University of Groningen
Investigation of nuclear forces in d + p elastic and p + d break-up reactions at
intermediate energies
Mardanpour-Mollalar, Hossein
IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to
cite from it. Please check the document version below.
Document Version
Publisher's PDF, also known as Version of record
Publication date:
2008
Link to publication in University of Groningen/UMCG research database
Citation for published version (APA):
Mardanpour-Mollalar, H. (2008). Investigation of nuclear forces in d + p elastic and p + d break-up
reactions at intermediate energies s.n.
Copyright
Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the
author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).
Take-down policy
If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately
and investigate your claim.
Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the
number of authors shown on this cover page is limited to 10 maximum.
Download date: 15-06-2017
RIJKSUNIVERSITEIT GRONINGEN
Investigation of nuclear forces in d~ + p
elastic and p~ + d break-up reactions at
intermediate energies
Proefschrift
ter verkrijging van het doctoraat in de
Wiskunde en Natuurwetenschappen
aan de Rijksuniversiteit Groningen
op gezag van de
Rector Magnificus, dr. F. Zwarts,
in het openbaar te verdedigen op
Vrijdag 16 Mei 2008
om 14:45 uur
door
Hossein Mardanpour-Mollalar
geboren op 21 September 1979
te Tabriz, Iran
Promotor:
Prof. dr. N. Kalantar-Nayestanaki
Co Promotor:
Dr. J. G. Messchendorp
Beoordelingscommissie:
Prof. dr. M. N. Harakeh
Prof. dr. P. U. Sauer
Prof. dr. H. Paetz gen. Schieck
The cover picture is designed by Samira Zamani. Samira is a master student
of fine arts at Transart institute in Linz (Austria).
Druk: Facilitairbedrijf, RUG, Groningen, April 2008.
To my dear parents: Hasan and Zahra
and my teachers
Contents
1 General introduction
1.1 Study of 3NF effects in elastic scattering . . . . . . . . . . . . . . . . . . . .
1.2 Study of 3NF effects in the break-up reactions . . . . . . . . . . . . . . . . .
1.3 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 Elements of the nuclear potential
2.1 Scattering theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 Nucleon-Nucleon scattering . . . . . . . . . . . . . . . . . . . . . .
2.1.2 Evaluating the cross section from scattering theory . . . . . . . . .
2.1.3 Three-Nucleon (3N) scattering . . . . . . . . . . . . . . . . . . . .
2.1.4 Faddeev equations for a three-body system without a 3N potential
2.2 Partial Wave Analysis, PWA . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Nijmegen partial wave analysis (Nijm-PWA) . . . . . . . . . . . .
2.3 Nucleon-Nucleon potentials . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.1 Nijmegen potential . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.2 Argonne potential . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3.3 Bonn potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Three-Nucleon Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4.1 Hannover-Lisbon model of the ∆ . . . . . . . . . . . . . . . . . . .
2.4.2 Tucson-Melbourne, three-nucleon force (TM’) . . . . . . . . . . . .
2.4.3 Urbana-Illinois three-nucleon force . . . . . . . . . . . . . . . . . .
2.4.4 Other three-nucleon potentials (3NP) . . . . . . . . . . . . . . . .
2.5 Chiral perturbation theory (χPT) . . . . . . . . . . . . . . . . . . . . . .
2.6 Observables of the elastic-scattering process . . . . . . . . . . . . . . . . .
2.6.1 Scattering with spin- 12 particles . . . . . . . . . . . . . . . . . . . .
2.6.2 Scattering with spin-1 particles . . . . . . . . . . . . . . . . . . . .
2.7 Break-up observables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 Study of 3NF effects in d~ + p elastic scattering
3.1 Experimental procedure and data analysis . . . . . . .
~ α)10 B(2+ ) reaction with
3.1.1 Measurement of 12 C(d,
3.1.2 The D-room polarimeter measurements . . . .
3.1.3 The χ2 -fitting of the asymmetry measurements
3.2 Results and discussion . . . . . . . . . . . . . . . . . .
3.3 Comparison between data and theory . . . . . . . . .
v
. . . . .
SMART
. . . . .
. . . . .
. . . . .
. . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
1
3
4
7
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
9
9
10
11
12
14
16
16
17
17
18
19
20
21
23
23
25
25
27
28
29
31
.
.
.
.
.
.
35
35
37
41
43
45
52
vi
4 Experimental setup to study the p~ + d reaction at
4.1 The AGOR cyclotron . . . . . . . . . . . . . . . .
4.2 POLarized Ion Source (POLIS) . . . . . . . . . . .
4.3 The In-Beam Polarimeter (IBP) . . . . . . . . . .
4.4 BINA . . . . . . . . . . . . . . . . . . . . . . . . .
4.4.1 Mechanical components of BINA . . . . . .
4.4.2 Data acquisition of BINA . . . . . . . . . .
CONTENTS
KVI
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
5 Analysis of the p
~ + d elastic reaction
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . .
5.2 Kinematical phase space and particle identification . . .
5.3 Energy calibration . . . . . . . . . . . . . . . . . . . . .
5.3.1 Energy calibration of the forward scintillators . .
5.3.2 Energy calibration of the backward ball of BINA
5.4 The MWPC efficiency . . . . . . . . . . . . . . . . . . .
5.5 The elastic-scattering cross section . . . . . . . . . . . .
5.6 Vector-analyzing power in elastic p~ + d scattering . . . .
5.7 Analysis of the IBP data . . . . . . . . . . . . . . . . . .
5.7.1 Particle identification in the IBP detector . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
55
55
57
59
60
61
69
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
77
77
77
80
80
82
83
85
88
90
91
6 Analysis of the p
~ + d break-up reaction
6.1 Break-up kinematics and the S-curve . . . . . . . . . . . . . . .
6.2 Energy calibration of the E detectors for the break-up channel
6.2.1 Energy calibration of the forward E scintillators . . . .
6.2.2 Energy calibration of the backward ball . . . . . . . . .
6.3 Background analysis in the spectrum of the break-up reaction .
6.4 Energy projection on the S-curve . . . . . . . . . . . . . . . . .
6.5 The break-up cross section . . . . . . . . . . . . . . . . . . . . .
6.6 The scattering asymmetry and the analyzing power . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
95
95
96
96
99
100
104
106
107
7 Results and discussion of the p~ + d reactions obtained with BINA
7.1 Results and discussion of the p
~ + d elastic reaction . . . . . . . . . . .
7.2 Results and discussion of the p
~+d break-up reaction . . . . . . . . . .
7.3 A global comparison between the data and theoretical predictions . . .
7.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
111
111
113
126
129
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
8 Summary, conclusions, and outlook
A The interaction of particles with spin with an external magnetic field
A.1 Description of the polarization . . . . . . . . . . . . . . . . . . . . . . . .
A.1.1 Spin- 12 particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.1.2 Spin-1 particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.2 Hyperfine structure of the hydrogen atom . . . . . . . . . . . . . . . . . .
A.3 Hydrogen atom in the magnetic field: the Zeeman effect . . . . . . . . . .
B χ2 fitting of the polarization asymmetries
139
.
.
.
.
.
143
143
143
144
145
147
149
CONTENTS
vii
C The data acquisition of BINA
153
D The trigger unit of BINA
155
E The event structure of BINA
157
E.1 Analysis of a sample normal event in the experiments with BINA . . . . . . 157
E.2 Analysis of a scaler event in the experiments with BINA. . . . . . . . . . . 158
F Extracting the Cross Sections
161
Bibliography
163
Samenvatting
169
viii
CONTENTS