Tìm kiếm
Đang tải khung tìm kiếm
Kết quả 1 đến 1 của 1

    TIẾN SĨ Nghiên cứu phương trình trạng thái của chất hạt nhân cân bằng beta trong sao neutron và sao proto-neutron (Equation of state of the beta-stable nuclear matter for neutron and proto-neutron stars)

    D
    dream dream Đang Ngoại tuyến (18524 tài liệu)
    .:: Cộng Tác Viên ::.
  1. Gửi tài liệu
  2. Bình luận
  3. Chia sẻ
  4. Thông tin
  5. Công cụ
  6. Nghiên cứu phương trình trạng thái của chất hạt nhân cân bằng beta trong sao neutron và sao proto-neutron (Equation of state of the beta-stable nuclear matter for neutron and proto-neutron stars)

    Abstract
    This thesis presents the results of a consistent mean- eld study for
    the equation of state (EOS) of the -stable baryonic matter containing
    npe particles in the core of cold neutron star (NS) and hot proto-neutron
    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 different 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- eld 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 high-density medium was found
    also to affect the thermal properties of hot -stable baryonic matter of
    PNS signi cantly.
    Given the EOS of the crust of NS and PNS from the compressible
    liquid drop model and relativistic mean- eld 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
    -equilibrium were investigated at different temperatures and entropy per
    baryon S=A = 1; 2 and 4. The obtained results show consistently the
    strong impact of the nuclear symmetry energy and nucleon effective mass
    on the thermal properties and composition of hot PNS matter. Maximal
    iigravitation masses obtained with different EOS's for the neutrino-free -
    stable PNS at S=A = 4 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- eld description of the EOS of both the cold
    and hot asymmetric NM.
    iiiAcknowledgements
    First and foremost, I gratefully express my best thanks to my super-
    visor, 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. Jer^ome 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- eld 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
    ivVietnam, 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.
    vAbbreviations
    NM Nuclear matter
    ANM Asymmetric Nuclear matter
    EOS Equation of state
    HF Hartree-Fock
    BHF Bruckner Hartree-Fock
    D Direct
    EX Exchange
    NS Neutron star
    PNS Proto-neutron star
    n neutron
    p proton
    NN nucleon-nucleon
    IS Iso-scalar
    IV Iso-vector
    viContents
    Abstract . ii
    Acknowledgements . iv
    Abbreviations vi
    List of tables xi
    List of gures xix
    1 Introduction 1
    2 Hartree-Fock formalism for the mean- eld study of NM 9
    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 nite 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
    vii3 HF study of the -stable NS matter 40
    3.1 equilibrium constraint . 41
    3.2 EOS of the -stable npe matter 43
    3.2.1 Composition of the npe matter . 43
    3.2.2 The cooling of neutron star . 47
    3.2.3 Pressure of the -stable npe matter 49
    3.3 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
    4 Hartree-Fock study of hot nuclear matter 63
    4.1 Explicit HF expressions 66
    4.1.1 The nite range interactions . 66
    4.1.2 Zero-range Skyrme interaction 69
    4.2 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-
    namical properties of NM 79
    4.2.4 Entropy 83
    5 HF study of the -stable PNS matter 89
    5.1 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
    viiiConclusion 113
    References 118
    List of author's publications in the present research topic 129
    ixList of Tables
    2.1 Parameters of the central term V (C) (r 12 ) in the original M3Y
    Paris and M3Y-Pn (n=3,4,5) interactions [15] 15
    2.2 Parameters of the density dependence (2.20) of CDM3Yn
    interaction [8, 9] 17
    2.3 Ranges and strengths of Yukawa functions used in the ra-
    dial dependence of the M3Y-Paris, M3Y-P5, and M3Y-P7
    interactions [15, 16] 18
    2.4 Parameters of the density-dependent term v (DD) (n b ; r 12 )[15,
    16] . 19
    2.5 Ranges and strengths of Gaussian functions used in the ra-
    dial dependence of the D1S and D1N interactions [10, 11]. 21
    2.6 HF results for the NM saturation properties using the con-
    sidered effective NN interactions. The nucleon effective mass
    m
    
    =m is evaluated at  = 0 and E 0 = E(n 0 ;  = 0)=A. K sym
    is the curvature parameter of the symmetry energy (2.6),
    and K τ is the symmetry term of the nuclear incompressibil-
    ity (2.57) determined at the saturation density n δ of asym-
    metric NM . 29
    x3.1 Con guration of static neutron star given by different NS
    equations of state: maximum gravitational mass M G , radius
    R G , and moment of inertia I G ; maximum central densities
    n c ;  c and pressure P c ; total baryon number A; surface red-
    shift z surf ; binding energy E bind 56
    5.1 Properties of the -free and -trapped, -stable PNS at en-
    tropy per baryon S=A = 0; 1; 2 and 4, given by the solu-
    tions of the TOV equations using the EOS's based on the
    CDM3Y3, CDM3Y6 interactions [9] and their soft CDM3Y3s,
    CDM3Y6s versions [6]. M max and R max are the maximum
    gravitational mass and radius; n c ;  c ; P c , and T c are the
    baryon number density, mass density, total pressure, and
    temperature in the center of PNS. T s is temperature of the
    outer core of PNS, at baryon density  s  0:63  10 15 g/cm 3 .
    Results at S=A = 0 represent the stable con guration of cold
    (-free) NS [6] . 105
    5.2 The same as Table 5.1 but obtained with the EOS's based
    on the SLy4 version [19] of Skyrme interaction, M3Y-P7
    interaction parametrized by Nakada [16], and D1N version
    [18] of Gogny interaction 107
    xiList of Figures
    1.1 Structure of neutron star. (http://www.buzzle.com/articles/neutron-
    star-facts.html) 4
    1.2 Density dependence of the energy (per baryon) of NM en-
    ergy given by the HF calculation using the CDM3Y3 and
    CDM3Y6 versions [8] of the M3Y-Paris interaction, which
    are associated with the nuclear incompressibility K = 218
    and 252 MeV, respectively . 6
    2.1 Total NM energy per particle E=A at different neutron-
    proton asymmetries  given by the HF calculations using
    the CDM3Y3 (lower panel) and CDM3Y6 (upper panel) in-
    teractions. The solid circles are the saturation densities of
    the NM at the different neutron-proton asymmetries 30
    2.2 Total NM energy per particle E=A for symmetric NM (upper
    panel) and pure neutron matter (lower panel) given by the
    HF calculation using different interactions. The circles and
    crosses are results of the ab-initio calculation by Akmal,
    Pandharipande and Ravenhall (APR) [52] and microscopic
    Monter Carlo (MMC) calculation by Gandol et al. [53],
    respectively . 32
    xii2.3 Pressure of symmetric NM (upper panel) and pure neutron
    matter (lower panel) calculated in the HF approximation
    using the effective NN interactions given in Table 2.6. The
    shaded areas are the empirical constraints deduced from the
    HI
    ow data [59] 34
    2.4 HF results for the NM symmetry energies E sym (n b ) given
    by the density-dependent NN interactions under study. The
    shaded (magenta) region marks the empirical boundaries de-
    duced from the analysis of the isospin diffusion data and
    double ratio of neutron and proton spectra data of HI col-
    lisions [60, 61]. The square and triangle are the constraints
    deduced from the consistent structure studies of the GDR
    [62] and neutron skin [50], respectively. The circles and
    crosses are results of the ab-initio calculation by Akmal,
    Pandharipande and Ravenhall (APR) [52] and microscopic
    Monter Carlo (MMC) calculation by Gandol et al. [53],
    respectively . 36
    3.1 The fractions x j = n j =n b of constituent particles of the NS
    matter obtained from the solutions of Eqs. (3.4) and (3.6)
    using the mean- eld potentials given by the M3Y-P5 and
    D1N interactions 44
    3.2 The same as Fig. 3.1 but using the mean- eld potentials
    given by the M3YP7 and Sly4 interactions. The circles are
    n j values calculated at the maximum central densities n c
    given by the solution of the TOV equations . 45
    3.3 The same as Fig. 3.2 but using the mean- eld potentials
    given by the CDM3Y6 and its soft version interactions . 46
    xiii3.4 The proton fraction x p of the -stable NS matter obtained
    from the solutions of Eqs. (3.4) and (3.6) using the mean-
    eld potentials given by the stiff-type CDM3Yn and Sly4
    interactions. The circles are n p values calculated at the max-
    imum central densities n c given by the TOV equations. The
    thin lines are the corresponding DU thresholds (3.11) . 47
    3.5 The pressure inside the NS matter obtained with the in-
    medium NN interactions that give stiff (upper panel) and
    soft (lower panel) behavior of E sym (n b ), in comparison with
    the empirical data points deduced from the astronomical ob-
    servation of neutron stars [83]. The shaded band shows the
    uncertainties associated with the data determination. The
    circles are P values calculated at the corresponding maxi-
    mum central densities given by the TOV equations . 50
    3.6 The NS gravitational mass versus its radius in comparison
    with the empirical data (shaded contours) deduced by
    
    Ozel
    et al [83] from recent astronomical observations of neutron
    stars. The circles are values calculated at the maximum cen-
    tral densities. The thick solid (red) line is the limit allowed
    by General Relativity [79] . 53
    3.7 The same as Fig. 3.6, but in comparison with the empirical
    data (shaded contours) deduced by Steiner et al. [80] from
    the observation of the X-ray burster 4U 1608-52 . 54
    3.8 The gravitational mass M given by different EOS's of the NS
    matter plotted versus the corresponding total baryon mass
    M b . The shaded rectangle is the empirical value inferred
    from observations of the double pulsar PSR J0737-3059 by
    Podsiadlowski et al. [81] 58
    xiv3.9 The adiabatic sound velocity versus baryon density obtained
    with the EOS's given by the stiff-type (upper panel) and
    soft-type (lower panel) in-medium NN interactions. The
    thick solid (red) lines are the subluminal limit (v s 6 c),
    and the vertical arrows indicate the baryon densities above
    which the NS matter predicted by the M3Y-P7 interaction
    becomes superluminal (see details in the text) 61
    4.1 Free energy per particle F=A of symmetric nuclear matter
    (SNM) and pure neutron matter (PNM) at different temper-
    atures given by the HF calculation using the CDM3Y3 (right
    panel) and CDM3Y6 (left panel) interactions [9] (lines), in
    comparison with the BHF results (symbols) by Burgio and
    Schulze [27] . 71
    4.2 The same as Fig. 4.1 but for the HF results obtained with the
    M3Y-P5 (right panel) and M3Y-P7 (left panel) interactions
    parametrized by Nakada [15, 16] . 72
    4.3 The same as Fig. 4.1 but for the HF results obtained with
    the D1N version [18] of Gogny interaction (left panel) and
    SLy4 version [19] of Skyrme interaction (right panel) 73
    4.4 Pressure of ANM (upper panel) and PNM (lower panel) at
    T=0,20,40 MeV compare to the analysis of the collective
    data measured in relativistic HI collision [59] 74
    4.5 Free symmetry energy per particle F sym =A of pure neutron
    matter ( = 1) at different temperatures given by the HF
    calculations (4.29) using the CDM3Y3 and CDM3Y6 inter-
    actions [9] and their soft versions CDM3Y3s and CDM3Y6s
    [6] (lines), in comparison with the BHF results (symbols) by
    Burgio and Schulze [27] 75
    xv4.6 The same as Fig. 4.4 but for the HF results given by the
    M3Y-P5 and M3Y-P7 interactions parametrized by Nakada
    [15, 16], and the D1N version [18] of Gogny interaction and
    SLy4 version [19] of Skyrme interaction . 76
    4.7 Free symmetry energy (4.29) (lower panels) and internal
    symmetry energy (4.31) (upper panels) at different temper-
    atures, given by the HF calculations using the CDM3Y6
    interaction [9]. (F sym =A)= 2 curves must be very close if the
    quadratic approximation (4.30) is valid 77
    4.8 Density pro le of the neutron- (upper panel) and proton ef-
    fective mass (lower panel) at different neutron-proton asym-
    metries  given by the HF calculation using the CDM3Y6
    and CDM3Y3 interactions [9], and the D1N version of Gogny
    interaction [18], in comparison with the BHF results (sym-
    bols) by Baldo et al. [71] . 80
    4.9 The same as Fig. 4.8 but for the HF results obtained with
    the M3Y-P7 and M3Y-P5 interactions [15, 16], and the SLy4
    version [19] of Skyrme interaction . 81
    4.10 Density pro le of temperature in the isentropic and symmet-
    ric NM given by the HF calculation using different density
    dependent NN interactions, in comparison with that given
    by the approximation (4.34) for the fully degenerate Fermi
    (DF) system at T ≪ T F 82
    4.11 Density pro le of entropy per particle S=A of symmetric
    nuclear matter (SNM) and pure neutron matter (PNM) at
    different temperatures, deduced from the HF results (lines)
    obtained with the CDM3Y6 and CDM3Y3 interactions [9],
    in comparison with the BHF results by Burgio and Schulze
    (symbols) [27] 84
    xvi4.12 The same as Fig. 4.6 but for the HF results obtained with
    the M3Y-P7 and M3Y-P5 interactions [15, 16] 85
    4.13 The same as Fig. 4.6 but for the HF results obtained with
    the D1N version [18] of Gogny interaction and SLy4 version
    [19] of Skyrme interaction . 86
    4.14 Symmetry part of the entropy per particle (4.33) of pure
    neutron matter at different temperatures given by the CDM3Y3
    and CDM3Y6 interactions [9] and their soft CDM3Y3s and
    CDM3Y6s versions [6]. S sym =A is scaled by the correspond-
    ing temperature to have the curves well distinguishable at
    different T . 87
    5.1 Total pressure (5.10) of the isentropic -free (left panel) and
    -trapped (right panel) -stable PNS matter at different
    baryon densities n b and entropy per baryon S=A = 1; 2 and
    4. The EOS of the PNS crust is given by the RMF calcu-
    lation by Shen et al. [5], and the EOS of the uniform PNS
    core is given by the HF calculation using the CDM3Y6 in-
    teraction [9] (upper panel) and its soft CDM3Y6s version
    [6] (lower panel). The transition region matching the PNS
    crust with the uniform core is shown as the dotted lines 94
    5.2 Neutron-proton asymmetry  of the -free (left panels) and
    -trapped (right panels) -stable PNS matter at different
    baryon number densities n b and entropy per baryon S=A =
    1; 2 and 4. The EOS of the homogeneous PNS core is given
    by the HF calculation using the CDM3Y6 interaction [9] and
    its soft CDM3Y6s version [6] . 95
    xvii5.3 Entropy per baryon (upper panel) and temperature (lower
    panel) as function of baryon number density n b of the -
    stable PNS matter given by the CDM3Y6 interaction [13, 9]
    (thick lines) and its soft CDM3Y6s version [6] (thin lines)
    in the -free (left panel) and -trapped (right panel) cases. 96
    5.4 Particle fractions as function of baryon number density n b in
    the -free and -stable PNS matter at entropy per baryon
    S=A = 1; 2 and 4, given by the CDM3Y6 interaction [9]
    (upper panel) and its soft CDM3Y6s version [6] (lower panel). 97
    5.5 The same as Fig. 5.4 but for the -trapped, -stable matter
    of the PNS . 98
    5.6 The same as Fig. 5.4, but given by the SLy4 version [19] of
    Skyrme interaction (upper panel) and M3Y-P7 interaction
    parametrized by Nakada [16] (lower panel) 99
    5.7 The same as Fig. 5.6 but for the -trapped, -stable PNS
    matter 100
    5.8 Density pro le of neutron and proton effective mass in the -
    free and -stable PNS matter at entropy per baryon S=A =
    1; 2 and 4, given by the HF calculation using the CDM3Y6
    [9] and M3Y-P7 [16] interactions (left panel), the D1N ver-
    sion of Gogny interaction [18] (right panel) and SLy4 version
    [19] of Skyrme interaction (right panel) 102
    5.9 Density pro le of temperature in the -free and -stable
    PNS matter at entropy per baryon S=A = 1; 2 and 4, de-
    duced from the HF results obtained with the same density
    dependent NN interactions as those considered in Fig. 5.8. 103
    xviii5.10 Gravitational mass (in unit of solar mass M⊙) of the -
    stable, -free (left panel) and -trapped (right panel) PNS
    at entropy S=A = 1; 2 and 4 as function of the radius (in
    km), based on the EOS of the homogeneous PNS core given
    by the CDM3Y6 interaction [9] (upper panel) and its soft
    CDM3Y6s version [6] (lower panel). The circle at the end
    of each curve indicates the last stable con guration . 104
    5.11 The same as Fig. 5.10 but given by the CDM3Y3 interaction
    [9] (upper panel) and its soft CDM3Y3s version [6] (lower
    panel) 106
    5.12 The same as Fig. 5.10 but given by the SLy4 version of
    Skyrme interaction [19] (upper panel) and M3Y-P7 interac-
    tion parametrized by Nakada [16] (lower panel) . 108
    5.13 Delay time t BH from the onset of the collapse of a 40 M⊙
    progenitor until the black hole formation as function of the
    enclosed gravitational mass M G (open squares) given by the
    hydrodynamic simulation [76, 4], and M max values given by
    the solution of the TOV equations using the same EOS for
    the -free and -stable PNS at S=A = 4 (open circles). The
    M max values given by the present mean- eld calculation of
    the -free and -stable PNS at S=A = 4 using different den-
    sity dependent NN interactions are shown on the correlation
    line interpolated from the results of simulation . 111
    xixChapter 1
    Introduction
    With the physics of unstable neutron-rich nuclei being at the fore-
    front of modern nuclear physics, the determination of the equation of state
    (EOS) of asymmetric neutron-rich nuclear matter (NM) becomes also an
    important research goal in many theoretical and experimental studies. Al-
    though, in general concept, asymmetric NM is an idealized in nite uniform
    matter composed of strongly interacting baryons and (almost free) leptons
    at different mass densities and neutron-proton asymmetries, it is in fact a
    real physical condition existing in neutron stars which can be observed
    from Earth through their radiation of X-rays or radio signals. Up to now,
    about 2000 neutron stars have been detected (mostly as radio pulsars) in
    the Milky Way and Large Magellanic Cloud, with the observed gravitation
    mass of the most massive neutron stars reaching around or slightly above
    two solar masses (M G  2:01  0:04 M⊙). Above this value stars evolve
    into black holes. For different theoretical studies, such a large neutron star
    mass should be possible with the realistic EOS of neutron star matter.
    In the terrestrial laboratories, the interior of a heavy neutron-rich nucleus
    like lead or uranium can be considered as a small fragment of asymmetric
    NM, and some basic properties of asymmetric NM were deduced from the
    structure studies of heavy nuclei with neutron excess. Very important are
    12 Chapter 1. Introduction
    the saturation properties of NM, in particular, the internal energy pressure
    of the symmetric NM (in nite nuclear matter with the same neutron and
    proton densities) around the saturation baryon number density n 0  0:17
    fm
    3 . In terms of thermodynamics, EOS often means the dependence of
    the pressure P on the mass density  and temperature T of NM, while in
    the many-body studies of NM it is often discussed as the dependence of
    the internal NM energy on the baryon number density and temperature.
    From the nuclear astrophysics viewpoint, a realistic EOS of neutron
    star matter is a vital input for the astrophysical studies for the structure
    and formation of cold neutron star (NS) as well as hot proto-neutron star
    (PNS). Proto-neutron stars are compact and very hot and neutrino-rich
    stellar objects which have the shortest stellar life time in the Universe (it
    is around one minute between the birth of PNS following the gravitational
    collapse of a massive progenitor and the appearance of a black hole or
    a neutron star). Nevertheless, many complex physics phenomena occur
    during these seconds, with PNS contracting, cooling down and eventually
    losing all its neutrino content. Very important for the hydrodynamical
    modeling of a compact PNS or NS are its gravitational mass and radius in
    the hydrostatic equilibrium. With a given EOS of the -stable neutron rich
    matter, the mass-radius (M=R) relation of NS or PNS can be determined
    from the solution of the Tolman-Oppenheimer-Volkov (TOV) equations
    [1], which were derived from the Einstein theory of the general relativity
    assuming the spherical symmetry of the stellar object
    dP
    dr
    = G
    m
    r 2
    (
    1 +
    P
    c 2
    ) (
    1 +
    4Pr 3
    mc 2
    ) (
    1
    2Gm
    rc 2
    ) 1
    ;
    dm
    dr
    = 4r
    2
    ; (1.1)
    where G is the universal gravitational constant, P and  are the pressure
    and mass energy density of NS or PNS, r is the radial coordinate in the
    Schwarzschild metric, and m is the gravitational mass enclosed within the3
    sphere of radius r. As discussed below in the present thesis, the TOV equa-
    tions (1.1) are solved numerically using the realistic P() relation given by
    a chosen EOS of the matter inside NS or PNS. As such, EOS means not
    only P() but also the composition of the stellar matter. Nuclear astro-
    physics is an interdisciplinary eld that is actively developed and carried
    out at different nuclear physics centers in recent years [2]. The nuclear
    astrophysical modeling of the stellar object is based in many cases on the
    astrophysical observations and extrapolations of what we consider reliable
    physical knowledge of the EOS of NM tested in terrestrial laboratories.
    In fact, the combined use of the astrophysical and nuclear physics data in
    the astrophysical studies also offers a unique opportunity to test different
    theoretical nuclear models.
    In the hot environment of PNS, the entropy per baryon S=A is believed
    to be of the order of 1 or 2 Boltzmann constant k B [3] (in the present work
    we assume k B = 1). However, the recent astrophysical studies have sug-
    gested that S=A might well exceed 4 in the hot core of PNS during a failed
    supernova [4], when a very massive progenitor collapses directly to black
    hole. Such an environment is so extreme that neutrinos are rst trapped
    within the PNS matter in the beginning of the core collapse. Then, on a
    time scale of 10-20 s PNS is cooling down mainly through electron neutrino
    emission, and after about 40-50 s the PNS matter becomes transparent to
    neutrinos. For a newborn NS, the cooling via neutrino emission can take
    place for 100 to 10 5 years before the
    cooling period begins [1]. Thus,
    the knowledge about the EOS of the hot, asymmetric NM is vital for the
    astrophysics studies of both NS and PNS. From the surface of NS and
    PNS inwards, the baryon matter rst forms a low-density, inhomogeneous
    crust and, with the increasing baryon density, the matter gradually forms
    a uniform core (see Fig. 1.1).
    Given the EOS's of the crust of NS and PNS given by the compressible4 Chapter 1. Introduction
    Figure 1.1: Structure of neutron star.
    (http://www.buzzle.com/articles/neutron-star-facts.html)
    liquid drop model and relativistic mean- eld approach, respectively, dif-
    ferent EOS's of the uniform core of NS and PNS predicted in the present
    mean- eld approach have been used as the input for the TOV equations
    (1.1) to obtain the basic stellar characteristics in the hydrostatic equi-
    librium, like the M=R relation between the gravitational mass and radius,
    central matter density and pressure. These results were compared with the
    available empirical data to verify the reliability of the considered EOS's of
    asymmetric NM in the astrophysical modeling of NS and PNS.
    The key quantity to distinguish different nuclear EOS's of NM is the5
    nuclear mean- eld potential that can be obtained from a consistent mean-
    eld study, like the relativistic mean- eld (RMF) approach [5] or nonrela-
    tivistic Hartree-Fock (HF) formalism [6] based on the realistic choice of the
    nucleon-nucleon (NN) interaction in the high-density nuclear medium. To
    deduce an in-medium NN interaction starting from the free NN interaction
    to the form amenable for different nuclear structure and reaction calcu-
    lations still remains a challenge for the microscopic nuclear many-body
    theories. Therefore, most of the nuclear reaction and structure studies still
    use different kinds of the effective (density-dependent) NN interaction as
    in-medium interaction between nucleons. Microscopic many-body studies
    have shown consistently the strong effect by the Pauli blocking as well
    as higher-order NN correlations with the increasing baryon density. Such
    medium effects are normally considered as the physics origin of the em-
    pirical density dependence introduced into various versions of the effective
    NN interaction used in the HF mean- eld approaches. For example, the
    density dependent CDM3Yn versions [8, 9] of the M3Y interaction, which
    was originally constructed to reproduce the G-matrix elements of the Reid
    [10] and Paris [11] NN potentials in an oscillator basis.
    In searching for a realistic choice of the effective NN interaction for the
    consistent use in the mean- eld studies of NM and nite nuclei as well as
    in the nuclear reaction calculations, we have performed in the present work
    a systematic HF study of asymmetric NM at both zero and nite tempera-
    tures using the CDM3Yn interactions, which have been used mainly in the
    folding model studies of the nuclear scattering [8, 12, 13, 14], and the M3Y-
    Pn interactions carefully parametrized by Nakada [15, 16] for use in the
    HF studies of nuclear structure. For comparison, the same HF study has
    also been done with the D1S and D1N versions of the Gogny interaction
    [17, 18] and Sly4 version of the Skyrme interaction [19]. In the mean- eld
    studies, the EOS of NM is usually associated with density dependence of6 Chapter 1. Introduction
    the total energy of NM (per baryon) which is expressed as
    E
    A
    (n b ; ) =
    E
    A
    (n b ;  = 0) + E sym (n b )
    2
    + O(
    4
    ) + ::: (1.2)
    where the baryon number density (n b = n n + n p ) is the sum of the neutron
    and proton number densities,  = (n n n p )=n b is the asymmetry parame-
    ter, and E sym (n b ) is the so-called symmetry energy. A foremost requisite
    to the realistic in-medium NN interaction is that it should give the proper
    description of the saturation properties of symmetric NM, i.e., the binding
    energy of symmetric NM of around
    E
    A
    (n 0 ;  = 0)  16 MeV at the satu-
    ration density n 0 , like the HF results obtained with the density dependent
    CDM3Y3 and CDM3Y6 versions [8] of the M3Y-Paris interaction shown
    in Fig 1.2.
    0 1 2 3 4
    -20
    0
    20
    40
    60
    80
    E/A(MeV)
    0
    CDM3Y3 (K=218 MeV)
    CDM3Y6 (K=252 MeV)
    EOS for cold Nuclear Matter
    Figure 1.2: Density dependence of the energy (per baryon) of NM energy given by the
    HF calculation using the CDM3Y3 and CDM3Y6 versions [8] of the M3Y-Paris inter-
    action, which are associated with the nuclear incompressibility K = 218 and 252 MeV,
    respectively.
    Very vital quantity for the determination of the EOS of asymmetric
    NM is the nuclear symmetry energy, especially, the behavior of E sym (n b )7
    with the increasing baryon number density. Because the symmetry energy
    of NM is determined entirely by the isospin- and density dependence of the
    in-medium NN interaction, it is directly related to the realistic description
    of the structure of nite nuclei with neutron excess. Moreover, the knowl-
    edge of the symmetry energy of NM is essential for the determination of
    the chemical potentials of the constituent baryons and leptons that in turn
    determine the particle abundances in the stellar objects prior to or after
    the supernova [21]. The recent HF studies of NM [22] have shown that the
    density dependence of the symmetry energy of NM given by the effective
    NN interactions considered in the present work is associated with two dif-
    ferent (soft and stiff ) behaviors at high baryon densities. As a result, these
    two families predict very different behaviors of the proton-to-neutron ratio
    in the equilibrium that can imply two drastically different mechanisms
    for the neutron star cooling (with or without the direct Urca process). Fur-
    thermore, the difference in the NM symmetry energy is showing up also in
    the main properties of NS in the hydrostatic equilibrium [6] that are read-
    ily obtained from the solutions of the TOV equations (1.1). In this thesis,
    the strong impact of the nuclear symmetry energy to the basic properties
    of the NS matter as well as PNS matter is illustrated in details based on
    the results of a consistent HF study of the NS and PNS matter in the
    -equilibrium.
    Another fundamental physics quantity that also impacts the behav-
    ior of the high-density NM is the nucleon effective mass in the medium,
    which is determined by the density- and momentum- dependence of the
    single-nucleon or nucleon mean- eld potential [9, 23]. Microscopic studies
    of the single-nucleon potential in the high-density nuclear medium have
    shown the important link of the nucleon effective mass to different nuclear
    phenomena such as the dynamics of heavy-ion collisions at intermediate en-
    ergies, the damping of low-lying nuclear excitations and giant resonances .8 Chapter 1. Introduction
    as well as the thermodynamical properties of the collapsing stellar mat-
    ter [23]. Therefore, an interesting research topic discussed in this thesis is
    how the nucleon effective mass given by different density dependent NN
    interactions affects the basic properties of the asymmetric NM at zero and
    nite temperatures. In particular, the density pro les of the temperature
    and entropy of the hot stable PNS matter. The impact of symmetry
    energy as well as impact of nucleon effective mass to the properties of NS
    and PNS matter have been discussed in the two recent publishes by author
    of this thesis and collaborations [6, 7].
    The structure of this thesis is as follows: the next chapter presents the
    HF formalism for the mean- eld study of the EOS of asymmetric NM. The
    EOS of the -stable NS matter and its composition at zero temperature
    are discussed in Chapter 3, with the emphasis on the impact of the nu-
    clear symmetry energy. The results of a consistent HF study of the hot
    asymmetric NM and -stable PNS matter are presented in Chapters 4 and
    5, where the strong impact of the nuclear symmetry energy and nucleon
    effective mass on the thermal properties and composition of hot PNS mat-
    ter is investigated. In particular, the maximal gravitation masses obtained
    with different EOS's for the neutrino-free -stable PNS at the entropy per
    baryon S=A  4 were used to assess the time of the collapse of a very
    massive, hot PNS to black hole, based on the results of the hydrodynamic
    simulation of a failed supernova of the 40 M⊙ protoneutron progenitor.
    The summary of the present research and the main conclusions are given
    in the nal chapter.

    Xem Thêm: Nghiên cứu phương trình trạng thái của chất hạt nhân cân bằng beta trong sao neutron và sao proto-neutron (Equation of state of the beta-stable nuclear matter for neutron and proto-neutron stars)
    Nội dung trên chỉ thể hiện một phần hoặc nhiều phần trích dẫn. Để có thể xem đầy đủ, chi tiết và đúng định dạng tài liệu, bạn vui lòng tải tài liệu. Hy vọng tài liệu Nghiên cứu phương trình trạng thái của chất hạt nhân cân bằng beta trong sao neutron và sao proto-neutron (Equation of state of the beta-stable nuclear matter for neutron and proto-neutron stars) sẽ giúp ích cho bạn.
    #1
  7. Đang tải dữ liệu...

    Chia sẻ link hay nhận ngay tiền thưởng
    Vui lòng Tải xuống để xem tài liệu đầy đủ.

    Gửi bình luận

    ♥ Tải tài liệu

social Thư Viện Tài Liệu
Tài liệu mới

Từ khóa được tìm kiếm

Nobody landed on this page from a search engine, yet!

Quyền viết bài

  • Bạn Không thể gửi Chủ đề mới
  • Bạn Không thể Gửi trả lời
  • Bạn Không thể Gửi file đính kèm
  • Bạn Không thể Sửa bài viết của mình
  •  
DMCA.com Protection Status