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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 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