AL-ABDULLAH-DISSERTATION

175 Pages·2007·3.19 MB·English

EXTRACTING THE ASYMPTOTIC NORMALIZATION COEFFICIENTS
IN NEUTRON TRANSFER REACTIONS TO DETERMINE THE REACTION
RATES FOR 22Mg(p,γ)23Al AND 17F(p,γ)18Ne
A Dissertation
by
TARIQ ABDALHAMED AL-ABDULLAH
Submitted to the Office of Graduate Studies of
Texas A&M University
in partial fulfillment of the requirements for the degree of
DOCTOR OF PHILOSOPHY
August 2007
Major Subject: Physics
EXTRACTING THE ASYMPTOTIC NORMALIZATION COEFFICIENTS
IN NEUTRON TRANSFER REACTIONS TO DETERMINE THE REACTION
RATES FOR 22Mg(p,γ)23Al AND 17F(p,γ)18Ne
A Dissertation
by
TARIQ ABDALHAMED AL-ABDULLAH
Submitted to the Office of Graduate Studies of
Texas A&M University
in partial fulfillment of the requirements for the degree of
DOCTOR OF PHILOSOPHY
Approved by:
Chair of Committee, Carl A. Gagliardi
Committee Members, Robert E. Tribble
Joseph B. Natowitz
Che-Ming Ko
Head of Department, Edward Fry
August 2007
Major Subject: Physics
iii
ABSTRACT
Extracting the Asymptotic Normalization Coefficients in Neutron Transfer
Reactions to Determine the Reaction Rates for 22Mg(p,γ)23Al and 17F(p,γ)18Ne.
(August 2007)
Tariq Abdalhamed Al-Abdullah, B.S., Yarmouk University;
M.S., Yarmouk University
Chair of Advisory Committee: Dr. Carl A. Gagliardi
The nucleosynthesis of the β+-unstable 18F and 22Na nuclei in oxygen-neon novae is
considered one of the crucial subjects in the field of nuclear astrophysics. They are
produced in thermonuclear runaway processes via radiative proton-capture reactions
andmaybeejectedintothestellarmediumwhenthesuddenoutburstsoftheenvelope
occur. Recent observations with γ-ray telescopes, however, have not detected those
long-lived γ-ray emitters.
Theproblemistostudytheimportanceoftheratesofthe17F(p,γ)18Neand22Mg(p,γ)23Al
reactions that may influence the abundances of 18F and 22Na, respectively. To investi-
gate their productions, an indirect technique has been applied to determine these re-
actionratesatstellarenergiesthroughmeasurementsoftheasymptoticnormalization
coefficients (ANCs) in the mirror nuclear systems. The ANCs for 18O and 23Ne are
obtainedfromtheneutrontransferreactions13C(17O,18O)12Cand13C(22Ne,23Ne)12C
at 12 MeV/nucleon, respectively. The ANC of 13C, which represents the other vertex
in the transfer reactions, has also been measured to be C2 = 2.31±0.08 fm−1.
p
1/2
The differential cross-sections for the reaction 13C(22Ne,23Ne)12C because of transi-
iv
tions from the Jπ = 1− in 13C to the Jπ = 5+ and 1+ states in 23Ne, have been
2 2 2
detected. Optical model parameters for use in the DWBA calculations were obtained
from measurements of the elastic scatterings 22Ne+13C and 22Ne+12C at the same
energy. The extracted ANCs in 23Ne are transposed to their corresponding values in
23Al. The astrophysical S-factor S (0) was determined to be 961±105 eVb. The
1−22
reaction rate calculated from these results shows that the 22Mg(p,γ)23Al reaction may
reduce the production of 22Na in massive novae M ≈ 1.35 M .
(cid:12)
A similar procedure has been followed in studying the 13C(17O,18O)12C reaction.
The ANCs related to the Jπ = (0+,2+,4+,2+) states in 18Ne were determined from
1 1 1 2
their corresponding values in 18O, then used to calculate S (0) = 2.5±0.4 keVb.
1−17
These results show that the reaction rate of 17F(p,γ)18Ne is dominated by the direct
capture to the 2+ and 2+ states at astrophysical energies. The calculated reaction
2 1
rate is considered to be slow, which leads to an increase in the production of 18F in
oxygen-neon novae.
v
To my father and my mother
vi
ACKNOWLEDGMENTS
I would like to express my sincere gratitude to Prof. Carl A. Gagliardi who has been a
very generous and fair advisor. He has provided me with knowledge, encouragement,
and support that assisted me to earn this Ph.D. He gave me the opportunities to
interact with many researchers around the world and build several relationships that
may open the door to improve my career in the future. His bright and creative way
of thinking and addressing several important research issues inspired me all the time.
It was my fortune and pleasure to work under his supervision.
I also would like to convey my special thanks to Prof. R. E. Tribble for his advice,
guidance,andhelp,andProfs. J.NatwoitzandChe-MingKoforservingascommittee
members and for their valuable input to this work.
I would like to express my grateful appreciation to Prof. L. Trache for his patience
and tremendous support throughout my study years. He is a very nice, great, and
gracious person who shared his experience with me and showed me the proper ways
to solve the difficulties in my research. A similar vote of thanks and appreciation
goes to Prof. Florin Carstoiu who has done the theoretical part of the research, and
Dr. G. Tabacaru for his great help.
I would like to extend my thanks to the MDM group, Dr. Y.-W. Lui, Dr. H.
Clark, Dr. Y. Tokimoto, and Mr. X. Chen for their nice cooperation and generous
help in preparing the experimental setup. Special thanks are due to my friends and
collaborators, Dr. C. Fu and Mr. Y. Zhai.
vii
I would like to express my gratitude to the Hashemite University for their sponsorship
and providing me the option to pursue my Ph.D at Texas A&M University. I also
gratefully appreciate the financial support that I received from the Robert A. Welch
Foundation for five consecutive years.
viii
TABLE OF CONTENTS
CHAPTER Page
I INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . 1
A. The Nucleosynthesis of Elements . . . . . . . . . . . . . . 2
B. Thermonuclear Runaways in Oxygen Neon Novae . . . . . 7
C. CNO and HCNO Cycles . . . . . . . . . . . . . . . . . . . 10
D. The Ne-Na Cycle . . . . . . . . . . . . . . . . . . . . . . . 12
E. The Missing Evidence of 22Na . . . . . . . . . . . . . . . . 13
F. The Production of 18F . . . . . . . . . . . . . . . . . . . . 16
G. Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
H. Dissertation Outline . . . . . . . . . . . . . . . . . . . . . 18
II THEORY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
A. Kinematics of Nuclear Reactions . . . . . . . . . . . . . . . 19
B. Reaction Rates . . . . . . . . . . . . . . . . . . . . . . . . 20
1. Nonresonant Reactions . . . . . . . . . . . . . . . . . 21
2. Reaction Through Narrow Resonances . . . . . . . . . 25
C. Direct Measurements vs Indirect Measurements . . . . . . 27
D. Nuclear Reactions and DWBA Model . . . . . . . . . . . . 28
E. The Optical Potential and Elastic Scattering . . . . . . . . 30
F. The Woods-Saxon Potential . . . . . . . . . . . . . . . . . 32
G. The Double Folding Potential . . . . . . . . . . . . . . . . 33
H. Asymptotic Normalization Coefficients (ANC) . . . . . . . 36
I. The ANCs for 22Mg(p,γ)23Al from 13C(22Ne,23Ne)13C . . . 41
J. Extracting the ANC of 18Ne from Its Mirror 18O . . . . . . 46
III EXPERIMENTAL SETUP AND PROCEDURES . . . . . . . . 51
A. The Experiments . . . . . . . . . . . . . . . . . . . . . . . 51
B. The MDM Spectrometer and the Oxford Detector . . . . . 53
C. The Data Acquisition System and Electronics . . . . . . . 60
D. The Preliminary Analysis of the Raw Data . . . . . . . . . 64
E. Oxford Detector Calibrations . . . . . . . . . . . . . . . . 65
1. Position Calibration . . . . . . . . . . . . . . . . . . . 65
2. Angle Calibration . . . . . . . . . . . . . . . . . . . . 68
IV DATA ANALYSIS AND EXTRACTING THE ANCS . . . . . . 73
ix
CHAPTER Page
A. The Differential Cross Sections . . . . . . . . . . . . . . . . 73
B. The 13C(12C,13C)12C Experiment . . . . . . . . . . . . . . 75
1. Elastic Scattering Data . . . . . . . . . . . . . . . . . 76
2. The Woods-Saxon OMPs . . . . . . . . . . . . . . . . 79
3. The Double Folding Potential OMPs . . . . . . . . . . 84
4. The Strong Absorptive Optical Potential . . . . . . . . 86
5. The Semiclassical WKB Approximation . . . . . . . . 90
6. The 13C(12C,13C)12C Exchange Reaction . . . . . . . . 93
7. Extracting the ANC in 13C . . . . . . . . . . . . . . . 98
C. The 13C(22Ne,23Ne)12C Experiment . . . . . . . . . . . . . 102
1. Elastic Scattering of 22Ne+13C and 22Ne+12C . . . . . 102
2. Optical Model Potentials . . . . . . . . . . . . . . . . 103
3. Strong Absorption Profiles . . . . . . . . . . . . . . . 107
4. WKB Approximation . . . . . . . . . . . . . . . . . . 107
5. The Neutron Transfer Reaction . . . . . . . . . . . . . 108
6. Extracting the ANCs . . . . . . . . . . . . . . . . . . 114
D. The 13C(17O,18O)12C Experiment . . . . . . . . . . . . . . 118
1. Elastic Scattering of 17O+13C and 18O+12C . . . . . . 118
2. Optical Model Potentials . . . . . . . . . . . . . . . . 120
3. Strong Absorptive Optical Potentials . . . . . . . . . . 122
4. Semiclassical Approximation . . . . . . . . . . . . . . 123
5. Measuring the Neutron Transfer Reaction . . . . . . . 126
6. Extracting the ANCs . . . . . . . . . . . . . . . . . . 129
V ASTROPHYSICAL REACTION RATES AND CONCLUSIONS 136
A. The 22Mg(p,γ)23Al Reaction Rate . . . . . . . . . . . . . . 136
B. The Reaction Rate for 17F(p,γ)18Ne . . . . . . . . . . . . 142
C. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
VITA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
x
LIST OF TABLES
TABLE Page
I The Γ width for the resonance 3+ state in 18Ne from several
p
experimental studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
II Mirror states in 18Ne and 18O, where all the energies are in keV. . . . 49
III The best fit parameters of the Woods-Saxon optical model poten-
tial obtained from the analysis of the elastic scattering data for
12C+13C. The Coulomb-reduced radius is fixed to r = 1 fm. R
c V
and R are the rms radii of the real and imaginary potentials,
W
respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
IV The best fit optical model parameters for the folding potential
with various effective interactions, χ2, the total nuclear cross sec-
tion reaction, and the rms radii of the real and imaginary parts
and their corresponding volume integrals per pair of interacting
nucleons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
V The parameters of the Woods-Saxon optical model potential ob-
tainedfromtheanalysisoftheelasticscatteringdatafor22Ne+13C
and 22Ne+12C, where r = 1 fm for all potentials. . . . . . . . . . . . 106
c
VI The parameters of the Woods-Saxon optical model potentials ob-
tained from the analysis of the elastic scattering data for 17O+13C
and 18O+12C, where r = 1 fm for all potentials. . . . . . . . . . . . . 121
c
VII The binding energies (B.E.), the proton orbitals, and the ANCs
of the low-lying levels in 18Ne. . . . . . . . . . . . . . . . . . . . . . . 143