Barn (unit)

A barn (symbol: b) is a metric unit of area equal to 10−28 m2 (100 fm2). Originally used in nuclear physics for expressing the cross sectional area of nuclei and nuclear reactions, today it is also used in all fields of high-energy physics to express the cross sections of any scattering process, and is best understood as a measure of the probability of interaction between small particles. A barn is approximately the cross-sectional area of a uranium nucleus. The barn is also the unit of area used in nuclear quadrupole resonance and nuclear magnetic resonance to quantify the interaction of a nucleus with an electric field gradient. While the barn never was an SI unit, the SI standards body acknowledged it in the 8th SI Brochure (superseded in 2019) due to its use in particle physics.[1]

Barn
Unit systemparticle physics
Unit ofarea
Symbolb 
Named afterthe broad side of a barn
Conversions
1 b in ...... is equal to ...
   SI base units   10−28 m2
   non standard   100 fm2
   natural units   2.56819×10−3 MeV−2

Etymology

During Manhattan Project research on the atomic bomb during World War II, American physicists at Purdue University needed a secretive unit to describe the approximate cross-sectional area presented by the typical nucleus (10−28 m2) and decided on "barn". They considered this a large target for particle accelerators that needed to have direct strikes on nuclei, and the American idiom "couldn't hit the broad side of a barn" refers to someone whose aim is very bad.[2] Initially they hoped the name would obscure any reference to the study of nuclear structure; eventually, the word became a standard unit in nuclear and particle physics.[3][4]

Commonly used prefixed versions
Multiples and sub-multiples[5][6]
Unit Symbol m2 cm2
megabarn Mb 10−22 10−18
kilobarn kb 10−25 10−21
barn b 10−28 10−24
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

Other related units are the outhouse (1 μb, or 10−34 m2) and the shed (10−24 b (1 yb), or 10−52 m2), although these are rarely used in practice.[7]

Conversions

Calculated cross sections are often given in terms of gigaelectronvolts (GeV), via the conversion ħ2c2/GeV2 = 0.3894 mb = 38940 am2.

In natural units (where ħ = c = 1), this simplifies to GeV−2 = 0.3894 mb = 38940 am2.

barnGeV-2
1 mb2.56819 GeV−2
1 pb2.56819×10−9 GeV−2
0.389379 mb1 GeV−2
0.389379 pb1×10−9 GeV−2

SI units with prefix

In SI, one can use units such as square femtometers (fm2).

Conversion from SI units
1 pm2 = 10 kb
1 fm2 = 10 mb
1 am2 = 10 nb
1 zm2 = 10 fb
1 ym2 = 10 zb

Inverse femtobarn

The inverse femtobarn (fb−1) is the unit typically used to measure the number of particle collision events per femtobarn of target cross-section, and is the conventional unit for time-integrated luminosity. Thus if a detector has accumulated 100 fb−1 of integrated luminosity, one expects to find 100 events per femtobarn of cross-section within these data.

Consider a particle accelerator where two streams of particles, with cross-sectional areas measured in femtobarns, are directed to collide over a period of time. The total number of collisions will be directly proportional to the luminosity of the collisions measured over this time. Therefore, the collision count can be calculated by multiplying the integrated luminosity by the sum of the cross-section for those collision processes. This count is then expressed as inverse femtobarns for the time period (e.g., 100 fb−1 in nine months). Inverse femtobarns are often quoted as an indication of particle collider productivity.[8][9]

Fermilab produced 10 fb−1 in the first decade of the 21st century.[10] Fermilab's Tevatron took about 4 years to reach 1 fb−1 in 2005, while two of CERN's LHC experiments, ATLAS and CMS, reached over 5 fb−1 of proton–proton data in 2011 alone.[11][12][13][14][15][16] In April 2012 the LHC achieved the collision energy of 8 TeV with a luminosity peak of 6760 inverse microbarns per second; by May 2012 the LHC delivered 1 inverse femtobarn of data per week to each detector collaboration. A record of over 23 fb−1 was achieved during 2012.[17] As of November 2016, the LHC had achieved 40 fb−1 over that year, significantly exceeding the stated goal of 25 fb−1.[18] In total, the second run of the LHC has delivered around 150 fb−1 to both ATLAS and CMS in 2015–2018.[19]

Usage example

As a simplified example, if a beamline runs for 8 hours (28 800 seconds) at an instantaneous luminosity of 300×1030 cm−2⋅s−1 = 300 μb−1⋅s−1, then it will gather data totaling an integrated luminosity of 8640000 μb−1 = 8.64 pb−1 = 0.00864 fb−1 during this period. If this is multiplied by the cross-section, then a dimensionless number is obtained which would be simply the number of expected scattering events.

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See also

References
  1. "Non-SI units accepted for use with the SI, and units based on fundamental constants". SI brochure (8th edition). BIPM. May 2006. Retrieved 2009-03-13.
  2. "The Big Apple: "Can't hit the broad side of a barn" (baseball saying)". August 11, 2014.
  3. Mike Perricone (February 2006). "Signal to Background". Symmetry Magazine. 3 (1): 4. Archived from the original on 16 February 2009. Retrieved 2009-03-13.
  4. Doreen Wackeroth, Leila Belkora (ed.). "Cross Section" (PDF). High Energy Physics Made Painless. Fermilab Science Education Office. Retrieved 2009-03-13.CS1 maint: extra text: authors list (link)
  5. Russ Rowlett (September 1, 2004). "Units: S". How Many? A Dictionary of Units of Measurement. University of North Carolina at Chapel Hill. Retrieved 2009-12-14.
  6. Green, Jonathon (December 1987). Dictionary of Jargon. Routledge Kegan & Paul. p. 487. ISBN 0-7100-9919-3. Retrieved 2009-12-14.
  7. "Nuclear Glossary". Nuclear Glossary. 2004-05-27. Retrieved 2011-04-08.
  8. Kate Metropolis (July 21, 2004). "Understanding luminosity through 'barn', a unit that helps physicists count particle events". Stanford News Service. Retrieved 2009-03-13.
  9. Mason Inman, Emily Ball (April 16, 2004). "PEP-II's luminous life". SLAC. Archived from the original on June 2, 2009. Retrieved 2009-03-13.
  10. "10 Inverse Femtobarns: Celebration Time At Fermilab!". Science20.com. December 12, 2010. Retrieved 2011-04-08.
  11. "What will we do with all this data?". Pauline Gagnon, Quantum Diaries. October 17, 2011.
  12. "CDF, DZero reach 5 inverse femtobarns of luminosity". Fermilab Today. September 26, 2008. Retrieved 2011-07-23.
  13. "LHC experiments reach record data milestone". Symmetry magazine. June 17, 2011. Retrieved 2011-07-23.
  14. "Thanks to recent fine tuning, the LHC has delivered 2 inverse femtobarns of data already this year; peak luminosity is now over 2x10^33". CERN. August 5, 2011. Retrieved 2011-08-05.
  15. "LHC Report: 2 inverse femtobarns!". CERN Bulletin. 2011-08-05. Retrieved 2011-08-06.
  16. "LHC proton run for 2011 reaches successful conclusion". CERN Press Office. 2011-10-31. Retrieved 2011-10-31.
  17. "LHC luminosity plots". CERN. 2012-12-17. Archived from the original on 2013-02-19.
  18. "LHC smashes targets for 2016 run | CERN". home.cern. Retrieved 2016-11-02.
  19. "LHC Report: The final days of Run 2 | CERN". home.cern. Retrieved 2018-12-07.
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