The discussion revolves around the proportionality of a cross section in a physics context, specifically examining expressions involving sine functions and their implications in scattering theory.
Some participants have provided insights into the relationships between different expressions, while others express uncertainty about the next steps. There is an acknowledgment of the importance of specific parameters in determining the proportionality, but no consensus has been reached on the implications of the findings.
Participants note the significance of the angular dependence in scattering and the role of specific variables, such as the momentum transfer q. There is mention of a specific case where m=0, which is tied to the nature of the exchange boson.
No. But can you factor the first denominator?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?
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.alfredbester said:[tex]1 / (4psin^2(x) + m)(4psin^4(x) + m)[/tex]
Not sure what to do from there.
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 anyalfredbester 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.