Barebones Dirac equation

Project.toml

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+[deps]
+DifferentialEquations = "0c46a032-eb83-5123-abaf-570d42b7fbaa"

dirac.jl

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+using DifferentialEquations
+
+ħc = 197.327 # ħc in MeVfm
+M_n = 939.5654133 # Neutron mass in MeV/c2
+M_p = 938.2720813 # Proton mass in MeV/c2
+
+"The spherical Dirac equation that returns du=[dg, df] in-place where
+(g, f) are the reduced radial components evaluated at r,
+κ is the generalized angular momentum,
+M is the mass in MeV/c2,
+E in the energy in MeV,
+S(r) & V(r) are functions corresponding to scalar and vector potentials in MeV,
+r is the radius in fm.
+Reference: P. Giuliani, K. Godbey, E. Bonilla, F. Viens, and J. Piekarewicz, Frontiers in Physics 10, (2023)."
+function dirac!(du, (g, f), (κ, M, E, S, V), r)
+    du[1] = -(κ/r) * g + (E + M - S(r) - V(r)) * f / ħc
+    du[2] =  (κ/r) * f - (E - M + S(r) - V(r)) * g / ħc
+end
+
+"Solve the Dirac equation and return g(r=r_max)"
+function boundaryValue(κ, M, E, S, V, r_max, r_min=r_max/1000)
+    prob = ODEProblem(dirac!, [0, 1], (r_min, r_max))
+    sol = solve(prob, RK4(), p=(κ, M, E, S, V))
+    return sol(r_max)[1]
+end

test/dirac.jl

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+include("../dirac.jl")
+
+boundaryValue(-1, M_n, 940, r -> 0, r -> 0, 20)