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 While the barn never was an SI unit, the SI standards body acknowledged it in the 8th SI Brochure (superseded in 2019) due to its use in particle physics.
|Unit system||particle physics|
|Named after||the broad side of a barn|
|1 b in ...||... is equal to ...|
|SI base units||10−28 m2|
|non standard||100 fm2|
|natural units||2.56819×10−3 MeV−2|
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. 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.
Commonly used prefixed versionsEdit
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.
|1 mb||2.56819 GeV−2|
|1 pb||2.56819×10−9 GeV−2|
|0.389379 mb||1 GeV−2|
|0.389379 pb||1×10−9 GeV−2|
SI units with prefixEdit
In SI, one can use units such as square femtometers (fm2).
|1 pm2 = 10 kb|
|1 fm2 = 10 mb|
|1 am2 = 10 nb|
|1 zm2 = 10 fb|
|1 ym2 = 10 zb|
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.
Fermilab produced 10 fb−1 in the first decade of the 21st century. 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. 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. As of November 2016, the LHC had achieved 40 fb−1 over that year, significantly exceeding the stated goal of 25 fb−1. In total, the second run of the LHC has delivered around 150 fb−1 to both ATLAS and CMS in 2015–2018.
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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