Fixed some units
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mesons.jl
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mesons.jl
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@ -1,34 +1,35 @@
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using DifferentialEquations
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const ħc = 197.327 # ħc in MeVfm
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const ħc = 197.327 # MeVfm
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# Values defined in C. J. Horowitz and J. Piekarewicz, Phys. Rev. Lett. 86, 5647 (2001)
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# Values taken from Hartree.f (FSUGarnet) and
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const m_ρ = 763.0
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const m_ω = 782.5
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const m_s = 496.939473213388
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const m_γ = 0.000001000 # not defined in paper
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const g2_s = 110.349189097820
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const g2_v = 187.694676506801
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const g2_ρ = 192.927428365698
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const g2_g = 0.091701236 # not defined in paper
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const κ = 3.260178893447
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const λ = -0.003551486718 # LambdaSS
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const ζ = 0.023499504053 # LambdaVV
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const Λv = 0.043376933644 # LambdaVR
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const m_ρ = 763.0 # MeV/c2
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const m_ω = 782.5 # MeV/c2
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const m_s = 496.939473213388 # MeV/c2
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const m_γ = 0.000001000 # MeV/c2 # not defined in paper
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const g2_s = 110.349189097820 # units?
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const g2_v = 187.694676506801 # units?
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const g2_ρ = 192.927428365698 # units?
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const g2_g = 0.091701236 # units? # not defined in paper
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const κ = 3.260178893447 # units?
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const λ = -0.003551486718 # units? # LambdaSS
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const ζ = 0.023499504053 # units? # LambdaVV
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const Λv = 0.043376933644 # units? # LambdaVR
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const r_reg = 1E-9 # regulator for Green's functions in fm
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const r_reg = 1E-9 # fm # regulator for Green's functions
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"Green's function for Klein-Gordon equation"
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"Green's function for Klein-Gordon equation in natural units"
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greensFunctionKG(m, r, rp) = -(1 / m) * rp / (r + r_reg) * sinh(m * min(r, rp)) * exp(-m * max(r, rp))
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"Green's function for Poisson's equation"
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"Green's function for Poisson's equation in natural units"
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greensFunctionP(r, rp) = -rp^2 / (max(r, rp) + r_reg)
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"Solve the Klein-Gordon equation (or Poisson's equation when m=0) for a given a source function (as an array) where
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the other parameters are the same from mesons!(...)."
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m is the mass of the meson in MeV/c2,
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r_max is the r-cutoff in fm."
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function solveKG(m, source, r_max)
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greensFunction = m == 0 ? greensFunctionP : (r, rp) -> greensFunctionKG(m, r, rp)
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greensFunction = m == 0 ? greensFunctionP : (r, rp) -> greensFunctionKG(m / ħc, r, rp)
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mesh = range(0, r_max; length=length(source))
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greenMat = greensFunction.(transpose(mesh), mesh)
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return greenMat * source
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@ -50,14 +51,14 @@ function solveMesonWfs(ρ_sp, ρ_vp, ρ_sn, ρ_vn, r_max, divs, iterations=3)
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(src_Φ0, src_W0, src_B0) = (zeros(1 + divs) for _ in 1:3)
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for _ in 1:iterations
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@. src_Φ0 = g2_s * ((κ/2) * Φ0^2 + (λ/6) * Φ0^3 - (ρ_sp + ρ_sn)) / ħc
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Φ0 .= solveKG(m_s / sqrt(ħc), src_Φ0, r_max)
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@. src_Φ0 = g2_s * ((κ/2) * Φ0^2 + (λ/6) * Φ0^3 - (ρ_sp + ρ_sn))
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Φ0 .= solveKG(m_s, src_Φ0, r_max)
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@. src_W0 = g2_v * ((ζ/6) * W0^3 + 2 * Λv * B0^2 * W0 - (ρ_vp + ρ_vn)) / ħc
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W0 .= solveKG(m_ω / sqrt(ħc), src_W0, r_max)
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@. src_W0 = g2_v * ((ζ/6) * W0^3 + 2 * Λv * B0^2 * W0 - (ρ_vp + ρ_vn))
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W0 .= solveKG(m_ω, src_W0, r_max)
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@. src_B0 = g2_ρ * (2 * Λv * W0^2 * B0 - (ρ_vp - ρ_vn) / 2) / ħc
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B0 .= solveKG(m_ρ / sqrt(ħc), src_B0, r_max)
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@. src_B0 = g2_ρ * (2 * Λv * W0^2 * B0 - (ρ_vp - ρ_vn) / 2)
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B0 .= solveKG(m_ρ, src_B0, r_max)
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end
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return (Φ0, W0, B0, A0)
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@ -1,10 +1,10 @@
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using DifferentialEquations, Roots
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const ħc = 197.327 # ħc in MeVfm
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const M_n = 939.5654133 # Neutron mass in MeV/c2
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const M_p = 938.2720813 # Proton mass in MeV/c2
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const ħc = 197.327 # MeVfm
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const M_n = 939.5654133 # MeV/c2
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const M_p = 938.2720813 # MeV/c2
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const r_reg = 1E-6 # regulator for the centrifugal term in fm
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const r_reg = 1E-6 # fm # regulator for the centrifugal term
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"The spherical Dirac equation that returns du=[dg, df] in-place where
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u=[g, f] are the reduced radial components evaluated at r,
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@ -13,7 +13,7 @@ xs = test_data[:, 1]
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r_max = maximum(xs)
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divs = length(xs) - 1
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(Φ0, W0, B0, A0) = solveMesonWfs(ρ_sp, ρ_vp, ρ_sn, ρ_vn, r_max, divs, 3)
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(Φ0, W0, B0, A0) = solveMesonWfs(ρ_sp, ρ_vp, ρ_sn, ρ_vn, r_max, divs, 1)
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plot(xs, hcat(Φ0, W0, B0, A0), layout=4, label=["Φ0" "W0" "B0" "A0"])
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xlabel!("r (fm)")
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