Barn (unit)

Unit for cross sectional area used in high-energy physics

Barn

Unit system| particle physics
Unit of| area
Symbol| b
Named after| the broad side of a barn
Conversions
1 b in ...| ... is equal to ...
SI base units|    10−28 m2
equivalent|    100 fm2

A barn (symbol: b) is a metric unit of area equal to 10−28 m2 (100 fm2). This is equivalent to a square that is 10−14 m (10 fm) each side, or a circle of diameter approximately 1.128×10−14 m (11.28 fm).

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 While the barn never was an SI unit, the SI standards body acknowledged it in the 8th SI Brochure (superseded in 2019) due to its use in particle physics.[1]

## Etymology

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Image of a helium-4 nucleus; 4He has a very small cross-section, less than 0.01 barn.

During Manhattan Project research on the atomic bomb during World War II, American physicists Marshall Holloway and Charles P. Baker were working at Purdue University on a project using a particle accelerator to measure the cross sections of certain nuclear reactions. According to an account of theirs from a couple years later, they were dining in a cafeteria in December 1942 and discussing their work. They "lamented" that there was no name for the unit of cross section and challenged themselves to develop one. They initially tried eponyms, names of "some great men closely associated with the field" that they could name the unit after, but struggled to find one that was appropriate. They considered "Oppenheimer" too long (in retrospect, they considered an "Oppy" to perhaps have been allowable), and considered "Bethe" to be too easily confused with the commonly used Greek letter beta. They then considered naming it after John Manley, another scientist associated with their work, but considered "Manley" too long and "John" too closely associated with toilets. But this latter association, combined with the "rural background" of one of the scientists, suggested to them the term "barn", which also worked because the unit was "really as big as a barn". According to the authors, the first published use of the term was in a (secret) Los Alamos report from late June 1943, on which the two originators were co-authors.[2]

## Derived units and SI multiples

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The unit symbol for the barn (b) is also the IEEE standard symbol for bit, and both are commonly used with metric prefixes, which may give rise to ambiguity.

SI multiples of barn (b)  Submultiples  | Multiples

|

Value  | SI symbol  | Name  | Value  | SI symbol  | Name
10−1 b  | db  | decibarn  | 101 b  | dab  | decabarn
10−2 b  | cb  | centibarn  | 102 b  | hb  | hectobarn
10−3 b  | mb  | millibarn  | 103 b  | kb  | kilobarn
10−6 b  | μb  | microbarn  | 106 b  | Mb  | megabarn
10−9 b  | nb  | nanobarn  | 109 b  | Gb  | gigabarn
10−12 b  | pb  | picobarn  | 1012 b  | Tb  | terabarn
10−15 b  | fb  | femtobarn  | 1015 b  | Pb  | petabarn
10−18 b  | ab  | attobarn  | 1018 b  | Eb  | exabarn
10−21 b  | zb  | zeptobarn  | 1021 b  | Zb  | zettabarn
10−24 b  | yb  | yoctobarn  | 1024 b  | Yb  | yottabarn
10−27 b  | rb  | rontobarn  | 1027 b  | Rb  | ronnabarn
10−30 b  | qb  | quectobarn  | 1030 b  | Qb  | quettabarn

## Conversions

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Calculated cross sections are often given in terms of inverse squared gigaelectronvolts (GeV−2), 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.

barn | GeV−2

|

1 mb | 2.56819 GeV−2
1 pb | 2.56819×10−9 GeV−2
0.389379 mb | 1 GeV−2
0.389379 pb | 10−9 GeV−2

### SI units with prefix

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In SI, one can use units such as square femtometers (fm2). The most common SI prefixed unit for the barn is the femtobarn, which is equal to a tenth of a square zeptometer. Many scientific papers discussing high-energy physics mention quantities of fractions of femtobarn level.

Conversion from SI units  | SI  | barns

|

1 pm2 | 10 kb
1 fm2 | 10 mb
1 am2 | 10 nb
1 zm2 | 10 fb
1 ym2 | 10 zb
1 rm2 | 10 rb
Conversion to SI units  | Barns  | SI  | Other names

|
|

1 b  | 100 fm2
1 cb  | 1 fm2
1 mb  | 0.1 fm2 = 100000 am2
1 μb  | 100 am2 | outhouse[3]
1 nb  | 0.1 am2 = 100000 zm2
1 pb  | 100 zm2
1 fb  | 0.1 zm2 = 100000 ym2
1 ab  | 100 ym2
1 zb  | 0.1 ym2 = 100000 rm2
1 yb  | 100 rm2 | shed

## Inverse femtobarn

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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.[4][5]

Fermilab produced 10 fb−1 in the first decade of the 21st century.[6] 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.[7][8][9][10][11][12] 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.[13] As of November 2016, the LHC had achieved 40 fb−1 over that year, significantly exceeding the stated goal of 25 fb−1.[14] In total, the second run of the LHC has delivered around 150 fb−1 to both ATLAS and CMS in 2015–2018.[15]

### Usage example

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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 equal to the number of expected scattering events.

## See also

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* "Shake", a unit of time created by the same people at the same time as the barn
* Orders of magnitude (area)
* List of unusual units of measurement
* List of humorous units of measurement

## References

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1. ^ "Non-SI units accepted for use with the SI, and units based on fundamental constants". SI brochure (8th edition). BIPM. May 2006. Archived from the original on 2018-07-18. Retrieved 2009-03-13.
2. ^ M.G. Holloway and C.P. Baker, "Note on the origin of the term 'barn'"], LAMS-523 (submitted 13 September 1944, issued 5 March 1947). Reprinted as Holloway, M.G.; Baker, C.P. (1972). "How the barn was born". Physics Today. 25 (7): 9. doi:10.1063/1.3070918. The initial published report to feature the unit was C.P. Baker, M.G. Holloway, L.D.P. King, and R.E. Schreiber, "Cross section for the reaction 20(230, 240)10", [LAMS-2](https://permalink.lanl.gov/object/tr?what=info:lanl-repo/lareport/LA-00002-MS) (June 28, 1943), which also defines the unit in its abstract.
3. ^ Craig A. Stone, Ph.D. "Glossary". The Language of the Nucleus. Scientific Digital Visions, Inc. Archived from the original on 2007-06-30. Retrieved 2022-11-22.
4. ^ Kate Metropolis (July 21, 2004). "Understanding luminosity through 'barn', a unit that helps physicists count particle events". Stanford News Service. Archived from the original on 2009-05-10. Retrieved 2009-03-13.
5. ^ 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.
6. ^ "10 Inverse Femtobarns: Celebration Time At Fermilab!". Science20.com. December 12, 2010. Retrieved 2011-04-08.
7. ^ "What will we do with all this data?". Pauline Gagnon, Quantum Diaries. October 17, 2011.
8. ^ "CDF, DZero reach 5 inverse femtobarns of luminosity". Fermilab Today. September 26, 2008. Retrieved 2011-07-23.
9. ^ "LHC experiments reach record data milestone". Symmetry magazine. June 17, 2011. Retrieved 2011-07-23.
10. ^ "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.
11. ^ "LHC Report: 2 inverse femtobarns!". CERN Bulletin. 2011-08-05. Retrieved 2011-08-06.
12. ^ "LHC proton run for 2011 reaches successful conclusion". CERN Press Office. 2011-10-31. Retrieved 2011-10-31.
13. ^ "LHC luminosity plots". CERN. 2012-12-17. Archived from the original on 2013-02-19.
14. ^ "LHC smashes targets for 2016 run | CERN". home.cern. Retrieved 2016-11-02.
15. ^ "LHC Report: The final days of Run 2 | CERN". home.cern. Retrieved 2018-12-07.

## External links

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* IUPAC citation for this usage of "barn"