.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/core/plot_spectra_RaF.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_core_plot_spectra_RaF.py: Spectrum RaF ============ Calculating the optical spectrum of :math:`^{226}\text{RaF}` using spectroscopic constants. Radium monofluoride is of particular interest due to its applications in precision measurements with a heavy nucleus. .. GENERATED FROM PYTHON SOURCE LINES 12-17 .. code-block:: Python from MoleCool.spectra import Molecule, ElectronicStateConstants, cm2THz from MoleCool import pi, np, plt from copy import deepcopy .. GENERATED FROM PYTHON SOURCE LINES 19-40 Spectroscopic constants ----------------------- Literature: - [a] Garcia Ruiz 2020: "Spectroscopy of short-lived radioactive molecules". see Extended Data Table 2 in https://doi.org/10.1038/s41586-020-2299-4 using the relations :math:`\omega_e \chi_e\approx\omega_e^2/(4D_e)` and :math:`A_e\approx A_{00}`. - [b] Udrescu 2023: "Precision spectroscopy and laser cooling scheme of a radium-containing molecule" https://doi.org/10.1038/s41567-023-02296-w using the relations :math:`B_e\approx 3/2\,B_0 - 1/2\, B_1` and :math:`\alpha_e \approx B_0-B_1`. - [c] Petrov, Skripnikov 2020: "Energy levels of radium monofluoride RaF in external electric and magnetic fields to search for P- and T,P-violation effects" https://doi.org/10.1103/PhysRevA.102.062801 where the hyperfine tensor components are converted into Frosch and Foley parameters. - [2] Skripnikov 2020: "Nuclear magnetization distribution effect in molecules: Ra+and RaF hyperfine structure" - [5] Nuclear magnetic moments: https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.59.771 .. GENERATED FROM PYTHON SOURCE LINES 40-69 .. code-block:: Python X_cts = ElectronicStateConstants( const = { 'w_e' : 441.8, # [a] 'w_e x_e' : 1.6711, # [a] 'B_e' : 192.5175e-3, # [b] 'D_e' : 1.4e-7, # [a] 'alpha_e' : 1.0650e-3, # [b] 'gamma' : 5.8500e-3, # [b] 'b_F' : 3.2133e-3, # [c] 'c' : 0.6338e-3, # [c] }, unit = '1/cm', ) A_cts = ElectronicStateConstants( const = { 'T_e' : 14321.377, # [b] 'w_e' : 435.5, # [a] 'w_e x_e' : 1.635, # [a] 'A_e' : 2067.6000, # [a] 'p' : -0.4107, # [b] 'B_e' : 191.5375e-3, # [b] 'D_e' : 1.4e-7, # [a] 'alpha_e' : 1.0450e-3, # [b] }, unit = '1/cm', ) .. GENERATED FROM PYTHON SOURCE LINES 70-71 export all constants as dictionary: .. GENERATED FROM PYTHON SOURCE LINES 71-82 .. code-block:: Python X_cts.to_dict(exclude_default=False) # Or as a nice format using pandas.DataFrame: df = X_cts.show( formatting = 'non-zero', createHTML = 'cts_A', # to create a html file with nice format ) # which is the same as: X_cts .. raw:: html
value (1/cm) value (MHz)
vibration w_e 4.418000e+02 1.324483e+07
w_e x_e 1.671100e+00 5.009832e+04
rotation B_e 1.925175e-01 5.771529e+03
D_e 1.400000e-07 4.197094e-03
alpha_e 1.065000e-03 3.192790e+01
spin-rotation gamma 5.850000e-03 1.753786e+02
hyperfine b_F 3.213300e-03 9.633231e+01
c 6.338000e-04 1.900085e+01
Zeeman (no unit) g_S 2.002000e+00 2.002000e+00
g'_L 1.000000e+00 1.000000e+00


.. GENERATED FROM PYTHON SOURCE LINES 83-93 Setting up a molecule --------------------- The diatomic molecule :math:`^{226}\text{RaF}` has a single non-zero nuclear spin 1/2. We also set the temperature to 4 K which will affect the Boltzmann distribution of the calculated spectrum below. We also add two electronic states -- the ground state `X` and first excited state `A` with respective Hund's cases `b` and `a_p` (meaning well-defined parity eigenstates due to lambda doubling). The vibrational states :math:`\nu` are set to 0. .. GENERATED FROM PYTHON SOURCE LINES 93-117 .. code-block:: Python mol = Molecule( I1 = 0.5, # nuclear spin 1/2 label = '226 RaF', # label mass = 226+19, # temp = 4, ) mol.add_electronicstate( 'X', 2, 'Sigma', const = X_cts, nu = 0, Hcase = 'b', ) mol.add_electronicstate( 'A', 2, 'Pi', const = A_cts, nu = 0, Hcase = 'a_p', Gamma = 1/50e-9/(2*pi)*1e-6, # 50ns to in MHz [a] ) mol.build_states(Fmax = 4) print(mol) .. rst-class:: sphx-glr-script-out .. code-block:: none Molecule 226 RaF: with the nuclear spins I1 = 0.5, I2 = 0 and mass 245 u magnetic field strength: 0.00e+00G, temperature: 4.00K Including the following defined electronic states: * ground state X(^2)Sigma: - Hunds case b - open shell electronic state --> includes 18 states * excited state A(^2)Pi: - Hunds case a_p - open shell electronic state - linewidth: 2 pi * 3.18 MHz --> includes 32 states .. GENERATED FROM PYTHON SOURCE LINES 118-119 or just a single electonic state: .. GENERATED FROM PYTHON SOURCE LINES 119-120 .. code-block:: Python print(mol.X) .. rst-class:: sphx-glr-script-out .. code-block:: none ground state X(^2)Sigma: - Hunds case b - open shell electronic state --> includes 18 states .. GENERATED FROM PYTHON SOURCE LINES 121-123 The constants object ``X_cts`` (which is displayed above) is now also stored as the attribute ``const`` inside the :class:`~.spectra.ElectronicState` object: .. GENERATED FROM PYTHON SOURCE LINES 123-127 .. code-block:: Python print(type(mol.A.const)) # mol.A.const is the same as A_cts mol.A.const .. rst-class:: sphx-glr-script-out .. code-block:: none .. raw:: html
value (1/cm) value (MHz)
electronic energy offset T_e 1.432138e+04 4.293441e+08
vibration w_e 4.355000e+02 1.305596e+07
w_e x_e 1.635000e+00 4.901607e+04
rotation B_e 1.915375e-01 5.742150e+03
D_e 1.400000e-07 4.197094e-03
alpha_e 1.045000e-03 3.132831e+01
spin-orbit A_e 2.067600e+03 6.198509e+07
Lambda-doubling p -4.107000e-01 -1.231248e+04
Zeeman (no unit) g_S 2.002000e+00 2.002000e+00
g'_L 1.000000e+00 1.000000e+00


.. GENERATED FROM PYTHON SOURCE LINES 128-130 Electronic state ---------------- .. GENERATED FROM PYTHON SOURCE LINES 130-136 .. code-block:: Python mol.X.get_eigenstates( mixed_states = False, # transform basis to good Hund's case basis rounded = None, # better overview in table entries createHTML = False, # to export html file ) .. rst-class:: sphx-glr-script-out .. code-block:: none Calc Hamiltonian for X electronic state ..diagonalize it .. raw:: html
eigenvalue
L N J F
0 0.0 0.5 0.0 -0.002410
1.0 0.000803
1.0 0.5 1.0 0.377616
0.0 0.378712
1.5 1.0 0.385898
2.0 0.387677
2.0 1.5 2.0 1.142530
1.0 1.143833
2.5 2.0 1.156864
3.0 1.158533
3.0 2.5 3.0 2.291473
2.0 2.292839
3.5 3.0 2.311741
4.0 2.313363
4.0 3.5 4.0 3.824405
3.0 3.825803
4.5 4.0 3.850569
5.0 4.5 4.0 5.742733


.. GENERATED FROM PYTHON SOURCE LINES 137-139 Zeeman splitting plot ^^^^^^^^^^^^^^^^^^^^^ .. GENERATED FROM PYTHON SOURCE LINES 139-144 .. code-block:: Python mol.X.plot_Zeeman(np.linspace(0,70e-4,5)) plt.ylim(0.375,0.391) # mol.X.get_gfactors() .. image-sg:: /auto_examples/core/images/sphx_glr_plot_spectra_RaF_001.png :alt: plot spectra RaF :srcset: /auto_examples/core/images/sphx_glr_plot_spectra_RaF_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none Calc Hamiltonian for X electronic state ..diagonalize it Calc Hamiltonian for X electronic state ..diagonalize it Calc Hamiltonian for X electronic state ..diagonalize it Calc Hamiltonian for X electronic state ..diagonalize it Calc Hamiltonian for X electronic state ..diagonalize it (0.375, 0.391) .. GENERATED FROM PYTHON SOURCE LINES 145-147 Optical spectra --------------- .. GENERATED FROM PYTHON SOURCE LINES 147-152 .. code-block:: Python mol.build_states(Fmax = 11) mol.get_branratios(normalize = True) .. rst-class:: sphx-glr-script-out .. code-block:: none Calculating linestrengths in pure basis Calc Hamiltonian for X electronic state ..diagonalize it Calc Hamiltonian for A electronic state ..diagonalize it .. raw:: html
P -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1
Om 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 ... 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5
J 0.5 1.5 0.5 2.5 1.5 3.5 2.5 4.5 3.5 5.5 4.5 6.5 5.5 7.5 6.5 8.5 7.5 9.5 8.5 10.5 ... 1.5 2.5 2.5 3.5 3.5 4.5 4.5 5.5 5.5 6.5 6.5 7.5 7.5 8.5 8.5 9.5 9.5 10.5 10.5 11.5 11.5
F 0.0 1.0 2.0 1.0 1.0 0.0 2.0 3.0 2.0 1.0 3.0 4.0 2.0 3.0 5.0 4.0 3.0 4.0 5.0 6.0 4.0 5.0 6.0 7.0 6.0 5.0 7.0 8.0 6.0 7.0 8.0 9.0 7.0 8.0 10.0 9.0 8.0 9.0 11.0 10.0 ... 1.0 2.0 3.0 2.0 3.0 2.0 4.0 3.0 4.0 3.0 5.0 4.0 5.0 4.0 5.0 6.0 5.0 6.0 6.0 7.0 7.0 6.0 8.0 7.0 8.0 7.0 8.0 9.0 9.0 8.0 9.0 10.0 9.0 10.0 10.0 11.0 10.0 11.0 11.0 11.0
L N J F
0 0.0 0.5 0.0 0.000000e+00 2.222222e-01 0.000000e+00 8.180280e-27 5.807241e-25 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 1.111727e-01 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 ... 3.332717e-01 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
1.0 6.665434e-01 4.444855e-01 1.158603e-28 6.011897e-26 1.394918e-24 6.586482e-32 3.072336e-09 0.000000e+00 1.667837e-01 5.554529e-02 0.000000e+00 0.000000e+00 7.598170e-33 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 ... 1.666975e-01 4.998706e-01 0.000000e+00 6.151487e-09 0.000000e+00 1.072076e-20 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
1.0 0.5 1.0 1.701527e-32 1.525003e-24 1.979928e-01 1.058413e-02 4.893990e-01 4.762190e-01 1.341394e-31 0.000000e+00 1.361989e-28 1.418268e-26 0.000000e+00 0.000000e+00 6.675008e-03 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 ... 3.058791e-11 5.423055e-12 0.000000e+00 2.324046e-14 0.000000e+00 1.333522e-02 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
0.0 0.000000e+00 5.008218e-25 0.000000e+00 1.110495e-01 2.222222e-01 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 1.815770e-28 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 ... 3.893687e-11 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
1.5 1.0 1.061288e-31 1.531425e-27 2.192962e-02 4.895083e-01 1.060099e-02 5.237810e-01 4.360231e-30 0.000000e+00 1.371186e-29 1.020418e-26 0.000000e+00 0.000000e+00 1.734581e-01 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 ... 2.779582e-11 1.394314e-12 0.000000e+00 6.039313e-13 0.000000e+00 3.465317e-01 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
2.0 0.000000e+00 9.972735e-25 4.801490e-01 8.888691e-02 2.777778e-01 0.000000e+00 5.525872e-31 5.181086e-30 3.235843e-28 1.597233e-26 1.353925e-09 0.000000e+00 1.999882e-02 2.001593e-01 0.000000e+00 0.000000e+00 3.253860e-34 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 ... 7.784612e-12 4.542480e-12 6.968310e-13 6.972286e-14 3.998369e-01 4.000651e-02 0.000000e+00 2.259880e-09 0.000000e+00 2.808029e-24 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
2.0 1.5 2.0 0.000000e+00 2.741569e-01 3.517947e-28 4.025007e-26 8.731406e-25 0.000000e+00 3.760739e-03 2.134407e-01 4.960982e-01 5.457443e-02 3.542807e-31 0.000000e+00 1.378812e-31 6.109832e-30 0.000000e+00 0.000000e+00 2.662691e-03 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 ... 8.564528e-02 3.444133e-01 3.740491e-01 7.468456e-02 6.518883e-13 1.301594e-13 0.000000e+00 5.506243e-18 0.000000e+00 4.431260e-03 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
1.0 3.334566e-01 5.551449e-02 3.565747e-29 1.424008e-27 9.496249e-26 2.547179e-32 1.798670e-01 0.000000e+00 5.329390e-02 4.443623e-01 0.000000e+00 0.000000e+00 4.504572e-30 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 ... 3.333949e-01 4.005176e-02 0.000000e+00 3.601330e-01 0.000000e+00 6.276355e-13 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
2.5 2.0 0.000000e+00 3.620871e-03 1.966823e-30 1.313639e-26 3.524827e-26 0.000000e+00 4.964610e-01 1.091335e-02 3.772443e-03 3.343453e-01 2.621188e-29 0.000000e+00 1.187188e-29 1.450845e-31 0.000000e+00 0.000000e+00 2.016076e-01 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 ... 8.099059e-02 2.238280e-02 4.785531e-02 3.917604e-01 8.340167e-14 6.827554e-13 0.000000e+00 4.169092e-16 0.000000e+00 3.355161e-01 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
3.0 0.000000e+00 0.000000e+00 1.879918e-28 0.000000e+00 0.000000e+00 0.000000e+00 3.429097e-02 4.900455e-01 2.800517e-01 0.000000e+00 1.738628e-30 7.098268e-28 5.660333e-31 1.028684e-29 0.000000e+00 7.460488e-10 1.020520e-02 2.144903e-01 0.000000e+00 0.000000e+00 8.277905e-33 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 ... 0.000000e+00 9.328158e-02 4.351273e-01 3.046706e-02 7.583347e-13 5.309763e-14 9.127728e-13 2.113369e-17 3.569367e-01 1.700776e-02 0.000000e+00 1.121142e-09 0.000000e+00 4.335198e-21 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
3.0 2.5 3.0 0.000000e+00 0.000000e+00 2.780978e-01 0.000000e+00 0.000000e+00 0.000000e+00 3.565523e-31 1.183359e-29 1.864954e-28 0.000000e+00 1.910992e-03 2.216763e-01 1.989217e-02 4.978427e-01 0.000000e+00 2.222585e-30 3.814545e-31 7.389385e-28 0.000000e+00 0.000000e+00 1.429684e-03 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 ... 0.000000e+00 1.171003e-12 7.409155e-13 7.307116e-14 4.251323e-01 4.192774e-02 3.439280e-01 3.425720e-02 8.795064e-13 4.256768e-17 0.000000e+00 8.277012e-15 0.000000e+00 2.140565e-03 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
2.0 0.000000e+00 2.868909e-26 1.998034e-02 2.999712e-01 1.844546e-09 0.000000e+00 1.166987e-29 4.912145e-31 1.248853e-29 8.265199e-27 2.038931e-01 0.000000e+00 4.797793e-01 2.446632e-02 0.000000e+00 0.000000e+00 2.619854e-29 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 ... 1.168382e-11 8.430043e-14 3.798580e-14 7.439649e-13 2.179599e-02 4.268820e-01 0.000000e+00 3.403245e-01 0.000000e+00 4.228841e-16 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
3.5 3.0 0.000000e+00 0.000000e+00 1.850475e-03 0.000000e+00 0.000000e+00 0.000000e+00 6.389894e-30 8.927908e-32 1.065233e-30 0.000000e+00 4.984189e-01 6.530625e-03 3.001966e-01 1.919644e-03 0.000000e+00 2.760830e-28 6.757364e-29 2.139061e-29 0.000000e+00 0.000000e+00 2.148594e-01 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 ... 0.000000e+00 7.791903e-15 2.715541e-14 2.288575e-13 1.558159e-02 1.313169e-01 2.663055e-02 4.416034e-01 6.810070e-14 5.487323e-16 0.000000e+00 1.243907e-12 0.000000e+00 3.216938e-01 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
4.0 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 6.336713e-30 0.000000e+00 0.000000e+00 1.814664e-02 4.941743e-01 0.000000e+00 2.756121e-01 2.438607e-28 6.950858e-30 2.671511e-30 1.648633e-27 4.698697e-10 0.000000e+00 6.174618e-03 2.224729e-01 0.000000e+00 0.000000e+00 0.000000e+00 8.388611e-33 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 ... 0.000000e+00 0.000000e+00 2.399004e-13 0.000000e+00 1.376533e-01 0.000000e+00 4.626171e-01 1.699913e-02 1.183023e-12 2.112296e-17 3.232988e-13 3.580022e-14 3.330818e-01 9.258497e-03 6.592772e-10 0.000000e+00 6.132033e-22 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
4.0 3.5 4.0 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 2.743099e-01 0.000000e+00 0.000000e+00 1.618399e-30 1.657237e-27 0.000000e+00 6.375248e-30 2.268211e-01 1.153655e-03 1.021632e-02 4.985006e-01 2.488633e-29 0.000000e+00 1.358343e-30 2.478755e-28 0.000000e+00 0.000000e+00 0.000000e+00 8.912055e-04 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 ... 0.000000e+00 0.000000e+00 1.373070e-01 0.000000e+00 2.392971e-13 0.000000e+00 1.166747e-12 3.022789e-17 4.562525e-01 2.432650e-02 3.254513e-01 1.946962e-02 3.158924e-13 7.528399e-14 1.157925e-15 0.000000e+00 1.244922e-03 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
3.0 0.000000e+00 0.000000e+00 3.205560e-33 0.000000e+00 0.000000e+00 0.000000e+00 2.856203e-01 1.019200e-02 9.681309e-10 0.000000e+00 6.662237e-29 4.728503e-29 5.976319e-30 2.910068e-31 0.000000e+00 2.158100e-01 4.894647e-01 1.409310e-02 0.000000e+00 0.000000e+00 2.715430e-28 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 ... 0.000000e+00 3.224717e-10 5.111356e-03 1.429550e-01 8.908010e-15 2.491402e-13 3.387162e-14 5.709864e-16 1.324538e-02 4.595129e-01 0.000000e+00 3.243135e-01 0.000000e+00 1.254037e-12 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
4.5 4.0 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 1.098537e-03 0.000000e+00 0.000000e+00 3.903984e-29 5.162505e-30 0.000000e+00 2.498169e-34 4.345692e-03 4.992773e-01 2.858435e-01 1.160476e-03 6.143065e-27 0.000000e+00 6.225017e-28 4.033044e-30 0.000000e+00 0.000000e+00 0.000000e+00 2.225381e-01 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 ... 0.000000e+00 0.000000e+00 5.498778e-04 0.000000e+00 9.583204e-16 0.000000e+00 2.749818e-14 1.978273e-16 1.075307e-02 1.592055e-01 1.693557e-02 4.634327e-01 1.643815e-14 1.791975e-12 2.891392e-13 0.000000e+00 3.108629e-01 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
5.0 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 8.968545e-28 0.000000e+00 0.000000e+00 4.963108e-01 1.122913e-02 0.000000e+00 2.717556e-01 1.123099e-28 4.513607e-28 1.389258e-29 5.494511e-28 3.223891e-10 0.000000e+00 2.275698e-01 4.134173e-03 0.000000e+00 0.000000e+00 3.291081e-33 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 ... 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 4.163502e-13 0.000000e+00 1.628123e-01 0.000000e+00 4.755907e-01 1.076779e-02 4.616221e-13 4.163628e-14 5.379572e-15 1.000601e-14 5.783752e-03 3.178842e-01 4.309651e-10 0.000000e+00 0.000000e+00 4.900658e-23 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
5.0 4.5 5.0 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 2.707305e-01 0.000000e+00 0.000000e+00 5.476266e-28 7.038661e-30 0.000000e+00 8.986497e-28 7.712215e-04 2.303411e-01 6.205220e-03 4.987861e-01 2.787713e-30 0.000000e+00 4.593874e-28 1.924878e-29 0.000000e+00 0.000000e+00 6.084294e-04 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 ... 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 1.626785e-01 0.000000e+00 4.160080e-13 0.000000e+00 4.576272e-13 6.111292e-14 4.714750e-01 1.580476e-02 1.250590e-02 3.130343e-01 1.163196e-14 9.853349e-15 9.201218e-17 0.000000e+00 0.000000e+00 8.091417e-04 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
4.0 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 1.981005e-32 0.000000e+00 0.000000e+00 2.776303e-01 6.164349e-03 0.000000e+00 5.811109e-10 9.329529e-30 6.263722e-28 3.874125e-29 2.188723e-29 2.228520e-01 0.000000e+00 4.933940e-01 9.170438e-03 0.000000e+00 0.000000e+00 0.000000e+00 6.130689e-27 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 ... 0.000000e+00 0.000000e+00 5.058197e-22 0.000000e+00 2.902333e-10 0.000000e+00 3.710929e-03 1.668157e-01 9.489737e-15 2.072837e-16 8.569252e-15 1.834794e-12 8.828556e-03 4.745063e-01 3.126852e-01 0.000000e+00 2.908341e-13 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
5.5 5.0 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 7.239206e-04 0.000000e+00 0.000000e+00 7.976208e-31 3.666191e-28 0.000000e+00 2.412027e-30 4.997577e-01 3.099866e-03 2.779371e-01 7.768394e-04 1.168546e-27 0.000000e+00 6.720143e-30 1.387103e-26 0.000000e+00 0.000000e+00 2.275393e-01 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 ... 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 4.349947e-04 0.000000e+00 1.112386e-15 0.000000e+00 7.522312e-15 6.828517e-13 7.749936e-03 1.765961e-01 4.748440e-01 1.171012e-02 4.416610e-13 3.685982e-16 3.441054e-14 0.000000e+00 0.000000e+00 3.026013e-01 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
6.0 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 2.847146e-28 0.000000e+00 0.000000e+00 0.000000e+00 7.634063e-03 4.975794e-01 0.000000e+00 2.687937e-01 1.475032e-29 2.854604e-27 1.015563e-27 2.125826e-28 2.346771e-10 0.000000e+00 2.960512e-03 2.311128e-01 0.000000e+00 0.000000e+00 1.005121e-33 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 ... 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 1.736113e-13 0.000000e+00 1.788647e-01 0.000000e+00 7.411016e-03 4.826972e-01 6.893120e-15 1.519381e-14 4.484031e-16 2.083583e-14 3.073484e-01 3.943192e-03 0.000000e+00 3.026205e-10 0.000000e+00 9.771800e-24 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
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7.0 6.5 7.0 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 2.656452e-01 0.000000e+00 0.000000e+00 1.149271e-29 6.060683e-27 5.685230e-28 0.000000e+00 4.139165e-04 2.348368e-01 2.987589e-03 4.989532e-01 2.795058e-32 0.000000e+00 3.922456e-30 3.742933e-28 0.000000e+00 0.000000e+00 3.351960e-04 0.000000e+00 0.000000e+00 0.000000e+00 ... 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 1.901675e-01 0.000000e+00 5.985883e-15 9.305599e-16 3.290614e-14 4.853971e-01 8.183209e-03 2.974656e-01 6.387624e-03 9.541718e-16 2.062651e-16 8.318821e-20 0.000000e+00 0.000000e+00 4.176024e-04 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
6.0 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 3.002116e-32 0.000000e+00 0.000000e+00 0.000000e+00 2.689850e-01 2.953402e-03 0.000000e+00 2.733954e-10 2.520535e-27 6.126854e-29 4.986511e-30 7.492890e-27 2.307271e-01 0.000000e+00 4.964136e-01 4.778135e-03 0.000000e+00 0.000000e+00 9.858763e-28 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 ... 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 1.765784e-22 0.000000e+00 1.819269e-10 0.000000e+00 1.925539e-01 2.118043e-03 1.790979e-13 6.666940e-17 5.543931e-14 3.184293e-16 4.697138e-03 4.875252e-01 0.000000e+00 2.975269e-01 0.000000e+00 9.607552e-15 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
7.5 7.0 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 3.810788e-04 0.000000e+00 0.000000e+00 1.376808e-27 8.888677e-30 1.946623e-30 0.000000e+00 5.003062e-01 1.805065e-03 2.694906e-01 4.180620e-04 4.072421e-29 0.000000e+00 2.123674e-27 1.371833e-30 0.000000e+00 0.000000e+00 2.336609e-01 0.000000e+00 0.000000e+00 0.000000e+00 ... 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 2.728030e-04 0.000000e+00 8.586989e-18 2.239495e-14 3.062461e-16 4.517423e-03 1.969379e-01 6.550019e-03 4.857494e-01 2.101031e-17 1.568551e-14 5.798927e-17 0.000000e+00 0.000000e+00 2.911054e-01 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
8.0 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 3.283950e-27 0.000000e+00 0.000000e+00 4.187464e-03 4.989959e-01 0.000000e+00 2.647378e-01 1.866400e-31 1.481851e-27 1.700149e-29 7.507063e-28 0.000000e+00 1.401071e-10 1.731871e-03 2.357307e-01 0.000000e+00 0.000000e+00 ... 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 1.342556e-14 1.980399e-01 0.000000e+00 4.897586e-01 4.112986e-03 1.570985e-15 1.328140e-16 4.304836e-19 9.064099e-16 2.936810e-01 2.161023e-03 1.718756e-10 0.000000e+00 7.263227e-26 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
8.0 7.5 8.0 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 2.638569e-01 0.000000e+00 0.000000e+00 8.884808e-30 7.536745e-28 0.000000e+00 3.278972e-27 3.219823e-04 2.363543e-01 2.247011e-03 4.989509e-01 0.000000e+00 1.407692e-31 1.149456e-32 1.484140e-27 0.000000e+00 0.000000e+00 ... 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 1.984049e-01 1.345031e-14 0.000000e+00 1.568389e-15 2.031592e-16 4.889495e-01 6.291440e-03 4.888356e-03 2.922789e-01 9.020825e-16 9.737784e-19 1.354520e-19 0.000000e+00 3.203191e-04 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
7.0 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 2.527303e-31 0.000000e+00 0.000000e+00 2.663733e-01 2.217920e-03 2.039132e-10 0.000000e+00 2.111564e-27 3.624890e-30 1.368668e-27 3.508807e-29 2.331328e-01 0.000000e+00 4.970546e-01 3.683889e-03 0.000000e+00 0.000000e+00 3.949270e-29 0.000000e+00 0.000000e+00 0.000000e+00 ... 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 4.572701e-24 0.000000e+00 1.453294e-10 2.002937e-01 1.670707e-03 1.132609e-16 2.277655e-14 1.167728e-17 1.584612e-14 3.640421e-03 4.907229e-01 2.923862e-01 0.000000e+00 0.000000e+00 5.824442e-17 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
8.5 8.0 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 2.945083e-04 0.000000e+00 0.000000e+00 1.122781e-27 6.761853e-31 0.000000e+00 3.993808e-30 5.004926e-01 1.443229e-03 2.669785e-01 3.256459e-04 0.000000e+00 7.574338e-29 8.119488e-29 9.569886e-30 0.000000e+00 0.000000e+00 ... 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 2.214530e-04 1.501279e-17 0.000000e+00 1.156074e-17 6.567161e-15 3.604093e-03 2.033720e-01 4.885781e-01 5.165191e-03 1.594172e-17 9.732657e-17 1.213547e-16 0.000000e+00 2.869814e-01 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00
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11.0 10.5 11.0 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 2.601791e-01 0.000000e+00 0.000000e+00 0.000000e+00 1.329548e-26 4.908978e-30 ... 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 2.136612e-01 0.000000e+00 3.028468e-17 1.063477e-17 2.281772e-21 3.352882e-03 6.310456e-01 3.317953e-03 2.675728e-17
10.0 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 4.670567e-32 0.000000e+00 0.000000e+00 1.130962e-03 2.614706e-01 0.000000e+00 1.025595e-10 5.711138e-29 4.157098e-27 ... 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 2.521941e-25 8.177484e-11 0.000000e+00 2.147200e-01 9.303748e-04 9.079782e-17 1.318726e-19 1.572431e-15 9.083464e-24 4.957492e-01 2.511801e-03 3.627011e-01 2.924966e-15
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12.0 11.5 11.0 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 9.484776e-31 0.000000e+00 0.000000e+00 0.000000e+00 1.272896e-03 2.603888e-01 ... 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 9.672021e-27 0.000000e+00 6.946730e-11 2.178721e-01 1.009186e-03 6.910528e-16 3.645936e-24 5.157559e-15 6.378246e-01

46 rows × 88 columns



.. GENERATED FROM PYTHON SOURCE LINES 153-157 filtering transitions ^^^^^^^^^^^^^^^^^^^^^ the index filter argument internally utilizes the filter function :func:`~.spectra.multiindex_filter` .. GENERATED FROM PYTHON SOURCE LINES 157-166 .. code-block:: Python index_filter = ( dict(N = 1), dict(P = +1, Om = 0.5, J = 0.5), ) mol.get_branratios(normalize = False, index_filter = index_filter) .. rst-class:: sphx-glr-script-out .. code-block:: none Calculating linestrengths in pure basis .. raw:: html
P 1
Om 0.5
J 0.5
F 1.0 0.0
L N J F
0 1.0 0.5 1.0 1.468197 0.476219
0.0 0.666667 0.000000
1.5 1.0 0.031803 0.523781
2.0 0.833333 0.000000


.. GENERATED FROM PYTHON SOURCE LINES 167-168 similarly the eigeneneries can be extracted: .. GENERATED FROM PYTHON SOURCE LINES 168-177 .. code-block:: Python df2 = mol.get_E(index_filter = index_filter, recalc_branratios = False) f0 = df2.mean().mean() print(f"Mean frequency of cooling transition: {f0*cm2THz:.6f} THz") df2 # mol.X.nu = 1 # f0_repump = mol.get_E(index_filter = index_filter).mean().mean() # print(f"Mean frequency of repumping transition: {f0*cm2THz:.6f} THz") .. rst-class:: sphx-glr-script-out .. code-block:: none Mean frequency of cooling transition: 398.257789 THz .. raw:: html
P 1
Om 0.5
J 0.5
F 1.0 0.0
L N J F
0 1.0 0.5 1.0 13284.454774 13284.454774
0.0 13284.453678 13284.453678
1.5 1.0 13284.446492 13284.446492
2.0 13284.444713 13284.444713


.. GENERATED FROM PYTHON SOURCE LINES 178-183 Checking rotational leakage ^^^^^^^^^^^^^^^^^^^^^^^^^^^ Branching ratios for the state A(Om = 1/2, J = 1/2^+) decaying in any ground state (in percent). They reveal a vanishing probability of population leakage in any other ground state than X(N=1). .. GENERATED FROM PYTHON SOURCE LINES 183-189 .. code-block:: Python mol.get_branratios( index_filter = (dict(), dict(P = +1, Om = 0.5, J = 0.5)), recalc_branratios = False, ).round(6)*1e2 .. raw:: html
P 1
Om 0.5
J 0.5
F 1.0 0.0
L N J F
0 0.0 0.5 0.0 0.0000 0.0000
1.0 0.0000 0.0000
1.0 0.5 1.0 48.9399 47.6219
0.0 22.2222 0.0000
1.5 1.0 1.0601 52.3781
2.0 27.7778 0.0000
2.0 1.5 2.0 0.0000 0.0000
1.0 0.0000 0.0000
2.5 2.0 0.0000 0.0000
3.0 0.0000 0.0000
3.0 2.5 3.0 0.0000 0.0000
2.0 0.0000 0.0000
3.5 3.0 0.0000 0.0000
4.0 0.0000 0.0000
4.0 3.5 4.0 0.0000 0.0000
3.0 0.0000 0.0000
4.5 4.0 0.0000 0.0000
5.0 0.0000 0.0000
5.0 4.5 5.0 0.0000 0.0000
4.0 0.0000 0.0000
5.5 5.0 0.0000 0.0000
6.0 0.0000 0.0000
6.0 5.5 6.0 0.0000 0.0000
5.0 0.0000 0.0000
6.5 6.0 0.0000 0.0000
7.0 0.0000 0.0000
7.0 6.5 7.0 0.0000 0.0000
6.0 0.0000 0.0000
7.5 7.0 0.0000 0.0000
8.0 0.0000 0.0000
8.0 7.5 8.0 0.0000 0.0000
7.0 0.0000 0.0000
8.5 8.0 0.0000 0.0000
9.0 0.0000 0.0000
9.0 8.5 9.0 0.0000 0.0000
8.0 0.0000 0.0000
9.5 9.0 0.0000 0.0000
10.0 0.0000 0.0000
10.0 9.5 10.0 0.0000 0.0000
9.0 0.0000 0.0000
10.5 10.0 0.0000 0.0000
11.0 0.0000 0.0000
11.0 10.5 11.0 0.0000 0.0000
10.0 0.0000 0.0000
11.5 11.0 0.0000 0.0000
12.0 11.5 11.0 0.0000 0.0000


.. GENERATED FROM PYTHON SOURCE LINES 190-192 Plotting a simple spectrum ^^^^^^^^^^^^^^^^^^^^^^^^^^ .. GENERATED FROM PYTHON SOURCE LINES 192-203 .. code-block:: Python mol.calc_branratios(threshold=0.0) E, I = mol.calc_spectrum( limits = (f0-0.15,f0+0.1) ) plt.figure() plt.plot(mol.Eplt, mol.I) plt.xlabel('Frequency (cm$^{-1}$)') plt.ylabel('Intensity (arb. u.)') .. image-sg:: /auto_examples/core/images/sphx_glr_plot_spectra_RaF_002.png :alt: plot spectra RaF :srcset: /auto_examples/core/images/sphx_glr_plot_spectra_RaF_002.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none Calculating linestrengths in pure basis Text(38.347222222222214, 0.5, 'Intensity (arb. u.)') .. GENERATED FROM PYTHON SOURCE LINES 204-206 Nice spectrum with fortrat diagram ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ .. GENERATED FROM PYTHON SOURCE LINES 206-262 .. code-block:: Python # function to convert the xaxis units from cm^-1 to GHz with an offset def xconv(x): return (x * cm2THz - 398.258) * 1e3 # x-axis limits (always in units of cm^-1) limits = np.array([398.250, 398.260])/cm2THz fig, axs = plt.subplots(2,1, sharex=True) ax = axs[0] ### Plotting normal spectra mol.calc_branratios(threshold=0.0) # calculate branching ratios with Boltzmann for sigma, linewidth, color in zip([0, None], [0.8, 1.5], ['C0', 'k']): # calculate spectrum in a specific frequency range with Doppler broadening sigma E, I = mol.calc_spectrum( limits = limits, sigma = sigma, ) # plotting the spectrum ax.plot( xconv(E), I/I.max(), lw = linewidth, color = color, ) ### Plotting fortrat diagram ax = axs[1] # make a deep copy of the molecule as we modify the constants molf = deepcopy(mol) for const in [*ElectronicStateConstants.const_HFS, *ElectronicStateConstants.const_eq0Q]: molf.X.const[const] = 0 molf.X.eigenst_already_calc = False molf.calc_branratios(threshold=0.0) # calculate branching ratios with Boltzmann molf.plot_fortrat( ["N","J"], ax = ax, limits = limits, limits_unit = 'cm-1', branratio_TH = 1e-2, legend = True, xaxis_func = xconv, ) # residual annotations and labels: ax.set_ylim(top=11.9,bottom=-0.8) ax.grid(True, axis='y') ax.text(-0.1,6, "P$_1$", va='center', ha='right') ax.text(1.3,7.8, "$^\\text{P}$Q$_{12}$", va='center', ha='right') ax.text(-4.6,7.3, "$^\\text{Q}$R$_{12}$", va='bottom', ha='center') ax.text(-5,5.2, "Q$_1$", va='top', ha='center') ax.set_xlabel('Frequency (GHz)') ax.set_ylabel('Intensity (arb. u.)') .. image-sg:: /auto_examples/core/images/sphx_glr_plot_spectra_RaF_003.png :alt: plot spectra RaF :srcset: /auto_examples/core/images/sphx_glr_plot_spectra_RaF_003.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none Calculating linestrengths in pure basis Calculating linestrengths in pure basis Calc Hamiltonian for X electronic state ..diagonalize it Calculating linestrengths in pure basis Calculating linestrengths in pure basis Text(33.972222222222214, 0.5, 'Intensity (arb. u.)') .. GENERATED FROM PYTHON SOURCE LINES 263-265 Export properties for OBEs -------------------------- .. GENERATED FROM PYTHON SOURCE LINES 265-291 .. code-block:: Python mol.X.Fmax = 4 mol.A.Fmax = 4 vibr_values = { "vibrbranch": [ [0.996, 0.004], [0.004, 0.988], [1e-5, 0.008], [1e-6, 3e-5]], #[4] "vibrfreq": [ [752.760, 729.040], [778.453, 753.113], [805.745, 778.628], [834.787, 805.715]], } mol.export_OBE_properties( index_filter = (dict(N=1), dict(P=+1,Om=0.5,J=0.5)), fname = 'test_226RaF.json', HFfreq_offsets = [0,0], QuNrs_const = (['N'],['J']), # ([],[]), QuNrs_var = ([],[]), # (['J','F'],['F']) include_mF = False, vibr_values = vibr_values, rounded = 6, ) .. rst-class:: sphx-glr-script-out .. code-block:: none Calculating linestrengths in pure basis Calc Hamiltonian for X electronic state ..diagonalize it Calc Hamiltonian for A electronic state ..diagonalize it Calc Hamiltonian for X electronic state ..diagonalize it Calc Hamiltonian for X electronic state ..diagonalize it Calc Hamiltonian for X electronic state ..diagonalize it Calc Hamiltonian for A electronic state ..diagonalize it Calc Hamiltonian for A electronic state ..diagonalize it Calc Hamiltonian for A electronic state ..diagonalize it /home/docs/checkouts/readthedocs.org/user_builds/molecool-py/checkouts/latest/MoleCool/spectra.py:1314: UserWarning: Hcasebasis doesn't seem to be a good choice as the eigenstates are not diagonal (<75%). warnings.warn("Hcasebasis doesn't seem to be a good choice as the eigenstates are not diagonal (<75%).") {'mass': 245, 'level-specific': {'gs=X': {'v=0': {'N=1': {'gfac': [-0.468649, 0.0, 0.969165, 0.500492], 'HFfreq': [0.0, 32.867088, 248.303786, 301.634845], 'QuNrs': {'J': [0.5, 0.5, 1.5, 1.5], 'F': [1, 0, 1, 2]}}}}, 'exs=A': {'v=0': {'J=0.5': {'gfac': [-0.000333, -0.0], 'HFfreq': [0.0, 0.0], 'QuNrs': {'F': [1, 0]}}}, 'Gamma': 3.1830988618379066}}, 'transition-specific': {'gs=X <- exs=A': {'v=0 <- v=0': {'N=1 <- J=0.5': {'dMat_red': [[-1.211692, -0.690086], [-0.816497, 0.0], [-0.178334, 0.723727], [-0.912871, 0.0]], 'QuNrs_rows': {'J': [0.5, 0.5, 1.5, 1.5], 'F': [1, 0, 1, 2]}, 'QuNrs_cols': {'F': [1, 0]}}}, 'vibrbranch': [[0.996, 0.004], [0.004, 0.988], [1e-05, 0.008], [1e-06, 3e-05]], 'vibrfreq': [[752.76, 729.04], [778.453, 753.113], [805.745, 778.628], [834.787, 805.715]], 'QuNrs_rows': {'v': [0, 1, 2, 3]}, 'QuNrs_cols': {'v': [0, 1]}}}} .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 24.384 seconds) .. _sphx_glr_download_auto_examples_core_plot_spectra_RaF.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_spectra_RaF.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_spectra_RaF.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_spectra_RaF.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_