August 6, 2004  


Shedding Light on Luminosity

By Roger Erickson and Kate Metropolis

What on earth is an inverse femtobarn and what does it have to do with the number of events an accelerator produces?

Image by Alan Chou

Fittingly, it was in the farmlands of the Midwest that the term ‘barn’ was first applied to physics.  In December 1942, at a dinner on the campus of Purdue University, physicists M. G. Holloway and C. P. Parker were lamenting the lack of a catchy name for discussing the size of an atomic nucleus. They considered calling it the Oppenheimer or the Bethe, after physicists who were leading a project involving uranium cross sections.  The cross-sectional area of a uranium nucleus is about 10-24 square centimeters, a small area on the human scale but huge compared with the size of other atomic particles.  The barn, large compared with other farm buildings, came to mind.

'Barn' is easier to say than 'Oppenheimer' and does not, like 'Bethe', sound like the second letter of the Greek alphabet, which was already being used for several other physics quantities.  The name stuck and by June, 1943, 'barn' began appearing in internal technical reports at the secret laboratory at Los Alamos. 

‘Femto’ means a factor of 10-15 —a thousandth of a millionth of a millionth.  A femtobarn, then, is 10-39 square centimeters, an incomprehensibly small unit of area.  If you throw a projectile at a target, whether it is a neutron at a uranium nucleus, an electron at a positron or a tomato at a barn door, the larger the cross-sectional area of the target, the likelier you are to hit it.

Imagine you throw enough tomatoes at your farm building to get an average of two hits per square foot.  If the barn door is 10 feet by 15 feet, then the cross section for tomato/barndoor interactions is 150 square feet, and the number of tomatoes that splat on the door is given by:

150 square feet x 2 tomatoes per square foot = 300 tomato interactions

In this case, the integrated luminosity is 2 tomatoes per square foot (or 2 'inverse square feet').

You can calculate how many electron positron collisions in PEP-II make particles with b quarks in the BaBar detector in the same way. Multiply the cross section for those events (1.1 million femtobarns) by the integrated luminosity (at this writing, 250 events per femtobarn) and you get 275 million events.



The Stanford Linear Accelerator Center is managed by Stanford University for the US Department of Energy

Last update Wednesday August 04, 2004 by Emily Ball