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

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Figure 2.14: Neutron and proton density profiles for nuclei in the cold crust of a neutronstar. The optimum nucleus for each density ρ (fm −3 ) is shown, together with the pressure p(MeV fm −3 ), the total internal energy per baryon E (MeV), the charge radius R p (fm), theneutron skin thickness R n −R p , and the chemical potentials µ n ,µ p and µ e (MeV). N,Z andN nuc are defined in the text. R c is the Wigner-Seitz cell size and E β is the energy of uniformnuclear matter in beta equilibrium.36
Figure 2.15: Proton number per unit Wigner-Seitz cell for dense matter for the truncatedmodel is shown by the solid curve. The energy advantage (MeV/baryon, multiplied by 100)relative to uniform matter in beta equilibrium is shown by the dashed curve. The fillingfactor u, defined in Eq. (2.105) and multiplied by 100, is shown by the dotted curve.accounts for the wiggles shown in this figure. This figure also shows the filling factoru = ρ−ρ 0ρ 0 −ρ Rc, (2.105)which increases with density, and the energy advantage of nuclei over that of uniform nuclearmatter (both considered in beta equilibrium), ∆E = E −E β , which decreases with density.∆E decreases to zero before the filling factor approaches the value 1/2 for which mattermight expect to be turned inside out (Lamb et al.[15]).In general, the Wigner-Seitz cell size R c decreases with increasing density and the nuclearfilling factor in the absence of dripped nucleons, (R/R c ) 3 , where R ≈ (R n + R p )/2,therefore increases. However, the nuclear mass fraction decreases with density because ofdripped neutrons and, as a result, the filling factor u increases less rapidly than it would otherwise.The Coulomb energy decreases with density, and eventually nuclei become unstableto deformations. In the simple analysis of Ravenhall et al.[58], significant deformations fromsphericity occur when the filling factor is larger than about 1/8. From the results displayedhere, this occurs when ρ ≃ 0.06 fm −3 . At this point, the energy difference between nucleiand uniform matter is small, being only about 0.13 MeV per baryon, and the energy differenceeven disappears by densities near ρ = 0.09 fm −3 . Thus the density domain in whichsignificantly deformed nuclei appear is probably relatively small in this case. Lamb et al.[16]demonstrated that the nuclei will tend to turn “inside-out” when a filling factor larger than37
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 and 8: 3.3 Optimized Parameter Set . . . .
Page 9 and 10: List of Figures1.1 Mass and radius
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: 2.6.2 Dense Matter and the Wigner-S
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 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
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
Page 141 and 142:
D.1 Non-uniform electron density ap
Page 143 and 144:
Appendix ENuclear Quantities in Non
Page 145 and 146:
Table E.1: Non-relativistic Skyrme
Page 147 and 148:
[20] C.J. Pethick and D.G. Ravenhal
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