- Text
- Density,
- Neutron,
- Nuclei,
- Proton,
- Equilibrium,
- Dense,
- Numerical,
- Droplet,
- Bulk,
- Fraction,
- Physics

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

**Theory** **of** nuclear matter **of** neutron stars**and** core collapsing supernovaeA Dissertation PresentedbyYeunhwan LimtoThe **Graduate** Schoolin Partial Fulfillment **of** theRequirements**for** the Degree **of**Doctor **of** Philosophyin**Physics**Stony Brook UniversityJune 2012

- Page 2 and 3: Stony Brook UniversityThe Graduate
- Page 4 and 5: energy and the density derivative o
- Page 6 and 7: ContentsList of FiguresList of Math
- Page 8 and 9: 6.5 The Combined model . . . . . .
- Page 10 and 11: 5.1 Proton density profile of 208 P
- Page 12 and 13: ρ,ω µ ,σ ρ, ω, σ field respe
- Page 14 and 15: x i,oρ αv αB αuproton fraction
- Page 16 and 17: AcknowledgementsI deeply appreciate
- Page 18 and 19: to explain the existence of quark m
- Page 20 and 21: the thermodynamic identity, P = µ
- Page 22 and 23: Chapter 2The Finite-Range Force Mod
- Page 24 and 25: The bulk part is divided by kinetic
- Page 26 and 27: we can get the e−r/r 0interaction
- Page 28 and 29: (2.18), becomes∫E =[{∑d 3 2r 1
- Page 30 and 31: 2.3.3 Properties of Uniform MatterF
- Page 32 and 33: 2.3.5 Uniform Matter at Zero Temper
- Page 34 and 35: For values of S v = 31.63 MeV and S
- Page 36 and 37: as inside or I and the other phase
- Page 38 and 39: Figure2.3: Pressure isothermsaresho
- Page 40 and 41: Figure 2.5: Critical temperature as
- Page 42 and 43: pressure, and also the integrand, m
- Page 44 and 45: Q can be eliminated by combining Eq
- Page 46 and 47: where E sym is the density dependen
- Page 48 and 49: Figure 2.11: The same as Fig. 2.10
- Page 50 and 51: Figure 2.13: Neutron and proton den
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Figure 2.14: Neutron and proton den

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1/2 obtains, but this appears to be

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In the case of uniform matter, the

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is expected to be small, |Q 1 | ≤

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Solving, we haveα = 9 5 + 5B + 1 (

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Figure 3.1: Solid line shows the co

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Figure 3.3: Several experimental re

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181614FRTF II Critical TFRTF II fit

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Chapter 4Gaussian Type Finite Range

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where E B is the energy density for

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u = ρ/ρ 0 and x = ρ p /ρ,E B= 3

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Table 4.1: Interaction parameters w

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4.3 Nuclear matter and nuclei4.3.1

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Table 4.2: Comparsion of the result

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Since we assume that the momentum i

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the perturbation method and thermod

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Figure 4.9: The left panel shows th

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where λ = −ln(1 − 2m/r) and ν

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Chapter 5Nuclear Energy Density Fun

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Table 5.2: Parameters in SPM & SLy4

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Table 5.4: Neutron drip densities f

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Before the neutron drip, another ty

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2EKOPotentialSLy41.5M ( M O•)10.5

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These two tools can be combined to

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The derivative of E with respect to

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Figure 6.2: This is a contour plot

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2.52SGIISkkT8SkMSkT1SkT1sSkT2SkT3Sk

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M ( M O•)2.521.51M * = 0.811M * =

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specific heat) of the surface of sy

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Table 6.3: The chemical potential f

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the seven (ρ i ,x i ,r N ,x,ν n /

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is(f surf +f Coul = β(cs 2 ) 1/3 1

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0.20.180.160.140.12d=1d=2.0d=3d=1,i

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141210Phase diagram, Y p =0.45SLy4F

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Chapter 7ConclusionsThe nuclear equ

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Appendix AFinite Range IntegrationI

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This equation can be calculated by

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0.020.015N=40, SimpsonN=40, 1stN=40

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wherew 1i =w 2i =w 3i =w 4i =w 5i =

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wherei = r i +∆ e ri/a −e −r

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Appendix BJEL thermodynamic integra

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p mn n = 0 n = 1 n = 2 n = 3m = 0 5

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with differentials,( ) ∂p∂nT( )

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matter, and x Q is electron fractio

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Appendix DNumerical Techniques in H

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For R b < r < R c , we have∆µ p

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Other important quantities, S v and

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Bibliography[1] Barranco, M. & Buch

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[46] M. Kortelainen, T. Lesinski, J