Theory of Nuclear Matter for Neutron Stars and ... - Graduate Physics

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Table 5.2: Parameters in SPM & SLy4Parameters SPM SLy4t 0 -2719.7 -2488.91t 1 417.64 486.82t 2 -66.687 -545.39t 3 15042 13777.0ǫ 0.14416 1/6x0 0.16154 0.834x1 -0.047986 -0.344x2 0.027170 -1.000x3 0.13611 1.3545.2 Binding energy of single nucleusWe calculate the binding energy of a single nucleus such as 40 Ca, 90 Zr, and 208 Pb. Thesenuclei have closed shells so we can neglect shell effects.In a single nucleus, ρ outn,p = 0 since there are no dripped nucleons.0.10.08Charge density of 208 PbEDFPotentialSLy4ρ n , ρ p (fm -3 )0.060.040.0200 2 4 6 8 10r (fm)Figure 5.1: Proton density profile of 208 Pb.Table 5.3 shows the properties of a single nucleus from both experimental results and amodel calculation. In table 5.3, r ch is the charge radius, BE/A is the binding energy perbaryon, and δR is defined as r n − r p , where r n,p is the root-mean-square radius of neutronand proton. The density profiles for the single nucleus are given in Fig 5.1. Each modelagrees well with the experimental result. The PDP shows the maximum baryon density atthe center of the nucleus because of its mathematical expression. However, many of heavynuclei with large number of protons (e.g. 208 Pb) have maximum baryon density off the centerbecause of Coulomb repulsion. Thus PDP cannot show the exact density profile of a single74
Table 5.3: Nuclear properties of single nucleusNucleus Exp EKO SPM Sly440 Ca r ch (fm) 3.48 3.36 3.37 3.42BE/A (MeV) 8.45 8.51 8.51 8.14δR −0.06±0.05, −0.05±0.04 −0.03 −0.04 −0.0490 Zr r ch (fm) 4.27 4.23 4.23 4.28BE/A (MeV) 8.71 8.74 8.68 8.42δR 0.09±0.07 0.05 0.06 0.05208 Pb r ch (fm) 5.50 5.51 5.50 5.55BE/A (MeV) 7.87 7.85 7.74 7.56δR (fm) 0.12±0.05, 0.20±0.04 0.11 0.14 0.12nucleus. Except for the density profile, PDP can be used as an approximated density profileto find the charge radius, binding energy per baryon, and δR.5.3 Neutron Star CrustIn a neutron star, as the density increases, the pressure from degenerate electrons reaches apoint where the electrons can no longer support the gravitational collapse and the neutronsreplace the role of electrons soon after the neutron drip. The neutron drip divides the outercrust and inner crust of the neutron star. There is a phase transition around 0.5 ρ 0 [41]between inner crust and liquid core since the nuclear system favors the lowest energy state.Even though there might be sequential phase transition from spherical nuclei with a free ofneutrongas, cylindrical phase, slab, cylindrical hole, bubble touniformmatter, thedifferencein the energy density and press is negligible. Thus we consider the phase transition fromspherical nuclei phase to uniform nuclear matter. We can simply compare the energy densityof uniform nuclear matter with heavy nuclei with a free of neutron gas.5.3.1 Neutron dripThe neutron drips from heavy nuclei as their density increases. The drip point can besearched from a lower baryon density region. As the density increases, the neutron chemicalpotential increases, becomes positive, and neutrons start to drip. In case of protons, thechemical potential remains negative so there are never any dripped protons at T=0 MeV.Table 5.4 shows the neutron drip density for different models. In case of EKO, the neutronsstart to drip when ρ = 2.26×10 −4 fm −3 .Before the neutron drip, the total pressure comes from only electron contribution andsoon after the neutron drip, the pressure from dripped neutrons overwhelm the electroncontribution.75
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Theory of nuclear matter of neutron
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Abstract of the DissertationTheory
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To Jaenyeong, Jonghyun, and Jongbum
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3.3 Optimized Parameter Set . . . .
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List of Figures1.1 Mass and radius
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SymbolsNuclear Physics SymbolE ener
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ω δt 90−10QtT cTaylor expansion
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List of Tables1.1 Range of Tables .
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Chapter 1IntroductionStars give us
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Since the mass of neutron star is d
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shown in Fig. 1.2, LS220 is the onl
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density:p = ρ2ρ o[ K9µ n = −B
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nuclear energy density functional i
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2.3.2 Thermodynamic QuantitiesThe t
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point r and with momentum p isU n (
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Thus, in the case of zero temperatu
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For standard nuclear matter, u = 1
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a α L α U β L β U σ0.5882 1.11
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Figure 2.2: Bulk equilibrium of T =
Page 39 and 40: Figure 2.4: Coexistence curves for
Page 41 and 42: proton fraction x are irrelevant fo
Page 43 and 44: potential model analogue for the Ha
Page 45 and 46: with the convention that z II is th
Page 47 and 48: Figure 2.10: The surface tension of
Page 49 and 50: Figure 2.12: Contour plots of surfa
Page 51 and 52: 2.6.2 Dense Matter and the Wigner-S
Page 53 and 54: Figure 2.15: Proton number per unit
Page 55 and 56: Chapter 3Modified model† The trun
Page 57 and 58: We choose the value ǫ = 1/3. One m
Page 59 and 60: where∆V t = T oρ o[( ρρ o) ǫ[
Page 61 and 62: Q 1 to a small number also results
Page 63 and 64: where p = (S v ,L) and M ij = 1 ∂
Page 65 and 66: 3.4 Nuclear Surface TensionCompared
Page 67 and 68: 1.41.2FRTF II ω 0 , T=0 MeVFRTF II
Page 69 and 70: For the finite-range term, we use a
Page 71 and 72: Landau’s quasi-particle formula g
Page 73 and 74: The symmetry energy in nuclear matt
Page 75 and 76: Figure 4.2: The left figure shows t
Page 77 and 78: Figure 4.4: This figure shows the b
Page 79 and 80: Figure 4.5: In a neutron star, heav
Page 81 and 82: The energy exchange from the gradie
Page 83 and 84: Figure 4.8: The left panel shows th
Page 85 and 86: 4.5 Astrophysical application4.5.1
Page 87 and 88: 0.550.5GaussianFRTF IIFRTF I0.450.4
Page 89: neutron matter respectively. Those
Page 93 and 94: which aref Rc = a 0 +a 1 x+a 2 x 2
Page 95 and 96: parametrized[ht]504540EDF, Z nucFit
Page 97 and 98: Chapter 6Nuclear Equation of State
Page 99 and 100: Coulomb, and, symmetry part [24], i
Page 101 and 102: We can eliminate N s , leading to t
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Page 105 and 106: 2.52GSRsSGISIVSkaSkI1SkI2SkI3SkI5St
Page 107 and 108: HNsn, p, α,eFigure 6.7: In the Wig
Page 109 and 110: Table 6.1: Surface tension analytic
Page 111 and 112: free energy density for the alpha p
Page 113 and 114: Here s ′ = ∂s(u)/∂u.The minim
Page 115 and 116: 6.5.2 Determination of Coulomb surf
Page 117 and 118: gives analytic derivatives of therm
Page 119 and 120: 200180160Atomic number, Y p =0.45,
Page 121 and 122: for Fermi integral. This fitting fu
Page 123 and 124: A.1 Taylor expansion integrationThe
Page 125 and 126: thenwhere0u − i+1 = fu− i +J
Page 127 and 128: We separate the two integrals as in
Page 129 and 130: Each w i can be obtained[ae −∆/
Page 131 and 132: By expanding e r 0/a −e −r 0/a
Page 133 and 134: M 3 2a 0.433 1p 0 (e 2 /a) √ π/3
Page 135 and 136: of find exact polynomial expression
Page 137 and 138: Appendix CPhase coexistenceBulk equ
Page 139 and 140: To summarize, we need to solve 5 eq
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D.1 Non-uniform electron density ap
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Appendix ENuclear Quantities in Non
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Table E.1: Non-relativistic Skyrme
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[20] C.J. Pethick and D.G. Ravenhal
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Theory of Nuclear Matter for Neutron Stars and ... - Graduate Physics

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