed to link together uranium atoms and barns as both being relatively large compared to their surroundings, but it happened.

When sending descriptions of their experiments back and forth, scientists tried to avoid mentioning uranium. That’s because these messages could be caught and read by spies, and if Nazi scientists used uranium-related terms as clues, they could figure out what our patriotic researchers were up to. So as a code, our scientists used the word “barn” to mean a precise unit of area: 10-24 cm2, or 10-28 m2.

It’s hard to say if this worked or not. Of course, many of our Los Alamos secrets ended up being given to the Soviets anyway by communist spy Klaus Fuchs.* But I’d like to imagine a couple Nazi scientists scratching their heads reading our codes: “Warum sind die Amerikaner studieren Scheunen???

(Why are the Americans talking about barns???)

Through scientific osmosis after the war, “barn” stopped being a code word and became an accepted unit in the lexicon of research. It’s not an official SI unit, but it is officially accepted by their standards since physicists continue to use it regardless.

So that’s a barn – just a unit of area, like an acre or a square foot, but so much smaller – but what about the “inverse femto” parts?

Inverting The Femtobarn

Let’s get one explanation out of the way first. We’re all familiar with the “hour” unit of time. And you may remember from basic algebra that any fraction with a denominator (bottom number) of 1 is simply equal to the numerator (top number). So,

  • 1 / 1 = 1
  • 6 / 1 = 6
  • 555 / 1 = 555
  • x / 1 = x
  • etc.

In the same line of thinking, 1 hour / 1 is also equal to simply one hour.

We’re all also familiar with the unit of speed, miles per hour. Expressed mathematically, that’s miles / hours – if you travel 60 miles in 2 hours, you’re traveling at 60 miles / 2 hours = 30 miles per hour. If you travel 50 miles in 1 hour, that’s 50 / 1 = 50 miles per hour. The unit is “per hour”, which means that hour is on the bottom of the fraction.

Scientifically speaking, switching the top and the bottom of a fraction is called inverting it. 1 / 5 is the inverse form of 5 / 1, and 5 / 1 is the inverse form of 1 / 5. All it is, is flipping it around.

So what’s an inverse barn? It simply means that there’s something “per barn”. We just haven’t gotten to what quite yet.

Changing a barn to a femtobarn is simply making it much, much smaller. A barn is already small at 10-28 square meters, but a femtobarn is so, so, so, so tinier: 10-43 square meters, or 10-39 square centimeters. It’s nearly impossible to even imagine such a small unit of area. Think about the area of a city block, then about the area of a cross-section of one of the hairs on your head, and then extrapolate a million times smaller, and then another million times, and then a little more yet.

It’s a very small area. But this brings us to the inverse femtobarn. It’s a number of something per tiny little area.

So What Is It Used For?

The inverse femtobarn is used to measure effectiveness of particle accelerators, as mentioned above. These machines smash tiny particles together at super fast speeds and then watch what happens. These collision events are where the meat of the experiment is, where things get interesting – and inverse femtobarns are the way of stating how many of those interesting events happen per unit of area.

lhc_long_1

The Large Hadron Collider (Image: CERN)

As a metaphor, imagine you’re in a plane, flying over the countryside, and you have a whole bunch of watermelons – a hundred of them, to be precise. Unfortunately, the rear hatch comes loose during flight, and all the watermelons tumble out, one after the other!

Looking back down at your trail of fallen watermelons, you can see that you lost all 100 of them over an area of 20 acres. So, on average, that’s 5 watermelons per acre. And another way of saying “per acre” is 5 inverse acres. That’s how effective you were at littering watermelons across the countryside (way to go).

So if a particle accelerator’s inverse femtobarn count is high, they’re doing great – it means they’re getting a ton of collisions, which means much better results. In regular communications to the public, most accelerator labs prefer to just use the actual number of particle collisions, since that way they’re not stuck explaining all of the above, but that number will be less scientific overall.

In 2011, physicist Tommaso Dorigo announced that Fermilab reached 11 inverse femtobarns. How many collisions does this actually represent? To quote Dorigo about ten inverse femtobarns:

A mile-long stretch of sand, extending 100 meters into the land and with a depth of one meter, contains roughly the same number of sand grains as that number of collisions.

Then, in 2012, the LHC more than doubled that with 23 inverse femtobarns, and the number is only going up.

It takes that many collisions and more to probe the deepest secrets of particle physics that are currently accessible to us, such as the Higgs Boson.

Unit Conversions

For reference, here are conversions from barns to other units and back. Any SI prefix is acceptable with a barn.

Unit of Measurement        Symbol       m2            cm2      
yottabarn Yb 10−4 1
zettabarn Zb 10−7 10−3
exabarn Eb 10−10 10−6
petabarn Pb 10−13 10−9
terabarn Mb 10−16 10−12
gigabarn Mb 10−19 10−15
megabarn Mb 10−22 10−18
kilobarn kb 10−25 10−21
hectobarn hb 10−26 10−22
dekabarn dab 10−27 10−23
barn b 10−28 10−24
decibarn db 10−29 10−25
centibarn cb 10−30 10−26
millibarn mb 10−31 10−27
microbarn μb 10−34 10−30
nanobarn nb 10−37 10−33
picobarn pb 10−40 10−36
femtobarn fb 10−43 10−39
attobarn ab 10−46 10−42
zeptobarn zb 10−49 10−45
yoctobarn yb 10−52 10−48

But What If I Don’t Like Barns?

Not into barns? Don’t worry. As an extension of the farm-themed area units, scientists also created the smaller unit outhouse (equal to one microbarn, or 10-34 m2) and the even smaller unit shed (equal to one yoctobarn, or 10-52 m2). These units are not actually used very often, if ever, but I’m delighted to say that this is not a practical joke – it’s for real.

Modern physics!

Modern physics!

You probably won’t need to use the outhouse or the shed, but here are some conversion tables, just in case:

Unit of Measurement        m2            Outhouse Units           
yottabarn 10−4 1030 outhouses
zettabarn 10−7 1027 outhouses
exabarn 10−10 1024 outhouses: 1 yottaouthouse
petabarn 10−13 1021 outhouses: 1 zettaouthouse
terabarn 10−16 1018 outhouses: 1 exaouthouse
gigabarn 10−19 1015 outhouses: 1 petaouthouse
megabarn 10−22 1012 outhouses: 1 teraouthouse
kilobarn 10−25 109 outhouses: 1 gigaouthouse
hectobarn 10−26 108 outhouses
dekabarn 10−27 107 outhouses
barn 10−28 106 outhouses: 1 megaouthouse
decibarn 10−29 105 outhouses
centibarn 10−30 104 outhouses
millibarn 10−31 103 outhouses: 1 kilouthouse
10−32 102 outhouses: 1 hectouthouse
10−33 101 outhouses: 1 dekaouthouse
microbarn 10−34 1 outhouse
10−35 10-1 outhouses: 1 deciouthouse
10−36 10-2 outhouses: 1 centiouthouse
nanobarn 10−37 10-3 outhouses: 1 milliouthouse
picobarn 10−40 10-6 outhouses: 1 microuthouse
femtobarn 10−43 10-9 outhouses: 1 nanouthouse
attobarn 10−46 10-12 outhouses: 1 picouthouse
zeptobarn 10−49 10-15 outhouses: 1 femtouthouse
yoctobarn 10−52 10-18 outhouses: 1 attouthouse
10−55 10-21 outhouses: 1 zeptouthouse
10−58 10-24 outhouses: 1 yoctouthouse

 

Unit of Measurement        m2            Shed Units           
yottabarn 10−4 1046 sheds
zettabarn 10−7 1043 sheds
exabarn 10−10 1040 sheds
petabarn 10−13 1037 sheds
terabarn 10−16 1034 sheds
gigabarn 10−19 1031 sheds
megabarn 10−22 1028 sheds
kilobarn 10−25 1027 sheds
hectobarn 10−26 1026 sheds
dekabarn 10−27 1025 sheds
barn 10−28 1024 sheds: 1 yottashed
decibarn 10−29 1023 sheds
centibarn 10−30 1022 sheds
millibarn 10−31 1021 sheds: 1 zettashed
microbarn 10−34 1018 sheds: 1 exashed
nanobarn 10−37 1015 sheds: 1 petashed
picobarn 10−40 1012 sheds: 1 terashed
femtobarn 10−43 109 sheds: 1 gigashed
attobarn 10−46 106 sheds: 1 megashed
zeptobarn 10−49 103 sheds: 1 kiloshed
10−50 102 sheds: 1 hectoshed
10−51 101 sheds: 1 dekashed
yoctobarn 10−52 1 shed
10−53 10-1 sheds: 1 decished
10−54 10-2 sheds: 1 centished
10−55 10-3 sheds: 1 millished
10−58 10-6 sheds: 1 microshed
10−61 10-9 sheds: 1 nanoshed
10−64 10-12 sheds: 1 picoshed
10−67 10-15 sheds: 1 femtoshed
10−70 10-18 sheds: 1 attoshed
10−73 10-21 sheds: 1 zeptoshed
10−76 10-24 sheds: 1 yoctoshed

Conclusion

You may be wondering why Femtotechnology News wrote about the inverse femtobarn. Is it really just because it has the prefix “femto” in the name? That’s partially it; after all, our focus is “all things femto“, and that includes femtoscience as well as some less-related topics like this one. But there’s another reason, too.

The barn began as an attempt to hide our nuclear secrets from Nazi spies, and later became one of the best ways to measure efficiency in the most cutting edge machines known to humankind. If that’s not a story worth having on this website, then nothing is.

*Thanks to Michael Rudy for pointing out in the comments that Klaus Fuchs was a communist spy for the USSR, and not a Nazi spy for Germany as I had mistakenly had originally!

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Written by Ethan J. Hulbert

Ethan J. Hulbert is a scientist and marketing professional from Chicago, IL. Find out more about Ethan at ethanjhulbert.org.

  • Michael Rudy

    Great explanation! Klaus Fuchs was a communist who spied for the USSR though.

    • Oh gosh! Of course, I don’t know how I got that mixed around. Thanks for pointing this out, the article’s been updated!