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

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Figure 3.3: Several experimental result can restrict the S v and L. Our optimized S v and Lare in the white overlapped region in the middle of the figure [47].star observations [53]. There are also pure neutron matter calculations with purple polygons[54, 55]. This allowed region of S v and L will give important constraints to develop newnuclear force model in the future.48
3.4 Nuclear Surface TensionCompared with the truncated model, the modified model has a lower critical temperatureand surface tension. These properties will be used to construct E.O.S table using liquiddroplet approach. In the liquid droplet approach (chapter 6), the surface tension as a functionof T and proton fraction x is required.The critical temperature for asymmetric nuclear matter occurs when the dilute and densematter have the same density and proton fraction. In general, the proton fractions in bothdense and dilute matter is different each other except for symmetric nuclear matter. Thesurface tension can be obtained only numerically using Eq. (2.70).The surface tension for nuclear matter at finite temperature and given proton fraction canbe approximated [17] by[ ( ) 2 ] p Tω(x i ,T) = ω 0 (x i ) 1− . (3.30)T c (x i )For both the truncated model and the new model, p = 5/3 explains the numerical behaviorsvery well.The critical temperature at which both the dilute and dense phase have the same densityand proton fraction, is approximated byT c (x i ) = T c (x i = 0.5)(1+a(1−2x i ) 2 +b(1−2x i ) 4 +c(1−2x i ) 6 ). (3.31)The a, b, and c can be obtained by χ 2 minimization between the numerical result and fittingTable 3.1: The critical temperature analytic fitting functionModel T c,0 a b cTruncated 17.354 -0.5006 0.66126 -1.33316New 14.626 -0.4296 0.34216 -1.00298function. Fig. 3.4 shows the plot of critical temperature of numerical and fitting function.This fitting function is used to calculate finite temperature surface tension in Eq. (3.30).The surface tension at T = 0 MeV and Y p = 0.5 is also a function of proton factions. ω 0 canbe approximated with fractional function as in LS model,2·2 α +qω 0 (x i ) = ω 0 (x i = 0.5)x −α(3.32)i +q +(1−x i ) −αThe parameter α is left free so that we can choose from 2 to 4.0 and q is obtained from χ 2minimization. For both models, the best α’s are 3.6 and 3.7.49
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Theory of nuclear matter of neutron
Page 3 and 4:
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
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
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: where p = (S v ,L) and M ij = 1 ∂
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 and 90: neutron matter respectively. Those
Page 91 and 92: Table 5.3: Nuclear properties of si
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
Page 103 and 104: pressure from pure neutron matter,
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
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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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