Is cross section is proportional

In summary, the conversation discusses the cross section of a scattering process and its proportionality to various factors such as sin^4(x) and q^2. The conclusion is that the angular dependence of the scattering can be expressed by the Rutherford formula, with the condition that m = 0. The exchange boson is also mentioned as a factor in the determination of the cross section.
  • #1
alfredbester
40
0
If I show something that a cross section is proportional to:

[tex] 1 / (16p^2 sin^4( x) + 8mpsin^2 (x) + m^2) [/tex]

does it imply that the cross section is proportional to

[tex] 1 / sin^4 (x) [/tex] as well?
 
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  • #2
alfredbester said:
If I show something that a cross section is proportional to:

[tex] 1 / (16p^2 sin^4( x) + 8mpsin^2 (x) + m^2) [/tex]

does it imply that the cross section is proportional to

[tex] 1 / sin^4 (x) [/tex] as well?
No. But can you factor the first denominator?
 
  • #3
[tex] 1 / (4psin^2(x) + m)(4psin^2(x) + m) [/tex]

Not sure what to do from there.
 
  • #4
alfredbester said:
[tex] 1 / (4psin^2(x) + m)(4psin^4(x) + m) [/tex]

Not sure what to do from there.
The two factors in the denomnator are identical. What you have shown is that your thing is inversely proportional to the square of (4psin^2(x) + m). It is inversely proportiona to sin^4(x) only if m = 0. You could reach the same conclusion from your original expression, but it is a bit more evident when you factor it into a product of identical terms.
 
  • #5
That cause a problem then I was the scattering cross section is proportional to Mfi and

[tex] |M_{fi}|^2 /propto 1 / (q^2 + m^2)^2 [/tex]

Starting from the definition of q = [tex]p_{final} - p_{initial}.[/tex]

Show that the angular dependence of the scattering is then given simply by the Rutherford formula:CS= scattering cross secion

[tex] CS /propto 1 /(sin^4(\theta /2) [/tex]

I found [tex]q = 2psin(\theta /2)[/tex]
Since Mfi is proportional to the scattering CS I just tried sticking q into into the expression for [tex] |M_{fi}|^2 [/tex] as above but that clearly didn't work. I guess the wording angular dependence is key here.
 
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  • #6
alfredbester said:
That cause a problem then I was the scattering cross section is proportional to Mfi and

[tex] |M_{fi}|^2 /propto 1 / (q^2 + m^2)^2 [/tex]

Starting from the definition of q = [tex]p_{final} - p_{initial}.[/tex]

Show that the angular dependence of the scattering is then given simply by the Rutherford formula:CS= scattering cross secion

[tex] CS /propto 1 /(sin^4(\theta /2) [/tex]

I found [tex]q = 2psin(\theta /2)[/tex]
Since Mfi is proportional to the scattering CS I just tried sticking q into into the expression for [tex] |M_{fi}|^2 [/tex] as above but that clearly didn't work. I guess the wording angular dependence is key here.
I had no context for your question, and I'm not completely following what you are trying to do. I have to log off now. See if this helps you any

http://hyperphysics.phy-astr.gsu.edu/hbase/rutsca.html
 
  • #7
Thanks, I've got it now m=0 because the exchange boson is a photon :).
 

FAQ: Is cross section is proportional

1. Is cross section proportional to area?

Yes, cross section is proportional to area. This means that as the area of an object increases, so does its cross section, and vice versa.

2. How is cross section related to volume?

Cross section is not directly related to volume. Volume measures the amount of space an object occupies, while cross section measures the area of a slice through the object.

3. What is the significance of a proportional cross section?

A proportional cross section can provide important information about the shape and size of an object. It can also help with calculations and measurements, as well as understanding the physical properties of the object.

4. Can cross section be used to determine the density of an object?

Yes, cross section can be used in conjunction with other measurements, such as mass, to determine the density of an object. This is because density is defined as mass per unit of volume, and cross section can help calculate the volume of an object.

5. How does cross section play a role in physics and engineering?

Cross section is an important concept in physics and engineering as it helps to describe the behavior and properties of objects. It is used in fields such as optics, mechanics, and material science to analyze and understand how objects interact with different forces and energies.

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