(adsbygoogle = window.adsbygoogle || []).push({}); 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 [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.

2. Relevant 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.

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.

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# Homework Help: Born approx.

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