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

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6.5 The Combined model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 956.5.1 Equilibrium conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 956.5.2 Determination of Coulomb surface shape parameter D . . . . . . . . 996.5.3 Solving the equilibrium equations . . . . . . . . . . . . . . . . . . . . 996.6 Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1006.6.1 Energy density and pressure . . . . . . . . . . . . . . . . . . . . . . . 1016.6.2 Phase Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1016.6.3 Atomic number in the heavy nuclei . . . . . . . . . . . . . . . . . . . 1016.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1027 Conclusions 104A Finite Range Integration 106A.1 Taylor expansion integration . . . . . . . . . . . . . . . . . . . . . . . . . . . 107A.1.1 1D plane parallel nuclear matter . . . . . . . . . . . . . . . . . . . . . 107A.1.2 3D radial symmetric nuclear matter . . . . . . . . . . . . . . . . . . . 110B JEL thermodynamic integration 116C Phase coexistence 121D Numerical Techniques in Heavy Nuclei in Dense Matter 124D.1 Non-uniform electron density approximation . . . . . . . . . . . . . . . . . . 125D.2 Uniform electron density approximation . . . . . . . . . . . . . . . . . . . . 125E Nuclear Quantities in Non-relativistic Models 127E.1 Mathematical relations between nuclear parameters . . . . . . . . . . . . . . 127Bibliography 130viii
List of Figures1.1 Mass and radius relation of cold neutron stars . . . . . . . . . . . . . . . . . 21.2 Mass and radius relation of cold neutron stars in EOS . . . . . . . . . . . . . 42.1 The energy per baryon E and pressure p . . . . . . . . . . . . . . . . . . . . 162.2 Bulk equilibrium of T = 0 asymmetric nuclear matter . . . . . . . . . . . . . 212.3 Pressure isotherms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.4 Coexistence curves for asymmetric matter . . . . . . . . . . . . . . . . . . . 232.5 Critical temperature as a function of proton fraction . . . . . . . . . . . . . . 242.6 The surface density profile as a function of position . . . . . . . . . . . . . . 252.7 Surface tension and 90-10 surface thickness . . . . . . . . . . . . . . . . . . . 262.8 Surface neutron and proton density profiles . . . . . . . . . . . . . . . . . . 282.9 Surface tension and neutron skin thickness . . . . . . . . . . . . . . . . . . . 292.10 The surface tension of symmetric matter as a function of T . . . . . . . . . . 312.11 The surface tension of asymmetric matter as a function of T . . . . . . . . . 322.12 Contour plots of surface tesion and R n −R p . . . . . . . . . . . . . . . . . . 332.13 Neutron and proton density profiles for the nuclei . . . . . . . . . . . . . . . 342.14 Neutron and proton density profiles for nuclei in dense matter . . . . . . . . 362.15 Nuclear properties in dense matter . . . . . . . . . . . . . . . . . . . . . . . 373.1 S v and L contour plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463.2 Confidence interval of S v and L . . . . . . . . . . . . . . . . . . . . . . . . . 473.3 Experimentally allowed region of S v and L . . . . . . . . . . . . . . . . . . . 483.4 Numerical result and analytic fitting of the critical temperature . . . . . . . 503.5 Surface tension at T = 0 MeV as a given proton fraction . . . . . . . . . . . 514.1 Energy per baryon using Gaussian model . . . . . . . . . . . . . . . . . . . . 584.2 Semi-infinite nuclear matter surface properities . . . . . . . . . . . . . . . . . 594.3 Specific heat of uniform nuclear matter . . . . . . . . . . . . . . . . . . . . . 604.4 Density profiles of the close shell nuclei . . . . . . . . . . . . . . . . . . . . . 614.5 Heavy nuclei in dense matter . . . . . . . . . . . . . . . . . . . . . . . . . . . 634.6 Effective mass in the Wigner-Seitz cell . . . . . . . . . . . . . . . . . . . . . 634.7 Phase transition density in neutron star crust. . . . . . . . . . . . . . . . . . 664.8 Nuclear and quark matter coexistence . . . . . . . . . . . . . . . . . . . . . . 674.9 Mass and radius of Hybrid and Neutron stars . . . . . . . . . . . . . . . . . 684.10 Mass-radius of cold neutron stars . . . . . . . . . . . . . . . . . . . . . . . . 694.11 Moment of inertia of a cold neutron star . . . . . . . . . . . . . . . . . . . . 71ix
Page 1 and 2: Theory of nuclear matter of neutron
Page 3 and 4: Abstract of the DissertationTheory
Page 5 and 6: To Jaenyeong, Jonghyun, and Jongbum
Page 7: 3.3 Optimized Parameter Set . . . .
Page 11 and 12: SymbolsNuclear Physics SymbolE ener
Page 13 and 14: ω δt 90−10QtT cTaylor expansion
Page 15 and 16: List of Tables1.1 Range of Tables .
Page 17 and 18: Chapter 1IntroductionStars give us
Page 19 and 20: Since the mass of neutron star is d
Page 21 and 22: shown in Fig. 1.2, LS220 is the onl
Page 23 and 24: density:p = ρ2ρ o[ K9µ n = −B
Page 25 and 26: nuclear energy density functional i
Page 27 and 28: 2.3.2 Thermodynamic QuantitiesThe t
Page 29 and 30: point r and with momentum p isU n (
Page 31 and 32: Thus, in the case of zero temperatu
Page 33 and 34: For standard nuclear matter, u = 1
Page 35 and 36: a α L α U β L β U σ0.5882 1.11
Page 37 and 38: 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
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where∆V t = T oρ o[( ρρ o) ǫ[
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Q 1 to a small number also results
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where p = (S v ,L) and M ij = 1 ∂
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3.4 Nuclear Surface TensionCompared
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1.41.2FRTF II ω 0 , T=0 MeVFRTF II
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For the finite-range term, we use a
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Landau’s quasi-particle formula g
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The symmetry energy in nuclear matt
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Figure 4.2: The left figure shows t
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Figure 4.4: This figure shows the b
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Figure 4.5: In a neutron star, heav
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The energy exchange from the gradie
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Figure 4.8: The left panel shows th
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4.5 Astrophysical application4.5.1
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0.550.5GaussianFRTF IIFRTF I0.450.4
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neutron matter respectively. Those
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Table 5.3: Nuclear properties of si
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which aref Rc = a 0 +a 1 x+a 2 x 2
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parametrized[ht]504540EDF, Z nucFit
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Chapter 6Nuclear Equation of State
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Coulomb, and, symmetry part [24], i
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We can eliminate N s , leading to t
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pressure from pure neutron matter,
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2.52GSRsSGISIVSkaSkI1SkI2SkI3SkI5St
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HNsn, p, α,eFigure 6.7: In the Wig
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Table 6.1: Surface tension analytic
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free energy density for the alpha p
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Here s ′ = ∂s(u)/∂u.The minim
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6.5.2 Determination of Coulomb surf
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gives analytic derivatives of therm
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200180160Atomic number, Y p =0.45,
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for Fermi integral. This fitting fu
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A.1 Taylor expansion integrationThe
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thenwhere0u − i+1 = fu− i +J
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We separate the two integrals as in
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Each w i can be obtained[ae −∆/
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By expanding e r 0/a −e −r 0/a
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M 3 2a 0.433 1p 0 (e 2 /a) √ π/3
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of find exact polynomial expression
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Appendix CPhase coexistenceBulk equ
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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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