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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?
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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.
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