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Chapter 2. Relativistic Eikonal A(p, pN) Formalism 29ε pp21.510.50-0.5-1-1.51.510.5ε pn0-0.5-1-1.510 -1 1Proton momentum (GeV/c)Figure 2.6 The ratios of the real to the imaginary part of the central scattering amplitude A(∆) forproton-proton and proton-neutron scattering as a function of the proton lab momentum. The curves areglobal fits to the data. The data are from Ref. [68].and neutrons in the residual nucleus. This leaves us withŜIFSIRMSGA×(⃗r) ≃{ ∫ρ p (⃗r j )[ (d⃗r j 1 − Γ pp p 1 ,Z ⃗ b − ⃗ )b j θ (z − z j )res[ (× 1 − Γ Nk2 p k 2 , ⃗ b ′′ − ⃗ )b ′′jθ ( z ′′j − z ′′)]} Z res] ( [1 − Γ pp k 1 , ⃗ b ′ − ⃗ )b ′ j θ ( z ′ j − z ′)]{ ∫ρ n (⃗r j )[ (d⃗r j 1 − Γ pn p 1 ,N ⃗ b − ⃗ ) ] (b j θ (z − z j )[1 − Γ pn k 1 , ⃗ b ′ − ⃗ )b ′ j θ ( z ′ j − z ′)]res[ (× 1 − Γ Nk2 n k 2 , ⃗ b ′′ − ⃗ )b ′′jθ ( z ′′j − z ′′)]} N res. (2.78)