[SIZE="6"][SIZE="6"][FONT="Arial Black"]I have a relativistic scattering problem, where I got the scattering amplitude as follows,
f(θ)=-a*Cos(θ)
In order to extract the interaction potential, which I assumed to be radially symmetric, I apply Born's first order approximation which is,
V(r)=-(factor)*∫(q->0 to ∞)∫(θ->0 to π)Exp[i*q*r*Cos(θ)]*f(θ)*Sin(θ)dθ*(q^2)dq
Here, I wish to state that the first integral ∫(q->0 to ∞) can be written as ∫(q->0 to λ), being the cut off, for the physics of the problem that I am considering. So, one may not integrate upto ∞ for q, but upto λ as modes higher than cut off are irrelevant to the problem considered.
My questions,
1. What is the correct potential V(r) for the scattering amplitude f(θ)=-a*Cos(θ) obtained from relativistic scattering? Is Born approximation the correct way to get it?
2. I am sort of getting an imaginary potential for V(r). What is the physical significance of an imaginary potential in scattering problems?
3. Is there any approach for calculating V(r) from f(θ) in the relativistic case?
f(θ)=-a*Cos(θ)
In order to extract the interaction potential, which I assumed to be radially symmetric, I apply Born's first order approximation which is,
V(r)=-(factor)*∫(q->0 to ∞)∫(θ->0 to π)Exp[i*q*r*Cos(θ)]*f(θ)*Sin(θ)dθ*(q^2)dq
Here, I wish to state that the first integral ∫(q->0 to ∞) can be written as ∫(q->0 to λ), being the cut off, for the physics of the problem that I am considering. So, one may not integrate upto ∞ for q, but upto λ as modes higher than cut off are irrelevant to the problem considered.
My questions,
1. What is the correct potential V(r) for the scattering amplitude f(θ)=-a*Cos(θ) obtained from relativistic scattering? Is Born approximation the correct way to get it?
2. I am sort of getting an imaginary potential for V(r). What is the physical significance of an imaginary potential in scattering problems?
3. Is there any approach for calculating V(r) from f(θ) in the relativistic case?
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