For electrons of a few hundred MeV

PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Scattering theory · Scattering theory

The Nucleus Resolved, Ch How big a nucleus is, and what the mass surface knows

Problem

For electrons of a few hundred MeV, with β\beta essentially one, the first Born approximation for elastic scattering is adequate only where Zαfs≪1Z\alpha_{\rm fs} \ll 1, with αfs=1/137.036\alpha_{\rm fs} = 1/137.036. ((a)) Compute ZαfsZ\alpha_{\rm fs} for carbon (Z=6Z=6), tin (Z=50Z=50) and uranium (Z=92Z=92). ((b)) Given that lead (Z=82Z=82, Zαfs=0.60Z\alpha_{\rm fs} = 0.60) already shows the plane-wave minimum filled into a shoulder by the true Coulomb field, rank the three nuclei by how much the Born approximation can be trusted.

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