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44 Chapter 5. The Eikonal Final State 12 10 β 2 pp β 2 pp,β 2 pn [(GeV/c) 2 ] 8 6 4 β 2 pn β 2 pn (phase) 2 0 10 -1 1 10 Proton momentum [GeV/c] Figure 5.7 Slope parameters for pp and pn scattering. The solid and dashed lines are results of calculations that rely on the experimental data points, for pp and pn scattering, respectively. These experimental data points have been plotted for the pp scattering reaction. The dotted line is the result of a phase shift analysis of the pn scattering reaction. For references to the data points and calculations, see Ref. [6].
5.4. The Glauber Approach 45 shape of the elastic nucleon-nucleon cross section. The elastic scattering amplitude of Eq. (5.33) is directly related to the elastic differential cross section through the following expression d 2 σ el d∆ = 1 k 2 f |f el (∆)| 2 = σ2 tot(1 + ɛ 2 ) 16π 2 exp(−∆ 2 β 2 ) , (5.34) which is the standard high-energy approximation of the elastic differential cross section. Integrating this differential cross section leaves us with σ el = ∫ d 2 σ el d∆ d∆ = σ2 tot(1 + ɛ 2 ) 16π 2 β 2 . (5.35) This expression allows to derive the value of the slope parameter from the experimentally known values of the elastic cross section and the ratios of the real to imaginary part of the forward elastic scattering amplitudes. An example of such a calculation can be found in Fig. 5.8, that has been taken from Ref. [65]. In this reference use is made of a widely spread partial-wave analysis of nucleon-nucleon elastic scattering data by Arndt et al. [66, 67, 68, 69, 70]. We use the experimental values for ɛ pp and ɛ pn of Ref. [64] however; they can be found in Fig. 5.9. By analogy with the central amplitude, the spin-orbit amplitude can be parametrized as fpN s = γ k f σpN tot ( 4π (ɛs pN + i)exp − ∆2β pN s2 ) . (5.36) 2 Let us now consider the case of central scattering scattering. Inverting Eq. (5.29) leaves us with Γ(k f , ⃗ b) = 2π ik f ∫ d ⃗ ∆ (2π) 2 exp(−i⃗ ∆ ·⃗b)f E ( ⃗ ∆) . (5.37) Inserting the parametrization of Eq. (5.33) into this expression, gives us then the following expression for the profile function : Γ(k f , ⃗ b) = σtot pN (1 − iɛ ( pN) exp − 4πβ 2 pN b2 2β 2 pN ) . (5.38) In the analysis of the proton-nucleus scattering data, the spinless version of Glauber theory was very succesfull [5, 71]. As can be inferred from Fig. 5.6, the spin-dependent contributions to the proton scattering process are relatively weak for higher kinetic energies. All results that are presented in this work are obtained within the framework of the spinless version of the Glauber theory.
Page 1: De Eikonale Benadering in Dirac-Ge
Page 4 and 5: ii CONTENTS 10 Conclusion and Outlo
Page 6 and 7: 2 Chapter 1. Introduction the stron
Page 8 and 9: 4 Chapter 1. Introduction a wide Q
Page 10 and 11: 6 Chapter 2. Reaction Observables a
Page 12 and 13: 8 Chapter 2. Reaction Observables a
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
Page 37 and 38: 5.2. A Consistent Approach to Final
Page 39 and 40: 5.2. A Consistent Approach to Final
Page 41 and 42: 5.3. Optical Potentials and the Eik
Page 43 and 44: 5.3. Optical Potentials and the Eik
Page 45 and 46: 5.4. The Glauber Approach 41 where
Page 47: 5.4. The Glauber Approach 43 Figure
Page 51 and 52: 5.4. The Glauber Approach 47 ε pp
Page 53 and 54: 5.4. The Glauber Approach 49 1250 1
Page 55 and 56: 5.4. The Glauber Approach 51 so tha
Page 57 and 58: 5.4. The Glauber Approach 53 1.2 1
Page 59 and 60: 5.5. Higher Order Eikonal Correctio
Page 61 and 62: Chapter 6 Final State Interactions
Page 63 and 64: 6.1. 16 O(e, e ′ p) 15 N 59 d 5
Page 65 and 66: 6.1. 16 O(e, e ′ p) 15 N 61 ρ [(
Page 67 and 68: 6.1. 16 O(e, e ′ p) 15 N 63 12 C(
Page 69 and 70: 6.1. 16 O(e, e ′ p) 15 N 65 CEA w
Page 71 and 72: 6.1. 16 O(e, e ′ p) 15 N 67 Figur
Page 73 and 74: 6.1. 16 O(e, e ′ p) 15 N 69 0.4 0
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
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94 Chapter 8. Relativistic Effects
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Chapter 9 Nuclear Transparency The
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9.1. Theoretical Background 105 Req
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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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