Thesis Submitted for the Doctoral Degree of Science: Study of nuclear reactions for astrophysics

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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 matrix method used to determine reaction rate is also mentioned in this part.

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Nội dung Text: 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 ------ ------ 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
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-1
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. i-2
Symbols and abbreviation 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 (109 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. MΘ : Solar mass. MeV : Mega-electronVolt. MeV/u : Mega-electronVolt per nucleon. i-3
Symbols and abbreviation MHz : Mega-Hertz. MK : Mega-Kelvin (106 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. T1/2 : half-life of isotopes. T6 : temperature in the scale of 106 T9 : temperature in the scale of 109. TDC : time-to-digital converter. Tm : Tesla-meter (Magnetic field). i-4
Symbols and abbreviation 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 (4He). 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. i-5
Contents 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 22Mg + 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 i-6
Contents 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 i-7
Contents 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 24Mg ................................................. A-28 Appendix F: The rate of the 22Mg+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-8
List of figures Figure 1.1. Abundance ratio of isotopes to Silicon (106) in the Solar system. ..... 5 22 22 Figure 1.2. Potential of Mg and Mg(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 i-9
Figure 2.15. The yield of radioactive beam 22Mg is as a function of primary beam current of 20Ne. The error bar (7%) indicate the fluctuation of intensity of 22Mg due to small instability of 20Ne 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 22Mg12+ 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 20Ne10+ and 21Na11+. 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 20Ne10+, 21Na11+ and 22Mg12+. ................................ 58 Figure 3.4. Bragg curves of 22Mg, 21Na and 20 Ne were measured by the active target detector. The 22Mg12+ 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 22Mg at 18.48 MeV after passing through He+CO2 (10%) with different pressures. ......... 63 Figure 3.6b. The measured and calculated energy loss of alpha at 5.795 MeV after passing through He+CO2 (10%) with different pressures. ......... 63 Figure 3.7a. Fitting curve of energy loss of 22Mg was measured and calculated by SRIM2010. ..................................................................................... 64 i-10
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 θlab = 0 - 5 degrees. ..................................... 73 Figure 3.14. The excitation function of the alpha scattering cross sections in center-of-mass system at θlab = 5 - 10 degrees. ................................... 73 Figure 3.15. The best fitting curve by R-matrix analysis with Jπ of the first and the last resonances are 2+ and 0+, respectively ................................... 78 22 Figure 3.16. Reaction rates of the stellar reaction Mg(α,p)25Al 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 22Mg(p,γ)23Al 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-SMOKERWEB (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-11
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-12
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 22 Table 3.13. Rates corresponding to speed of reactions of Mg(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 i-13
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 22Mg 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 24Mg. ........................................................ A-28 22 Table F. The rate of the Mg+α interaction calculated by NON-SMOKER code ............................................................................................... A-29 i-14
Abstract 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 22Mg(α,p)25Al is a significant link. This reaction is very meaningful because it relates to not only the 26Si structure but also the celestial phenomena as well as the experimental technique, as described in 1
Abstract 22 section 1.5. There were two efforts to study the rate of Mg(α,p)25Al reaction [13, 14]. However, the results are still uncertain since the observed data relied on the beta decays of 26P 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 26Si obtained by 26P could not be used to calculate reaction rate of 22Mg(α,p)25Al in the temperature region T9 >1 GK because the energy levels are still low. The work in ref.[13] included a large 26 uncertainty above the alpha threshold of Si since the reaction rate was determined by the resonances that were assigned indirectly by using spin- parities of the mirror nucleus, 26Mg. In addition, the S-factor [15] needed for the reaction rate calculation was calculated from the quantum parameters of the 26 mirror nucleus. Because the information above the alpha threshold of Si corresponding to the region T9 > 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 22 the Mg+α reaction by using CRIB facility located at RIKEN, Japan. The reaction energy corresponded to the stellar condition of T9 > 0.5 GK. This work 26 investigated the Si structure above the alpha threshold and the rate of the stellar reaction 22Mg(α,p)25Al. Because the resonances of nuclei may be caused by the cluster structure [16, 17, 18], the α-cluster structure of resonance states in the 26Si nucleus was evaluated. For astrophysical aspects, the potential waiting point of 22Mg 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 22 22 of Na in meteorites could be revealed based on the rate of Mg(α,p)25Al 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 2
Abstract also mentioned in this part. The second chapter is the details of the 22 Mg(α,α)22Mg experiment. In this chapter, the methods and the setup of the 22 experiment are mentioned. The RI beam production of Mg is also reported here. In the last chapter, we describe the analysis and discussion about the 26 results. This chapter contains the experimental data of Si and their 22 astrophysical implications for the stellar reaction Mg(α,p)25Al. 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 22Mg+α interaction. 3
Chapter 1. Introduction 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 18th and 19th centuries, scientists fortified the ancients’ opinions via experiments in chemical reactions. However, in the years at the end of the 19th 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, 4