Rutherford Scattering cross section

It's possible that the problem itself is incorrect or there is a typo. It may be worth double checking with your professor or classmates to see if anyone else has encountered this issue.In summary, the conversation revolves around integrating the Rutherford cross section over the backward hemisphere to obtain 4pi(sigma0(E)). The user runs into trouble with the limits of integration and questions their solution, but ultimately concludes that their solution is correct. There may be a possibility of a typo or error in the problem itself.
  • #1
SuperPokenerd
8
0

Homework Statement


Integrate the rutherford cross section over the backward hemisphere to get 4pi(sigma0(E))


Homework Equations



Rutherford cross section is sigma0(E)/sin^4(theta/2)

The Attempt at a Solution


When I integrate this with the limits pi/2 to pi i get sigma0(E)*(8/3) i don't know what I'm doing wrong.
 
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  • #2
Are you sure you have your integration limits correct?
 
  • #3
I thought so, since the problem says that theta goes between pi/2 and pi i.e. large angle scattering is from 90-180 degrees. I don't see how I'm supposed to get it to be 4pi instead of 8/3.
 
  • #4
Never mind my previous response, I was confusing this with a different problem I was solving earlier.

As near as I can tell, your solution appears to be correct.
 
  • #5


It seems that you have made a small mistake in your integration. When integrating the Rutherford cross section over the backward hemisphere, the limits of integration should be from pi to 2pi, not from pi/2 to pi. This is because the backward hemisphere covers the angle range from pi to 2pi. Therefore, the correct result of the integration should be 4pi*sigma0(E), which is the expected result. I hope this clarifies your confusion.
 

Related to Rutherford Scattering cross section

What is the Rutherford Scattering cross section?

The Rutherford Scattering cross section is a measure of the probability that a charged particle will scatter off of a target nucleus at a certain angle. It is a fundamental concept in nuclear and particle physics, and is used to study the structure of atomic nuclei.

How is the Rutherford Scattering cross section calculated?

The Rutherford Scattering cross section is calculated using the Rutherford formula, which takes into account the charge and energy of the incident particle, as well as the size and charge of the target nucleus. It is also dependent on the scattering angle and the scattering potential.

What is the significance of the Rutherford Scattering cross section?

The Rutherford Scattering cross section is significant because it helped to prove the existence of the atomic nucleus and paved the way for the development of the nuclear model of the atom. It also provides important information about the size and structure of atomic nuclei.

What factors affect the Rutherford Scattering cross section?

The Rutherford Scattering cross section is affected by the energy and charge of the incident particle, the size and charge of the target nucleus, and the scattering angle. It is also influenced by the type of interaction between the incident particle and the target nucleus, such as electromagnetic or strong nuclear force.

How is the Rutherford Scattering cross section used in research?

The Rutherford Scattering cross section is used in a wide range of research fields, including nuclear and particle physics, materials science, and medical physics. It is used to study the structure of atomic nuclei, the properties of materials, and to develop new technologies such as proton therapy for cancer treatment.

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