Homework Help: Born approx.

1. Dec 26, 2009

MathematicalPhysicist

1. The problem statement, all variables and given/known data
Consider a non-relativistic scattering of a particle of mass m and charge e from a fixed distibution of charge $$\rho(r)$$. Assume that the charge distribution is neutral, $$\int d^3r \rho(r) =0$$, it's spherically symmetric, and the second moment is defined as:
$$A=\int d^3r r^2\rho(r)$$.
Use the Born approximation to derive the differential cross section for the scattering of a particle of wave vector k.

2. Relevant equations
Let $$q=2ksin(\theta/2)$$ and the amplitude of the differential cross section to be:
$$f(\theta)=(-2m/(q\hbar^2))\int_{0}^{\infty} rV(r)sin(qr)dr$$
(for a spherically symmetric potential).
N.B
theta is the scattering angle.

3. The attempt at a solution
To do the calculation all I need to know is what is the potential,
now the constant A has magnitude of charge times displacement squared, which means eA/r^3 will give units of potetnial energy, but when I insert this I get that the integral doesnt converge, am I wrong here?
If it were the first moment then the integral will converge (the known intgral of sin(x)/x on the etire real line).
Any suggestions here?

Thanks in advance.

2. Dec 29, 2009

MathematicalPhysicist

Anyone?

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook