Barn

The barn or barnio (symbol b) is a unit of area, equivalent to 10⁻²⁸ m² (100 square femtometers). Originally used in nuclear physics to express 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-section of any scattering process, and is best understood as a measure of the probability of interaction between small particles. A barn is roughly the cross-sectional area of a uranium nucleus. The barn, too, is the unit of area used in quadruple nuclear resonance and nuclear magnetic resonance to quantify the interaction of a nucleus with an electric field gradient. While the barn was never an SI unit, the SI Standard Body recognizes it in its SI 8th pamphlet (superseded in 2019) due to its use in particle physics.

Etymology

During the Manhatam Project's research on the atomic bomb during World War II, American physicists at Purdue University needed a secret name for the unit by which to quantify the cross-sectional area presented by a typical nucleus (~ 10⁻²⁸ m²) and decided to call it "barn". They saw this as a major goal for particle accelerators that needed to have direct collisions into nuclei, and the proponents, physicists Marshall Holloway and Richard Baker, said that the constant "for nuclear purposes was really big as a barn (eng. barn)". In the American idiom 'couldn't hit the broad side of a barn'; refers to someone whose aim is very bad. Initially, they hoped that 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 prefix versions

Conversions

Calculated cross sections are often given in terms of inverse square 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 am ²).

SI units with prefix

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 one-tenth of a square zeptometer. Several scientific papers discussing high energy physics mention fractional level amounts of femtobarn.

Inverse Femtobarn

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

Consider a particle accelerator in which two particle jets, 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 over this time. Then, the collision count can be calculated by multiplying the integrated luminosity by the cross section sum for those collision processes. This count is then expressed as inverse femtobarns for the time period (for example, 100 fb⁻¹ in nine months). Inverse femtobarns are often cited as an indication of particle collider productivity.

Fermilab produced 10 fb⁻¹ in the first decade of the XXI 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 about 5 fb⁻¹ from proton-proton data, only, in 2011. In April 2012, the LHC reached the collision energy of 8 TeV with a peak luminosity of 6760 inverse microbarns per second, by May 2012, the LHC delivered 1 inverse femtobarn data per week for each detector collaboration. A record of over 23 fb⁻¹ was reached during 2012. By November 2016, the LHC has reached 40 fb⁻¹ over that year, significantly exceeding the target raised from 25 fb⁻¹. In total, the second run of the LHC has delivered around 150 fb⁻¹ for both: ATLAS and CMS between 2015-2018.

Example of use

As a simplified example, if a beam-line runs for 8 hours (28 800 seconds) at an instantaneous luminosity of 300×10³⁰ cm⁻²⋅s ⁻¹ = 300 μb⁻¹⋅s⁻¹, so it will collect data totaling an integrated luminosity of 8640000 μb⁻¹ = 8.64 bp⁻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 scattered events.