Discussion
Validity of first-Born approximation for central force potential is :
Answer: C
The first Born approximation is valid for large incident energy and weak scattering potential.
The Born approximation replaces the true wave inside the potential by the incident plane wave. That is accurate only if the potential distorts the wave little, which requires a weak potential, and if the particle passes quickly, which a high energy ensures. A common criterion is \(|V|a/\hbar v \ll 1\), where \(a\) is the range and \(v\) the speed.
A strong potential at low energy is the opposite regime, where partial-wave methods are used. The approximation is not universal, so 'any central potential' and 'independent of energy and potential' are wrong.
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