MINISTRY OF EDUCATION AND TRAINING

MINISTRY OF SCIENCE AND TECHNOLOGY

VIETNAM ATOMIC ENERGY INSTITUTE






 Nguyen Ngoc Duy
STUDY OF NUCLEAR REACTIONS
FOR ASTROPHYSICS
Thesis Submitted for
the Doctoral Degree of Science

Subject: Atomic and Nuclear Physics.
Code number: 62 44 05 01 Thesis Submitted for
the Doctoral Degree of Science
Thesis Supervisors
1. Ass.Prof. Le Hong Khiem
2. Ass.Prof. Vuong Huu Tan Hanoi - 2013i-1
Statement of authorship
scientist but also a very kind supervisor. He always very nicely gives me clear
and patient guidance that helps me to conduct my research. He supports me in
science as well as finance to study and perform the experiment of this work
during I stay in Japan.
I also owe my thanks to Dr. Pham Dinh Khang, Ass.Prof. Nguyen Nhi
Dien and Dr. Phu Chi Hoa who give me many meaningful advices and help me
to finish the PhD course. Thanks to their kind encouragement and organization
for the thesis committee.
It would be inappropriate not to mention Dr. Nguyen Xuan Hai, Dr. Dam
Nguyen Binh and Mr. Nguyen Duy Ly for their kind discussion. I must
emphasize their readiness to share their knowledge and experience.
I would also like to thank all of our collaborators at the CRIB facility for
their help to perform my experiment successfully. I especially thank Dr.
Hidetoshi Yamaguchi and David Miles Kahl at CNS who helped me with their
best efforts during the beam time.
Last but not least, I thank my family and my friends for supporting me all
the time. This thesis is as a present sent to my lovely departed father. Although
he was very sore because of cancer, during his hospital time, he encouraged me
a lot.
Symbols and abbreviation

i-3
List of Symbols and Abbreviations ADC : Analoge – Digital Converter.
CAMAC : Computer Automated Measurement and Control.

MHz : Mega-Hertz.
MK : Mega-Kelvin (10
6
K)
mm : millimeter.
msr : mili-steradian.
mV : mili-Volt.
n : neutron or the number of events.
nm : nano-meter (10
-9
m)
ns : nano-second (10
-9
s)
NSCL : National Superconducting Cyclotron Laboratory (Michigan USA)
p : proton.
pC : pico-Coulomb (10
-12
C).
ps : pico-second (10
-12
s).
PID : Particle Identification.
q : charge of particles.
RF : Radio Frequency of accelerator.
RI : Radioactive Ion.
s : second.
sccm : Standard Cubic Centimeters per Minute.
sr : steradian (solid angle).
T : temperature or Tesla.

µ : reduce mass of nuclear system.
µm : micrometer = 10
-6
m.
µs : microsecond = 10
-6
s.
ν : neutrino.
π : constant = 3.141516(15).
^ : AND logic.
yrs : years.
amu : atomic mass unit.
Contents

i-6
CONTENTS

Overview 1
Chapter 1. Introduction 4
1.1. Origin of matter in the universe 4
1.2. Nucleosynthesis on stars 6
1.2.1. Hydrogen burning 6
1.2.2. Helium burning 10
1.2.3. Nucleosynthesis involving up to Fe 11
1.2.4. Nucleosynthesis involving beyond Fe 14
1.3. Type II Supernovae 16
1.4. X-ray Bursts 17

Chaper 2. Experimental measurement of
22
Mg + α
αα
α reaction 31
2.1. Experimental method 31
2.1.1. Estimation of the interest energy region 31
2.1.2. Thick target in inverse kinematic mechanism 32
2.1.3. CRIB spectrometer 33
Contents

i-72.1.4. Particle detector 37
2.1.4.1. Beam monitor PPAC 37
2.1.4.2. Design of the silicon-detector telescopes 39
2.1.4.3. Design the active-gas-target detector GEM-MSTPC 41
2.2. Experimental setup 44
2.2.1. Setup of
22
Mg + α reaction 44
2.2.2. Electronic system 47
2.3. Data Acquisition 49
2.4. Radioactive Ion beam production of
22
Mg 50
2.4.1. Estimation of the production reactions 50
2.4.2.
22

25
Al 81
Conclusion and Outlook 89
Contents

i-8List of Publications 92
Bibliography 94
Appendix
Appendix A: Energy calibration and Energy loss correction A-1
Appendix B: Several main computer codes which were used for data
analysis A-3
Appendix C: Geometry solution for scattering angles A-23
Appendix D: Transformation between the Laboratory and the Center-of-Mass
Frame A-26
Appendix E: A part of energy levels of
24
Mg A-28
Appendix F: The rate of the
22
Mg+α interaction calculated by NON-SMOKER
code A-29
Appendix G: Several photos during this work A-30
Appendix H: The proof of the experiment at CRIB facility A-32 i-9


Figure 2.6. An image of SSD with 16 strips is similar to the 8-strips SSD. 39
Figure 2.7. Schematic of downstream telescopes (a) and side telescopes (b). 40
Figure 2.8. Main structure of the active-target detector GEM-MSTPC 42
Figure 2.9. Schematic of proportional counter region with GEM foils and read-
out pad structure. 42
Figure 2.10. Setup of the experiment using GEM-MSTPC 45
Figure 2.11. Top view of detector system inside the reaction chamber 45
Figure 2.12. A diagram of electronic system for the experiment. 47
Figure 2.13. The diagram of electronic system for trigger and DAQ. The TDC
and ADC were installed in VME and CAMAC, while the Flash ADCs
COPPER were mounted in VME 48
Figure 2.14. Timing chart of the coincident gate for out-put trigger. 49

i-10Figure 2.15. The yield of radioactive beam
22
Mg is as a function of primary
beam current of
20
Ne. The error bar (7%) indicate the fluctuation of
intensity of
22
Mg due to small instability of
20
Ne from the ion source
HyperECR 51
Figure 2.16. The plot shows particle identification at F2 based on time of flight
(ToF) and energy E from measured data (a) and simulation (b). It

Na
11+
and
22
Mg
12+
. 58
Figure 3.4. Bragg curves of
22
Mg,
21
Na and
20
Ne were measured by the active
target detector. The
22
Mg
12+
was gated by using the windows of ∆E-
Pad number 59
Figure 3.5. Identification of ejectiles coming from the reaction by the ∆E-E
method 61
Figure 3.6a. The measured and calculated energy loss of
22
Mg at 18.48 MeV
after passing through He+CO
2
(10%) with different pressures. 63
Figure 3.6b. The measured and calculated energy loss of alpha at 5.795 MeV
after passing through He+CO

of the first and
the last resonances are 2
+
and 0
+
, respectively 78
Figure 3.16. Reaction rates of the stellar reaction
22
Mg(α,p)
25
Al calculated by
resonant states in 26Si from the alpha scattering measurement in the
energy region corresponding to stellar temperature of 1.0 - 2.5 GK.
The result which is out of the temperature range is extrapolation. 83
Figure 3.17. Reaction rates for
22
Mg(p,γ)
23
Al reported in ref [105] 83
Figure 3.18. Reaction rates were calculated from the experimental cross sections
in this work (solid line) and from the statistical cross sections obtained
by NON-SMOKER
WEB
(dash line) 86
Figure 3.19. S-factor as a function of energy 87
Figure C.1. Geomertry of the detector setup A-24
Figure C.2. A sketch of SSD telescopes including segments which are used to
calculate the scattering angles. A-24
Figure D.1. The relationship between laboratory and center-of-mass frames A-26


i-13
List of tables

Table 1.1. A summary of pp-chain in Hydrogen burning process 7
Table 1.2. List of main reaction chains of hydrogen burning in CNO and Hot
CNO cycles 8
Table 2.1. Parameters of Gamow windows in the interest energy region 31
Table 2.2. Details of CRIB design 34
Table 2.3. Operating bias which were Alied to the GEM-MSTPC during the

Al,
22
Mg(α,p)
25
Al and beta decay. 85
Table 3.14. S-factor S(E) at the resonances were determined in this work 88

i-14Table A1. The parameters of the energy calibration for SSD strips. A-1
Table A2.1. Energy loss of alpha measured and calculated by SRIM2010 was
used for the correction. A-2
Table A2.2. Energy loss of
22
Mg measured and calculated by SRIM2010 was
used for the correction. A-2
Table C. A part of results of geometry calculation with the reaction points in the
middle of active target (pad number 23, 24). A-25
Table E. Apart of energy levels of
24
Mg. A-28
Table F. The rate of the
22
Mg+α interaction calculated by NON-SMOKER
code A-29Abstract
1

22
Mg(
α
,p)
25
Al is a significant link. This reaction
is very meaningful because it relates to not only the
26
Si structure but also the
celestial phenomena as well as the experimental technique, as described in
Abstract
2section 1.5. There were two efforts to study the rate of
22
Mg(
α
,p)
25
Al reaction
[13, 14]. However, the results are still uncertain since the observed data relied
on the beta decays of
26
P or (p,t) reaction are far from the Gamow window (see
section 1.7), which corresponds to the temperature range of Supernovae and X-
ray Burst environments. The excited states of
26
Si obtained by
26

α
reaction by using CRIB facility located at RIKEN, Japan. The
reaction energy corresponded to the stellar condition of T
9
> 0.5 GK. This work
investigated the
26
Si structure above the alpha threshold and the rate of the
stellar reaction
22
Mg(
α
,p)
25
Al. Because the resonances of nuclei may be caused
by the cluster structure [16, 17, 18], the α-cluster structure of resonance states in
the
26
Si nucleus was evaluated. For astrophysical aspects, the potential waiting
point of
22
Mg in the nucleosynthesis [19], the existence of the gamma ray 1.275
MeV as well as the anomalies in the Ne-E problem [20, 21] and the abundance
of
22
Na in meteorites could be revealed based on the rate of
22
Mg(
α
,p)

α
,p)
25
Al. The final
section of the thesis is the conclusion of the present study as well as the future
plan to continue doing research on the
22
Mg+α interaction. Chapter 1. Introduction
4
Chapter 1. Introduction

1.1. Origin of matter in universe
The origin of matter is still an interest question of human history. There
were some hypotheses in the ancient world. According to Eastern philosophy,
the matter was built from five basic elements: metal (gold), wood, water, fire
and earth. Whereas, ancient Greece thought that all matters were created from
air, water, fire and earth. The ideas prove that people tried to explain the origin
of matter in the universe. And it is worth noting that in order to discover the
universe it is necessary to understand the origin of matter. More than 2400 years
ago, Democritus, a Greek philosopher, reasoned that a matter could not be
divided forever, it has a limit piece named “atomos”. His idea was similar to
another one supposed by Paramu, an Indian philosopher. They all thought that
matter, including planets and stars, should be constructed by a lot of small
pieces (atomos) by the time via different mechanisms. During the 18

particles via nucleosynthesis.
formation and evolution of objects in the universe is to study the
isotopes in nature.
By investigating
the planets
and the celestial objects,
As can be seen in Fig.
1
Solar system is very high. In the mass region above Iron,
are also set as peaks at
stars, nucleonsynthesis is still going on process. There
nucleosynthesis i
n stars pla

Figure 1.1.
Abundance ratio of isotopes to Silicon (10
5

and neutrons.
Such kinds of
particles are also observed in
either nuclear reactions or particle collision in high energy accelerator
cosmic ray
s are the windows of the
universe. The cosmological
observation indicates that we can study
the univ
erse on the Earth, from
uclear physics is a key to access
to the

Chapter 1. Introduction
particles are also observed in
either nuclear reactions or particle collision in high energy accelerator
s.
universe. The cosmological
erse on the Earth, from
the Sun
cosmos.

matter on stars is also composed
to atoms, nucleus
s to understand the
formation and evolution of objects in the universe is to study the
abundance of
recorded on
the Earth,
e of their
evolution.
, the abundance ratio of light elements
to Silicon in the
abundance
of isotopes
a imply
that in the
fore, study of
the
an important role in discovering
the universe.

the

1 1 1
0.42 ,
e
H H D e MeV
υ
+
+ → + + +2 1 3
1 1 2
5.49 .
D H He MeV
γ
+ → + +

The chain is continued with one of three possible transformations in the latter
sense, which are named pp1, pp2 and pp3. Depending on the stellar temperature,
the second step bridges to other branches as shown in table 1.1. The probability
of pp1, pp2 and pp3 are 86%, 14% and 0.11% in the Sun, respectively.

Chapter 1. Introduction
7Table 1.1. A summary of pp-chain in Hydrogen burning process.
pp1 chain pp2 chain pp3chain
p(p,e
+
υ)d p(p,e

7
Be(p,γ)
8
B

7
Li(p,α)α
8
B(β
+
υ)
8
Be

8
Be(α)α

The energy of Hydrogen burning is independent from details of
conversion. This process releases an energy of Q = 4m
H
- m
He
= 26.731 MeV,
where m
H
and m
He
are masses of proton and Helium, respectively. Depending on
the temperature of a star, energy released in such synthesis is distributed to
space outside stars into two main forms: photons and neutrinos. Photon emission

12
C(p,γ)
13
N(β
+
ν)
13
C(p,γ)
14
N(p,γ)
15
O(β
+
ν)
15
N(p,α)
12
C
CNO-II
14
N(p,γ)
15
O(β
+
ν)
15
N(p,γ)
16
O(p,γ)
17

F(β
+
ν)
17
O(p,γ)
18
F(β
+
ν)
18
O(p,γ)
19
F(p,α)
16
O
HCNO cycles
HCNO-I
12
C(p,γ)
13
N(p,γ)
14
O(β
+
ν)
14
N(p,γ)
15
O(β
+

ν)
15
N(p,γ)
16
O(p,γ)
17
F(p,γ)
18
Ne(β
+
ν)
18
F(p,α)
15
ONeNa-MgAl cycles
As a result of pp-chain and CNO cycles, the temperature and density of the
core are risen up quickly in stars. In this stage, some Ne and Mg isotopes are
synthesized. At the temperature of 30 MK, the hydrogen burning can continue
with these elements via NeNa - MgAl cycles. This phenomenon happens in most
of the second or third generation stars. Typically, the reaction chains use Ne, Na,
Mg and Al to produce a
4
He from four protons. The cycles are known as
following reactions:
Chapter 1. Introduction
9



In the first chain, the
(
)
22 23
,
Ne p Na
γ
reaction is significant to understand
astrophysical phenomenon of
23
Na abundance in the universe. It should be
emphasized that the nucleus
23
Na is the only stable isotope of sodium elements.
In addition, scientists predict that there is a cosmic ray with an energy of 1.275
MeV [25] existing in the cosmos from the product of
(
)
22 22
Na Ne
β υ
+
. The beta-
decay is also thought to be a reason for the different ratios of
22
Ne/
20
Ne in
meteorites. Such astrophysical phenomena are thought to be skipped by the

1/2
= 10
6
yrs). The probability of the ground state is
approximately 85%. It is worth noting that most of isotopes emitted in the cycles
have a short lifetime, except
26
Al at the ground state. Therefore, the nucleus
26
Al
is an evidence of recent nucleosynthesis on the Galaxy [26]. On the other hand,
the beta-decay via
26 26
( )
m
Al Mg
β υ
+
is not related to the gamma-ray of 1.809
MeV which is emitted from the excited nucleus
26
Mg [27]. This gamma line
comes from the path of beta-decay of
26
Al
g
and it was first detected by the
HEAO-3 satellite in 1982 [28]. The observation of this gamma line indicates
that the nucleosynthesis in stars certainly going through the MgAl cycles.
Because of the high Coulomb barrier, the NeNa-MgAl cycles does not play