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60 Chapter 6. Final State Interactions and the Eikonal Approximation CC1 operator RPWIA CEA OMEA RMSGA Udias Kelly 1p 3/2 0.59 (0.56) 0.53 (1.19) 0.96 (1.78) 0.96 (0.75) 0.71 0.67 1p 1/2 0.53 (0.48) 0.50 (0.58) 0.79 (0.60) 0.80 (0.38) 0.73 0.72 CC2 operator 1p 3/2 0.61 (1.59) 0.62 (2.80) 1.01 (3.48) 1.01 (2.19) 1p 1/2 0.53 (0.56) 0.57 (1.09) 0.82 (1.04) 0.82 (0.95) Table 6.1 The spectroscopic factors for the 16 O(e, e ′ p) reaction of Ref. [15], as obtained with a χ 2 procedure. The reduced χ 2 (i.e. the χ 2 per degree of freedom) is given between brackets. The spectroscopic factors obtained by Udias et al. in Ref. [86], and by Kelly in Ref. [45] are also given by comparison. deals with final state interactions (FSI’s). In the eikonal calculations, the dips of the RPWIA calculations are filled in, and, at low missing momenta the RPWIA cross sections are reduced. These two features reflect nothing but the usual impact of the final state interactions on the A(e, e ′ p) angular cross sections. The limitations of the consistent eikonal calculations (q ≫ k i ) are immediately visible at higher missing momenta (p m ≥ 250 MeV/c). Here, the eikonal cross sections largely overshoot both the RPWIA results and the data and should by no means be considered realistic. It is worth remarking that the data closely follow the trend set by the RPWIA curves. As a matter of fact, whereas the eikonal calculations predict huge effects from final state interactions at large transverse missing momenta, the data seem to suggest rather the opposite effect. One may wonder whether the observed behaviour of the consistent eikonal results at higher missing momenta in Fig. 6.1 is a mere consequence of the small-angle approximation contained in Eq. (5.13), or whether the adopted model assumptions for computing the scattering states is also (partly) at the origin of this pathological behaviour. To address this question, we have performed calculations for various fixed recoil angles θ defined as cos θ = ⃗p m · ⃗q |⃗p m ||⃗q| . (6.1) The results are displayed in terms of the reduced cross section which is defined in the standard fashion as the differential cross section, divided by a kinematical factor times the “CC1” off-shell electron-nucleon cross section σeN cc1 of Ref. [39]. This cross section is defined as [ ( Q σeN cc1 4 Q 2 = σ Mott q 4 w C + 2q 2 + θ ) tan2 e w T 2
6.1. 16 O(e, e ′ p) 15 N 61 ρ [(GeV/c) -3 ] 16 O(e,e′p) 15 N(1p 3/2 -1) 10 2 1 θ = 0 o 10 2 10 -2 10 -4 1 10 -2 10 -4 θ = 45 o RPWIA CEA 1 10 -2 10 -4 10 2 θ = 90 o 0 100 200 300 400 500 p m [MeV/c] Figure 6.2 The reduced cross section for the 16 O(e, e ′ p) 15 N(1p −1 3/2 ) reaction versus missing momentum at three values of the recoil angle θ. A fixed outgoing proton momentum of | ⃗ k f | = 1 GeV/c was considered. The solid line shows the consistent eikonal calculation, while the dashed one shows RPWIA results.
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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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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
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Page 41 and 42: 5.3. Optical Potentials and the Eik
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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
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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
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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
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Page 75 and 76: 6.2. 12 C(e, e ′ p) 11 B 71 0 -0.
Page 77 and 78: 6.2. 12 C(e, e ′ p) 11 B 73 ρ [(
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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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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