Barn (unit)

A barn (symbol b) is a unit of area. Originally used in nuclear physics for expressing the cross sectional area of nuclei and nuclear reactions, today it is 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 defined as 10⁻²⁸ m² (100 fm²) and 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 is not an SI unit, it is accepted for use with the SI due to its continued use in particle physics.^[1] It is one of the very few units which are accepted to be used with SI units, and one of the most recent units to have been established (cf. the knot and the bar, other non-SI units acceptable in limited circumstances).^[2]

Two related units are the outhouse (10⁻³⁴ m², or 1 μb) and the shed (10⁻⁵² m², or 1 yb),^[3] although these are rarely used in practice.

Etymology

The etymology of the unit barn is whimsical. During wartime research on the atomic bomb, American physicists at Purdue University who were deflecting neutrons off uranium nuclei, (similar to Rutherford scattering) described the uranium nucleus as "big as a barn". Physicists working on the project adopted the name "barn" for a unit equal to 10⁻²⁴ square centimetres, about the size of a uranium nucleus. Initially they hoped the American slang name would obscure any reference to the study of nuclear structure; eventually, the word became a standard unit in particle physics.^[4][5]

Commonly used prefixed versions

Conversion to SI units

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 (or "outhouse"[6])	μb	10−34	10−30
nanobarn	nb	10−37	10−33
picobarn (or "silo")	pb	10−40	10−36
femtobarn	fb	10−43	10−39
attobarn	ab	10−46	10−42
zeptobarn	zb	10−49	10−45
yoctobarn (or "shed"[7][8])	yb	10−52	10−48

Conversions

Calculated cross sections are often written in units of ħ²c²/GeV² (approximately 0.3894 mb).

SI units with prefix

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

Conversion from squared prefixed 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 a measurement of particle collision events per femtobarn. One inverse femtobarn is equal to around 70 million million (70 x 10¹²) collisions.^[9] Over a period of time, two streams of particles with a cross-sectional area, measured in femtobarns, are directed to collide. The total number of collisions is 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 effectiveness.^[10][11] Fermilab has produced 10 fb⁻¹ in the last decade.^[12] Fermilab's Tevatron took about 4 years to reach 1 fb⁻¹ in 2005, while the Large Hadron Collider experiments ATLAS and CMS reached over 5 inverse femtobarns of proton-proton data in 2011 alone.^{[13][14][15][16][17][18]}

Usage example

As a simplified example, if a beamline runs for 8 hours (28,800 seconds) at an instantaneous luminosity of 300 × 10³⁰ cm⁻²s⁻¹ = 300 μb⁻¹s⁻¹, then it will gather data totaling an integrated luminosity of 8,640,000 μb⁻¹ = 8.64 pb⁻¹ during this period. "By next year, collisions will be occurring – if all continues to go well – at a rate producing what physicists call one "inverse femtobarn," best described as a colossal amount of information for analysts to ponder."^[19]

See also

• Orders of magnitude (area)
• List of unusual units of measurement

References

1. ^ "Chapter 4.1: Non-SI units accepted for use with the SI, and units based on fundamental constants". SI brochure (8th edition). BIPM. May 2006. http://www.bipm.org/en/si/si_brochure/chapter4/4-1.html. Retrieved 2009-03-13. 
2. ^ "Table 8. Other non-SI units". SI brochure (8th edition). BIPM. May 2006. http://www.bipm.org/en/si/si_brochure/chapter4/table8.html. Retrieved 2009-03-13. 
3. ^ "Nuclear Glossary". Nuclear Glossary. 2004-05-27. http://www.nuclearglossary.com/nuclearglossary_reactions.html. Retrieved 2011-04-08. 
4. ^ Mike Perricone (February 2006). "Signal to Background". Symmetry Magazine 3 (1): 4. http://www.symmetrymagazine.org/cms/?pid=1000258. Retrieved 2009-03-13. 
5. ^ Doreen Wackeroth, Leila Belkora (ed.). "Cross Section". High Energy Physics Made Painless. Fermilab Science Education Office. http://ed.fnal.gov/painless/pdfs/cross.pdf. Retrieved 2009-03-13. 
6. ^ "An Exceptional Nuclear Glossary". Nuclearglossary.com. 2006-11-25. http://www.nuclearglossary.com/abcs/nuclearglossary_O.html#outhouse. Retrieved 2011-04-08. 
7. ^ Russ Rowlett (September 1, 2004). "Units: S". How Many? A Dictionary of Units of Measurement. University of North Carolina at Chapel Hill. http://www.unc.edu/~rowlett/units/dictS.html. Retrieved 2009-12-14. 
8. ^ Green, Jonathon (December 1987). Dictionary of Jargon. Routledge Kegan & Paul. p. 487. ISBN 0710099193. http://books.google.com/?id=P0QOAAAAQAAJ&pg=PA487. Retrieved 2009-12-14. 
9. ^ "LHC achieves 2011 data milestone". CERN. June 17, 2011. http://press.web.cern.ch/press/PressReleases/Releases2011/PR06.11E.html. Retrieved 2011-07-23. 
10. ^ Kate Metropolis (July 21, 2004). "Understanding luminosity through 'barn', a unit that helps physicists count particle events". Stanford News Service. http://news-service.stanford.edu/news/2004/july21/femtobarn-721.html. Retrieved 2009-03-13. 
11. ^ Mason Inman, Emily Ball (April 16, 2004). "PEP-II's luminous life". SLAC. http://www2.slac.stanford.edu/tip/special/PEP-II-04-16-04.htm. Retrieved 2009-03-13. 
12. ^ "10 Inverse Femtobarns: Celebration Time At Fermilab!". Science20.com. December 12, 2010. http://www.science20.com/quantum_diaries_survivor/10_inverse_femtobarns_celebration_time_fermilab. Retrieved 2011-04-08. 
13. ^ "What will we do with all this data?". Pauline Gagnon, Quantum Diaries. October 17, 2011. http://www.quantumdiaries.org/2011/10/17/what-will-we-do-with-all-this-data/. 
14. ^ "CDF, DZero reach 5 inverse femtobarns of luminosity". Fermilab Today. September 26, 2008. http://www.fnal.gov/pub/today/archive_2008/today08-09-26.html. Retrieved 2011-07-23. 
15. ^ "LHC experiments reach record data milestone". Symmetry magazine. June 17, 2011. http://www.symmetrymagazine.org/breaking/2011/06/17/lhc-experiments-reach-record-data-milestone/. Retrieved 2011-07-23. 
16. ^ "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. http://twitter.com/#!/CERN/status/99405126694993920. Retrieved 2011-08-05. 
17. ^ "LHC Report: 2 inverse femtobarns!". CERN Bulletin. 2011-08-05. http://cdsweb.cern.ch/record/1372204. Retrieved 2011-08-06. 
18. ^ "LHC proton run for 2011 reaches successful conclusion". CERN Press Office. 2011-10-31. http://www.interactions.org/cms/?pid=1031152. Retrieved 2011-10-31. 
19. ^ CERN scientists eye parallel universe breakthrough, Reuters, October 20, 2010, http://www.reuters.com/article/2010/10/20/us-science-cern-idUSTRE69J35X20101020, retrieved 2011-07-26 

External links

• IUPAC citation for this usage of "barn"
• barn