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MathematicalPhysicist
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Homework Statement
Consider a non-relativistic scattering of a particle of mass m and charge e from a fixed distibution of charge [tex]\rho(r)[/tex]. Assume that the charge distribution is neutral, [tex]\int d^3r \rho(r) =0[/tex], it's spherically symmetric, and the second moment is defined as:
[tex]A=\int d^3r r^2\rho(r)[/tex].
Use the Born approximation to derive the differential cross section for the scattering of a particle of wave vector k.
Homework Equations
Let [tex]q=2ksin(\theta/2)[/tex] and the amplitude of the differential cross section to be:
[tex]f(\theta)=(-2m/(q\hbar^2))\int_{0}^{\infty} rV(r)sin(qr)dr[/tex]
(for a spherically symmetric potential).
N.B
theta is the scattering angle.
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 doesn't 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.