The resonance

PHYSICS · Multi-part · Fermi University Physics · Particle Physics & Quantum Fields · Particles, interactions and experiment · Particles, interactions and experiment

Particle Physics, Ch Resonances, widths and the Breit-Wigner line shape

Problem

The Δ(1232)\Delta(1232) resonance, seen in π+p\pi^+p scattering, has full width at half maximum Γ=117 MeV\Gamma = 117\,\mathrm{MeV} and peak cross section σpeak=195 mb\sigma_{\rm peak} = 195\,\mathrm{mb}. Use the Breit-Wigner form σ(E)=σpeak1+(2(E−Mc2)Γ)2.\sigma(E) = \dfrac{\sigma_{\rm peak}}{1 + \left(\dfrac{2(E-Mc^2)}{\Gamma}\right)^2}. ((a)) Find the mean lifetime of the Δ\Delta. ((b)) Find the energy offsets E−Mc2E - Mc^2 at which the cross section has fallen to one tenth of its peak value.

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