# Scattering Cross Section

## Main Question or Discussion Point

I'm just wondering what the difference is between a cross section and a scattering cross section? Or is there any? I can't seem to find anywhere that clears it up, in fact theres a whole section on scattering cross sections in Kibble and Berkshire but they don't define it once :P

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QuantumPion
Gold Member
A cross section, in nuclear physics, refers to any particular interaction probability (or depending on the context, could refer to the total cross section for all interactions). A scattering cross section is one particular interaction probability. For example, the total cross section = scattering cross section + absorption cross section. The scattering cross section can be further broken down to elastic and inelastic scattering. The absorption cross section can be broken down to the absorption and fission cross sections, and so forth.

Ken G
Gold Member
Perhaps it would also help to define what "scattering" is-- usually, scattering means the light is not destroyed, instead it simply has its direction changed. This can be further broken down into types of scattering that don't change the frequency of the light (called "elastic" or "resonant" scattering), and those that do, but in many cases you can neglect the change in frequency so just imagine that scattering does nothing but change the direction of the individual photons involved.

Khashishi
I don't think the literature is totally consistent on this, but intuitively, "scattering" refers to a process in which the initial and final particles are the same, but perhaps with different momenta, whereas cross section could refer to any process.

So as opposed to what i would have considered a cross section to be before (a 2d slice of a 3d object) a cross section in terms of scattering is a probability that particles will undergo scattering? Surely they should have just defined a new word for that :P

Bobbywhy
Gold Member
rshalloo, not just particles get scattered.

Waves also scatter off objects. Radar microwaves scatter off a metal aircraft (called the "radar cross section") and some of the reflected energy goes back to the radar set where gets detected as a target. Sonar behaves similarly: acoustic waves travel from the active sonar transmitter, hit the target (submarine's acoustic cross section) and scatter in the same way radar waves do. You can imagine that the "broadside" aspect of a sub would reflect much more energy than the bow or stern aspect would. Same with radar and aircraft.

Ah yes that makes sense!
Thats really cool, I suppose sometimes when trying to wrap my head around these things I tend to forget how awesome their applications are!

QuantumPion
Gold Member
So as opposed to what i would have considered a cross section to be before (a 2d slice of a 3d object) a cross section in terms of scattering is a probability that particles will undergo scattering? Surely they should have just defined a new word for that :P
A physical cross section is a 2-dimensional area that represents how large a target the object is. However in nuclear physics it is often the case that the effective cross section can be much larger than the physical cross section, due to quantum mechanical effects. Or if you are talking about radar cross sections for example, the radar cross section of a stealth fighter will be much smaller than its physical cross section. The reason why these are all called cross sections and not something else is because they are still measured in units of area as if their real cross sections were physical cross sections for the purpose of determining interaction effects.

scattering cross sections

So would it make sense to calculate the cross section from an observer's/radar platform's view by the angles that each point makes with the observer/radar platform view?

However, this seems rather limited, because a point in space may be part of a plane that is facing different directions. and it seems strange that the radar cross section return would be the same for the same point, regardless of which orientation the plane the point is part of is facing.

In other words, what would be a good formula/model to calculate the effective cross section? I see all sorts of formulas about angles, but I am thinking about whether the orientation of the surface matters, as mentioned above.

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QuantumPion
Gold Member
So would it make sense to calculate the cross section from an observer's/radar platform's view by the angles that each point makes with the observer/radar platform view?

However, this seems rather limited, because a point in space may be part of a plane that is facing different directions. and it seems strange that the radar cross section return would be the same for the same point, regardless of which orientation the plane the point is part of is facing.

In other words, what would be a good formula/model to calculate the effective cross section? I see all sorts of formulas about angles, but I am thinking about whether the orientation of the surface matters, as mentioned above.
I don't know how they calculate the effective radar cross section of a stealth fighter although my first guess would be that it's just the average of its front, side, top, bottom and rear radar cross sections.

Bobbywhy
Gold Member
I also have no idea how to calculate an aircraft's radar cross-section. I can tell you how it is measured, however. One method is to use an exact scale model of the aircraft built with the same materials.
Then illuminate it with radar and measure the scattered (reflected) energy. The radar's frequency (wavelength) is chosen to be proportional to the expected search radar frequency. A second method, used in the final development stage, is to affix the entire aircraft on a vertical stanchion and rotate it while measuring the actual radar cross-section with real search radar(s). It's quite a sight to see and it avoids the uncertainties of calculations.

I also have no idea how to calculate an aircraft's radar cross-section. I can tell you how it is measured, however. One method is to use an exact scale model of the aircraft built with the same materials.
Then illuminate it with radar and measure the scattered (reflected) energy. The radar's frequency (wavelength) is chosen to be proportional to the expected search radar frequency. A second method, used in the final development stage, is to affix the entire aircraft on a vertical stanchion and rotate it while measuring the actual radar cross-section with real search radar(s). It's quite a sight to see and it avoids the uncertainties of calculations.
Hmm it seems strange that it couldn't be modeled accurately. People model the electric and magnetic fields inside hollow superconducting cavities used in particle accelerators, so I don't see why the same sort of computational approaches wouldn't work for an airplane. I bet there's a good PhD thesis in there.