L In elastic e- µ¯ scattering the interaction of the muon is characterized by the vertex can be applied to factor iey (F

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L In Elastic E U Scattering The Interaction Of The Muon Is Characterized By The Vertex Can Be Applied To Factor Iey F 1 (168.02 KiB) Viewed 21 times

L In elastic e- µ¯ scattering the interaction of the muon is characterized by the vertex can be applied to factor iey (Feynman rule 1). The method ( electron-proton scattering by replacing the factor iey of the muon vertex by the factor -ie [7°F (4²) + 5 F2(a² No¹ an]. -ie[yºF Kp 2mp -F₂(9²)ioq [ប where q is the momentum transfer four-vector of the electron, and Kp is the anomalous magnetic moment of the proton in units of the Bohr magneton. F₁(q²) and F₂(q2) are form factors representing the internal structure of the proton, with F₁(0) = F₂(0) = 1, so that for q→ 0, i.e. a stationary proton interacting with static electric and magnetic fields, the proton has the correct electrostatic and magnetostatic interactions. Show that in the laboratory frame in which the proton is initially at rest the differential cross-section for elastic scattering of electrons of energy E(»m₂) is given by the Rosenbluth cross-section - 1 do do [₁ 2E 1 + sin² mp 1₁ ΦΩ ΦΩ K²/ x {[F{(4²) _ \_/ 4²°F}(q?} ] _ _ {F}(@?) + x,F2(q?}]}³ tam² 2} F₁(q²) q²F²(q²) 9² 2m² [F₁(q²) x₂F₂(q²)]² 4m² Here is the angle of scattering, and (do/dn') is the Mott cross-section with Z= 1 and v= 1.