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120 Chapter 9. Nuclear Transparency 1.15 1s 1/2 Q 2 (GeV) 2 1p 3/2 Q 2 (GeV) 2 1.1 1p 1/2 z lj (IA) / z lj (IA+2N) 1.05 1 0.95 0.9 0.85 0 0.25 0.5 0.75 1 0 0.25 0.5 0.75 1 0 0.25 0.5 0.75 1 Q 2 (GeV) 2 Figure 9.7 The predicted sensitivity of the extracted spectroscopic factors to effects beyond the impulse approximation in the 16 O(e, e ′ p) reaction. Parallel kinematics ( ⃗ k f ‖⃗q) and quasielastic conditions were imposed. The dashed line includes only central correlations, whereas the solid curve also includes tensor correlations. The dot-dashed calculation accounts only for meson exchange currents, whereas the dotted line includes meson and ∆-isobar exchange currents, central and tensor correlations. This picture was taken from [123].
Chapter 10 Conclusion and Outlook In this work we have outlined a fully relativistic eikonal framework for modelling semi-exclusive A(e, e ′ p) reactions from spherical nuclei at intermediate and high four-momentum transfers Q 2 . We have carried out a wide range of 12 C(e, e ′ p) and 16 O(e, e ′ p) calculations for a variety of kinematical conditions, thereby covering fourmomentum transfers in the range 0.1 ≤ Q 2 ≤ 20 (GeV/c) 2 . Our model has proven to be a very flexible framework as it can be used in conjunction with relativistic optical potentials or within a Glauber multiple-scattering approach, which are two substantially different techniques to deal with final state interactions. To our knowledge all Glauber calculations reported in literature are performed within a non-relativistic and factorized scheme. Our approach can accommodate dynamical relativity, and all calculations were performed within a fully unfactorized model. This means that in our theoretical considerations we do not formally separate the proton-nucleus interaction from the nuclear dynamics. In addition to the Glauber and optical potential approach we developed a consistent eikonal model (CEA) in which the bound and scattering states were derived from the same Dirac equation. Our results illustrate that the validity of the CEA is confined to proton emission in a cone with a relatively small opening angle about the direction of the virtual photon’s momentum. At first sight, this observation put serious constraints on the applicability of the Glauber method, that is based on the eikonal approximation, for modelling the final state interactions in high-energy (e, e ′ p) reactions from nuclei. However, although this consistent treatment minimizes the effects of spurious states, it can only take elastic contributions into account. It turned out that the implementation of inelastic contributions in the exit channels is needed to fully appreciate the limits of the Glauber model. To that purpose we have extended the eikonal formalism to include optical (complex) potentials that are constructed by global fits to the available nucleon-nucleus data. This method of dealing with final state interactions has shown to extend the applicability of the eikonal method far 121
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De Eikonale Benadering in Dirac-Ge
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ii CONTENTS 10 Conclusion and Outlo
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2 Chapter 1. Introduction the stron
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4 Chapter 1. Introduction a wide Q
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6 Chapter 2. Reaction Observables a
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8 Chapter 2. Reaction Observables a
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10 Chapter 2. Reaction Observables
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Chapter 3 Relativistic Bound State
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3.1. Formalism 15 content to the me
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3.2. Results 17 12 C 16 O proton ne
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3.2. Results 19 have verified that
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3.2. Results 21 where the positive
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3.2. Results 23 Figure 3.4 Nucleon
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26 Chapter 4. Off-Shell Electron-Pr
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28 Chapter 4. Off-Shell Electron-Pr
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Chapter 5 The Eikonal Final State I
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5.2. A Consistent Approach to Final
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5.2. A Consistent Approach to Final
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5.3. Optical Potentials and the Eik
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5.3. Optical Potentials and the Eik
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5.4. The Glauber Approach 41 where
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5.4. The Glauber Approach 43 Figure
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5.4. The Glauber Approach 45 shape
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5.4. The Glauber Approach 47 ε pp
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5.4. The Glauber Approach 49 1250 1
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5.4. The Glauber Approach 51 so tha
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5.4. The Glauber Approach 53 1.2 1
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5.5. Higher Order Eikonal Correctio
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Chapter 6 Final State Interactions
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6.1. 16 O(e, e ′ p) 15 N 59 d 5
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6.1. 16 O(e, e ′ p) 15 N 61 ρ [(
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6.1. 16 O(e, e ′ p) 15 N 63 12 C(
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6.1. 16 O(e, e ′ p) 15 N 65 CEA w
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6.1. 16 O(e, e ′ p) 15 N 67 Figur
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Page 79 and 80: 6.2. 12 C(e, e ′ p) 11 B 75 P n P
Page 81 and 82: Chapter 7 Off-Shell Ambiguities A m
Page 83 and 84: 79 momentum region. Since these exc
Page 85 and 86: 81 R L [fm 3 ] R T [fm 3 ] R TT [fm
Page 87 and 88: 83 R L [fm 3 ] R T [fm 3 ] 0.04 0.0
Page 89 and 90: 85 manner, we will from here on onl
Page 91 and 92: 87 R CC1/CC2 R CC1/CC2 R CC1/CC2 R
Page 93 and 94: 89 The relation obtained in Eq. (7.
Page 95: 91 A LT 1 0.5 0 OMEA (CC2) OMEA (CC
Page 98 and 99: 94 Chapter 8. Relativistic Effects
Page 107 and 108: Chapter 9 Nuclear Transparency The
Page 109 and 110: 9.1. Theoretical Background 105 Req
Page 111 and 112: 9.1. Theoretical Background 107 few
Page 113 and 114: 9.2. Review of Experimental Results
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Page 117 and 118: 9.3. Nuclear Transparency Calculati
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Page 127 and 128: 123 with increasing Q 2 the uncerta
Page 129 and 130: Bibliography [1] V. Pandharipande,
Page 131 and 132: Bibliography 127 [42] J. Kelly, Phy
Page 133 and 134: Bibliography 129 [85] A. Saha, W. B
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