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]
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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.
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]
| 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 | 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 |
Calculated cross sections are often written in units of ħ2c2/GeV2 (approximately 0.3894 mb).
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 a measurement of particle collision events per femtobarn of target cross-section, and is the conventional unit for time-integrated luminosity.
In a particle accelerator 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 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 productivity.[9][10]
Fermilab has produced 10 fb−1 in the first decade of the 21st century.[11] 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.[12][13][14][15][16][17]
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 = 0.00864 fb−1 during this period.