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3.3. A(p, pN) Differential Cross Sections 42real part of S IFSI10.90.80.70.60.50.40.30.20.10θ = 45 o , φ = 0 o1 2 3 4 5 6r (fm)real part of S IFSI10.90.80.70.60.50.40.30.20.1r = 3 fm, θ = 90 oreal part of S IFSI10.90.80.70.60.50.40.30.20.1φ (deg)r = 4 fm, φ = 0 o00 20 40 60 80 100 120 140 160 180EDAD1EDAD2EDAI00 50 100 150 200 250 300 350θ (deg)Figure 3.6 The sensitivity of the real part of the complete IFSI factor for neutron knockout from 12 Cto the adopted choice for the parametrization of the optical potentials. Results of ROMEA calculationswith the EDAD1 (solid curve), EDAD2 (dashed curve), and EDAI (dot-dashed curve) optical potentialsare shown. Kinematics as in Fig. 3.1.looking at the complete IFSI factor in Fig. 3.1: the attenuation effect is clearly larger for θ ≥ 90 ◦ .Apart from breaking the symmetry around θ = 90 ◦ , the IFSI also narrow the peak in the θdependence. Of course, these IFSI effects are most pronounced for the lowest lying 1s 1/2 level.3.3 Numerical Results for A(p, pN) Differential Cross Sections3.3.1 12 C, 16 O, and 40 Ca(p, 2p) and (p, pn) at 1 GeVThe PNPI experiment [114] was carried out with an incident proton beam of energy 1 GeV. Thescattered proton was detected at θ 1 = 13.4 ◦ with a kinetic energy between 800 and 950 MeV,while the knocked-out nucleon was observed at θ 2 = 67 ◦ having a kinetic energy below 200 MeV.Figs. 3.10–3.12 display a selection of differential cross section results as a function of thekinetic energy of the most energetic nucleon in the final state. The EDAI optical potential [46]was used for the ROMEA calculations. The other parametrizations of Ref. [46] produce similarpredictions, whereas the RMSGA approach fails to give an adequate description of the databecause of the low kinetic energy of the ejected nucleon. Since the experiment of Ref. [114]only measured relative cross sections, the ROMEA results were normalized to the experimentaldata.The ROMEA calculations reproduce the shapes of the measured differential cross sections.
Chapter 3. IFSI and A(p, pN) Differential Cross Sections 43real part of S IFSI0.80.60.40.2real part of S IFSI0.80.60.40.2150θ (deg)10050012345r (fm)6150θ (deg)10050012345r (fm)6real part of S IFSI0.80.60.40.20real part of S IFSI0.80.60.40.20150θ (deg)10050012345r (fm)6150θ (deg)10050012345r (fm)6Figure 3.7 As in Fig. 3.1, but using the RMSGA method.Furthermore, comparison of the RPWIA and ROMEA calculations shows that the effect of theIFSI is twofold. First, IFSI result in a reduction of the RPWIA cross section that is both level andA dependent. From the figures it is clear that ejection of a nucleon from a deeper lying levelleads to stronger initial- and final-state distortions. This reflects the fact that the incoming andoutgoing nucleons encounter more obstacles when a deeper lying bound nucleon is probed.The A dependence also conforms with our expectations, i.e., the IFSI effects are larger for heaviernuclei. Besides the attenuation, the IFSI also make the measured missing momentum differentfrom the initial momentum of the struck nucleon. As can be inferred from Fig. 3.13, thismomentum shift leads to an asymmetry between the positive and negative missing-momentumside of the momentum distribution. Note that a positive missing momentum corresponds top mx = k 1 sin θ 1 + k 2 sin θ 2 cos φ 2 > 0.3.3.2 40 Ca(p, 2p) at 460 MeVNext, we focus on a 40 Ca(p, 2p) experiment conducted at the EFI facility in Chicago by Tyrén etal. [115]. The impinging proton had a kinetic energy of T p1 = 460 MeV, while the outgoing pro-
Page 1: FACULTEIT WETENSCHAPPENA RELATIVIST
Page 8 and 9: Contentsiv
Page 10 and 11: 2mechanism is obtained than in incl
Page 12 and 13: 4rely on partial-wave expansions of
Page 15 and 16: Chapter 2Relativistic Eikonal Descr
Page 18 and 19: 2.1. Observables and Kinematics 10w
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Page 24 and 25: 2.1. Observables and Kinematics 16d
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Page 44 and 45: 3.1. The IFSI Factor 36sence of ini
Page 46 and 47: 3.1. The IFSI Factor 38imaginary pa
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Page 62 and 63: 54Figure 4.1 The beam-momentum depe
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Page 68 and 69: 4.3. Color Transparency 60of CT. Th
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Page 72 and 73: 4.3. Color Transparency 64with p th
Page 74 and 75: 4.4. Nuclear Transparency Results 6
Page 80 and 81: 4.5. Outlook 72the 7 Li and 12 C da
Page 82 and 83: 4.5. Outlook 7410.812 C0.6Transpare
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Page 86 and 87: 5.1. The A(e, e ′ p) Matrix Eleme
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92be transformed into an amplitude
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A.2. Pauli Matrices 94A.2 Pauli Mat
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96pseudo-scalar π mesons, as well
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980.11ρ chg(e/fm 3 )0.080.060.0440
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100with∫D r,θ (r, θ) ≡dφ sin
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Bibliography 102[12] R. A. Arndt, I
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Bibliography 104[43] E. D. Cooper,
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Bibliography 106[71] R. J. Glauber,
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Bibliography 108[104] S. J. Wallace
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Bibliography 110[132] C. Baglin et
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Bibliography 112[163] K. Wijesooriy
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Bibliography 114[195] L. L. Frankfu
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Bibliography 116[227] J. Botts, J.-
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Bibliography 118
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Nederlandstalige samenvatting 120
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Nederlandstalige samenvatting 122we
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Nederlandstalige samenvatting 1246
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