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56 Chapter 5. The Eikonal Final State − (∇ 2 χ)g − 2 ⃗ ∇ · ⃗∇g = 0 . (5.71) To solve this set of equations, we introduce the following expansions : χ(⃗r) = ⃗ k · ⃗r + χ 0 (⃗r) + χ 1 (⃗r) + . . . , (5.72) g(⃗r) = g 0 (⃗r) + g 1 (⃗r) + g 2 (⃗r) + . . . , (5.73) where χ n (⃗r), g n (⃗r) ∝ k −n . The lowest, first and second-order solutions read ∫ z χ 0 = − V dz ′ , (5.74) −∞ g 0 = 1 (5.75) χ 1 = − 1 2E g 1 = − 1 2E χ 2 = − 1 2E g 2 = − 1 2E ∫ z −∞ ∫ z −∞ ∫ z −∞ ∫ z −∞ [S 2 − V 2 + 2MS + ( ⃗ ∇χ 0 ) 2 ]dz ′ (5.76) [∇ 2 χ 0 − ⃗σ · ⃗∇(S − V )σ z ]dz ′ (5.77) [2 ⃗ ∇χ 0 · ⃗∇χ 1 − M 2 E ∇ zχ 0 ]dz ′ (5.78) [(∇ 2 χ 0 )g 1 + (∇ 2 χ 1 )g 0 + 2 ⃗ ∇χ 0 · ⃗∇g 1 − 1 E ⃗σ · ⃗∇(S − V ){σ z Eg 1 + ⃗σ · ⃗∇χ 0 g 0 } + M + S − V E 2 ⃗σ · ⃗∇(S − V )σ z Eg 0 ]dz ′ . (5.79)
Chapter 6 Final State Interactions and the Eikonal Approximation In the previous chapter we have discussed various methods to treat the final state interactions in exclusive A(e, e ′ p) reactions. In this chapter all of these different approximations will be put to a stringent test. This will be done by comparing calculated A(e, e ′ p) observables with exclusive 16 O(⃗e, e ′ ⃗p) and 12 C(⃗e, e ′ ⃗p) data that have recently been collected at Jefferson Lab (JLAB) and the Stanford Linear Accelerator (SLAC) facility. 6.1 16 O(e, e ′ p) 15 N We start our (e, e ′ p) investigations within the relativistic eikonal approximation for the kinematics of an 16 O(e, e ′ p) experiment that was recently performed at Jefferson Lab (E89-003) [15]. The main objectives of this experiment were to determine [15, 85] • the limits of the validity of the single-particle model of valence proton knockout • the effects of relativity and spinor distortion on valence proton knockout using the diffractive character of the A LT asymmetry (with the term “diffractive” we refer to the behaviour of the experimental asymmetry at higher missing momenta) • the bound state wave function and spectroscopic factors for knockout from the valence shells • the longitudinal component of the (e, e ′ p) cross section at higher missing energies (through the R T L response function). 57
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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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Page 14 and 15: 10 Chapter 2. Reaction Observables
Page 17 and 18: Chapter 3 Relativistic Bound State
Page 19 and 20: 3.1. Formalism 15 content to the me
Page 21 and 22: 3.2. Results 17 12 C 16 O proton ne
Page 23 and 24: 3.2. Results 19 have verified that
Page 25 and 26: 3.2. Results 21 where the positive
Page 27: 3.2. Results 23 Figure 3.4 Nucleon
Page 30 and 31: 26 Chapter 4. Off-Shell Electron-Pr
Page 32 and 33: 28 Chapter 4. Off-Shell Electron-Pr
Page 35 and 36: Chapter 5 The Eikonal Final State I
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Page 45 and 46: 5.4. The Glauber Approach 41 where
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Page 51 and 52: 5.4. The Glauber Approach 47 ε pp
Page 53 and 54: 5.4. The Glauber Approach 49 1250 1
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Page 69 and 70: 6.1. 16 O(e, e ′ p) 15 N 65 CEA w
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Page 75 and 76: 6.2. 12 C(e, e ′ p) 11 B 71 0 -0.
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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
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9.1. Theoretical Background 107 few
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9.2. Review of Experimental Results
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9.2. Review of Experimental Results
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9.3. Nuclear Transparency Calculati
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Chapter 10 Conclusion and Outlook I
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123 with increasing Q 2 the uncerta
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Bibliography [1] V. Pandharipande,
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Bibliography 127 [42] J. Kelly, Phy
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Bibliography 129 [85] A. Saha, W. B
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