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Isospin Symmetry Breaking in Sd Shell Nuclei

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Isospin Symmetry Breaking in Sd Shell Nuclei Num´ero d’ordre: 4446 TH ESE` pr´esent´ee `a L’Université Bordeaux I Ecole Doctorale des Sciences Physiques et de l’Ing enieure´ par Yek Wah LAM (Yi Hua LAM 藍藍藍乙乙乙華華華) Pour obtenir le grade de DOCTEUR Sp ecialit´ e´ Astrophysique, Plasmas, Nucl eaire´ Isospin Symmetry Breaking in sd Shell Nuclei Soutenue le 13 decembre 2011 tel-00777498, version 1 - 17 Jan 2013 Apr`es avis de: M. Piet Van ISACKER DR, CEA, GANIL Rapporteur externe M. Frederic NOWACKI DR, CNRS, IHPC, Strasbourg Rapporteur externe Devant la commission d’examen form´ee de: M. Bertram BLANK DR, CNRS, CEN Bordeaux-Gradignan Pr´esident M. Michael BENDER DR, CNRS, CEN Bordeaux-Gradignan Directeur de th`ese M. Van Giai NGUYEN DR, CNRS, IPN, Orsay Examinateurs M. Piet Van ISACKER DR, CEA, GANIL M. Frederic NOWACKI DR, CNRS, IHPC, Strasbourg Mme. Nadezda SMIRNOVA Maˆıtre de Conf´erences, Universit´eBordeaux I 2011 CENBG Dedicated to my beloved wife Mei Chee Chan ഋऍ޲ , and my dear son Yu Xuan Lam ᙔᒕ侍 , without whose consistent encouragement and total sacrifice, this thesis would have never been touched by the light. And dedicated to the late Peik Ching Ho Ֆᅸమ , my grandma who loved me most, tel-00777498, version 1 - 17 Jan 2013 and lost her beloved hubby during WW2, and rebuilt our family determinantly. 2 Acknowledgments As a mechanical engineering graduate, I opted not to follow the ordinary trend of graduates. Most of them have a rather easy life with high income, whereas I have chosen a different path of life – pursuing theoretical physics career – the so-called abnormal path in ordinary Malaysians perspective. And I have to be ready that there is no guarantee for the future... No matter how many impedences and how challenging the path is, I keep my faith on Him and trust His guidance. I thank God for His grace and faithful love. Throughout the moment I pursue the PhD thesis, He has sent many angels to me, like Patrick AURENCHE (LAPTH, Annecy) whom I knew since 2003, and Vincent BRETON (LPC, Clermont-Ferrand) known in 2007. I appreciate their consistent concerns about my stay and research work in France, and Vincent’s prayers. Moreover, I am deeply indebted to Nadya A. SMIRNOVA, who is my sister in Christ, and is my sister in life and nuclear physics. Special thank to her, Etienne CAURIER, and Frederic NOWACKI for introducing me to nuclear shell model; and Piet Van Isacker for fruitful discussion in dynamical symmetry breaking and Wigner’s supermultiplet theory. Meanwhile, I would like to thank Michael BENDER, who is the mean-field approach expert, and seems to be my big brother, who fight for me with the bureaucratics. He works together with Philippe tel-00777498, version 1 - 17 Jan 2013 QUENTIN, Bernard HASS, and Arnaud GAUFFIER for securing financial support from the embassy of France in Malaysia. Besides, I thank Bertram BLANK and J´erˆome GIOVINAZZO for the calculation of exper- imental uncertainties, as well as fruitful discussions about isospin-forbidden proton emissions; and Johnny PINSON and Catherine SEZNEC for I.T. support. I thank Benoit AVEC in sharing his knowledge of mean-field approach, and Julien LE BLOAS for his workstation, hence I managed to push many results during the last stage of PhD; and Patricia GABINSKI for her support to file a lawsuit to la CAF about their discriminate decision on my beloved son. Finally, I won the lawsuit. Special thanks for the juniors, who work in other laboratories, have helped me to obtain some very important articles. They are Casey CHEW Soo Hoon ( 周淑芬) (TU Munich, Germany), Marc CHEONG (Monash Univ., Australia), and HOANG Ngoc Duy (Lund Univ., Sweden). 3 I would like to thank pastor Alan DAVEY, who accompanied me to apply the Domofrance apartment; and sister Nadya, who volunteered herself to be the apartment guarantor. There were more than 20000 applicants in the waiting list. With His blessing, I came across with Matthias LAMBERT, the town-council housing agent, who helped me to secure an apartment within two weeks. I moved in to the apartment exactly on the day I moved out from the student hostel. No extra money was needed as it was not a prior moving in to the apartment. Besides, I really appreciate the only British pastoral team in Bordeaux, i.e., Alan DAVEY and family, Benjamin GRIFFIN (who brought a firm and heavy desktop alone upto 17th floor to me) and family, Fiona STEWARD for all furnitures provided for us and for the Chinese Christian Fellowship (CCF). I deeply appreciate brothers and sisters in Christ from CCF, who are our comrades in Christ in every evangelistic movements, who fervently prays for us in many difficulties and great times here, who helped us to negotiate with the Pr´efecture to extend our stay, who are playmates of my beloved son, who shared life experiences with us, who walked with us during my wife’s miscarriage and the demise of my grandma, who have experienced His grace and kept faith on Him. They are Andy CHEUNG Kin Wah ( 張建華), his beloved wife Kitty and daughter Sharon CHEUNG Hoi Lam ( 張凱琳), ZHANG Sen ( 張森) and TU Yi Fei ( 涂軼菲), WU Ying (吳瑩), WANG Jin Long ( 王金龍), YAN Shi Bo ( 閻士博), FU Hua ( 付華), WANG Yi Yang (王暘), Dr. WANG Xin Nin ( 王欣寧), LIN Yin ( 林殷), BAI Yu ( 白玉), ZHU Yue Hong ( 朱 月虹), Annie CHENG ( 程哲), Helene CHEN ( 陳薈茹), WAN Zhe ( 萬吉吉), SHI Jia Wei ( 石 嘉偉 楊偉雲 馬成剛 趙欣 YANG Wei Yun ( ), MA Cheng Gang ( ), ZHAO Xin ( ), Franc ֒ois LIU ,( (劉鴻輝), WANG Yuan Jie ( 王元捷), Fabrice CHANG Regine ( 張和君), Ammie ZHAO ( 趙張 始初), and 黃俊生, 徐榮心, etc... Throughout the PhD thesis, the funding from the France embassy in Malaysia was not stable. Special thanks to brothers and sisters in Christ from Malaysia for their consistent love, prayers and offers of financial support, they are June CHEN Siew Jung ( 曾秀蓉), TAN Chong Wei ( 陳仲偉), LIM Wai Kheong ( 林偉強) and Grace YAP ( 葉珍珠), LONG Yin Wah ( 龍豔 tel-00777498, version 1 - 17 Jan 2013 華), LOKE Chee Hoo ( 陸志豪), WONG Hiong Kwan ( 黃向群) and family, Cillia YONG ( 楊 鳳展), Theresa LAU Wai Hing and family, 黃詩豪 and family, HONG Yee Min, YONG Nyuk Fue ( 楊玉慧) and family, Amy WONG ( 黃新嵐), Hii Hee Ling ( 許慧玲) and family, pastor LAI Kam Poh ( 黎錦波) and family, 賴長桂, 馬姐妹, 陳秀苟, 英秀霞, 劉福坤, 歐麗珍, 陳東蓮, Amy, 符興財 and 羅桂珠, 黃麗珍, 張耀玲 and family. Thanks to DU Ling Guo ( 杜靈國) and ZHANG Li Na ( 張麗娜) whom we have shared many good moments in Bordeaux, and thanks to post-doctorates, REN Yong Xiang ( 任勇 祥) and LIANG Li Yuan ( 梁麗媛), and YIN Cong Ling ( 尹從嶺), who pass down very useful information to me and concern about my financial status in France. And thanks to my supportive good friends: EU Theng Hong ( 尤騰豐), KHOO Eng Yow ( 邱 涌耀) and family, EU Choon Leng ( 尤俊龍) and family, KOH Peng Hooi ( 高炳輝) and family, LIM Lee San ( 林麗珊), WONG Kit Ping ( 黃潔冰) and family, TAN Hui Li ( 陳慧麗), LEE Wei Ching ( 李惠婧), etc. for their consistent spiritual and offers of monetary supports. 4 We would like to thank aunty 周彩蓮, my mom-in-law 周彩金, cousins-in-law 簡榮華 and family, 簡榮渭 and family, 簡麗蓉 and family, for their fervent prayers and offers of financial support for our family. Very special thank to my beloved wife and my little son, and my young sister LY Kim Quyen ( 李金娟), my family brothers LAM Wan Wah ( 藍萬華), Siew Hui ( 秀慧) and family, LAM Choong Wah ( 藍中華) and CHAY Jing Jing ( 謝晶晶), LAM Cai Wah ( 藍才華), and my parents LAM Pin Kok ( 藍平國) and TANG Fong Har ( 鄧芳霞), my aunt LAM Shun Yin ( 藍順 英); and to my beloved grandma, who passed away on the day of my CEA-Saclay presentation (27 April 2011). I would like to appreciate those who oppose, humiliate, and defame me in the past. Such discouragements do not bring me down, instead, they become my strengths to pursue my destiny. And very... very special thanks to the almighty Lord Jesus Christ for everything He has granted to me and family. ஭ࡌ๮ລᜄΌ๮׌л亼ᖕ ॷȋȋ䦄㪑Ƞ੔෫ξӽȡכ ऩᚶᇝਜᖂǴكᏢਢ஍ᐕதॸၰǴ຀ ਡ౛҂ૈ໦Ѧ፞Ǵϼ߃ଁࢂШύ௃Ǵ ਜξ፯ᅰίख़рǴเ៏ᡫѠ΋ТܴǴ ணҗऩ৴ᆎύཀǴόᜫ亼ᖕܰᘾ䷡Ƕ tel-00777498, version 1 - 17 Jan 2013 LAM Yi Hua ( 藍乙華) 5 tel-00777498, version 1 - 17 Jan 2013 6 Contents Couverture 1 Acknowledgments 3 Contents 7 1 Isospin Symmetry and Its Breaking in Nuclear Structure 13 1.1 Isospin Formalism .................. 14 1.2 Isospin Symmetry Breaking ............... 19 1.3 Physics Motivation .................. 22 tel-00777498, version 1 - 17 Jan 2013 2 Nuclear Shell Model and the Construction of Isospin Non-Conserving Hamil- tonian 27 2.1 Nuclear Shell Model .................. 28 2.2 Large Scale Shell Model Calculations ............ 41 2.3 Second Quantization ................. 44 2.4 Residual Interaction .................. 45 2.5 Construction Formalism of Isospin Non-Conserving Hamiltonian .... 49 7 Contents 3 Experimental Isobaric Multiplet Mass Equation Coefficients 59 3.1 IMME Fitting Procedure ................ 60 3.2 IMME b and c Coefficients ................ 62 3.3 Tabulation of the IMME Coefficients ............ 69 Results 73 4 Fit of INC Hamiltonian to Experimental b and c Coefficients 75 4.1 Fitting procedure .................. 76 4.2 Results of the Fit of INC Hamiltonian to Experimental b and c Coefficients 77 4.3 Remarks ..................... 85 5 Staggering Effects in b and c Coefficients 87 5.1 Fitted b and c coefficients ................ 88 5.2 Staggering Effects of b and c Coefficients ........... 92 5.3 Remarks ..................... 111 tel-00777498, version 1 - 17 Jan 2013 Applications of the INC Hamiltonian 113 6 Masses and extension of the IMME beyond the quadratic form 115 6.1 Introduction ...................
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