How to Calculate Scattering Amplitude in the Born Approximation?

[wgdtelr]

The scattering amplitude in the Born approximation is as
f(θ) = (-2m / (h/2π )2 K ) * integral 0 to ∞ (r sin Kr V(r) dr)

Substituting V (r) = -V0 exp(-r2/2a2)

We get f(θ) = (-mVoa3√π / 2(h/2π) ) * exp (-k2a2sin2θ/2 )

Differential crossection dσ / dΩ = / f(θ) /^2

= (-mVoa3√π / 2(h/2π) )2 * exp (-2k2a2sin2θ/2 )

can u please give the intermediate calculations.

 

[Cyosis]

First of all show us what you have tried so far. What you've shown so far is full of ambiguities making it impossible to do an accurate calculation. For example the 2K in your first equation is it a part of the denominator or a part of the numerator. If you would type it into your calculator it would be part of the numerator, but for some reason many people think it's supposed to be part of the denominator. Next up I take r2 is r^2 and not 2r? etc.

I could do the intermediate calculations, but what is the point, besides it being against forum regulations. Where are you stuck? We can take it from there.