From 6deee7e47c77452cb75f7b8df49ca1fcfc6b9d06 Mon Sep 17 00:00:00 2001
From: Nuwan Yapa <yapanuwan@gmail.com>
Date: Fri, 21 Jun 2024 10:58:51 -0400
Subject: [PATCH] Regular instead of r_min

---
 dirac.jl      | 15 ++++++++-------
 test/Pb208.jl |  4 ++--
 2 files changed, 10 insertions(+), 9 deletions(-)

diff --git a/dirac.jl b/dirac.jl
index 929e8e0..908a4f8 100644
--- a/dirac.jl
+++ b/dirac.jl
@@ -4,6 +4,8 @@ using DifferentialEquations, Roots
 M_n = 939.5654133 # Neutron mass in MeV/c2
 M_p = 938.2720813 # Proton mass in MeV/c2
 
+const r_reg = 1E-6 # regulator for the centrifugal term in fm
+
 "The spherical Dirac equation that returns du=[dg, df] in-place where
     u=[g, f] are the reduced radial components evaluated at r,
     κ is the generalized angular momentum,
@@ -17,23 +19,22 @@ function dirac!(du, u, (κ, p, E, Φ0, W0, B0, A0), r)
     common1 = E - W0(r) - (p - 0.5) * B0(r) - p * A0(r)
     common2 = M - Φ0(r)
     (g, f) = u
-    du[1] = -(κ/r) * g + (common1 + common2) * f / ħc
-    du[2] =  (κ/r) * f - (common1 - common2) * g / ħc
+    du[1] = -(κ/(r + r_reg)) * g + (common1 + common2) * f / ħc
+    du[2] =  (κ/(r + r_reg)) * f - (common1 - common2) * g / ħc
 end
 
 "Solve the Dirac equation and return g(r=r_max) for given scalar and vector potentials where
     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,
     the other parameters are the same from dirac!(...)."
-function boundaryValue(κ, p, E, Φ0, W0, B0, A0, r_max, r_min=r_max/1000)
-    prob = ODEProblem(dirac!, [0, 1], (r_min, r_max))
+function boundaryValue(κ, p, E, Φ0, W0, B0, A0, r_max,)
+    prob = ODEProblem(dirac!, [0, 1], (0, r_max))
     sol = solve(prob, RK4(), p=(κ, p, E, Φ0, W0, B0, A0))
     return sol(r_max)[1]
 end
 
 "Find all bound energies between E_min (=0) and E_max (=mass) where
     the other parameters are the same from dirac!(...)."
-function findEs(κ, p, Φ0, W0, B0, A0, r_max, r_min=r_max/1000, E_min=0, E_max=(p ? M_p : M_n))
-    f(E) = boundaryValue(κ, p, E, Φ0, W0, B0, A0, r_max, r_min)
+function findEs(κ, p, Φ0, W0, B0, A0, r_max, E_min=0, E_max=(p ? M_p : M_n))
+    f(E) = boundaryValue(κ, p, E, Φ0, W0, B0, A0, r_max)
     return find_zeros(f, (E_min, E_max))
 end
diff --git a/test/Pb208.jl b/test/Pb208.jl
index 1dde58d..6ab004a 100644
--- a/test/Pb208.jl
+++ b/test/Pb208.jl
@@ -18,10 +18,10 @@ A_interp = linear_interpolation(xs, As)
 κ = -1
 p = true
 r_max = maximum(xs)
-E_min = 850
+E_min = 880
 E_max = 939
 
-boundEs = findEs(κ, p, S_interp, V_interp, R_interp, A_interp, r_max, r_max/1000, E_min, E_max)
+boundEs = findEs(κ, p, S_interp, V_interp, R_interp, A_interp, r_max, E_min, E_max)
 println("bound E = $boundEs")
 
 Es = collect(E_min:0.5:E_max)