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1 year ago in Particle Physics By Anisha

What does it mean when the differential scattering cross-section blows up in the forward direction?

In analyzing potential scattering in quantum mechanics, I keep encountering this divergence in the forward direction. Mathematically, it's clear from the Rutherford formula, but I'm struggling with the physical picture. Does it imply an infinite probability? That can't be right, so what reality does this mathematical feature represent?

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By Shahruddin Jafri Answered 1 year ago

This is a classic and important subtlety. The divergence isn't a physical infinity but a mathematical artifact of modeling an infinite-range force, like the Coulomb potential, acting across an infinite volume. In reality, no potential has truly infinite range; it's always screened or truncated. Physically, it signifies that for such forces, very small-angle scattering events are overwhelmingly the most probable. In any real experiment, your detector has a finite angular resolution. You integrate the cross-section from your minimum resolvable angle, not from zero, which gives a finite, measurable total cross-section. The divergence points to the dominance of weak, glancing interactions.

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What does it mean when the differential scattering cross-section blows up in the forward direction?

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