Study of the (e,e'p) quasielastic reaction in complex nuclei: theory and experiment

UNIVERSIDAD COMPLUTENSE DE MADRID

FACULTAD DE CIENCIAS FÍSICAS
Departamento de Física Atómica, Molecular y Nuclear





STUDY OF THE (e,e’p) QUASIELASTIC
REACTION IN COMPLEX NUCLEI: THEORY AND
EXPERIMENT.


MEMORIA PARA OPTAR AL GRADO DE DOCTOR
PRESENTADA POR

Joaquín López Herraiz


Bajo la dirección del doctor

José Manuel Udías Moinelo


Madrid, 2010



ISBN: 978-84-693-8348-3 © Joaquín López Herraiz, 2010



Universidad Complutense de Madrid
Facultad de Ciencias Físicas
Dpto. de Física Atómica, Molecular y Nuclear













STUDY OF THE (e,e’p)
QUASIELASTIC REACTION
IN COMPLEX NUCLEI:
THEORY AND EXPERIMENT





JOAQUÍN LÓPEZ HERRAIZ




Tesis dirigida por el profesor
Dr. José Manuel Udías Moinelo


Madrid, March 2010

Abstract
Study of the (e,e‟p) Quasielastic
Reaction in Complex Nuclei:
Theory and Experiment

Joaquín López Herraiz

Experimental coincidence cross section and transverse-longitudinal asymmetry A TL
16 12 208have been obtained for the quasielastic (e,e'p) reaction in O, C, and Pb in constant q-
ω kinematics in the missing momentum range -350 < p < 350 MeV/c. In these miss
experiments, performed in experimental Hall A of the Thomas Jefferson National
Accelerator Facility (JLAB), the beam energy and the momentum and angle of the
scattered electrons were kept fixed, while the angle between the proton momentum and
the momentum transfer q was varied in order to map out the missing momentum
distribution.
The experimental cross section and A asymmetry have been compared with Monte TL
Carlo simulations based on Distorted Wave Impulse Approximation (DWIA) calculations
with both relativistic and non-relativistic spinor structure. The spectroscopic factors
obtained for both models are in agreement with previous experimental values, while A TL
measurements favor the relativistic DWIA calculation.
This thesis describes the details of the experimental setup, the calibration of the
spectrometers, the techniques used in the data analysis to derive the final cross sections
and the A , the ingredients of the theoretical calculations employed and the comparison of TL
the results with the simulations based on these theoretical models.

Thesis Supervisor: José Manuel Udías Moinelo


Contents

1. Introduction ................................................................................................................................................. 11
1.1. Electron Scattering ............................... 11
1.2. Inclusive Electron Scattering - (e,e’) .................................................................................................... 13
1.3. Exclusive Electron ing - (e,e'p) . 14
1.4. Kinematics ........................................... 15
1.5. Mechanisms of the (e,e’p) Reaction ..... 20
1.5.1. Impulse Approximation ............................................................................................................... 21
1.5.2. Coulomb Distortion ..................... 23
1.5.3. Mean Field and Correlations ...... 24
16 12 2081.6. Results from Previous (e,e'p) Experiments on O, C and Pb ........................................................ 26
161.6.1. Previous O(e,e'p) experiments .................................................................. 26
121.6.2. Previous C(e,e'p) experiments .. 29
2081.6.3. Previous Pb(e,e'p) experiments ............................... 31
1.7. Physics Motivation and Objectives of these Experiments .................................... 33
1.7.1. General Motivation ..................................................................................... 33
161.7.2. Experiment E00-102 - (e,e'p) on O ........................... 34
208 121.7.3. Expt E06-007 - (e,e'p) on Pb and C .......................................... 35
1.8. General Description of the Experimental Setup ................... 36
1.8.1. Experiment E00-102 .................................................................................... 36
1.8.2. Expt E06-007 ................................ 38
2. Theory .......................................................... 39
2.1. Single-Photon Approximation .............................................................................. 39
2.2. Impulse Approximation (IA) ................................................ 39
2.3. One-body operator ............................................................................................... 41
2.4. Beyond the Impulse Approximation .................................... 41
2.5. Mean field approximation .................... 42
2.6. Relativistic Mean Field ........................ 43
2.7. Spectroscopic Factors ........................................................................................................................... 45
2.8. Beyond mean field ............................... 46
2.9. Final State Interaction: Optical Potential ............................. 50
2.10. Factorization ......................................................................................................................................... 53
2.11. Negative energy components ............... 55
2.12. Off-shell ambiguity .............................. 57
2.13. Gauge invariance ambiguity ................. 58
2.14. Proton Form Factors ............................................................................................................................. 59
22.15. Study of the Q dependence of the Spectroscopic Factors ................................... 60
2.16. Relativistic vs. Non-Relativistic Calculations ...................... 62
3. Simulations .................................................................................................................................................. 65
3.1. Introduction .......... 65
3.2. MCEEP ................ 67
3.3. RDWIA Response Functions + MCEEP .............................................................................................. 68
3.4. Example of the enhanced MCEEP simulations for the E89-003 experiment ...................................... 69
3.4.1. Pinhole acceptances .................................................... 69
3.4.2. Impact of the acceptances on the results ..................................................................................... 70
3.5. Input file parameters ............................ 71
3.5.1. Beam parameters ......................... 71
3.5.2. Internal collimators ..................................................... 71
3.6. Energy Loss and Radiative Effects ...................................................................... 72
4. Description of the Experimental Setup ..................................... 75
4.1. Overview .............................................................................................................. 75
4.2. Accelerator ........... 76
4.3. Hall A Setup ......................................... 77

4.4. Beamline .............................................................................................................................................. 78
4.4.1. Beam Current Measurement ........ 78
4.4.2. Beam Position Measurement ....... 80
4.4.3. Beam Energy Measurement ......... 81
4.4.4. Beam Rastering System ............................................................................................................... 82
4.5. Target System ...................................... 84
4.5.1. Experiment E00-102 .................... 84
4.5.2. Expt E06-007 86
4.6. High Resolution Spectrometers ............................................................................................................ 88
4.7. Detector Packages ................................................................................................................................ 90
4.7.1. Scintillators . 90
4.7.2. Trigger system ............................. 91
4.7.3. Vertical Drift Chambers .............................................................................................................. 93
4.8. Data Acquisition................................... 96
4.9. Data Analysis Software ........................ 97
4.10. Coordinate Systems .............................................................................................. 99
4.10.1. Ha