Scattering Amplitude Wave equation: Solution is: Green’s function satisfies the point source equation: Solution:
The total scattered wave function is an integral equation which can be solved by means of a series of iterative approximations, known as Born Series. - Zero-order Solution: - First order solution: And so on…
In real scattering experiment Where r is the distance from the target to the detector and r’ is the size of the target. So we approximate:
If the potential is spherically symmetric: So, solving the Schrodinger equation in first-order Born approximation, the differential cross-section is given by above equation for a spherically symmetric potential. The potential is weak enough that the scattered wave is only slightly different from incident plane wave. For s-wave scattering scattering amplitude = -b scattering length
Question: Use Born approximation for Coulomb potential and derive the classical Rutherford scattering formula.