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Chapter 2. Relativistic Eikonal A(p, pN) Formalism 15so that the RPWIA differential A(p, 2p) cross section of Eq. (2.2) can be written in the crosssectionfactorized form(d 5 ) RPWIAσ≈ sM A−1 k 1 k 2f −1 2j + 1recdE k1 dΩ 1 dΩ 2 M p M A p 1 4πHere, s is the Mandelstam variable for the pp scattering.(dσ pNdΩ( )|˜α nκ (p m )| 2 dσppdΩc.m.. (2.30)In)the numerical calculations presented in Chapter 3, the free proton-nucleon cross sectionis obtained from the SAID code [12, 13] at an effective laboratory kinetic energy ofc.m.T efflab = s − 4M 2 p2M p(2.31)and a c.m. scattering angle θ c.m. given bycos θ c.m. =t − u√ (s− 4M 2 p) [ (4M 2 p −t−u) 2s− 4M 2 p] , (2.32)with s, t, and u the Mandelstam variables for the pp scattering. For the nuclear transparencycalculations of Chapter 4, the phenomenological parametrization of Ref. [67], which is moresuitable at large s (s ≥ 7 GeV 2 ) and c.m. scattering angle θ c.m. ≈ 90 ◦ , is used (see Eq. (4.8)).2.1.3 Treatment of the IFSI: Factorization Assumption and the Distorted MomentumDistributionThe factorized RPWIA result of Eq. (2.30) adopts an oversimplified description of the reactionmechanism. The momentum distribution 2j+14π|˜α nκ (p m )| 2 , which represents the probability offinding a proton in the target nucleus with missing momentum ⃗p m , is modified by the scatteringsof the incoming and outgoing protons in the nucleus. Therefore, it is necessary to incorporatethe effects of these IFSI in the model.In this section, the differential A(p, 2p) cross section is written in a factorized form takingIFSI effects into account. The relativistic eikonal methods used for dealing with the IFSI effectswill be discussed in depth in the forthcoming sections. Two methods will be used. The relativisticoptical model eikonal approximation (ROMEA) is the subject of Section 2.2, whereas therelativistic multiple-scattering Glauber approximation (RMSGA) is discussed in Section 2.3.In both versions of the relativistic eikonal framework for A(p, pN) reactions (ROMEA andRMSGA), the antisymmetrized initial- and final-state (A + 1)-body wave functions,Ψ ⃗p 1,m s1i ,gsA+1(⃗r 0 , ⃗r 1 , . . . , ⃗r A )[= ÂŜ p1 (⃗r 0 , ⃗r 2 , . . . , ⃗r A ) e i⃗p 1·⃗r 0u(⃗p 1 , m s1i ) Ψ gsA (⃗r 1, ⃗r 2 , . . . , ⃗r A )](2.33)andΨ ⃗ k 1 ,m s1f , ⃗ k 2 ,m s2fA+1(⃗r 0 , ⃗r 1 , . . . , ⃗r A ) = Â[Ŝ † k1 (⃗r 0, ⃗r 2 , . . . , ⃗r A ) e i⃗ k 1·⃗r 0u( ⃗ k 1 , m s1f )× Ŝ† k2 (⃗r 1, ⃗r 2 , . . . , ⃗r A ) e i⃗ k 2·⃗r 1u( ⃗ k 2 , m s2f ) Ψ J R M RA−1(⃗r 2 , . . . , ⃗r A )], (2.34)