Quantum Physics For Dummies, Revised Edition
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In quantum physics, once you relate the angles of the scattered particles in the lab frame and the center-of-mass frame, you can translate the differential cross section — the bull's eye when you're aiming to scatter the particles at a particular angle — between the lab and center-of-mass frames.

The differential area

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is infinitesimal in size, and it stays the same between the two frames. But the angles that make up

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the scattering angle, vary when you translate between frames. You get to take a look at how that works now, relating the lab differential cross section:

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to the center-of-mass differential cross section:

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In the lab frame,

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And in the center-of-mass frame,

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Because

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the following equation is true:

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Putting that equation with the equations for the lab frame and the center-of-mass frame, you have

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Because you have cylindrical symmetry here,

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You've already seen that

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You can also show that

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About This Article

This article is from the book:

About the book author:

Steven Holzner is an award-winning author of technical and science books (like Physics For Dummies and Differential Equations For Dummies). He graduated from MIT and did his PhD in physics at Cornell University, where he was on the teaching faculty for 10 years. He’s also been on the faculty of MIT. Steve also teaches corporate groups around the country.

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