What is the Cross Section Calculus for Proton-Electron Scattering?

In summary, In the book "Gauge Theories of the strong, weak, and electromagnetic interactions" by Chris Quigg, the calculus of the scattering of proton-electron is exposed in chapter 7, section 3, page 168. The result in the lab frame is given by the equation \frac{\mbox d^2\sigma}{\mbox d E^\prime\mbox d\Omega^\prime} =\frac1{16\pi^2}\frac{E^\prime}{E}\bar{|\mathcal M|}^2. The Rosenbluth cross section is commonly used in this type of calculation, and it involves complex algebra with gamma matrices. For beginners, the book "Introduction
  • #1
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In the book "Gauge Theories of the strong, weak, and electromagnetic interactions" by Chris Quigg the calculus of the scattering of proton-electron is esbosed (chapter 7, section 3 , pag 168).

He get the result (in the lab frame):

[tex] \frac{\mbox d^2\sigma}{\mbox d E^\prime\mbox d\Omega^\prime} =\frac1{16\pi^2}\frac{E^\prime}{E}\bar{|\mathcal M|}^2[/tex].

I'm new to this kind of calculus, but couldn't get this.

Does Anyone have a suggestion?.

Thanks in advance
 
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  • #2
It's called the Rosenbluth cross section. Basic QED and field theory books, e.g Bjorken and Drell, Gross, etc. go into the derivation in great detail. Check out Google. The big deal is the algebra required to deal with the gamma matrices.

Regards,
Reilly Atkinson
 
  • #3
If you are really new to this kind of stuff (undergrad level), I highly recommend:

D. Griffiths, "Introduction to elementary particles", J. Wiley & Sons (1987.).

I liked all other Griffiths' books (Electrodynamics, Quantum mechanics) and this one is no exception. For more advanced level I'd say go with Bjorken and Drell (that would be for graduate level).
 

1. What is cross section calculus?

Cross section calculus is a mathematical method used to calculate the area of a shape or object when it is intersected by a plane. It involves using integration techniques to determine the area of the shape's cross section.

2. How is cross section calculus used in science?

Cross section calculus is commonly used in physics and engineering to calculate the properties of 3-dimensional objects and systems. It is also used in various fields of science, such as biology and geology, to analyze and measure the structures of organisms and geological formations.

3. What are the key concepts in cross section calculus?

The key concepts in cross section calculus include integration, limits, and area under a curve. These concepts are used to determine the area of a cross section by dividing the shape into infinitesimally small sections and summing their areas together.

4. What are some examples of applications of cross section calculus?

Cross section calculus is used in numerous real-world applications, such as calculating the volume of a solid object, determining the moment of inertia of a rotating body, and analyzing the structural integrity of buildings and bridges. It is also used in fields like medicine to measure the volume of organs and blood vessels.

5. What are the benefits of using cross section calculus?

Cross section calculus provides a precise and accurate method for calculating the area of complex shapes and objects. It also allows for the analysis of 3-dimensional structures, making it a valuable tool in various fields of science and engineering. Additionally, the use of integration techniques can be applied to a wide range of problems, making it a versatile tool for solving complex mathematical problems.

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