CROSS SECTIONS

Rotating detector or spectrometer to measure differential cross sections (angular distributions) in fixed-target experiments.


For colliding beams only the total cross section can be measured and the detector arrays surround the collision region insofar as is possible. (For obvious reasons a cylindrical geometry is generally adopted!)
Below is a model of the Atlas detector at the LHC.  Note human figures for scale.




A differential cross section, protons on 58Ni nuclei, elastic scattering.  The standard unit for cross sections is the millibarn (mb), which is equal to 0.1 fm2, with a fm being 10-15 m. Physicists refer to a fm as a Fermi, but its technical name is femtometer.  I am hoping you know what a steradian is!



Total cross sections for p + p.

The Mandelstam variable s is the square of the total center-of-momentum energy of the process. Also sometimes displayed for differential cross sections is the Mandelstam variable t, which is the square of the four-momentum transfer in the process.


Why all particle physics experiments are done with colliding beams...

See the class notes, first set, linked on the main course page, for details on calculating absolute experimental values for differential and total cross sections, dσ/dΩ and σ.  [Also given in the text.]
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