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Fields and densities read off from s::system

This commit is contained in:
Nuwan Yapa 2025-02-18 16:54:55 -05:00
parent 5e7bbd124e
commit b7dd47eab8
8 changed files with 40 additions and 46 deletions
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11
mesons.jl
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@ -38,14 +38,13 @@ end
"Iteratively solve meson equations and return the wave functions u(r)=[Φ0(r), W0(r), B0(r), A0(r)] where
divs is the number of mesh divisions so the arrays are of length (1+divs),
ρ_sp, ρ_vp are the scalar and vector proton densities as arrays,
ρ_sn, ρ_vn are the scalar and vector neutron densities as arrays,
Φ0, W0, B0, A0 are the mean-field potentials (couplings included) in MeV as as arrays,
r is the radius in fm,
An initial guess initial_sol=(Φ0, W0, B0, A0) can be provided to speed up convergence (permuting!).
the inital solutions are read from s and the final solutions are saved in-place.
Reference: P. Giuliani, K. Godbey, E. Bonilla, F. Viens, and J. Piekarewicz, Frontiers in Physics 10, (2023)"
function solveMesonWfs(ρ_sp, ρ_vp, ρ_sn, ρ_vn, s::system, iterations=10; initial_sol=(zeros(1 + divs) for _ in 1:4))
(Φ0, W0, B0, A0) = initial_sol
function solveMesonFields!(s::system, iterations=10)
(Φ0, W0, B0, A0) = (s.Φ0, s.W0, s.B0, s.A0)
(ρ_sp, ρ_vp, ρ_sn, ρ_vn) = (s.ρ_sp, s.ρ_vp, s.ρ_sn, s.ρ_vn)
(src_Φ0, src_W0, src_B0, src_A0) = (zero_array(s) for _ in 1:4)
# A0 doesn't need iterations

25
nucleons.jl
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@ -27,7 +27,9 @@ end
divs is the number of mesh divisions so solution would be returned as a 2×(1+divs) matrix,
shooting method divides the interval into two partitions at r_max/2, ensuring convergence at both r=0 and r=r_max,
the other parameters are the same from dirac!(...)."
function solveNucleonWf(κ, p, E, Φ0, W0, B0, A0, s::system; shooting=true, normalize=true)
function solveNucleonWf(κ, p, E, s::system; shooting=true, normalize=true)
(Φ0, W0, B0, A0) = fields_interp(s)
if shooting
@assert s.divs % 2 == 0 "divs must be an even number when shooting=true"
prob = ODEProblem(dirac!, [0, 1], (s.r_max, s.r_max / 2))
@ -62,8 +64,9 @@ end
"Returns a function that solves the Dirac equation and returns g(r=r_max) where
r_max is the outer boundary in fm,
the other parameters are the same from dirac!(...)."
function boundaryValueFunc(κ, p, Φ0, W0, B0, A0, s::system; dtype=Float64, algo=Tsit5())
function boundaryValueFunc(κ, p, s::system; dtype=Float64, algo=Tsit5())
prob = ODEProblem(dirac!, convert.(dtype, [0, 1]), (0, s.r_max))
(Φ0, W0, B0, A0) = fields_interp(s)
func(E) = solve(prob, algo, p=(κ, p, E, Φ0, W0, B0, A0), saveat=[s.r_max], save_idxs=[1])[1, 1]
return func
end
@ -71,21 +74,21 @@ end
"Find all bound energies between E_min (=0) and E_max (=mass) where
tol_digits determines the precision for root finding and the threshold for identifying duplicates,
the other parameters are the same from dirac!(...)."
function findEs(κ, p, Φ0, W0, B0, A0, s::system, E_min=0, E_max=(p ? M_p : M_n), tol_digits=5)
func = boundaryValueFunc(κ, p, Φ0, W0, B0, A0, s)
function findEs(κ, p, s::system, E_min=0, E_max=(p ? M_p : M_n), tol_digits=5)
func = boundaryValueFunc(κ, p, s)
Es = find_zeros(func, (E_min, E_max); xatol=1/10^tol_digits)
return unique(E -> round(E; digits=tol_digits), Es)
end
"Find all orbitals and return two lists containing κ values and corresponding energies for a single species where
the other parameters are defined above"
function findAllOrbitals(p, Φ0, W0, B0, A0, s::system, E_min=0, E_max=(p ? M_p : M_n))
function findAllOrbitals(p, s::system, E_min=0, E_max=(p ? M_p : M_n))
κs = Int[]
Es = Float64[]
# start from κ=-1 and go both up and down
for direction in [-1, 1]
for κ in direction * (1:100) # cutoff is 100
new_Es = findEs(κ, p, Φ0, W0, B0, A0, s, E_min, E_max)
new_Es = findEs(κ, p, s, E_min, E_max)
if isempty(new_Es); break; end
append!(Es, new_Es)
append!(κs, fill(κ, length(new_Es)))
@ -120,11 +123,11 @@ l_κ(κ::Int) = abs(κ) - (κ < 0) # since true = 1 and false = 0
"Calculate scalar and vector densities of a nucleon species on [0,r_max] divided into (divs+1) points and returns them as vectors (ρ_s, ρ_v) where
the arrays κs, Es, occs tabulate the energies and occupation numbers corresponding to each κ,
the other parameters are defined above"
function calculateNucleonDensity(κs, Es, occs, p, Φ0, W0, B0, A0, s::system)
function calculateNucleonDensity(κs, Es, occs, p, s::system)
ρr2 = zeros(2, s.divs + 1) # ρ×r² values
for (κ, E, occ) in zip(κs, Es, occs)
wf = solveNucleonWf(κ, p, E, Φ0, W0, B0, A0, s; shooting=true, normalize=true)
wf = solveNucleonWf(κ, p, E, s; shooting=true, normalize=true)
wf2 = wf .* wf
ρr2 += (occ / (4 * pi)) * wf2 # 2j+1 factor is accounted in the occupancy number
end
@ -141,8 +144,8 @@ end
"Solve the Dirac equation and calculate scalar and vector densities of a nucleon species where
the other parameters are defined above"
function solveNucleonDensity(p, Φ0, W0, B0, A0, s::system, E_min=800, E_max=939)
κs, Es = findAllOrbitals(p, Φ0, W0, B0, A0, s, E_min, E_max)
function solveNucleonDensity(p, s::system, E_min=800, E_max=939)
κs, Es = findAllOrbitals(p, s, E_min, E_max)
occs = fillNucleons(Z_or_N(s, p), κs, Es)
return calculateNucleonDensity(κs, Es, occs, p, Φ0, W0, B0, A0, s)
return calculateNucleonDensity(κs, Es, occs, p, s)
end

17
system.jl
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@ -18,11 +18,11 @@ mutable struct system
ρ_sn::Vector{Float64}
ρ_vn::Vector{Float64}
"Dummy struct to define the mesh"
system(r_max, divs) = new(0, 0, r_max, divs, [Float64[] for _ in 1:8]...)
"Initialize an unsolved system"
system(Z, N, r_max, divs) = new(Z, N, r_max, divs, [zeros(1 + divs) for _ in 1:8]...)
"Dummy struct to define the mesh"
system(r_max, divs) = system(0, 0, r_max, divs)
end
"Get mass number of nucleus"
@ -73,18 +73,17 @@ function solve_system(s::system; reinitialize_densities=true, monitor_print=true
while true
# mesons
@time "Meson fields" solveMesonWfs(s.ρ_sp, s.ρ_vp, s.ρ_sn, s.ρ_vn, s, isnan(E_total_previous) ? 50 : 5; initial_sol = (s.Φ0, s.W0, s.B0, s.A0))
(S_interp, V_interp, R_interp, A_interp) = fields_interp(s)
@time "Meson fields" solveMesonFields!(s, isnan(E_total_previous) ? 50 : 5)
# protons
@time "Proton spectrum" (κs_p, Es_p) = findAllOrbitals(true, S_interp, V_interp, R_interp, A_interp, s)
@time "Proton spectrum" (κs_p, Es_p) = findAllOrbitals(true, s)
occs_p = fillNucleons(s.Z, κs_p, Es_p)
@time "Proton densities" (s.ρ_sp, s.ρ_vp) = calculateNucleonDensity(κs_p, Es_p, occs_p, true, S_interp, V_interp, R_interp, A_interp, s)
@time "Proton densities" (s.ρ_sp, s.ρ_vp) = calculateNucleonDensity(κs_p, Es_p, occs_p, true, s)
# neutrons
@time "Neutron spectrum" (κs_n, Es_n) = findAllOrbitals(false, S_interp, V_interp, R_interp, A_interp, s)
@time "Neutron spectrum" (κs_n, Es_n) = findAllOrbitals(false, s)
occs_n = fillNucleons(s.N, κs_n, Es_n)
@time "Neutron densities" (s.ρ_sn, s.ρ_vn) = calculateNucleonDensity(κs_n, Es_n, occs_n, false, S_interp, V_interp, R_interp, A_interp, s)
@time "Neutron densities" (s.ρ_sn, s.ρ_vn) = calculateNucleonDensity(κs_n, Es_n, occs_n, false, s)
if monitor_plot
for s in p.series_list

11
test/Pb208_meson_flds.jl
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@ -16,16 +16,17 @@ plot(xs_bench, hcat(Φ0_bench, W0_bench, B0_bench, A0_bench), layout=4, label=["
# format: x Rhos(n) Rhov(n) Rhot(n) Rhos(p) Rhov(p) Rhot(p)
test_data = readdlm("test/Pb208DensFSUGarnet.csv")
xs = test_data[:, 1]
ρ_sn = test_data[:, 2]
ρ_vn = test_data[:, 3]
ρ_sp = test_data[:, 5]
ρ_vp = test_data[:, 6]
r_max = maximum(xs)
divs = length(xs) - 1
s = system(r_max, divs)
(Φ0, W0, B0, A0) = solveMesonWfs(ρ_sp, ρ_vp, ρ_sn, ρ_vn, s, 200) # many iterations needed without an initial solution
s.ρ_sn = test_data[:, 2]
s.ρ_vn = test_data[:, 3]
s.ρ_sp = test_data[:, 5]
s.ρ_vp = test_data[:, 6]
(Φ0, W0, B0, A0) = solveMesonFields!(s, 200) # many iterations needed without an initial solution
plot!(xs, hcat(Φ0, W0, B0, A0), layout=4, label=["Φ0" "W0" "B0" "A0"])
xlabel!("r (fm)")

6
test/Pb208_nucleon_basic.jl
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@ -21,17 +21,15 @@ s.W0 = Vs
s.B0 = Rs
s.A0 = As
(S_interp, V_interp, R_interp, A_interp) = fields_interp(s)
E_min = 850
E_max = 939
boundEs = findEs(κ, p, S_interp, V_interp, R_interp, A_interp, s, E_min, E_max)
boundEs = findEs(κ, p, s, E_min, E_max)
binding_Es = (p ? M_p : M_n) .- boundEs
println("binding energies = $binding_Es")
func = boundaryValueFunc(κ, p, S_interp, V_interp, R_interp, A_interp, s)
func = boundaryValueFunc(κ, p, s)
Es = collect(E_min:0.5:E_max)
boundaryVals = [func(E)^2 for E in Es]

6
test/Pb208_nucleon_dens.jl
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@ -21,14 +21,12 @@ s.W0 = Vs
s.B0 = Rs
s.A0 = As
(S_interp, V_interp, R_interp, A_interp) = fields_interp(s)
(ρ_sp, ρ_vp) = solveNucleonDensity(true, S_interp, V_interp, R_interp, A_interp, s)
(ρ_sp, ρ_vp) = solveNucleonDensity(true, s)
p_sp = plot(rs(s), ρ_sp, xlabel="r (fm)", label="ρₛₚ(r) calculated")
p_vp = plot(rs(s), ρ_vp, xlabel="r (fm)", label="ρᵥₚ(r) calculated")
(ρ_sn, ρ_vn) = solveNucleonDensity(false, S_interp, V_interp, R_interp, A_interp, s)
(ρ_sn, ρ_vn) = solveNucleonDensity(false, s)
p_sn = plot(rs(s), ρ_sn, xlabel="r (fm)", label="ρₛₙ(r) calculated")
p_vn = plot(rs(s), ρ_vn, xlabel="r (fm)", label="ρᵥₙ(r) calculated")

4
test/Pb208_nucleon_spectrum.jl
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@ -22,12 +22,10 @@ s.W0 = Vs
s.B0 = Rs
s.A0 = As
(S_interp, V_interp, R_interp, A_interp) = fields_interp(s)
E_min = 800
E_max = 939
κs, Es = findAllOrbitals(p, S_interp, V_interp, R_interp, A_interp, s, E_min, E_max)
κs, Es = findAllOrbitals(p, s, E_min, E_max)
Ebinds = (p ? M_p : M_n) .- Es
occ = fillNucleons(Z_or_N(s, p), κs, Es)

6
test/Pb208_nucleon_wf.jl
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@ -21,15 +21,13 @@ s.W0 = Vs
s.B0 = Rs
s.A0 = As
(S_interp, V_interp, R_interp, A_interp) = fields_interp(s)
E_min = 800
E_max = 939
groundE = findEs(κ, p, S_interp, V_interp, R_interp, A_interp, s, E_min, E_max) |> minimum
groundE = findEs(κ, p, s, E_min, E_max) |> minimum
println("ground state E = $groundE")
wf = solveNucleonWf(κ, p, groundE, S_interp, V_interp, R_interp, A_interp, s)
wf = solveNucleonWf(κ, p, groundE, s)
gs = wf[1, :]
fs = wf[2, :]