Study of nuclear reaction for astrophysics

MINISTRY OF EDUCATION AND TRAINING MINISTRY OF SCIENCE AND TECHNOLOGY

VIETNAM ATOMIC ENERGY INSTITUTE

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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

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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

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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

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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.

Symbols and abbreviation

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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).

Symbols and abbreviation

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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.

Contents

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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

Contents

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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

Contents

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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

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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

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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 20Ne 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

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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

Figure 3.16. Reaction rates of the stellar reaction 22Mg(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

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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

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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,

22Mg(α,p)25Al and beta decay. ............................................................ 85

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