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Chapter 3. IFSI and A(p, pN) Differential Cross Sections 41|S IFSI( 40 Ca)|/|S IFSI( 12 C)|0.80.60.40.2150θ (deg)100500r (fm)1 2 3 4 5 6 7 8Figure 3.5 The ratio of the 40 Ca absolute value of the complete IFSI factor to the 12 C one as a function ofr and θ. The results are for proton emission from the Fermi level and φ = 0 ◦ , and were obtained withinthe ROMEA model using the EDAD1 optical potential of Ref. [46]. Kinematics as in Fig. 3.1.folded with a relativistic bound-state wave function φ α1 (⃗r). As the particles experience lessIFSI close to the nuclear surface, one obtains a stronger reduction of the quasifree cross sectionfor nucleon knockout from a level which has a larger fraction of its density in the nuclearinterior. This will become apparent in Fig. 3.8, but even more so in Section 3.3.1.Fig. 3.8 shows a function δ r (r) which represents the contribution of the nuclear region withradial coordinate r to the differential cross section. The procedure for calculating this function issimilar to the method exposed in Ref. [118] and is developed in Appendix C. Comparison of theupper and lower panels illustrates that IFSI mechanisms make the A(p, 2p) cross sections reflectsurface mechanisms, unlike the A(e, e ′ p) reaction where the weakly interacting electron probesthe entire nuclear volume and only the outgoing proton interacts with the residual system.Apart from the shift to higher r, the IFSI brings about a strong reduction in the magnitude ofthe cross sections, whereby the Fermi level is least affected. Even though δ r (r) is concentratedin the surface region, the average density seen through this reaction still amounts to 0.069 fm −3(0.080 fm −3 ) or 32% (45%) of the central density in the case of 1s 1/2 knockout from 12 C ( 40 Ca).In the case of emission from the Fermi level, on the other hand, the average density is only 12%(13%) of the central density for a 12 C ( 40 Ca) target.In Fig. 3.9 we show which (r, θ) coordinates of the collision point provide the largest contributionsto the cross section. The kinematics was the same as in Fig. 3.8 and the ROMEAcalculations used the EDAD1 optical potential. As can be inferred from the left panels, thecontributions to the RPWIA cross sections are symmetric around θ = 90 ◦ . The IFSI not onlyshift the maximum in δ r,θ to higher r, but also to lower values of θ. This can be explained by