diff --git a/dirac.jl b/dirac.jl index 590e0ad..a96307a 100644 --- a/dirac.jl +++ b/dirac.jl @@ -9,34 +9,34 @@ M_p = 938.2720813 # Proton mass in MeV/c2 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, +Φ0(r) & W0(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 +function dirac!(du, (g, f), (κ, M, E, Φ0, W0), r) + du[1] = -(κ/r) * g + (E + M - Φ0(r) - W0(r)) * f / ħc + du[2] = (κ/r) * f - (E - M + Φ0(r) - W0(r)) * g / ħc end "Solve the Dirac equation and return g(r=r_max) for given scalar and vector potentials where 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, +Φ0(r) & W0(r) are functions corresponding to scalar and vector potentials in MeV, r_max is the outer boundary in fm, r_min (=r_max/1000) is inside boundary in fm which cannot be 0 due to the centrifugal term." -function boundaryValue(κ, M, E, S, V, r_max, r_min=r_max/1000) +function boundaryValue(κ, M, E, Φ0, W0, 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)) + sol = solve(prob, RK4(), p=(κ, M, E, Φ0, W0)) return sol(r_max)[1] end "Find all bound energies between E_min (=0) and E_max (=M) where κ is the generalized angular momentum, M is the mass in MeV/c2, -S(r) & V(r) are functions corresponding to scalar and vector potentials in MeV, +Φ0(r) & W0(r) are functions corresponding to scalar and vector potentials in MeV, r_max is the outer boundary in fm, r_min (=r_max/1000) is inside boundary in fm which cannot be 0 due to the centrifugal term." -function findEs(κ, M, S, V, r_max, r_min=r_max/1000, E_min=0, E_max=M) - f(E) = boundaryValue(κ, M, E, S, V, r_max, r_min) +function findEs(κ, M, Φ0, W0, r_max, r_min=r_max/1000, E_min=0, E_max=M) + f(E) = boundaryValue(κ, M, E, Φ0, W0, r_max, r_min) return find_zeros(f, (E_min, E_max)) end