How to prove the width of a resonance using the cross section of a S wave?

[ziad1985]

Homework Statement

The total cross section of a S wave is given by the following equation
Sigma=(pi/k)*(b^2)/((E-En)^2+(b/2)^2))
prove that b is the width of the resonance.

Homework Equations

Nothing that is the only thing

The Attempt at a Solution

I already solved the question using basic calculation.
For E=En i get the maximum of Sigma , for half of that maximum , i get a second degree equation of E, when solving it i get 2 solution representing that half maximum(E1 & E2) , the difference between E1 and E2 , E1-E2=b
But I'm not really comfortable with the way i did it , I know i got the solution , but I'm looking for another way , something more to do with physics.
idea anyone?

 

[Meir Achuz]

You did it correctly. Somtimes physics depends on simple math.