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Scattering Cross Sections

Inasmuch as we are going to discuss modern ELEMENTARY PARTICLE PHYSICS later on, it is appropriate to stop for a moment and contemplate Rutherford's classic experiment, for the art of interpreting the distributions of SCATTERING ANGLES when a beam of one type of particle in a well-defined initial state is slammed into a target composed of other types of particles is essentially the entire experimental repertoire of the modern Particle Physicist.

Consider: the goal of the experimenter is to learn more about the structure of particles that are, individually, too small to be detected with a microscope. [If the particle is much smaller in size than the wavelength  $\lambda$  of the light used in the microscope, the best it can do is scatter the light into spherical outgoing wavefronts ( HUYGENS' PRINCIPLE), from which we can learn nothing about the shape of the particle itself. The approved terminology for this limitation is that the RESOLUTION of the microscope can never be finer than the wavelength of the light it uses.] So how can we learn anything about the shape of the object particle? By SCATTERING other particles off it!

Imagine that there is an object hidden from sight behind a thin piece of paper; you have a BB gun which you can use to bounce BBs off the object. You get to to see which way the BBs bounce, and if you have a more fancy apparatus you may get to measure their velocities (momenta) before and after their collisions with the object; moreover, if any bits fly off the object as a result of a BB collision, you get to measure their directions and momenta as well. This is essentially the situation of the Particle Physicist. We may have a variety of PARTICLE BEAMS ranging from electrons to heavy nuclei, with energies ranging from a few eV to many GeV (billions of eV) or even TeV (trillions of eV) per particle - corresponding to peashooters, BB guns, rifles, howitzers and rail guns - but the only way we can use them is to shoot ``blind'' at our target particles and study the SCATTERING DISTRIBUTION.

You should try to imagine for yourself some qualitative phenomena you might look for to test various hypotheses about the target object - starting with Rutherford's test for ``plum puddings'' vs. hard-kernel ATOMIC NUCLEI. I will not attempt to develop the arcane terminology of scattering theory here, but I will mention the basic paradigm: the thing one can measure and describe most easily about a particle is the area it presents to an incoming beam; we call this the SCATTERING CROSS SECTION and measure it in area units such as BARNS [one BARN $\equiv$ (10^-13 cm)² or 10^-30 m²)] -- about the size of an average nucleus.^23.7