******************* 786 **************************** c Ref: "Electron-Ion Recombination Rate Coefficients and Photoionization Cross Sections for Astrophysically Abundant Elements. XII. Na IX, Na X, Mg X, and Mg XI for UV and X-ray modeling", Sultana N. Nahar, Astrophys. J. Suppl. 167, 315 (2006) c **************************************************** c Na XI : Energies, Oscillator strengths and decay rates for allowed (E1) and forbidden (E2,E3,M1,m2) transitions (1s to 4f) Process: Na XI + h\nu <-> Na XI* Contents of the file (contains both LS and fine structure transitions): --------------------- i) Table 1 - Ion Information and Configuration Set: ii) LS Term Energies (Relative to the ground) iii) Transitions in pure LS coupling - Oscillator Strengths: iv) Fine Structure energies: relativistic(BP): v-a) Same Spin-Multiplicity Dipole allowed E1 (E1d) fine structure transitions v-b) Fine structure intercombination (E1i) transitions vi) Forbidden Electric Octupole E3 & Magnetic Quadrupole M2 transitions: vii) Forbidden Electric Quadrupole E2 & Magnetic Dipole M1 transitions: --------------------------------------------------------------------------- i) Table 1 - Ion Information and Configuration Set: --------------------------------------------------- Ion: nz = 11, nelc = 1 Total No of LS terms= 10 Configuration set: 10 configurations: first**** spectroscopic, rest**** correlation 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f Number of orbitals = 10 Scaling parameters of the orbitals: 1.00000(1s) 1.00000(2s) 1.00000(2p) 1.00000(3s) 0.00000(3p) 1.00000(3d) 1.00000(4s) 1.00000(4p) 1.00000(4d) 1.00000(4f) -------------------------------------------------------------------------- ii) LS Term Energies (Relative to the ground) ---------------------------------------------- i SLP E(Rel,Ry) cfg# 1 2Se 0.000000 1 2 2Po 90.750046 3 3 2Se 90.750046 2 4 2De 107.555595 6 5 2Po 107.555603 5 6 2Se 107.555603 4 7 2Fo 113.437546 10 8 2De 113.437546 9 9 2Po 113.437546 8 10 2Se 113.437546 7 No of first LS terms optimized = 10 -------------------------------------------------------------------------- iii) Transitions in pure LS coupling - Oscillator Strengths: ------------------------------------------------------------ Table Explanation: ------------------ LSi:CFi -> Initial LS term & configuration number as in Table 1 LSf:CFf -> Final LS term & configuration number as in Table 1 fL, fV -> oscillator strengths in length and velocity forms -------------------- Ni LSi:CFi Nf LSf:CFf Ei Ef aji(s-1) fL fV %diff 1 2Se: 1 2 2Po: 3 0.0000 90.7500 9.177E+12 4.16E-01 4.16E-01 0.0E+00 1 2Se: 1 5 2Po: 5 0.0000 107.5556 2.450E+12 7.91E-02 7.91E-02 0.0E+00 1 2Se: 1 9 2Po: 8 0.0000 113.4375 9.988E+11 2.90E-02 2.90E-02 1.7E-02 2 2Po: 3 4 2De: 6 90.7500 107.5556 9.470E+11 6.96E-01 6.96E-01 4.8E-04 2 2Po: 3 6 2Se: 4 90.7500 107.5556 9.248E+10 1.36E-02 1.36E-02 2.5E-02 2 2Po: 3 8 2De: 9 90.7500 113.4375 3.021E+11 1.22E-01 1.22E-01 1.0E-06 2 2Po: 3 10 2Se: 7 90.7500 113.4375 3.777E+10 3.04E-03 3.05E-03 1.6E-01 3 2Se: 2 5 2Po: 5 90.7500 107.5556 3.288E+11 4.35E-01 4.35E-01 2.3E-03 3 2Se: 2 9 2Po: 8 90.7500 113.4375 1.416E+11 1.03E-01 1.03E-01 9.7E-03 4 2De: 6 7 2Fo:10 107.5556 113.4375 2.020E+11 1.02E+00 1.02E+00 4.7E-06 4 2De: 6 9 2Po: 8 107.5556 113.4375 5.091E+09 1.10E-02 1.10E-02 2.5E-06 5 2Po: 5 8 2De: 9 107.5556 113.4375 1.031E+11 6.18E-01 6.18E-01 2.7E-04 5 2Po: 5 10 2Se: 7 107.5556 113.4375 2.689E+10 3.22E-02 3.22E-02 1.9E-06 6 2Se: 4 9 2Po: 8 107.5556 113.4375 4.490E+10 4.85E-01 4.85E-01 1.0E-03 LS transitions: Number of oscillator strengths = 14 ----------------------------------------------------------------------------- iv) Fine Structure energies: relativistic(BP): ----------------------------------------------- ie SLp(cf#) g k*cm E(Ry) 1 2Se( 1) 2 0.0 0.00000E+00 2 2Po( 3) 2 9973381.0 9.08841E+01 3 2Se( 2) 2 9973396.0 9.08843E+01 4 2Po( 3) 4 9978738.0 9.09330E+01 5 2Po( 5) 2 11821900.0 1.07729E+02 6 2Se( 4) 2 11821905.0 1.07729E+02 7 2De( 6) 4 11823479.0 1.07743E+02 8 2Po( 5) 4 11823480.0 1.07743E+02 9 2De( 6) 6 11824008.0 1.07748E+02 10 2Po( 8) 2 12468661.0 1.13623E+02 11 2Se( 7) 2 12468663.0 1.13623E+02 12 2De( 9) 4 12469323.0 1.13629E+02 13 2Po( 8) 4 12469324.0 1.13629E+02 14 2Fo(10) 6 12469546.0 1.13631E+02 15 2De( 9) 6 12469546.0 1.13631E+02 16 2Fo(10) 8 12469657.0 1.13632E+02 ------------------------------------------------------------------------ v-a) Same Spin-Multiplicity Dipole allowed E1 (E1d) fine structure transitions -------------------------------------------------------- Table Explanation: ----------------- SLpCi -> initial symmetry (2S+1)Lpi(parity) & configuration number as in Table 1 SLpCi -> final symmetry (2S+1)Lpi(parity) & configuration number as in Table 1 fij, S, aji -> Oscillator strength fij, line strengh S & transition probability aji for electic dipole E1 same-spin transition ------------------------ Nj Ni SLpCj SLpCi gj gi wl(A) Ej(Ry) Ei(Ry) fij S aji(s-1) 2 1 2Po 3 2Se 1 2 2 10.03 90.88 0.00 1.38E-01 9.111E-03 9.16E+12 4 1 2Po 3 2Se 1 4 2 10.02 90.93 0.00 2.76E-01 -1.819E-02 9.16E+12 4 3 2Po 3 2Se 2 4 2 18720.48 90.93 90.88 2.41E-03 2.972E-01 2.29E+04 5 1 2Po 5 2Se 1 2 2 8.46 107.73 0.00 2.59E-02 1.443E-03 2.42E+12 5 3 2Po 5 2Se 2 2 2 54.10 107.73 90.88 1.44E-01 5.137E-02 3.29E+11 6 2 2Se 4 2Po 3 2 2 54.10 107.73 90.88 1.33E-02 4.754E-03 3.04E+10 6 4 2Se 4 2Po 3 2 4 54.25 107.73 90.93 1.37E-02 9.818E-03 6.23E+10 7 2 2De 6 2Po 3 4 2 54.05 107.74 90.88 6.92E-01 -2.465E-01 7.91E+11 7 4 2De 6 2Po 3 4 4 54.21 107.74 90.93 6.95E-02 4.960E-02 1.58E+11 7 5 2De 6 2Po 5 4 2 63307.39 107.74 107.73 2.68E-03 1.116E+00 2.23E+03 8 1 2Po 5 2Se 1 4 2 8.46 107.74 0.00 5.21E-02 -2.902E-03 2.43E+12 8 3 2Po 5 2Se 2 4 2 54.05 107.74 90.88 2.87E-01 -1.021E-01 3.27E+11 8 6 2Po 5 2Se 4 4 2 63478.03 107.74 107.73 4.27E-03 1.784E+00 3.53E+03 9 4 2De 6 2Po 3 6 4 54.19 107.75 90.93 6.25E-01 -4.462E-01 9.47E+11 9 8 2De 6 2Po 5 6 4 189545.84 107.75 107.74 8.05E-04 2.008E+00 9.96E+01 10 1 2Po 8 2Se 1 2 2 8.02 113.62 0.00 9.27E-03 4.890E-04 9.61E+11 10 3 2Po 8 2Se 2 2 2 40.08 113.62 90.88 3.35E-02 8.843E-03 1.39E+11 10 6 2Po 8 2Se 4 2 2 154.62 113.62 107.73 1.60E-01 1.630E-01 4.47E+10 10 7 2Po 8 2De 6 2 4 155.00 113.62 107.74 9.20E-03 1.877E-02 5.11E+09 11 2 2Se 7 2Po 3 2 2 40.08 113.62 90.88 2.81E-03 7.410E-04 1.17E+10 11 4 2Se 7 2Po 3 2 4 40.16 113.62 90.93 3.00E-03 1.587E-03 2.48E+10 11 5 2Se 7 2Po 5 2 2 154.62 113.62 107.73 3.15E-02 3.211E-02 8.80E+09 11 8 2Se 7 2Po 5 2 4 154.99 113.62 107.74 3.24E-02 6.618E-02 1.80E+10 12 2 2De 9 2Po 3 4 2 40.07 113.63 90.88 1.21E-01 -3.187E-02 2.51E+11 12 4 2De 9 2Po 3 4 4 40.15 113.63 90.93 1.21E-02 6.400E-03 5.01E+10 12 5 2De 9 2Po 5 4 2 154.46 113.63 107.73 6.13E-01 -6.230E-01 8.56E+10 12 8 2De 9 2Po 5 4 4 154.84 113.63 107.74 6.17E-02 1.258E-01 1.72E+10 12 10 2De 9 2Po 8 4 2 150978.55 113.63 113.62 4.80E-03 4.770E+00 7.02E+02 13 1 2Po 8 2Se 1 4 2 8.02 113.63 0.00 1.88E-02 -9.900E-04 9.72E+11 13 3 2Po 8 2Se 2 4 2 40.07 113.63 90.88 6.71E-02 -1.772E-02 1.39E+11 13 6 2Po 8 2Se 4 4 2 154.46 113.63 107.73 3.18E-01 -3.237E-01 4.45E+10 13 7 2Po 8 2De 6 4 4 154.84 113.63 107.74 1.81E-03 3.684E-03 5.03E+08 13 9 2Po 8 2De 6 4 6 154.96 113.63 107.75 1.10E-02 3.365E-02 4.58E+09 13 11 2Po 8 2Se 7 4 2 151407.11 113.63 113.62 5.98E-03 5.959E+00 8.70E+02 14 7 2Fo10 2De 6 6 4 154.78 113.63 107.74 1.02E+00 -2.071E+00 1.89E+11 14 9 2Fo10 2De 6 6 6 154.91 113.63 107.75 4.84E-02 1.481E-01 1.35E+10 14 12 2Fo10 2De 9 6 4 449799.41 113.63 113.63 8.45E-04 5.004E+00 1.86E+01 15 4 2De 9 2Po 3 6 4 40.15 113.63 90.93 1.09E-01 -5.775E-02 3.01E+11 15 8 2De 9 2Po 5 6 4 154.78 113.63 107.74 5.55E-01 -1.131E+00 1.03E+11 15 13 2De 9 2Po 8 6 4 450432.88 113.63 113.63 1.45E-03 8.575E+00 3.17E+01 16 9 2Fo10 2De 6 8 6 154.88 113.63 107.75 9.68E-01 -2.962E+00 2.02E+11 16 15 2Fo10 2De 9 8 6 898720.25 113.63 113.63 4.02E-04 7.144E+00 2.49E+00 No of non-zero E1 transitions = 42 (I1 = 42) No of E1 transitions including (SD=0)= 42 No of lines in the table = 65 v-b) Fine structure intercombination (E1i) transitions ------------------------------------------------------ Fine structure E1i intercombination transitions in Breit-Pauli approx: Ni Nj SLpCi SLpCj gi gj wl(A) Ei(Ry) Ej(Ry) fij S aji(s-1) Number of intercombination transitions, E1i = 0 ------------------------------------------------------------------------------ vi) Forbidden Electric Octupole E3 & Magnetic Quadrupole M2 transitions: Table Explanation: ----------------- SLpCi -> initial symmetry (2S+1)Lpi(parity) & configuration number as in Table 1 SLpCi -> final symmetry (2S+1)Lpi(parity) & configuration number as in Table 1 SE3, AE3 -> line strengh S & transition probability A for electic octupole E3 transition SM2, AM2 -> line strengh S & transition probability A for magnetic quadrupole M2 transition ------------------------ Ni Nj SLpCi SLpCj gi gj wl(A) SE3 AE3 SM2 AM2 s-1 s-1 9 2 2De 6 2Po 3 6 2 54.04 -1.09E-01 4.24E+03 6.31E+00 3.40E+04 10 9 2Po 8 2De 6 2 6 155.12 -2.13E+00 1.55E+02 4.88E-01 4.05E+01 14 1 2Fo10 2Se 1 6 2 8.02 3.07E-07 7.53E+03 0.00E+00 0.00E+00 14 3 2Fo10 2Se 2 6 2 40.06 -8.48E-02 2.68E+04 0.00E+00 0.00E+00 14 6 2Fo10 2Se 4 6 2 154.41 9.70E+00 2.43E+02 0.00E+00 0.00E+00 15 2 2De 9 2Po 3 6 2 40.06 4.06E-05 1.28E+01 8.18E-01 1.97E+04 15 5 2De 9 2Po 5 6 2 154.41 -9.34E+00 2.34E+02 1.59E+01 4.51E+02 16 1 2Fo10 2Se 1 8 2 8.02 -4.09E-07 7.53E+03 0.00E+00 0.00E+00 16 3 2Fo10 2Se 2 8 2 40.06 1.13E-01 2.68E+04 0.00E+00 0.00E+00 16 6 2Fo10 2Se 4 8 2 154.38 -1.29E+01 2.43E+02 0.00E+00 0.00E+00 16 7 2Fo10 2De 6 8 4 154.76 -3.52E+00 6.51E+01 5.05E+01 1.06E+03 No of non-zero M2/E3 transitions = 11 Total number of M2/E3 transitions = 16 ---------------------------------------------------------------------------- vii) Forbidden Electric Quadrupole E2 & Magnetic Dipole M1 transitions: ----------------------------------------------------- Table Explanation: ----------------- SLpCi -> initial symmetry (2S+1)Lpi(parity) & configuration number as in Table 1 SLpCi -> final symmetry (2S+1)Lpi(parity) & configuration number as in Table 1 SE2, AE2 -> line strengh S & transition probability A for electric quadrupole E2 transition SM1, AM1 -> line strengh S & transition probability A for magnetic dipole M1 transition ------------------------ Ni Nj SLpCi SLpCj gi gj wl SE2 AE2 SM1 AM1 A s-1 s-1 3 1 2Se 1 2Se 2 2 2 10.03 0.00E+00 0.00E+00 -4.89E-06 6.54E+04 4 2 2Po 3 2Po 3 2 4 18668.72 -3.26E-02 6.04E-06 -1.33E+00 1.38E+00 5 2 2Po 3 2Po 5 2 2 54.10 0.00E+00 0.00E+00 -1.50E-07 1.28E+01 5 4 2Po 3 2Po 5 4 2 54.25 -2.37E-02 4.23E+07 -4.33E-06 3.66E+02 6 1 2Se 1 2Se 4 2 2 8.46 0.00E+00 0.00E+00 -1.33E-06 2.97E+04 6 3 2Se 2 2Se 4 2 2 54.10 0.00E+00 0.00E+00 -5.72E-07 4.87E+01 7 1 2Se 1 2De 6 2 4 8.46 -1.10E-04 1.07E+09 4.42E-08 4.93E+02 7 3 2Se 2 2De 6 2 4 54.05 1.00E-01 9.10E+07 -1.24E-07 5.30E+00 8 2 2Po 3 2Po 5 2 4 54.05 2.32E-02 2.11E+07 -1.80E-06 7.67E+01 8 4 2Po 3 2Po 5 4 4 54.21 2.36E-02 2.11E+07 -2.17E-06 9.18E+01 8 5 2Po 5 2Po 5 2 4 63272.24 -1.18E+00 4.87E-07 -1.33E+00 3.55E-02 9 1 2Se 1 2De 6 2 6 8.46 1.65E-04 1.07E+09 0.00E+00 0.00E+00 9 3 2Se 2 2De 6 2 6 54.04 -1.50E-01 9.11E+07 0.00E+00 0.00E+00 9 7 2De 6 2De 6 4 6 189231.03 -2.47E-01 2.86E-10 -2.40E+00 1.59E-03 10 2 2Po 3 2Po 8 2 2 40.08 0.00E+00 0.00E+00 -4.67E-08 9.78E+00 10 4 2Po 3 2Po 8 4 2 40.16 -2.19E-03 1.76E+07 -1.04E-06 2.17E+02 10 5 2Po 5 2Po 8 2 2 154.62 0.00E+00 0.00E+00 -4.52E-08 1.65E-01 10 8 2Po 5 2Po 8 4 2 155.00 -4.79E-01 4.50E+06 -3.94E-06 1.43E+01 11 1 2Se 1 2Se 7 2 2 8.02 0.00E+00 0.00E+00 -6.63E-07 1.73E+04 11 3 2Se 2 2Se 7 2 2 40.08 0.00E+00 0.00E+00 -2.05E-07 4.30E+01 11 6 2Se 4 2Se 7 2 2 154.62 0.00E+00 0.00E+00 -1.44E-07 5.24E-01 11 7 2De 6 2Se 7 4 2 154.99 -7.70E-02 7.23E+05 -1.76E-11 6.39E-05 11 9 2De 6 2Se 7 6 2 155.12 -1.17E-01 1.09E+06 0.00E+00 0.00E+00 12 1 2Se 1 2De 9 2 4 8.02 -5.25E-05 6.64E+08 2.05E-08 2.68E+02 12 3 2Se 2 2De 9 2 4 40.07 2.17E-03 8.82E+06 -3.31E-08 3.47E+00 12 6 2Se 4 2De 9 2 4 154.46 1.40E+00 6.68E+06 -1.22E-08 2.23E-02 12 7 2De 6 2De 9 4 4 154.84 3.12E-01 1.47E+06 -2.60E-07 4.73E-01 12 9 2De 6 2De 9 6 4 154.96 -1.34E-01 6.31E+05 -8.49E-07 1.54E+00 13 2 2Po 3 2Po 8 2 4 40.07 2.06E-03 8.38E+06 -3.52E-07 3.69E+01 13 4 2Po 3 2Po 8 4 4 40.15 2.20E-03 8.86E+06 -6.96E-07 7.25E+01 13 5 2Po 5 2Po 8 2 4 154.46 4.69E-01 2.24E+06 -2.58E-06 4.72E+00 13 8 2Po 5 2Po 8 4 4 154.84 4.77E-01 2.25E+06 -6.58E-07 1.20E+00 13 10 2Po 8 2Po 8 2 4 150878.03 -1.31E+01 7.05E-08 -1.33E+00 2.62E-03 14 2 2Po 3 2Fo10 2 6 40.06 3.16E-02 8.57E+07 0.00E+00 0.00E+00 14 4 2Po 3 2Fo10 4 6 40.15 -9.07E-03 2.44E+07 3.42E-08 2.38E+00 14 5 2Po 5 2Fo10 2 6 154.41 -2.52E+00 8.05E+06 0.00E+00 0.00E+00 14 8 2Po 5 2Fo10 4 6 154.78 7.24E-01 2.28E+06 -5.15E-08 6.25E-02 15 1 2Se 1 2De 9 2 6 8.02 7.88E-05 6.65E+08 0.00E+00 0.00E+00 15 3 2Se 2 2De 9 2 6 40.06 -3.27E-03 8.87E+06 0.00E+00 0.00E+00 15 6 2Se 4 2De 9 2 6 154.41 -2.10E+00 6.69E+06 0.00E+00 0.00E+00 15 7 2De 6 2De 9 4 6 154.78 1.33E-01 4.20E+05 -2.63E-07 3.19E-01 15 9 2De 6 2De 9 6 6 154.91 5.36E-01 1.68E+06 -1.30E-06 1.57E+00 15 12 2De 9 2De 9 4 6 449539.53 -3.97E+00 6.05E-11 -2.40E+00 1.19E-04 16 4 2Po 3 2Fo10 4 8 40.15 5.45E-02 1.10E+08 0.00E+00 0.00E+00 16 8 2Po 5 2Fo10 4 8 154.76 -4.34E+00 1.03E+07 0.00E+00 0.00E+00 16 14 2Fo10 2Fo10 6 8 897683.25 -1.35E+00 4.86E-13 -3.43E+00 1.60E-05 Number of E2,M1 transitions = 46 Total number of transitions (including non-spectroscopic) = 53 NT= total number of forbidden (E2,M1,E3,M2) transitions = 46 + 11 = 57 Net allowed (E1) and forbidden (E2,M1,E3,M2) transitions = = 42 + 57 = 99