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Chapter 2. Relativistic Eikonal A(p, pN) Formalism 27Cross section (mb)10 210σ totσ elppCross section (mb)10 210σ totσ elpn10 -1 1 10Proton momentum (GeV/c)Figure 2.4 Total and elastic cross sections for proton-proton and proton-neutron scattering as a functionof the proton lab momentum. The data were taken from Ref. [95]. The solid (dashed) curve is our globalfit to the elastic (total) cross section.Eq. (2.62) are scarce and not free of ambiguities due to spin effects. Therefore, in our calculations,the slope parameters are determined through the following relation( ) 2 ( )σpNtot 1 + ɛ 2 pNβ 2 pN =16π σ elpN. (2.75)This parametrization can be derived from the theoretical shape of the elastic pN cross sectionas follows. Expression (2.63) for the elastic scattering amplitude leads to( ) 2 ( )dσpNeld(∆ 2 ) = π ∣ ∣ ∣∣A( ∆) ⃗ ∣∣2 σpNtot 1 + ɛ 2 pN=k 2 exp ( −β 216πpN∆ 2) . (2.76)Integrating this standard high-energy approximation of the elastic differential cross sectionresults in∫σpN el =(dσelpNd(∆ 2 ) d(∆2 ) =σ totpN) 2 ( )1 + ɛ 2 pN16πβ 2 pN, (2.77)so that the slope parameter is given by Eq. (2.75). In Fig. 2.5, the slope parameters obtainedthrough this expression are compared with those determined directly through Eq. (2.62).