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12.8: General Notes on Scattering in the Born Approximation

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    The square well illustrates some general feature of scattering in the Born approximation:

    • Born approximation is based on perturbation theory, so works best for high energy particles.
    • Scattering depends on \(V^2_0\), so both attractive and repulsive potentials behave the same.
    • At high energy, cross section is inversely proportional to the energy \((E = \hbar^2 k^2/2m)\)
    • Dependence on \(k\) and \(\theta\) arises only through the combination \(\chi = 2k \sin \frac{\theta}{2}\). Thus as energy increases, the scattering angle \(\theta\) is reduced and the scattered beam becomes more peaked in the ‘straight on’ direction.
    • Angular dependence depends on the range of the potential \(a\) but not on the strength \(V_0\).
    • Total cross section depends on both range \(a\) and depth \(V_0\) of the potential.

    This page titled 12.8: General Notes on Scattering in the Born Approximation is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Graeme Ackland via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.