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Implemented determinant and removed boundary value

This commit is contained in:
Nuwan Yapa 2025-02-19 12:49:43 -05:00
parent b8e82644a8
commit df8ed2fe12
2 changed files with 16 additions and 11 deletions
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19
nucleons.jl
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@ -78,13 +78,18 @@ function solveNucleonWf(κ, p::Bool, E, s::system; shooting=true, normalize=true
return wf return wf
end end
"Returns a function that solves the Dirac equation and returns g(r=r_max) where "Returns a function that solves the Dirac equation in two partitions and returns
r_max is the outer boundary in fm, the determinant of [g_left(r) g_right(r); f_left(r) f_right(r)],
the other parameters are the same from dirac!(...)." where is r is in fm."
function boundaryValueFunc(κ, p::Bool, s::system; dtype=Float64, algo=Tsit5()) function determinantFunc(κ, p::Bool, s::system, r::Float64=s.r_max/2, algo=Tsit5())
prob = ODEProblem(dirac!, convert.(dtype, [0, 1]), (0, s.r_max))
(f1, f2) = optimized_dirac_potentials(p, s) (f1, f2) = optimized_dirac_potentials(p, s)
func(E) = solve(prob, algo, p=(κ, E, f1, f2), saveat=[s.r_max], save_idxs=[1])[1, 1] prob_left = ODEProblem(dirac!, [0.0, 1.0], (0, r))
prob_right = ODEProblem(dirac!, [0.0, 1.0], (s.r_max, r))
function func(E)
u_left = solve(prob_left, algo, p=(κ, E, f1, f2), saveat=[r])
u_right = solve(prob_right, algo, p=(κ, E, f1, f2), saveat=[r])
return u_left[1, 1] * u_right[2, 1] - u_right[1, 1] * u_left[2, 1]
end
return func return func
end end
@ -92,7 +97,7 @@ end
tol_digits determines the precision for root finding and the threshold for identifying duplicates, tol_digits determines the precision for root finding and the threshold for identifying duplicates,
the other parameters are the same from dirac!(...)." the other parameters are the same from dirac!(...)."
function findEs(κ, p::Bool, s::system, E_min=850.0, E_max=938.0, tol_digits=5) function findEs(κ, p::Bool, s::system, E_min=850.0, E_max=938.0, tol_digits=5)
func = boundaryValueFunc(κ, p, s) func = determinantFunc(κ, p, s)
Es = find_all_zeros(func, E_min, E_max; partitions=20, tol=1/10^tol_digits) Es = find_all_zeros(func, E_min, E_max; partitions=20, tol=1/10^tol_digits)
return unique(E -> round(E; digits=tol_digits), Es) return unique(E -> round(E; digits=tol_digits), Es)
end end

8
test/Pb208_nucleon_basic.jl → test/Pb208_shooting.jl
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@ -29,10 +29,10 @@ boundEs = findEs(κ, p, s, E_min, E_max)
binding_Es = (p ? M_p : M_n) .- boundEs binding_Es = (p ? M_p : M_n) .- boundEs
println("binding energies = $binding_Es") println("binding energies = $binding_Es")
func = boundaryValueFunc(κ, p, s) func = determinantFunc(κ, p, s)
Es = collect(E_min:0.5:E_max) Es = collect(E_min:0.1:E_max)
boundaryVals = [func(E)^2 for E in Es] dets = [func(E)^2 for E in Es]
plot(Es, boundaryVals, yscale=:log10, label="g(r_max)^2") plot(Es, dets, yscale=:log10, label="determinant^2")
vline!(boundEs, label="bound E") vline!(boundEs, label="bound E")
xlabel!("E (MeV)") xlabel!("E (MeV)")