Nghiên cứu một số phản ứng hạt nhân cần thiết cho thiên văn học

Nghiên cứu một số phản ứng hạt nhân cần thiết cho thiên văn học

VIETNAM ATOMIC ENERGY INSTITUTE

-


    -

Nguyen Ngoc Duy

STUDY OF NUCLEAR REACTIONS

FOR ASTROPHYSICS

Thesis Submitted for the Doctoral Degree of Science

VIETNAM ATOMIC ENERGY INSTITUTE

-


    -

Nguyen Ngoc Duy

STUDY OF NUCLEAR REACTIONS

Hanoi - 2013

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

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

List of Symbols and Abbreviations

torr : unit of pressure (torricelli)

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 26Si and 22Mg(α,α)22Mg scattering 17

1.5.1 Reaction rate of 22Mg(α,p)25Al 18

1.5.2 Distribution of 26Al in the Galaxy 19

1.5.3 Reaction rate of 25Al(p,γ)26Si 20

1.5.4 Nuclear structure of 26Si 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 + αα 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

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 22Mg + α reaction 44

2.2.2 Electronic system 47

2.3 Data Acquisition 49

2.4 Radioactive Ion beam production of 22Mg 50

2.4.1 Estimation of the production reactions 50

2.4.2 22Mg 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 22Mg(α,α)22Mg 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 22Mg(α,α)22Mg reaction 75

3.6 Excited states above the alpha threshold of 26Si 79

3.7 Rate of the stellar reaction 22Mg(α,p)25Al 81

Conclusion and Outlook 89

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

code A-29 Appendix G: Several photos during this work A-30 Appendix H: The proof of the experiment at CRIB facility A-32

List of figures

Figure 1.1 Abundance ratio of isotopes to Silicon (106) in the Solar system 5

Figure 1.2 Potential of 22Mg and 22Mg(α,p)25Al reaction in the hydrongen burning via NeNa-MgAl cycles 19

Figure 1.3 Nuclear level scheme of 26Si and its mirror nucleus, 26Mg 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

Figure 2.15 The yield of radioactive beam 22Mg is as a function of primary

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

contaminants 52 Figure 2.17 The histogram indicates X-position of the particles on the PPACa at

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

∆E-Pad number 59 Figure 3.5 Identification of ejectiles coming from the reaction by the ∆E-E

method 61

Figure 3.6b The measured and calculated energy loss of alpha at 5.795 MeV

by SRIM2010 64

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

Figure 3.14 The excitation function of the alpha scattering cross sections in

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 3.18 Reaction rates were calculated from the experimental cross sections

in this work (solid line) and from the statistical cross sections obtained

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

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

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 (22Mg + α) interaction at Ecm = 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 26Si determined in this work were compared with previous studies in ref [13] and ref [14] 79

Table 3.10 Energy levels of 12C in range of 0 - 15 MeV 80

Table 3.11 Resonance strengths of resonances above alpha-threshold of 26Si 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 22Mg(p,γ)23Al, 22 Mg(α,p)25Al and beta decay 85

Table 3.14 S-factor S(E) at the resonances were determined in this work 88

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

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

code A-29

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

celestial phenomena as well as the experimental technique, as described in

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

section 1.7), which corresponds to the temperature range of Supernovae and

GK because the energy levels are still low The work in ref.[13] included a large

determined by the resonances that were assigned indirectly by using

reaction rate calculation was calculated from the quantum parameters of 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

by the cluster structure [16, 17, 18], the α-cluster structure of resonance states in

MeV as well as the anomalies in the Ne-E problem [20, 21] and the abundance

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

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

here In the last chapter, we describe the analysis and discussion about the

section of the thesis is the conclusion of the present study as well as the future

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

centuries, scientists fortified the ancients’ opinions via experiments in chemical

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 acceleratorTherefore, cosmic ray

observation indicates that we can study

and stars, and nuclear 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 in stars pla

Figure 1.1 Abundance ratio of isotopes to Silicon (10

and neutrons Such kinds of particles are also observed in either nuclear reactions or particle collision in high energy accelerator

cosmic rays are the windows of the universe The cosmological observation indicates that we can study the universe 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 tasks to understand the formation and evolution of objects in the universe is to study the

By investigating the results that were recorded onand the celestial objects, we can predict the course 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 phenomena imply

stars, nucleonsynthesis is still going on process Therefore, study of

n stars plays an important role in discovering

Abundance ratio of isotopes to Silicon (10 6 ) in the

particles are also observed in either nuclear reactions or particle collision in high energy accelerators

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

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

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:

1H +1H →1D e+ + + +υe 0.42MeV,

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

Table 1.1 A summary of pp-chain in Hydrogen burning process

The energy of Hydrogen burning is independent from details of

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,

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]

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

HCNO cycles

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,

following reactions:

In addition, scientists predict that there is a cosmic ray with an energy of 1.275

The

meteorites Such astrophysical phenomena are thought to be skipped by the

M g p γ Al plays an important role in study the age of galaxies

approximately 85% It is worth noting that most of isotopes emitted in the cycles

is an evidence of recent nucleosynthesis on the Galaxy [26] On the other hand,

( )

m

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

ratios in meteorites [29]

1.2.2 Helium burning

In the next stage following the hydrogen burning, the star core is filled with a large number of helium Whilst in outer layers of stars the hydrogen burning still occurs Helium inside the star core is a source of the nucleosynthesis of heavy nuclei Under extreme hot environment (T = 100 MK)

the nucleosynthesis starts consuming helium to produce massive elements,

follows:

8,

number of alphas in this stage of stars, the second phase of the helium burning

reason to explain disappearance of stable isotopes with the mass number of A =

8 in the universe

Investigation of the helium burning process is useful to explain some astrophysical phenomena For example, there is no isotope existing in the universe with a mass number of A = 5 The reaction of protons and helium

result of helium burning, stable light elements in the mass region of A = 6 - 11 are skipped in this process Therefore, the abundance of these isotopes is very small in the universe In addition, the result in ref [31] points out that speed of

important for understanding the helium burning process, there is no experiment

performed because of very short life of the unstable nucleus Therefore, the

16

,

,

above, because of the high Coulomb barrier, alpha capture process beyond the

The energy of a star does not depend on helium burning process but it is subsidiary to the hydrogen burning one Although helium burning process is unimportant for the energy aspect, it plays a crucial role in the synthesis of the

under gravitation the core filled with C and O is gradually attracted and it becomes more condensed Hence, the earliest stage in the growth of a star is formed by a CO core, such as White Dwarf stars

1.2.3 Nucleosynthesis before the appearance of Iron

As mentioned above, the helium is consumed and the ashes of carbon and oxygen exist in the stellar environments at the end of the helium burning stage Materials are gravitationally contracted and the temperature rises up in the core

of stars There are some possible fusion reactions which can occur, such as

12

The first interaction initials the next stage of the nucleonsynthesis because

of the lowest Coulomb barrier From this reaction, the compound nucleus of

24

Mg at high excited states is formed Subsequently, there are not only light

projectiles (α, p, n) but also heavy residuals (20Ne, 23Na, 23Mg, 22Ne, 16O)

isotopes Such kind of those reactions is named carbon burning The conditions

of the temperature, material density and star mass, in this process are 0.5 - 1 GK,

converted into other isotopes via this process

When carbon fuel is consumed at the end of the carbon burning process, the elements in a mass range of A = 12 - 26 are distributed in the environments

In this stage, the star core is contracted to the White Dwarf size and temperature rises up around 1.8 GK which is referred to photodisintegration Hence, it is easy to liberate light particles, such as protons and alphas, into the environment via (γ,p) or (γ,α) reactions In principle, it is theoretically assumed that the next

,

a number of alphas and protons are liberated in the stellar environment, there is

rates This process is implied to the neon burning

The nucleosynthesis evolving up to the neon burning becomes more complicated The series of the reactions in this process often temporarily stop at unstable isotopes which are easy to decay into other particles As a result of the

There is a large number of oxygen in the last scenario of the neon

the lowest Coulomb barrier (12.53 MeV) among the induced elements above, the stage following the neon burning is the oxygen ignition In the process, two

16

The compound nucleus has high excited states because of large mass excess (16.5 MeV) Consequently, there are a lot of light particles and residuals

31

P(p,α) 28 Si, etc… All kinds of these reactions are referred to the oxygen burning The main source of the elements in the mass range of A = 29 - 42 is

are iteratively produced in the process, they have a high abundance (54% and 28%) after the oxygen ignition These isotopes are consumed when the fuel of oxygen and temperature are around 10% and 2.5 GK, respectively [34] The

and neutrinos, to increase the temperature in the core

When oxygen fuel is exhausted at the end of the burning, there are a lot of silicon and sulfur isotopes existing in the stellar environment At the moment, the core shrinks to increase the temperature and density Under the conditions of

should be paid an attention to the large number of liberated gamma ray in the

rays is dominant before the core temperature rises up to the necessary value (1.7

number of light particles such as protons, neutrons and alphas from the decays

of the compound nuclei, which are created by gamma capture Consequently, those light particles participate in the secondary reactions to form massive

elements up to Fe This process is named silicon burning

Silicon fuel is consumed via both two main reaction chains as follows:

isotope of Fe is generated The process is known as the chain of

During the silicon burning, the core loses an amount of energy resisting gravitational contract As a result, the core filled with heavy elements (iron and nickel) is contracted because there is no power to support it after the silicon burning In this case, the core is able to become a neutron star or black hole depending on its mass The outer shells explode and generate a large number of neutrons, which participate in the nucleosynthesis beyond iron

1.2.4 Nucleosynthesis beyond Iron

After formation of the core, the nucleosynthesis via thermonuclear

previous processes participate strongly in the burning processes occurring in outer layers These reactions generate a lot of light particles which are consumed

by heavy particles in the stellar environment to produce heavier elements beyond Fe These processes are divided into three main kinds of nucleosynthesis: s-process, r-process and p-process

Since the neutron has no charge, heavy particle with a mass of A picks it up

staying nearby the drip line in the nuclear chart In the scope of the end of silicon burning, the condition allows beta decays to be the dominant The

neutron capture occurs slowly, so-called s-process (slow neutron-capture

170

into two groups based on mass number A, A < 90 and A > 90 The first group is

one often occurs in shell burning regions of asymptotic giant branch (AGB)

In the s-process, the density of neutrons is quite low The study in ref.[23]

,

,

neutrons for the process

In contrast to the s-process, when neutron density and temperature increase

so-called r-process (rapid neutron-capture process) Therefore, there are a large

number of neutron-rich isotopes to be synthesized There are two reactions,

The r-process produced series neutron-rich nuclei which decay into lighter

isotopes with a mass around 74 are also the candidates for photodisintegration

via (γ,n) to synthesize proton-rich nuclei [39], named gamma process These

nuclei can be formed via neither s-process nor r-process [40] And most of these

construct proton-rich nuclei is proton capture, (p,γ) or (p,n), of seed elements The (p,γ) reaction dominates over the (p,n) one All reactions evolving via both (p,γ), (p,n) and (γ,n) are named p-process At the end of this process most of the

heavy isotopes are distributed in the stellar environment

1.3 Type II supernovae

The formation of a star goes through many burning processes starting from the hydrogen burning up to the silicon burning which leads to creating a core of Iron-Nickel In the core, there is no further fusion reaction generating energy When the nuclear fuel is exhausted, the core is contracted under

and some heavy nuclei can capture free electrons, and the photodisintegration of the heavy nuclei may occurs These nuclear processes provide the pressure to prevent the collapse of stars, so-called degeneracy pressure However, the equilibrium is kept only in a limited time due to the lack of energy generating outward strength As a result, stars tend to contract into the core When the core

broken At that moment, massive stars collapse rapidly together with a violent explosion The core will involve to a neutron star or a black hole if the mass of

the type II supernova

In the supernova scope, ashes from the explosion including all kinds of particles, such as light particles and the elements in the Fe group They participate in most of the nuclear burning processes, as mentioned in the previous sections In addition, because of high temperature and density, the nucleosynthesis involving via CNO and NeNa-MgAl can transform into the rp-

or αp-process The elements heavier than Iron are also synthesized via s-, r- and p-process in the supernova environment

1.4 X-ray burst

The present model describes an X-ray burst as a binary system, in which a low-mass star (the companion) moves around a neutron star, a white dwarf, or a black hole Because of extreme gravitational potential, the neutron star plays a role of a compact object and the companion star tends toward the object Subsequently, material from the companion moves into the neutron star to create

an accretion disk Under extreme temperature and pressure, the material on the surface of the neutron star is burned rapidly The burning processes of the light particles occur violently When the accretion disk ignites explosively to heat the neutron star up to the temperature around 1 GK, an X-ray burst is fluxed toward the universe, so-called X-ray burst Once the burst ejected to the outside of the binary system, another accretion disk is re-created and the emission of X-ray burst is repeated It is worth noting that, in case of White Dwarfs, the burning process extremely occurs with the hydrogen layer, instead of the helium one Most of the X-ray bursts have a time scale of several hours or days At the end

of the stage, all light elements are converted into heavy isotopes and the rich nuclei beyond Fe can be produced [43]

proton-According to the evolution of an X-ray binary system, the nucleosynthesis happening on the surface of the compact object is similar to other processes applied to the young stars, except the time scale Among those processes, the hydrogen burning often occurs via hot CNO or NeNa-MgAl cycles rather than the pp-chains in case of the White Dwarf Any breakout from the cycles can change behaviors of the evolution Therefore, study nucleosynthesis on X-ray

burst gives understanding of the growth of the binary stars

1.5 Motivation of the study of 26 Si and 22 Mg(ααα,ααα) 22

Mg scattering

22

Mg(α,p) 25 Al and 25 Al(p,γ) 26

Si reactions, as well as the existence of 26Al in the

Galaxy The rates of these reactions can be determined via the resonance states

of 26Si This information can be obtained directly via the scattering of

22 Mg(α,α) 22

Mg Furthermore, the data of 26Si above the alpha threshold is expected to give valuable knowledge of the nuclear substructure, especially the

Mg is very essential for

1.5.1 Reaction rate of 22 Mg(ααα,p) 25

Al

During nucleosynthesis in stars, a series of (α,p) reactions set in the explosive hydrogen burning stage under high temperature and high density condition, such as X-ray bursts and type II supernovae One of the major

considerably on the cosmic observation [44] as well as the isotopic anomalies of

22

Ne in the Ne-E problem

22

Mg(β + ) 22 Na, 22 Mg(α,p) 25 Al, and 22 Mg(p,γ) 23 Al Because of the small Q-value

23

Al(γ,p) 22 Mg prevents the significant flow going through the 22 Mg(p,γ) 23 Al

theoretically investigated but it is confusing Otherwise, since the (α,p) reaction has a high rate, it skips the beta decay As results, the (α,p) reaction effects on

22

22

Na was thought to have been observed by the gamma ray but satellites cannot

detect it [45] The waiting-point potential of 22Mg and 22 Mg(α,p) 25

Al reaction in

the hydrogen burning via NeNa-MgAl cycles is pointed out in Fig 1.2

in the energy region above α-threshold are required However, the experimental

determine such data [46, 47] but the energy region was not high enough for the study of the reaction in the temperature region of Supernova and X-ray bursts

was not measured directly

Figure 1.2 Potential of 22 Mg and 22 Mg(α,p) 25 Al reaction in the hydrogen

burning via NeNa-MgAl cycles

1.5.2 Distribution of 26 Al in galaxy

isomer and ground states Since the ground state has a long lifetime, it is a

the galaxies is still under debate The studies in ref [48, 49] point out the major source should be the classical novae Whilst the results in ref [50] suggest that

the main contributor of 26Al comes from type II supernovae In such cases, the

1.5.3 Reaction rate of 25 Al(p,γ γγγ) 26

Si

The 25 Al(p,γ) 26 Si reaction relates to the nucleus 26Alg (T1/2 = 7.2 × 105 years)

in galaxies, which decays to 26Mg at the first excited state releasing gamma ray

of 1.809 MeV In addition, as the nucleosynthesis evolves up to 26Si, similar to

22

Mg, there are three possible ways for 26Si: proton capture, alpha capture and beta decay Under condition of stellar environment, there is a competition between 26 Si(p,γ) 27 P reaction and beta decay of 26Si If the decay is faster than the others, galactic 26Al can be produced However, the states of 26Al, isomer

26

Alm or ground state 26Alg, depend on resonance states of 26Si It should be emphasized that only the ground state 26Alg decays to the first state of 26Mg which can flux the characteristic gamma ray The isomer decays directly to the ground state of 26Mg without gamma emission

Another way for production of the cosmic ray is the proton capture of 25Mg

to produce 26Alg decaying to the first excited state of 26Mg to release the photon

of 1.809 MeV This gamma ray was detected again by the telescope COMPTEL

on NASA’s CGRO spacecraft in 1993 This evidence indicates that there may be two processes for the existence of 26Alg in galaxies which are essentially studied

If the rate of the 25 Al(p,

25

Mg, the excited states of

With details described above,

understand the mechanism of the

gamma ray This astrophysical aspect is supported strongly by

corresponding to stellar conditions

1.5.4 Structure of the

Figure 1.3 Nuclear level scheme of

In nuclear physics, the

the study of the 26Si nuclear

Al(p,γ) 26 Si reaction dominates over the

the excited states of 26Si become crucial in mechanism of

described above, the 25 Al(p,γ) 26 Si reaction is very significant

mechanism of the production of 26Al and the characteristic This astrophysical aspect is supported strongly by

corresponding to stellar conditions

the 26 Si isotope above the ααα-threshold

Nuclear level scheme of 26 Si and its mirror nucleus,

In nuclear physics, the 22 Mg(α,α) 22 Mg reaction also plays a

Si nuclear structure in the energy region above the alpha

reaction dominates over the proton capture of

Si become crucial in mechanism of 26Alg production

reaction is very significant to

Al and the characteristic This astrophysical aspect is supported strongly by the data of 26Si

Si and its mirror nucleus, 26 Mg.

reaction also plays a crucial role in

in the energy region above the alpha

emission threshold, Ethr = 9.164 MeV As mentioned above, the information of

26

Si is very important for both astrophysics and nuclear physics Because of limited data above 9.164 MeV, the cluster structure of 26Si is still uncertain There are several resonance states in the interest energy region obtained in the works in ref.[13, 14] but such states have a large uncertainty because lack of data for the spin-parity assignment

The proton-rich nucleus of 26Si is predicted to have a lot of levels above the alpha threshold, compared to the mirror nucleus 26Mg, over 152 levels, as shown

in Fig 1.3 In addition, it is believed that the α-cluster structure existed in 26Si because of the α-cluster threshold rule [51] The results of cross section calculation based on non-statistical model of Breit-Wigner [52] indicate that the

α-cluster is a possible reason of the large resonance cross section of the

22

Mg(α,p) 25 Al reaction.

1.6 The goals of this work

As discussed above, nuclear physics is a key to study astrophysics In this thesis, we surveyed the fundamental evolution of stars via nuclear reaction chains In which, nuclear reactions important for explanation of the astrophysical phenomena are pointed out, such as α+α, 8Be+α, 25Mg(p,γ) 26 Al,

25

Al(p,γ)26Si, 22 Mg(α,p) 25 Al,…as mentioned in the previous sections In addition,

although the 26Si plays a crucial role both in astrophysics and nuclear physics, there are few data in the energy region above the α-threshold obtained Therefore, we measured resonance states of the 26Si nucleus in the energy region located above 9.164 MeV, corresponding to the stellar temperature of T9 = 0.5 - 2.5 GK in type II Supernovae and X-ray Burst, see Fig.1.3 for details By using these resonance states we determined the rate of the significant stellar reaction

the experimental data of the 26Si nucleus, which relates to the astrophysical aspects, at CRIB [55, 56] This study was submitted and defended by myself in the PAC (Program Advisory Committee) meeting at RIKEN under the proposal

No AVF-NP1006 (Appendix H)

1.7 Stellar reaction rate

In stellar environment, a plasma stage containing various isotopes and electrons exists under thermodynamic equilibrium The velocity of particles follows Maxwellian distribution as described in ref [57]:

( )

3

2 2

In which, E is the value at which the particles have the largest probability

The reaction rate N A σv of a pair of particles, in the unit of cm 3 s -1 , of the reaction described as a+ → +A b B is given by:

where, N a and N A are density of particles a and A in a stellar plasma

environment, respectively σ ( )v is the nuclear reaction cross section

corresponding to velocity v

By using relevant velocity transformation and reduced mass µ of the system, the reaction rate per particle pair can be written in terms of energy by the following equation:

in which, reduced mass is given by a A

1.7.1 Non-resonant reaction rate

As we known, an electric potential exists in the interaction of two charge particles When a nuclear reaction occurs, the nuclei are repelled by the potential named Coulomb barrier In the stellar environment, energy of particles is low, from hundreds keV to few MeV For example, in stars like the Sun (1.5 MK), the energy of particles is in order of keV, whilst in the supernovae (~ 9 GK), energy of nuclei is a few hundred keV These values are lower than the Coulomb barrier However, there is a chance for a nuclear reaction occurs via the quantum tunnel effect [58] This phenomenon depends strongly on penetrability of particles given by the equation [59]:

l

kr P

=

where, k is the wave number, r is the separation between two particles, F l and G l

are regular and irregular solutions of coulomb function According to quantum mechanics, the probability of penetration depends on energy of particles can be obtained by [59]: