Undefined angles for Compton scattering

[doctorado]

Homework Statement

Hello, I need to find which values for θ and ψ are not defined for the Compton scattering. Where θ is the angle of the electron and ψ is the angle for the photon.

Homework Equations

I have attached the formulas I´m using.
http://tinypic.com/view.php?pic=v4z2qf&s=5

The Attempt at a Solution

According to me ψ≠0 , since the photon´s angle would not be modified and therefore there would be no scattering.
I have also done some graphs using Matlab and they show that θ ≠ ∏/2 and θ≠∏.
I´m using radians.
I have determined algebraically that tan(ψ/2)= sen (ψ/2)/cos(ψ/2). Therefore cos(ψ/2)≠0.
ψ/2≠ ∏/2. So ψ≠∏. However I have heard about "backscattering" happening in the practice, so I´m a bit confused since the math shows it is not possible but yet it is.

P.D. English is not my mother language so I apologize for any grammar or any other kind of mistake.

 

[mark726]

Thank you for your question. I can confirm that your findings are correct. The values for θ and ψ that are not defined for Compton scattering are:

1. θ = π/2 and θ = π: These angles correspond to the electron being scattered at a right angle, which is not possible in Compton scattering.

2. ψ = 0: This angle corresponds to the photon not being scattered at all, which means there is no Compton scattering occurring.

In terms of backscattering, this phenomenon does occur in practice but it is important to note that it is not a result of the mathematical equations being incorrect. Backscattering happens when the photon and electron have a head-on collision, which is not accounted for in the mathematical equations used for Compton scattering. Therefore, we can say that the values for θ and ψ are not defined for backscattering as well.

I hope this helps clarify your confusion. Keep up the good work in your studies!