THÔNG TIN TÀI LIỆU
MINISTRY OF MIMISTRY OF SCIENCE AND EDUCATION AND TECHNOLOGY TRAINING VIETNAM ATOMIC ENERGY INSTITUTE PhD THESIS presented by Ngo Hai Tan EQUATION OF STATE OF THE BETASTABLE NUCLEAR MATTER IN NEUTRON STARS AND PROTO-NEUTRON STARS Supervisor: Prof Dao Tien Khoa Abstract This thesis presents the results of a consistent mean-field study for the equation of state (EOS) of the β-stable baryonic matter containing npeµν particles in the core of cold neutron star (NS) and hot protoneutron star (PNS) Within the non-relativistic Hartree-Fock formalism, different choices of the in-medium, density-dependent nucleon-nucleon (NN) inter- action have been used Although the considered density dependent NN interactions have been well tested in numerous nuclear structure and/or reaction studies, they give rather di fferent behaviors of the nuclear sym- metry energy at high baryonic densities which were discussed in the lit- erature as the stiff and soft scenarios for the EOS of asymmetric NM A strong impact of the nuclear symmetry energy to the mean-field prediction of the cooling scenario for NS and thermodynamic properties of the PNS matter has been found in our study In addition to the nuclear symmetry energy, the nucleon effective mass in the highdensity medium was found also to affect the thermal properties of hot βstable baryonic matter of PNS significantly Given the EOS of the crust of NS and PNS from the compressible liquid drop model and relativistic mean-field approach, respectively, the different EOS’s of the core of NS and PNS were used as input for the Tolman-Oppenheimer-Volkov equations to obtain the structure of NS and PNS in the hydrostatic equilibrium, in terms of the gravitational mass, radius, central baryonic density, pressure and temperature For the PNS matter, both the neutrino-free and neutrino-trapped baryonic matters in β-equilibrium were investigated at different temperatures and entropy per baryon S/A = 1, and The obtained results show consistently the strong impact of the nuclear symmetry energy and nucleon e ffective mass on the thermal properties and composition of hot PNS matter Maximal ii gravitation masses obtained with different EOS’s for the neutrino-free βstable PNS at S/A = were used to assess the time of the collapse of a very massive PNS to black hole, based on the results of the hydrodynamic simulation of a failed supernova of the 40 M⊙ protoneutron progenitor The effective, density dependent CDM3Yn interaction has been shown to be quite reliable in the mean-field description of the EOS of both the cold and hot asymmetric NM iii Acknowledgements First and foremost, I gratefully express my best thanks to my supervisor, Prof Dao Tien Khoa for his longtime tutorial supervision of my research study at the Institute for Nuclear Science and Technology (INST) in Hanoi, ever since I graduated from Hanoi University of Pedagogy Prof Khoa has really inspired me to pursuit research in nuclear physics by his deep knowledge in teaching and coaching his students and young collabo- rators, and his strict demand on every detail of the research work I would also like to thank Dr J´eroˆme Margueron from IPN Lyon for his collabo- ration work in the topic of my PhD Thesis and support of my short visit to IPN Lyon as well as my attendance at some international meetings in Europe I have gained good skills of the nuclear physics research during my short visits to IPN Orsay and IPN Lyon, and I am deeply grateful to Prof Nguyen Van Giai from IPN Orsay for his help and encouragement I would like to thank my fellow PhD student, Ms Doan Thi Loan, who gave very important contribution to our common research project on the mean-field description of the equation of state of nuclear matter We have accomplished together many interesting tasks and share a lot of joint memories during the years working at INST as PhD students I wish to express my thanks also to my colleagues in the nuclear physics center at INST, in particular, Dr Do Cong Cuong and Mr Nguyen Hoang Phuc for their useful discussions and kind friendship that made the working atmosphere in our group very pleasant and lively The helpful discussions on different physics problems with Dr Bui Minh Loc, a frequent visitor at INST from University of Pedagogy of Ho Chi Minh City, are also thankfully acknowledged The present research work has been supported, in part, by National Foundation for Science and Technology Development (NAFOSTED) of iv Vietnam, Groupe de Physique Theorique of IPN Orsay at Universite Paris- Sud XI Orsay and IPN Lyon, the Palse program of Lyon University, the LIA collaboration in nuclear physics research between MOST of Vietnam and CNRS and CEA of France I am also grateful to INST and Nuclear Training Center of VINATOM for hosting my research stay at INST within the PhD program of VINATOM v Abbreviations NM Nuclear matter ANM Asymmetric Nuclear matter EOS Equation of state HF Hartree-Fock BHF Bruăckner Hartree- Fock DDirect EX Exchange NS Neutron star PNS Proto-neutron star n neutron p proton NN nucleon-nucleon IS Iso-scalar IV Iso-vector vi Contents Abstract ii Acknowledgements iv Abbreviations vi List of tables xi List of figures xix Introduction Hartree-Fock formalism for the mean-field study of NM 2.1 Effective density-dependent NN interaction 13 2.1.1 CDM3Yn effective interaction 14 2.1.2 M3Y-Pn interactions 18 2.1.3 Gogny interaction 20 2.1.4 Skyrme interaction 22 2.2 Explicit Hartree-Fock expressions 23 2.2.1 The finite range interactions 23 2.2.2 Zero-range Skyrme interaction 26 2.3 HF results for the cold asymmetric nuclear matter 27 2.3.1 Saturation properties 27 2.3.2 Total energy of cold NM 31 2.3.3 Nuclear matter pressure 33 2.3.4 Symmetry energy 35 vii HF study of the β-stable NS matter 40 3.1 β equilibrium constraint 41 3.2 EOS of the β-stable npeµ matter 43 3.2.1 Composition of the npeµ matter 43 3.2.2 The cooling of neutron star 47 3.2.3 Pressure of the β-stable npeµ matter 49 Cold neutron star in hydrodynamical equilibrium 51 3.3.1 Mass-radius relation 52 3.3.2 Total baryon mass 57 3.3.3 Surface red-shift 59 3.3.4 Binding energy 60 3.3.5 Causality condition 60 3.3 Hartree-Fock study of hot nuclear matter 4.1 Explicit HF expressions 4.2 66 4.1.1 The finite range interactions 66 4.1.2 Zero-range Skyrme interaction 69 HF results for the EOS of hot ANM 70 4.2.1 Helmholtz free energy 70 4.2.2 Free symmetry energy 75 4.2.3 Impact of nucleon effective mass on the thermaldy- 4.2.4 namical properties of NM 79 Entropy 83 HF study of the β-stable PNS matter 5.1 63 89 β equilibrium constraint 90 5.2 EOS of PNS matter 93 5.2.1 Impact of the free symmetry energy 93 5.2.2 Impact of the in-medium nucleon effective mass 101 5.3 Proto-neutron star in the hydrodynamical equilibrium 103 viii Conclusion 113 References 118 List of author’s publications in the present research topic .129 ix List of Tables 2.1 Parameters of the central term V (C)(r12) in the original M3Y Paris and M3Y-Pn (n=3,4,5) interactions [15] 2.2 Parameters of the density dependence (2.20) of CDM3Yn interaction [8, 9] 2.3 15 17 Ranges and strengths of Yukawa functions used in the radial dependence of the M3Y-Paris, M3Y-P5, and M3Y-P7 interactions [15, 16] 2.4 Parameters of the density-dependent term v(DD)(nb, r12)[15, 16] 2.5 19 Ranges and strengths of Gaussian functions used in the radial dependence of the D1S and D1N interactions [10, 11] 2.6 18 21 HF results for the NM saturation properties using the considered effective NN interactions The nucleon effective mass m∗/m is evaluated at δ = and E0 = E(n0, δ = 0)/A Ksym is the curvature parameter of the symmetry energy (2.6), and Kτ is the symmetry term of the nuclear incompressibility (2.57) determined at the saturation density nδ of asymmetric NM x 29
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