thesis submitted for the doctoral degree of science study of nuclear reactions for astrophysics

MINISTRY OF EDUCATION AND TRAINING

MINISTRY OF SCIENCE AND TECHNOLOGY

VIETNAM ATOMIC ENERGY INSTITUTE
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



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Nguyen Ngoc Duy



STUDY OF NUCLEAR REACTIONS
FOR ASTROPHYSICS






Thesis Submitted for
the Doctoral Degree of Science

Hanoi – 2013
MINISTRY OF EDUCATION AND TRAINING

MINISTRY OF SCIENCE AND TECHNOLOGY

VIETNAM ATOMIC ENERGY INSTITUTE











Nguyen Ngoc Duy


STUDY OF NUCLEAR REACTIONS
FOR ASTROPHYSICS

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 - 2013


i-1






Statement of authorship

I hereby certify that the present dissertation is my own research
work under guidance of my supervisors. All the data and results
presented in this dissertation are true and correct. They are based on
the results and conclusions of eleven papers written in co-
authorship with my collaborators. All of them have been published
in peer-review journals and science reports. These results have also
been reported at European Nuclear Physics Conference 2012 and
seminars in Romania, Japan and Vietnam. This approbation process
guarantees that these results have never been published by anyone
else in any other works or articles. Some results from other studies
used to compare and discuss with our new data are noted clearly as
references.


Nguyen Ngoc Duy

i-2



Acknowledgements

First, I would like to thank my supervisors in Vietnam, Ass.Prof. Le Hong
Khiem and Ass.Prof. Vuong Huu Tan. They are my good supervisors since they
are always able to give me kind suggestions and talk with me like a friend. As
the supervisors, they are very kind to give me scientific knowledge. They give
me a chance to go abroad to study at many classes and attend many wonderful
conferences. They teach and direct me carefully to complete this thesis.
Second, I would like to give my deeply thank to my supervisor in Japan,
Prof. Dr. Shigeru Kubono at the University of Tokyo. He is not only a famous

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.

cm : centimeter.
enA : electron-nanoAmpere.
eµA : electron-microAmpere.
FADC : Flash ADC.
Fm : Fermi (10
-15
m).
g : gram.
GK : Giga Kelvin (10
9
K)
GSI : The GSI Helmholtz Centre for Heavy Ion Research.
GEM : Gas-Electron Multiplier.
HDD : Hard disk.
JINA : Joint Institute for Nuclear Astrophysics-Michigan State University
K : temperature scale Kelvin.
k : Boltzman constant.
keV : kilo-electron-Volt.
kHz : kilo Hertz.
kV : kilo-Volt.
M
Θ
: Solar mass.
MeV : Mega-electronVolt.
MeV/u : Mega-electronVolt per nucleon.
Symbols and abbreviation

i-4

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.

T
1/2
: half-life of isotopes.
T
6
: temperature in the scale of 10
6

T
9
: temperature in the scale of 10
9
.
TDC : time-to-digital converter.
Tm : Tesla-meter (Magnetic field).
Symbols and abbreviation

i-5


torr : unit of pressure (torricelli).
TRIUMF : Canada's national laboratory for particle and nuclear physics.
V : Volt.
v : velocity.
VME : Computer control interface for data acquisition of experiment.
α : alpha particle (
4
He).
β : Beta decay.
γ : gamma-ray.

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

1.5. Motivation of the study of
26
Si and
22
Mg(α,α)
22
Mg scattering 17
1.5.1. Reaction rate of
22
Mg(α,p)
25
Al 18
1.5.2. Distribution of
26
Al in the Galaxy 19
1.5.3. Reaction rate of
25
Al(p,γ)
26
Si 20
1.5.4. Nuclear structure of
26
Si above α-threshold 21
1.6. The goals of this work 22
1.7. Stellar reaction rate 23
1.7.1. Non-resonant reaction rate 24
1.7.2. Resonant reaction rate 26
1.7.2.1. Narrow resonance 27
1.7.2.2. Broad resonance 28
1.8. R-matrix method 29

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-7


2.1.4. 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

Mg beam production 51
Chapter 3. Data Analysis and Results. 55
3.1. Energy calibration 56
3.2. Particle Identification 58
3.2.1. RI beam identification 58
3.2.2. Ejectiles identification 59
3.3. Energy loss correction 61
3.4. Data analysis of
22
Mg(α,α)
22
Mg 64
3.4.1. Analysis algorithm 64
3.4.2. Computer codes for data analysis 67
3.4.3. Kinematics solution 68
3.4.4. Energy uncertainty 69
3.4.5. Solid angle 70
3.4.6. Beam events 72
3.4.7. Differential cross section and resonances 72
3.5. R-matrix analysis for
22
Mg(α,α)
22
Mg reaction 75
3.6. Excited states above the alpha threshold of
26
Si 79
3.7. Rate of the stellar reaction
22
Mg(α,p)

25
Al 81
Conclusion and Outlook 89
Contents

i-8


List 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

List of figures

Figure 1.1. Abundance ratio of isotopes to Silicon (10
6
) in the Solar system. 5
Figure 1.2. Potential of
22
Mg and
22
Mg(α,p)
25
Al reaction in the hydrongen
burning via NeNa-MgAl cycles. 19
Figure 1.3. Nuclear level scheme of
26
Si and its mirror nucleus,
26
Mg 21
Figure 1.4. Gamow window is as a result of high energies following Maxwellian
distribution and Coulomb barrier penentrability of particles. 26
Figure 1.5. Resonant reaction is processed via compound mechanism. 26
Figure 1.6. An enhance of the narrow resonance 28
Figure 2.1. Illustration of excitation function measurement by using thick target
in inverse kinematics. 32
Figure 2.2. A plane view of the CRIB separator. 33
Figure 2.3. Design of the cryogenic gas target system at CRIB. 35
Figure 2.4. Side view of the Wien Filter structure 36
Figure 2.5. Structure of the monitor PPAC. 38

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-10


Figure 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

points out that the
22
Mg
12+
can be distinguished easily from other
contaminants. 52
Figure 2.17. The histogram indicates X-position of the particles on the PPACa at
F3 plane. Here, the main contaminants are only primary beam
20
Ne
10+

and
21
Na
11+
. We can distinguish the interested beam by RF signal and
energy at F3. 52
Figure 2.18. The beam was focused on the target at the F3 focal plane. 52
Figure 3.1. Energy spectrum of triple-alpha source was measured by strip No.4.
The inset shows correlation between alpha energy and channel of the
calibration. 56
Figure 3.2. Calibration of high-gain region with triple-alpha source 57
Figure 3.3. Calibration of low-gain region during experiment schedule with the
RI beam including
20
Ne
10+
,
21

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

2
(10%) with different pressures. 63
Figure 3.7a. Fitting curve of energy loss of
22
Mg was measured and calculated
by SRIM2010. 64

i-11


Figure 3.7b. Fitting curve of energy loss of alpha which was measured and
calculated by SRIM2010 64
Figure 3.8. Data channels in each event which is needed to be extracted in the
algorithm 65
Figure 3.9. Gating 22Mg beam based on energy loss distribution in one pad 66
Figure 3.10. Schematic of the kinematic solutions. 68
Figure 3.11. Energy uncertainty as a function of reaction energy at different
angles 70
Figure 3.12. The illustration of solid angle determination in a given angular
range 71
Figure 3.13. The excitation function of the alpha scattering cross sections in
center-of-mass system at θ
lab
= 0 - 5 degrees. 73
Figure 3.14. The excitation function of the alpha scattering cross sections in
center-of-mass system at θ
lab
= 5 - 10 degrees. 73
Figure 3.15. The best fitting curve by R-matrix analysis with J
π

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-12


Photo G.1. Analog signal from readout pad of GEM-MSTPC. A-30

Photo G2. The production target vessel and liquid nitrogen bottle were being
prepared for the experiment at CRIB. A-30
Photo G3. GEM-MSTPC inside F3 chamber A-30
Photo G4. A part of electronic system for DAQ of the experiment. A-31
Photo G5. Preparation for the experiment. A-31

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

experiment 46
Table 3.1. Energies of alpha emitted from the isotopes in the source 56
Table 3.2. The calibrated parameters for the low- and high-gain regions. 57
Table 3.3. The open channels of (
22
Mg + α) interaction at E
cm
= 3.0 MeV 59
Table 3.4. Fitting parameters of measurement and SRIM calculation 63
Table 3.5. Format of the file containing parameters of each event 65
Table 3.6. Relative energies of resonances obtained from the excitation function
of cross sections, which would be used to input into AZURE code 75
Table 3.7. The initial parameters of Eresonances for AZURE 77
Table 3.8. The initial parameters of the entrance channel for AZUR . 77
Table 3.9. The resonant states in
26
Si determined in this work were compared
with previous studies in ref [13] and ref [14]. 79
Table 3.10. Energy levels of
12
C in range of 0 - 15 MeV 80
Table 3.11. Resonance strengths of resonances above alpha-threshold of
26
Si 82
Table 3.12. Reaction rates of resonances calculated from the experimental cross
sections measured in this work 84
Table 3.13. Rates corresponding to speed of reactions of
22
Mg(p,γ)
23

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-14


Table 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-29


Abstract
1

Abstract

Nuclear physics plays an important role in the improvement of the world.
There are many useful applications of the nuclear physics in industry,
agriculture, medicine, etc Besides, nuclear physics is a powerful tool to study
astrophysics. Since all materials are constructed from nuclei, it is possible to
study stars, supernovae and cosmological phenomena by using nuclear reactions
in laboratories on the Earth. Therefore, the study of nuclear reactions is
important not only for physics but also for astrophysics, so-called nuclear
astrophysics. According to the cosmic observation and nuclear mechanisms, the
stellar evolution models including a lot of nuclear processes are supposed [1, 2].
There are many reaction chains during the nucleosynthesis in stars, which
include sensitive reactions at which the evolution can change its behavior to
grow upon other branches.
The implication of nuclear physics for astrophysics was thought to have
been taken place since the late of 1950s from the seminal works of Burbidge,
Burbidge, Fowler, and Hoyle in their famous paper [3] and independently by
Cameron[4]. However, these works were relied on theoretical prediction of
astronomy, astrophysics and nuclear physics. It is necessary to perform
experimental research to confirm the theory. There are many accelerator
facilities with modern spectrometers which were built for measurements of
nuclear astrophysics, such as TRIUMF [5] in Canada, JINA [6] and NSCL [7] in
the United States of America, CRIB [8] in Japan, GSI [9] in Germany, etc…In
Vietnam, a Tandem accelerator located at Hanoi University of Science is being
constructed to use for undergraduate training and study of nuclear astrophysics.
In the rp-process of the nucleosynthesis in Supernovae [10, 11] and X-ray
Bursts [12], the stellar reaction

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
2


section 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

P could not be
used to calculate reaction rate of
22
Mg(
α
,p)
25
Al in the temperature region T
9
>1
GK because the energy levels are still low. The work in ref.[13] included a large
uncertainty above the alpha threshold of
26
Si since the reaction rate was
determined by the resonances that were assigned indirectly by using spin-
parities of the mirror nucleus,
26
Mg. In addition, the S-factor [15] needed for the
reaction rate calculation was calculated from the quantum parameters of the
mirror nucleus. Because the information above the alpha threshold of
26
Si
corresponding to the region T
9
> 0.5 GK seems to be empty up to date, the
calculated rates of the stellar reaction is still uncertain.
In such research scenario, we decided to perform a direct measurement of
the
22
Mg+

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)

25
Al
obtained in this study.
This dissertation is constructed by an overview, three chapters and the
conclusion. The general knowledge of nuclear physics, astrophysics and the
goals of this work are mentioned in the first chapter. The basic theory of the
stellar reaction rate and the R-matrix method used to determine reaction rate is
Abstract
3


also mentioned in this part. The second chapter is the details of the
22
Mg(
α
,
α
)
22
Mg experiment. In this chapter, the methods and the setup of the
experiment are mentioned. The RI beam production of
22
Mg is also reported
here. In the last chapter, we describe the analysis and discussion about the
results. This chapter contains the experimental data of
26
Si and their
astrophysical implications for the stellar reaction
22
Mg(

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

th
and 19
th

centuries, scientists fortified the ancients’ opinions via experiments in chemical
reactions. However, in the years at the end of the 19
th
century, ancient atomic
theory was changed when John Thomson discovered electrons in 1897. He
pointed out that the atom’s structure includes two kinds of smaller particles:
electrons and protons. Fifteen years later, Rutherford found out the atomic
nucleus and in 1932 Chadwick proved the existence of neutrons. The origin of
matter, now, is clearer in consideration.
Nowadays, by using a lot of instruments and high energy accelerators,
scientists discovered deeply inside the atom and the nucleus together with
particles which have a microscopic scale and “special” properties. In addition,
scientists study matter not only on the earth, in laboratories, but also in the
universe by observation and measurement. Astrophysicists demonstrate that the
universe is expanding [22] and there are a lot of cosmic rays including pions,

muons, positrons
and neutrons.
either nuclear reactions or particle collision in high energy accelerator
Therefore,
cosmic ray
observation indicates that we can study
and stars, and n
uclear physics is a key to access
As mentioned above,
and

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

cosmos.
As mentioned above,
matter on stars is also composed
particles via nucleosynthesis.
One of the first task
s to understand the
formation and evolution of objects in the universe is to study the
By investigating
the results that were
recorded on
and the celestial objects,
we can predict the cours
e of their
1
.1
, the abundance ratio of light elements
Solar system is very high. In the mass region above Iron,
abundance
are also set as peaks at
Fe, Ge, Sr, etc…These phenomen
a imply
stars, nucleonsynthesis is still going on process. There
fore, study of
n stars pla
ys
an important role in discovering
Abundance ratio of isotopes to Silicon (10
6
) in
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

Solar system.
Chapter 1. Introduction
6


1.2. Nucleosynthesis on stars
Nucleosynthesis after the Big Bang was proposed in 1930s by two famous
scientists, Bethe and Critchfield, since they discovered thermonuclear reaction
of four Hydrogens to produce a Helium particle. According to their model, the
nucleosynthesis can be divided into four main processes: Hydrogen burning,
Helium burning, element production up to Fe and isotope production beyond Fe.
1.2.1. Hydrogen burning
In the sense of one second after the Big Bang, the earliest nucleus built is
Hydrogen and the universe was filled with a large number of protons. In
addition, there are a lot of protons in the outer layers of stars. Under such
conditions, the fusion of four protons produces helium, so-called Hydrogen
burning.There are three main transformations from protons to Helium in
Hydrogen burning process: proton-proton chain (pp-chain), CNO cycles and
NeNa-MgAl cycle. Each kind of synthesis depends typically on the density,
temperature and catalyst of the stellar environments. For example, the process
occurs in the core of stars with the temperature in a range of 8-55 MK, while the
temperature in shells of AGB stars [23] is around 45 - 100 MK; for star mass M
lower than Solar mass M
Θ
, the pp-chain is dominant and, inversely, the
dominant is the CNO and NeNa-MgAl cycles.
Proton-proton chains (pp-chains)
The synthesis of Helium via pp-chain starts with two first steps:

1 1 2

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
7


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

+
υ)d p(p,e
+
υ)d
d(p,γ)
3
He d(p,γ)
3
He d(p,γ)
3
He
3
He(
3
He,2p)α
3
He(α,γ)
7
Be
3
He(α,γ)
7
Be

7
Be(e
-
,υ)
7
Li

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

often occurs in the stars in which the temperature is approximately 1 GK and the
neutrino deliverance takes place in the stellar environment of 0.5 GK. The
fusion energy in a star prevents collapse due to its gravitation.
CNO cycles
In the scenario of the inner layers of stars, there are heavier elements,
such as Li, Be, B, C, N and O. The stars’ mass grows up (above 1.3 M
Θ
) and the
density of the core becomes higher. At the same sense, temperature of stars rises
up rapidly (above 15 MK) based on the released energy of the previous process.
In these conditions, the dominant of the hydrogen burning process is the CNO
cycle. The intermediaries of Carbon, Nitrogen and Oxygen play roles as
catalysts in this process. The released energy during the cycle is 25.0 MeV,
smaller than the one in the pp-chain. This energy difference is caused by the
energy lost via neutrino emission [24].
Chapter 1. Introduction
8


The CNO cycles are very sensitive with temperature. The cycles are
divided into two cycles based on the temperature of stars, namely Cold CNO
(CNO) and Hot CNO (HCNO). The CNO cycles mainly occur during the
temperature lower than 100 MK, whereas the HCNO ones dominate in the range
of 100 - 400 MK. There are four types of CNO and three types of HCNO as
listed in table 1.2.

Table 1.2. List of main reaction chains of hydrogen burning in
CNO and Hot CNO cycles
CNO cycles
CNO-I

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,α)
14
N
CNO-III
15
N(p,γ)
16
O(p,γ)
17
F(β
+
ν)
17
O(p,γ)
18
F(β
+
ν)
18
O(p,α)
15
N
CNO-IV
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,α)
12
C

HCNO-II
15
O(β
+
ν)
15
N(p,γ)
16
O(p,γ)
17
F(β
+
ν)
17
O(p,γ)
18
F(p,α)
15
O

HCNO-III
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
O


NeNa-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

(
)
(
)
(
)
(
)
(
)
(
)
20 21 21 22 22 23 20
, , , , .
Ne p Na Ne p Na Ne p Na p Ne
γ β υ γ β υ γ α
+ +

24 25 25 26 27 27 24
( , ) ( ) ( , ) ( , ) ( ) ( , ) .
Mg p Al Mg p Al p Si Al p Mg
γ β υ γ γ β υ α
+ +

24 25 25 26 26 27 24
( , ) ( ) ( , ) ( ) ( , ) ( , ) .
Mg p Al Mg p Al Mg p Al p Mg
γ β υ γ β υ γ α
+ +

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

breakout reaction
22
Mg(
α
,p)
25
Al. The NeNa-MgAl can bridge to other chains by
22
Mg(
α
,p)
25
Al if this reaction has a high rate. For the two last chains, the proton
capture
25 26
( , )
Mg p Al
γ
plays an important role in study the age of galaxies

since it produces isotope of
26
Al in two states, isomer (
26
m
Al
, half life T
1/2
= 6.35
s) and ground state (T

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

a main role in the energy source of stars. However, they are important not only
in production of seed isotopes in the isotope group of
20
Ne –
27
Al but also in
explanation of Ne-E problem and anomalies of the
26
Mg/
24
Mg and
26
Al/
27
Al
ratios in meteorites [29].