475 lines
13 KiB
Python
Executable File
475 lines
13 KiB
Python
Executable File
#!/usr/bin/env python3
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from boundState import BoundState
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from solveSE import WoodsSaxonPot, CoulombPotential, SpinOrbit_Pot, WS_SurfacePot
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import matplotlib.pyplot as plt
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# boundState = BoundState(16, 8, 1, 0, 1, 0, 0.5, -3.273)
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# boundState = BoundState(16, 8, 1, 0, 0, 2, 2.5, -4.14)
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# boundState.SetPotential(1.10, 0.65, -6, 1.25, 0.65, 1.30)
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# boundState.FindPotentialDepth(-75, -50, 0.1)
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# # boundState.PrintWF()
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# boundState.PlotBoundState()
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# exit()
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from distortedWave import DistortedWave
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# dw = DistortedWave("60Ni", "p", 30)
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# dw.ClearPotential()
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# dw.AddPotential(WoodsSaxonPot(-47.937-2.853j, 1.20, 0.669), False)
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# dw.AddPotential(WS_SurfacePot(-6.878j, 1.28, 0.550), False)
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# dw.AddPotential(SpinOrbit_Pot(-5.250 + 0.162j, 1.02, 0.590), False)
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# dw.AddPotential(CoulombPotential(1.258), False)
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# dw = DistortedWave("60Ni", "d", 60)
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# dw.PrintInput()
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# dw.ClearPotential()
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# dw.AddPotential(WoodsSaxonPot(-81.919, 1.15, 0.768), False)
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# dw.AddPotential(WoodsSaxonPot(-4.836j, 1.33, 0.464), False)
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# dw.AddPotential(WS_SurfacePot(-8.994j, 1.373, 0.774), False)
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# dw.AddPotential(SpinOrbit_Pot(-3.557, 0.972, 1.011), False)
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# dw.AddPotential(CoulombPotential(1.303), False)
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# dw.CalScatteringMatrix()
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# dw.PrintScatteringMatrix()
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# dw.PlotDCSUnpolarized(180, 1)
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# exit()
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# for i in range(1, 19):
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# theta = 10*i
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# # ruth = dw.RutherFord(theta)
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# # coulAmp = dw.CoulombScatterintAmp(theta)
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# dw.CalLegendre(theta)
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# nuAmp1 = dw.NuclearScatteringAmp(-0.5, 0.5, 14)
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# nuAmp2 = dw.NuclearScatteringAmp(0.5, -0.5, 14)
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# # dsc = dw.DCSUnpolarized(theta, 14)
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# # print(f"{theta:3.0f}, {nuAmp1:15.5f}, {nuAmp2:15.5f}, {dsc:10.6f}, {ruth:10.6f}")
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# print(f"{theta:3.0f}, {nuAmp1:15.5f}, {nuAmp2:15.5f}")
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import sys, os
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import re
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import numpy as np
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from scipy.integrate import simpson
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import matplotlib.pyplot as plt
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sys.path.append(os.path.join(os.path.dirname(__file__), '../Cleopatra'))
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from IAEANuclearData import IsotopeClass
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from clebschGordan import clebsch_gordan, quantum_factorial, obeys_triangle_rule
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from sympy.physics.quantum.cg import wigner_9j
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# Woods-Saxon
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v = 0
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r0 = 0
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a = 0
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vi = 0
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ri0 = 0
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ai = 0
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# Woods-Saxon Surface
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vsi = 0
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rsi0 = 0
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asi = 0
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# Spin-orbit
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vso = 0
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rso0 = 0
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aso = 0
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vsoi = 0
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rsoi0 = 0
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asoi = 0
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# Coulomb
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rc0 = 0
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def AnCai(A : int, Z : int, E : float):
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global v, r0, a, vi, ri0, ai, vsi, rsi0, asi, vso, rso0, aso, vsoi, rsoi0, asoi, rc0
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A3 = A**(1./3.)
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v = 91.85 - 0.249*E + 0.000116*pow(E,2) + 0.642 * Z / A3
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r0 = 1.152 - 0.00776 / A3
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a = 0.719 + 0.0126 * A3
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vi = 1.104 + 0.0622 * E
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ri0 = 1.305 + 0.0997 / A3
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ai = 0.855 - 0.1 * A3
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vsi = 10.83 - 0.0306 * E
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rsi0 = 1.334 + 0.152 / A3
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asi = 0.531 + 0.062 * A3
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vso = 3.557
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rso0 = 0.972
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aso = 1.011
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vsoi = 0.0
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rsoi0 = 0.0
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asoi = 0.0
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rc0 = 1.303
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def Koning(A : int, Z : int, E : float, Zproj : float):
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global v, r0, a, vi, ri0, ai, vsi, rsi0, asi, vso, rso0, aso, vsoi, rsoi0, asoi, rc0
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N = A-Z
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A3 = A**(1./3.)
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vp1 = 59.3 + 21.*(N-Z)/A - 0.024*A
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vn1 = 59.3 - 21.*(N-Z)/A - 0.024*A
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vp2 = 0.007067 + 0.00000423*A
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vn2 = 0.007228 - 0.00000148*A
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vp3 = 0.00001729 + 0.00000001136 * A
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vn3 = 0.00001994 - 0.00000002 * A
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vp4 = 7e-9 # = vn4
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vn4 = vp4
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wp1 = 14.667 + 0.009629*A
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wn1 = 12.195 + 0.0167*A
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wp2 = 73.55 + 0.0795*A # = wn2
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wn2 = wp2
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dp1 = 16 + 16.*(N-Z)/A
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dn1 = 16 - 16.*(N-Z)/A
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dp2 = 0.018 + 0.003802/(1 + np.exp((A-156.)/8)) # = dn2
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dn2 = dp2
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dp3 = 11.5 # = dn3
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dn3 = dp3
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vso1 = 5.922 + 0.003 * A
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vso2 = 0.004
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wso1 = -3.1
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wso2 = 160
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epf = -8.4075 + 0.01378 *A
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enf = -11.2814 + 0.02646 *A
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rc = 1.198 + 0.697/pow(A3,2) + 12.995/pow(A3,5)
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vc = 1.73/rc * Z / A3
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v = vp1*(1 - vp2*(E-epf) + vp3*pow(E-epf,2) - vp4*pow(E-epf,3)) + vc * vp1 * (vp2 - 2*vp3*(E-epf) + 3*vp4*pow(E-epf,2))
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#neutron
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if Zproj == 0 :
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v = vn1*(1 - vn2*(E-enf) + vn3*pow(E-enf,2) - vn4*pow(E-enf,3))
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r0 = 1.3039 - 0.4054 / A3
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a = 0.6778 - 0.000148 * A
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vi = wp1 * pow(E-epf,2)/(pow(E-epf,2) + pow(wp2,2))
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if Zproj == 0 :
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vi = wn1 * pow(E-enf,2)/(pow(E-enf,2) + pow(wn2,2))
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ri0 = 1.3039 - 0.4054 / A3
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ai = 0.6778 - 0.000148 * A
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vsi = dp1 * pow(E-epf,2)/(pow(E-epf,2)+pow(dp3,2)) * np.exp(-dp2*(E-epf))
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if Zproj == 0 :
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vsi = dn1 * pow(E-enf,2)/(pow(E-enf,2)+pow(dn3,2)) * np.exp(-dn2*(E-enf))
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rsi0 = 1.3424 - 0.01585 * A3
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asi = 0.5187 + 0.0005205 * A
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if Zproj == 0:
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asi = 0.5446 - 0.0001656 * A
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vso = vso1 * np.exp(-vso2 * (E-epf))
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if Zproj == 0:
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vso = vso1 * np.exp(-vso2 * (E-enf))
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rso0 = 1.1854 - 0.647/A3
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aso = 0.59
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vsoi = wso1 * pow(E-epf,2)/(pow(E-epf,2)+pow(wso2,2))
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if Zproj == 0 :
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vsoi = wso1 * pow(E-enf,2)/(pow(E-enf,2)+pow(wso2,2))
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rsoi0 = 1.1854 - 0.647/A3
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asoi = 0.59
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rc0 = rc
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def ConvertLSym(LSym :str) -> int:
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if LSym == "s" :
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return 0
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elif LSym == "p" :
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return 1
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elif LSym == "d" :
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return 2
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elif LSym == "f" :
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return 3
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elif LSym == "g" :
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return 4
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elif LSym == "h" :
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return 5
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elif LSym == "i" :
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return 6
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elif LSym == "j" :
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return 7
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elif LSym == "k" :
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return 8
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else :
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return -1
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#==========================================
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nu_A = "16O"
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nu_a = "d"
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nu_b = "p"
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nu_B = "17O"
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ELabPreU = 10 # MeV/u
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Ex = 0.87
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J_B = "1/2+"
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orbital = "1s1/2"
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import time
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start_time = time.time() # Start the timer
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iso = IsotopeClass()
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A_A, Z_A = iso.GetAZ(nu_A)
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A_a, Z_a = iso.GetAZ(nu_a)
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A_b, Z_b = iso.GetAZ(nu_b)
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A_B, Z_B = iso.GetAZ(nu_B)
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A_x = abs(A_a - A_b)
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Z_x = abs(Z_a - Z_b)
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mass_A = iso.GetMassFromSym(nu_A)
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mass_a = iso.GetMassFromSym(nu_a)
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mass_b = iso.GetMassFromSym(nu_b)
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mass_B = iso.GetMassFromSym(nu_B)
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mass_x = iso.GetMassFromAZ( A_x, Z_x)
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if A_A < A_B : # (d,p)
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A_c = A_A
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Z_c = Z_A
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BindingEnergy = mass_B - mass_A - mass_x + Ex
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else: #(p,d)
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A_c = A_B
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Z_c = Z_B
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BindingEnergy = mass_A - mass_B - mass_x
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sym_A = iso.GetSymbol(A_A, Z_A)
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sym_B = iso.GetSymbol(A_B, Z_B)
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spin_A_str = iso.GetJpi(A_A, Z_A)
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spin_B_str = J_B
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spin_A = float(eval(re.sub(r'[+-]', '', spin_A_str)))
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spin_B = float(eval(re.sub(r'[+-]', '', J_B)))
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if A_a == 2 and Z_a == 1:
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spin_a = 1.0
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spin_b = 0.5
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else:
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spin_a = 0.5
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spin_b = 1.0
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s = 0.5 # spin of x, neutron or proton
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#=================== digest orbital
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match = re.search(r'[a-zA-Z]', orbital) # Find first letter
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if match:
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index = match.start() # Get position of the first letter
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node = int(orbital[:index])
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l_sym = orbital[index:index+1]
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j_sym = orbital[index+1:]
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j = eval(j_sym)
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l = ConvertLSym(l_sym)
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#==== check the angular conservasion
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passJ = False
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if obeys_triangle_rule(spin_A, spin_B, j):
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passJ = True
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else:
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print(f"the orbital spin-J ({j}) does not consver J({nu_A}) + J({nu_B}) = {spin_A} + {spin_B}.")
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passS = False
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if obeys_triangle_rule(spin_a, spin_b, s):
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passS = True
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else:
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print(f"the orbital spin-s ({s})does not consver S({nu_a}) + S({nu_b}) = {spin_a} + {spin_b}.")
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passl = False
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if obeys_triangle_rule(j, s, l):
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passl = True
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else:
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print(f"the orbital spin-l ({l})does not consver J({j}) + J({s}).")
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if passJ == False or passS == False or passl == False :
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print("Fail angular momentum conservation.")
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exit()
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reactionStr = f"{nu_A}({spin_A_str})({nu_a},{nu_b}){nu_B}({Ex:.3f}|{spin_B_str}, {orbital}) @ {ELabPreU:.1f} MeV/u"
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print("==================================================")
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print(reactionStr)
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Q_value = mass_A + mass_a - mass_b - mass_B - Ex
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print(f"Transfer Orbtial : {orbital}")
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print(f"Q-value : {Q_value:10.6f} MeV")
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print(f"Binding : {BindingEnergy:10.6f} MeV")
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#=================== find the maximum L for partial wave
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mass_I = mass_A * mass_a / (mass_A + mass_a) # reduced mass of incoming channel
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hbarc = 197.3269788 # MeV.fm
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k_I = np.sqrt(2*mass_I * A_a * ELabPreU)/hbarc # wave number of incoming channel
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touching_Radius = 1.25*(A_A**(1./3) + A_a**(1./3)) + 10 # add 10 fm
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maxL = int(touching_Radius * k_I) # maximum partial wave
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print(f"max L : {maxL}")
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#================== Bound state
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print("====================== Bound state ")
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boundState = BoundState(A_c, Z_c, A_x, Z_x, node, l, j, BindingEnergy)
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boundState.SetPotential(1.10, 0.65, -6, 1.25, 0.65, 1.30)
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boundState.FindPotentialDepth(-70, -55, 0.1)
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# # boundState.PrintWF()
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# boundState.PlotBoundState()
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# exit()
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#================== incoming wave function
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print("====================== Incoming wave function ")
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AnCai(A_A, Z_A, A_a * ELabPreU)
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dwI = DistortedWave(nu_A, nu_a, ELabPreU * A_a)
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dwI.maxL = maxL
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dwI.PrintInput()
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dwI.ClearPotential()
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dwI.AddPotential(WoodsSaxonPot(-v, r0, a), False)
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dwI.AddPotential(WoodsSaxonPot(-1j*vi, ri0, ai), False)
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dwI.AddPotential(WS_SurfacePot(-1j*vsi, rsi0, asi), False)
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dwI.AddPotential(SpinOrbit_Pot(-vso , rso0, aso), False)
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dwI.AddPotential(SpinOrbit_Pot(- 1j* vsoi, rsoi0, asoi), False)
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dwI.AddPotential(CoulombPotential(rc0), False)
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dwI.PrintPotentials()
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sm_I, wfu_I = dwI.CalScatteringMatrix()
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dwI.PrintScatteringMatrix()
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# dwI.PlotDistortedWave(1, 1, 20)
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# dwI.PlotScatteringMatrix()
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#================= outgoing wave function
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print("====================== Outgoing wave function ")
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Koning(A_B, Z_B, A_a*ELabPreU + Q_value - Ex, Z_b)
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dwO = DistortedWave(nu_B, nu_b, ELabPreU * A_a + Q_value - Ex)
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dwO.maxL = maxL
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dwO.ClearPotential()
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dwO.AddPotential(WoodsSaxonPot(-v, r0, a), False)
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dwO.AddPotential(WoodsSaxonPot(-1j*vi, ri0, ai), False)
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dwO.AddPotential(WS_SurfacePot(-1j*vsi, rsi0, asi), False)
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dwO.AddPotential(SpinOrbit_Pot(-vso , rso0, aso), False)
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dwO.AddPotential(SpinOrbit_Pot(- 1j* vsoi, rsoi0, asoi), False)
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dwO.AddPotential(CoulombPotential(rc0), False)
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dwO.PrintPotentials()
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sm_O, wfu_O = dwO.CalScatteringMatrix()
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dwO.PrintScatteringMatrix()
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# dwO.PlotDistortedWave(1, 1.5, 20)
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end_time = time.time() # End the timer
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print(f"Time used {(end_time - start_time) * 1000:.2f} milliseconds")
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#=================== Calculate radial integral
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print("====================== Calculating Radial integrals")
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def FormatSpin(spin : float) -> str:
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if int(2*spin) % 2 == 0 :
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return f"{int(spin):+d}"
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else:
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return f"{int(2*spin):+d}/2"
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spin_a = dwI.spin_a
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spin_b = dwO.spin_a
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radialInt = np.zeros((maxL+1, int(2*spin_a+1), int(2*spin_b+1)), dtype=complex)
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bs = boundState.GetBoundStateWF()
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for L in range(0, maxL+1):
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for index1 in range(0, len(wfu_I[L])):
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wf1 = wfu_I[L][index1]
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for index2 in range(0, len(wfu_O[L])):
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wf2 = wfu_O[L][index2]
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# if L == 0 and index1 == 2 and index2 == 1 :
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# for i in range(0, len(bs)):
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# if i%50 == 0 :
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# print(bs[i], wf1[i], wf2[i], bs[i]* wf1[i]* wf2[i])
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pf1 = np.exp(1j*dwI.CoulombPhaseShift(L))
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pf2 = np.exp(1j*dwI.CoulombPhaseShift(L))
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integral = simpson (bs*wf1*wf2, dx=boundState.dr)
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radialInt[L][index1][index2] = integral * pf1 * pf2
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#print radial integral
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for index1 in range(0, int(2*spin_a) + 1):
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for index2 in range(0, int(2*spin_b) + 1):
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print(f"======================= J1 = L{FormatSpin(index1-spin_a)}, J2 = L{FormatSpin(index2-spin_b)}")
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for L in range(0, maxL+1):
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J1 = L + index1 - spin_a
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J2 = L + index2 - spin_b
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print(f"{L:2d}, {J1:4.1f}, {J2:4.1f}, {np.real(radialInt[L][index1][index2]):12.4e} + {np.imag(radialInt[L][index1][index2]):12.4e}I")
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# Plot radial integral
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fig, axes = plt.subplots(int(2*spin_b+1), int(2*spin_a+1), figsize=(6*int(2*spin_a+1), 4*int(2*spin_b+1)))
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for index2 in range(0, int(2*spin_b) + 1):
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for index1 in range(0, int(2*spin_a) + 1):
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haha = []
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l_list = []
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for L in range(0, maxL+1):
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J1 = L + index1 - spin_a
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J2 = L + index2 - spin_b
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if J1 < 0 or J2 < 0 :
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continue
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l_list.append(L)
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haha.append(radialInt[L][index1][index2])
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axes[index2, index1].plot(l_list, np.real(haha), label="Real", marker='o')
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axes[index2, index1].plot(l_list, np.imag(haha), label="Imag", marker='x')
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axes[index2, index1].legend()
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axes[index2, index1].set_xlabel('L')
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axes[index2, index1].set_ylabel('Value')
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axes[index2, index1].set_title(f'Radial Int. vs L for Spin J1 = L{FormatSpin(index1-spin_a)}, J2 = L{FormatSpin(index2-spin_b)}.')
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axes[index2, index1].set_xlim(-1, maxL+1)
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axes[index2, index1].grid()
|
|
|
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plt.tight_layout()
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plt.show(block=False)
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input("Press Enter to continue...")
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|
|
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def Gamma(L1, J1, L2, J2, m, ma, mb):
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if int(L1 + L2 + l)%2 != 0:
|
|
return 0
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else:
|
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fact0 = wigner_9j(j, l, s, J1, L1, spin_a, J2, L2, spin_b)
|
|
if fact0 == 0:
|
|
return 0
|
|
else:
|
|
fact1 = pow(-1, m) * np.power(1j, L1-L2-l) * (2*L2+1) * np.sqrt((2*l+1)*(2*s+1)*(2*L1+1)*(2*J2+1))
|
|
fact2 = np.sqrt( quantum_factorial(L2-m) / quantum_factorial(L2+m) )
|
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fact3 = clebsch_gordan(J2, mb-m, j, m-mb+ma, J1, ma)
|
|
fact4 = clebsch_gordan(L1, 0, spin_a, ma, J1, ma)
|
|
fact5 = clebsch_gordan(L2, -m, spin_b, mb, J2, mb-m)
|
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fact6 = clebsch_gordan(L1, 0, l, 0, L2, 0)
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|
return fact0 * fact1 * fact2 * fact3 * fact4 * fact5 * fact6
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|
|
|
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|
def Beta(m, ma, mb, theta_deg):
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|
return 0
|
|
|
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|