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 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 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, the SI standards body accepts its use with SI units due to its continued use in particle physics.

Etymology

The etymology of the unit barn is whimsical: during wartime research on the atomic bomb, 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." This was particularly applicable because 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 terrible. 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 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	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	yb	10−52	10−48

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.

Conversions

Calculated cross sections are often given in terms of gigaelectronvolts (GeV), via the conversion ħ²c²/GeV² = 0.3894 mb = 38 940 am².

In natural units (where ħ = c = 1), this simplifies to GeV^-2 = 0.3894 mb = 38 940 am².

SI units with prefix

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

Conversion from 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 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 this data.

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.

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.

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 = 0.008 64 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.

See also

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

External links

• IUPAC citation for this usage of "barn"