PhD Thesis: Elastic Scattering at Low Energy Within Microscopic Nuclear Models

VIETNAM NATIONAL UNIVERSITY HCMC UNIVERSITY OF SCIENCE ELASTIC SCATTERING AT LOW ENERGY WITHIN THE MICROSCOPIC NUCLEAR STRUCTURE MODELS (Mô tả tán xạ đàn hồi ở năng lượng thấp sử dung các mẫu vi mô cấu trúc hạt nhân) PhD THESIS OF PHYSICS HOCHIMINH CITY - 2023 VIETNAM NATIONAL UNIVERSITY HCMC UNIVERSITY OF SCIENCE ELASTIC SCATTERING AT LOW ENERGY WITHIN THE MICROSCOPIC NUCLEAR STRUCTURE MODELS Speciality: Atomic and Nuclear Physics Code: 62 44 05 01 Reviewer 1: GS. Lé Van Hoang Reviewer 2: PGS. Nguyén Xuan Hai Reviewer 3: PGS. D6 Quang Binh Independent reviewer 1: PGS.

Nguyén Xuan Hai Independent reviewer 2: TS. Nguyén Ngoc Anh SUPERVISORS 1. Associate Professor Tran Viet Nhan Hao 2. Professor Philippe Quentin HOCHIMINH CITY - 2023 DECLARATION I, Nguyen Hoang TUNG, hereby declare that the details mentioned in this thesis with the title, "ELASTIC SCATTERING AT LOW-ENERGY WITHIN THE MICROSCOPIC NUCLEAR STRUCTURE MODELS" are true and cor- rect to the best of my knowledge, and the work presented in it is my own.

I take full responsibility for the accuracy of the particulars mentioned. I confirm that: » This work was done wholly or mainly during my candidature for a research degree at this University. e Where any part of this thesis has previously been submitted for a degree or other qualification at this University or any other institutions, this has been clearly stated. e Where I have consulted the published work of others, this is always clearly attributed.

e Where I have quoted from the work of others, the source is always given. With the exception of such quotations, this thesis is entirely my own work. » Ï have acknowledged all main sources of help. e Where the thesis is based on work done by myself jointly with others, I have made clear exactly what was done by others and what I have contributed myself.

Signed: Name: ii ACKNOWLEDGMENTS What is LUCK? At any personal experiences which had specific definitions for their own ones. To me, I have been being the luckiest person for over seven years in my life that I met many great people who helped, guided, and inspired me. Without their support, I would have accomplished much less, if anything at all. I would like, foremost, to express my thanks to Assoc.

Tran Viet Nhan Hao for being the supervisor of this thesis. I am grateful for his constant care of my scientific problems and attention paid to the progress in my research as well as for the help in the development of numerical tools necessary in our work. I appreciate frequent discussions as well as the corrections and comments con- cerning this dissertation. I am specifically thankful to Professor Philippe Quentin who agreed to be the co-supervisor of this thesis.

I am especially grateful for his ideas, enthusiasm, vital discussions and clarifications. His corrections of the text of this thesis and critical remarks contributed strongly to the actual contents of this work. I would also like to express my gratitude to my sisters, my parents for their love and support, especially my mom, who always gives her endless supporting to my studying route for years. Hué City, November 2021 11 TABLE OF CONTENTS DECLARATION.

ii TABLE OF CONTENTS. iii LIST OF ABBREVIATIONS. iv LIST OFEIGURES. V LIST OF TABLES.

OPTICAL POTENTIAL 4 11 Phenomenological optical potenHal.2 Microscopic optical potentlal.21 Ab initio approaches .2 Nuclear matter approach.3 Nuclear structure approach. SELF-CONSISTENT MEAN FIELD AND BEYOND 18 2.1 Self-consistent mean-field.3 Effective phenomenological Skyrme interactions .2 Nuclear implementation of density functional theory .3 Beyond mean-field approach .4 Schrödinger equations for microscopic optical potential .3 Proton elastic scattering .4 The role of velocity-dependent and spin-orbit terms .5 The role of central term and density-dependent term.6 The role of momentum-density dependent term. CONCLUSIONS 62 PUBLISHED PAPERS 64 REFERENCES 65 APPENDIX A. Explicit calculation of the PVC vertex 71 APPENDIX B.

Analyzing power 72 lv LIST OF ABBREVIATIONS BCS Bardeen Cooper Schrieffer HF Hartree Fock HFB Hartree Fock Bogoliubov KD Koning-Delaroche MOP Microscopic Optical Potential NA nucleon-nucleus NN nucleon-nucleon OM Optical Model OP Optical Potential NSM Nuclear Structure Model POP Phenomenological Optical Potential PVC Particle-vibration Coupling QRPA Quasi Random Phase Approximation RPA Random Phase Approximation SCMF Self-consistent Mean Field SHF Skyrme Hartree Fock LIST OF FIGURES Figure.1 Mass operator calculated by Green function.2 Diagrammatic representation of the self-energy and the second-order self-energy. This Figure is extracted from Ref.1 Angular distributions of neutron elastic scattering by 1O, 40Ca, 48Ca, and 2°8Pb at different incident energies below 50 MeV. The solid curves show the results of the MOP calculations using the SLy5 interaction. The calculated results for ?°°Pb using the same MOPs are adopted from Fig.

The experimental data are the tabulated cross-sections taken from Ref. These figures are extracted from Ref.2 Angular distributions of proton elastic scattering by !%O, 40Ca, “Ca, and 7°8Pb at different incident energies below 50 MeV. The solid curves show the results of the MOP calculations using the SLy5 interaction. The experimental data are the tabulated cross-sections taken from Ref.

These figures are extracted from Ref.3 Same with Figure 3.2 but for analyzing power. These figures are extracted from Ref.4 The absorption W(R,s = 0) for neutron elastic scattering by !%O, #°Ca, 48Ca, and ?°8Pb at low incident energies. These figures are extracted from Ref.5 Angular distributions of neutron elastic scattering by '°O, 40Ca, 48Ca, and ?°8Pb at different incident energies below 50 MeV. The interaction SLy5 has been used.

The solid (dashed) curve shows the calculation with (without) #4,f¿ terms, respectively. The experimental data points are taken from Ref. These figures are extracted from Ref.6 Same with Fig.5 but for analyzing power. These figures are extracted from Ref.7 The absorption W(R,s = 0) for neutron elastic scattering by 1°O, #°Ca, 48Ca, and ?°°Pb at low incident energies.

The solid (dashed) curve shows the calculation with (without) spin-orbit term, respectively. These figures are extracted from Ref.8 Angular distributions of neutron elastic scattering by !8O, 40Ca, 48Ca, and ?°°Pb at different incident energies below 50 MeV. The interaction SLy5 has been used. The dotted dashed (solid) curve shows the calculation with (without) spin-orbit terms, re- spectively.

The dashed line shows the calculation without spin- orbit term in both RPA and PVC. The experimental data points are taken from Ref. These figures are extracted from Ref.9 Same with Fig.8 but for analyzing power. These figures are extracted from Ref.10 The calculated W(R,s = 0) for neutron elastic scattering by !6O at low incident energies.

The linepoints curve shows the calculation with the full effective SLy5 Skyrme interaction. The solid curve shows the calculation without spin-orbit term. The dot short dashed line shows the calculation without ¢;,t2 term. The dashed line (dot dot dashed line) shows the calculation without to (t3) term, respectively.

The calculated results for t1,t2,Wo using the same MOPs are adapted from [82].11 The calculated W(R,s = 0) for neutron elastic scattering by “Ca at low incident energies. The linepoints curve shows the calculation with the full effective SLy5 Skyrme interaction. The solid curve shows the calculation without spin-orbit term. The dot short dashed line shows the calculation without t;,t2 term.

The dashed line (dot dot dashed line) shows the calculation without to (t3) term, respectively. The calculated results for t1,t2,Wo using the same MOPs are adapted from |§2].12 The calculated W(R,s = 0) for neutron elastic scattering by “®Ca at low incident energies. The linepoints curve shows the calculation with the full effective SLy5 Skyrme interaction. The solid curve shows the calculation without spin-orbit term.

The dot short dashed line shows the calculation without t,,t2 term. The dashed line (dot dot dashed line) shows the calculation without to (t3) term, respectively. The calculated results for t1,t2,Wo using the same MOPs are adapted from |§2].13 The calculated W(R,s = 0) for neutron elastic scattering by 2°8Pb at low incident energies. The linepoints curve shows the calculation with the full effective SLy5 Skyrme interaction.

The solid curve shows the calculation without spin-orbit term. The dot short dashed line shows the calculation without t,,t2 term. The dashed line (dot dot dashed line) shows the calculation without to (t3) term, respectively. The calculated results for f1,fa, Wo using the same MOPs are adapted from [82].14 Angular distributions of neutron elastic scattering by !°Q at low incident energies.

The linepoints curve shows the calcula- tion with the full effective Skyrme interaction. The solid curve shows the calculation without spin-orbit term. The dot short dashed line shows the calculation without t),t2 term. The dashed line (dot dot dashed line) shows the calculation without to (ts) term, respectively.

The experimental data points are taken from Ref. The calculated results for t),t2,Wo using the same MOPSs are adapted from |§2].15 Angular distributions of neutron elastic scattering by 4°Ca at low incident energies. The linepoints curve shows the calcula- tion with the full effective Skyrme interaction. The solid curve shows the calculation without spin-orbit term.

The dot short dashed line shows the calculation without í,fs term. The dashed line (dot dot dashed line) shows the calculation without tp (t3) term, respectively. The experimental data points are taken from Ref. The calculated results for t),t2,Wo using the same MOPs are adapted from |§82]|.16 Angular distributions of neutron elastic scattering by “8Ca at low incident energies.

The linepoints curve shows the calcula- tion with the full effective Skyrme interaction. The solid curve shows the calculation without spin-orbit term. The dot short dashed line shows the calculation without ¢1,t2 term. The dashed line (dot dot dashed line) shows the calculation without tp (t3) term, respectively.

The experimental data points are taken from Ref. The calculated results for t1,t2,Wo using the same MOPs are adapted from |82].17 Angular distributions of neutron elastic scattering by ?°°Pb at low incident energies. The linepoints curve shows the calcula- tion with the full effective Skyrme interaction. The solid curve shows the calculation without spin-orbit term.

The dot short dashed line shows the calculation without í,fs term. The dashed line (dot dot dashed line) shows the calculation without to (ts) term, respectively. The experimental data points are taken from Ref. The calculated results for t1,t2,Wo using the same MOPs are adapted from |§2].18 Analyzing power of neutron elastic scattering by !%O at low incident energies.

The linepoints curve shows the calculation with the full effective Skyrme interaction. The solid curve shows the calculation without spin-orbit term. The dot short dashed line shows the calculation without t,,t2 term. The dashed line (dot dot dashed line) shows the calculation without to (t3) term, respectively.

The experimental data points are taken from Ref. The calculated results for t),t2,Wo using the same MOPs are adapted from [82]. eee eee Figure.19 Analyzing power of neutron elastic scattering by “°Ca at low incident energies. The linepoints curve shows the calculation with the full effective Skyrme interaction.

The solid curve shows the calculation without spin-orbit term. The dot short dashed line shows the calculation without t,,t2 term. The dashed line (dot dot dashed line) shows the calculation without to (t3) term, respectively. The experimental data points are taken from Ref.

The calculated results for t),t2,Wo using the same MOPs are adapted from [82]), 2.20 Analyzing power of neutron elastic scattering by “*Ca at low incident energies. The linepoints curve shows the calculation with the full effective Skyrme interaction. The solid curve shows the calculation without spin-orbit term. The dot short dashed line shows the calculation without í,fa term.

The dashed line (dot dot dashed line) shows the calculation without tp (t3) term, respectively. The experimental data points are taken from Ref. The calculated results for t1,t2,Wo using the same MOPs are adapted from [82]), 2.21 Analyzing power of neutron elastic scattering by ?°°Pb at low incident energies. The linepoints curve shows the calculation with the full effective Skyrme interaction.

The solid curve shows the calculation without spin-orbit term. The dot short dashed line shows the calculation without ¢,,t2 term. The dashed line (dot dot dashed line) shows the calculation without to (t3) term, respectively.