c ******************* 786 **************************** c Ref: "Electron-Ion Recombination Rate Coefficients, Photoionization Cross Sections for Astrophysically Abundant Elements. VII. Relativistic calculations for O VI and O VII for UV and X-ray modeling", Sultana N. Nahar, A.K. Pradhan, Astrophys. J. Suppl. 149, 239 (2003) c **************************************************** c O VIII : Energies, Oscillator strengths and decay rates for allowed (E1) and forbidden (E2,E3,M1,m2) transitions (1s to 4f) Process: O VIII + h\nu <-> O VIII* 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 = 8, 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 48.000015 3 3 2Se 48.000027 2 4 2De 56.888901 6 5 2Se 56.888905 4 6 2Po 56.888935 5 7 2Fo 60.000011 10 8 2De 60.000011 9 9 2Po 60.000015 8 10 2Se 60.000015 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 48.0000 2.567E+12 4.16E-01 4.16E-01 0.0E+00 1 2Se: 1 6 2Po: 5 0.0000 56.8889 6.854E+11 7.91E-02 7.91E-02 0.0E+00 1 2Se: 1 9 2Po: 8 0.0000 60.0000 2.794E+11 2.90E-02 2.90E-02 1.7E-02 2 2Po: 3 4 2De: 6 48.0000 56.8889 2.649E+11 6.96E-01 6.96E-01 4.8E-04 2 2Po: 3 5 2Se: 4 48.0000 56.8889 2.587E+10 1.36E-02 1.36E-02 2.5E-02 2 2Po: 3 8 2De: 9 48.0000 60.0000 8.452E+10 1.22E-01 1.22E-01 1.0E-06 2 2Po: 3 10 2Se: 7 48.0000 60.0000 1.057E+10 3.04E-03 3.05E-03 1.6E-01 3 2Se: 2 6 2Po: 5 48.0000 56.8889 9.200E+10 4.35E-01 4.35E-01 2.3E-03 3 2Se: 2 9 2Po: 8 48.0000 60.0000 3.962E+10 1.03E-01 1.03E-01 4.9E-03 4 2De: 6 7 2Fo:10 56.8889 60.0000 5.650E+10 1.02E+00 1.02E+00 4.7E-06 4 2De: 6 9 2Po: 8 56.8889 60.0000 1.424E+09 1.10E-02 1.10E-02 2.5E-06 5 2Se: 4 9 2Po: 8 56.8889 60.0000 1.256E+10 4.85E-01 4.85E-01 4.1E-03 6 2Po: 5 8 2De: 9 56.8889 60.0000 2.884E+10 6.18E-01 6.18E-01 5.1E-03 6 2Po: 5 10 2Se: 7 56.8889 60.0000 7.519E+09 3.22E-02 3.22E-02 1.6E-02 LS transitions: Number of oscillator strengths = 14 Number of default fine structure levels = 16 ----------------------------------------------------------------------------- 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 5271508.0 4.80375E+01 3 2Se( 2) 2 5271511.0 4.80375E+01 4 2Po( 3) 4 5273005.0 4.80512E+01 5 2Se( 4) 2 6248159.0 5.69374E+01 6 2Po( 5) 2 6248161.0 5.69374E+01 7 2De( 6) 4 6248600.0 5.69414E+01 8 2Po( 5) 4 6248604.0 5.69415E+01 9 2De( 6) 6 6248748.0 5.69428E+01 10 2Po( 8) 2 6589924.0 6.00518E+01 11 2Se( 7) 2 6589925.0 6.00518E+01 12 2De( 9) 4 6590110.0 6.00535E+01 13 2Po( 8) 4 6590110.0 6.00535E+01 14 2Fo(10) 6 6590172.0 6.00541E+01 15 2De( 9) 6 6590172.0 6.00541E+01 16 2Fo(10) 8 6590203.0 6.00544E+01 ------------------------------------------------------------------------ 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 18.97 48.04 0.00 1.38E-01 1.728E-02 2.56E+12 4 1 2Po 3 2Se 1 4 2 18.96 48.05 0.00 2.77E-01 -3.453E-02 2.56E+12 4 3 2Po 3 2Se 2 4 2 66943.34 48.05 48.04 1.28E-03 5.622E-01 9.49E+02 5 2 2Se 4 2Po 3 2 2 102.39 56.94 48.04 1.35E-02 9.075E-03 8.56E+09 5 4 2Se 4 2Po 3 2 4 102.55 56.94 48.05 1.37E-02 1.846E-02 1.73E+10 6 1 2Po 5 2Se 1 2 2 16.00 56.94 0.00 2.61E-02 2.753E-03 6.80E+11 6 3 2Po 5 2Se 2 2 2 102.39 56.94 48.04 1.45E-01 9.746E-02 9.20E+10 7 2 2De 6 2Po 3 4 2 102.34 56.94 48.04 6.94E-01 -4.678E-01 2.21E+11 7 4 2De 6 2Po 3 4 4 102.50 56.94 48.05 6.95E-02 9.385E-02 4.41E+10 7 6 2De 6 2Po 5 4 2 227761.34 56.94 56.94 1.41E-03 2.109E+00 9.04E+01 8 1 2Po 5 2Se 1 4 2 16.00 56.94 0.00 5.24E-02 -5.522E-03 6.82E+11 8 3 2Po 5 2Se 2 4 2 102.34 56.94 48.04 2.88E-01 -1.943E-01 9.18E+10 8 5 2Po 5 2Se 4 4 2 224595.95 56.94 56.94 2.28E-03 3.374E+00 1.51E+02 9 4 2De 6 2Po 3 6 4 102.49 56.94 48.05 6.26E-01 -8.445E-01 2.65E+11 9 8 2De 6 2Po 5 6 4 693615.19 56.94 56.94 4.16E-04 3.796E+00 3.84E+00 10 1 2Po 8 2Se 1 2 2 15.17 60.05 0.00 9.46E-03 9.450E-04 2.74E+11 10 3 2Po 8 2Se 2 2 2 75.85 60.05 48.04 3.39E-02 1.691E-02 3.93E+10 10 5 2Po 8 2Se 4 2 2 292.60 60.05 56.94 1.61E-01 3.098E-01 1.25E+10 10 7 2Po 8 2De 6 2 4 292.98 60.05 56.94 9.18E-03 3.542E-02 1.43E+09 11 2 2Se 7 2Po 3 2 2 75.85 60.05 48.04 2.92E-03 1.458E-03 3.38E+09 11 4 2Se 7 2Po 3 2 4 75.93 60.05 48.05 3.02E-03 3.021E-03 6.99E+09 11 6 2Se 7 2Po 5 2 2 292.60 60.05 56.94 3.19E-02 6.138E-02 2.48E+09 11 8 2Se 7 2Po 5 2 4 292.98 60.05 56.94 3.23E-02 1.247E-01 5.02E+09 12 2 2De 9 2Po 3 4 2 75.84 60.05 48.04 1.21E-01 -6.056E-02 7.03E+10 12 4 2De 9 2Po 3 4 4 75.92 60.05 48.05 1.21E-02 1.214E-02 1.40E+10 12 6 2De 9 2Po 5 4 2 292.44 60.05 56.94 6.15E-01 -1.185E+00 2.40E+10 12 8 2De 9 2Po 5 4 4 292.82 60.05 56.94 6.17E-02 2.381E-01 4.80E+09 12 10 2De 9 2Po 8 4 2 537764.38 60.05 60.05 2.54E-03 9.010E+00 2.93E+01 13 1 2Po 8 2Se 1 4 2 15.17 60.05 0.00 1.90E-02 -1.900E-03 2.76E+11 13 3 2Po 8 2Se 2 4 2 75.84 60.05 48.04 6.78E-02 -3.385E-02 3.93E+10 13 5 2Po 8 2Se 4 4 2 292.44 60.05 56.94 3.21E-01 -6.173E-01 1.25E+10 13 7 2Po 8 2De 6 4 4 292.82 60.05 56.94 1.82E-03 7.014E-03 1.42E+08 13 9 2Po 8 2De 6 4 6 292.94 60.05 56.94 1.10E-02 6.362E-02 1.28E+09 13 11 2Po 8 2Se 7 4 2 538371.94 60.05 60.05 3.18E-03 1.126E+01 3.65E+01 14 7 2Fo10 2De 6 6 4 292.76 60.05 56.94 1.02E+00 -3.919E+00 5.27E+10 14 9 2Fo10 2De 6 6 6 292.89 60.05 56.94 4.84E-02 2.802E-01 3.76E+09 15 4 2De 9 2Po 3 6 4 75.92 60.05 48.05 1.09E-01 -1.094E-01 8.44E+10 15 8 2De 9 2Po 5 6 4 292.77 60.05 56.94 5.55E-01 -2.141E+00 2.88E+10 16 9 2Fo10 2De 6 8 6 292.86 60.05 56.94 9.69E-01 -5.604E+00 5.65E+10 No of non-zero E1 transitions = 39 (I1 = 39) No of E1 transitions including (SD=0)= 39 No of lines in the table = 61 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 ------------------------ Forbidden E3 and M2 transitions in Breit-Pauli approximation: Ni Nj SLpCi SLpCj gi gj wl(A) SE3 AE3 SM2 AM2 s-1 s-1 9 2 2De 6 2Po 3 6 2 102.33 -7.40E-01 3.30E+02 1.20E+01 2.65E+03 10 9 2Po 8 2De 6 2 6 293.10 -1.44E+01 1.22E+01 9.14E-01 3.15E+00 14 1 2Fo10 2Se 1 6 2 15.17 7.78E-06 2.20E+03 0.00E+00 0.00E+00 14 3 2Fo10 2Se 2 6 2 75.83 -5.72E-01 2.08E+03 0.00E+00 0.00E+00 14 5 2Fo10 2Se 4 6 2 292.39 6.59E+01 1.89E+01 0.00E+00 0.00E+00 15 2 2De 9 2Po 3 6 2 75.83 7.67E-05 2.79E-01 1.55E+00 1.54E+03 15 6 2De 9 2Po 5 6 2 292.39 -6.37E+01 1.83E+01 3.03E+01 3.52E+01 16 1 2Fo10 2Se 1 8 2 15.17 -1.04E-05 2.20E+03 0.00E+00 0.00E+00 16 3 2Fo10 2Se 2 8 2 75.83 7.63E-01 2.08E+03 0.00E+00 0.00E+00 16 5 2Fo10 2Se 4 8 2 292.36 -8.78E+01 1.89E+01 0.00E+00 0.00E+00 16 7 2Fo10 2De 6 8 4 292.74 -2.39E+01 5.09E+00 9.56E+01 8.28E+01 No of non-zero M2/E3 transitions = 11 Total number of M2/E3 transitions = 15 ---------------------------------------------------------------------------- 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 18.97 0.00E+00 0.00E+00 -1.36E-06 2.69E+03 4 2 2Po 3 2Po 3 2 4 66786.14 -1.17E-01 3.69E-08 -1.33E+00 3.02E-02 5 1 2Se 1 2Se 4 2 2 16.00 0.00E+00 0.00E+00 -3.68E-07 1.21E+03 5 3 2Se 2 2Se 4 2 2 102.39 0.00E+00 0.00E+00 -1.60E-07 2.02E+00 6 2 2Po 3 2Po 5 2 2 102.39 0.00E+00 0.00E+00 -4.20E-08 5.27E-01 6 4 2Po 3 2Po 5 4 2 102.55 -8.46E-02 6.26E+06 -1.21E-06 1.52E+01 7 1 2Se 1 2De 6 2 4 16.00 -3.92E-04 1.57E+08 1.25E-08 2.05E+01 7 3 2Se 2 2De 6 2 4 102.34 3.59E-01 1.34E+07 -3.47E-08 2.18E-01 8 2 2Po 3 2Po 5 2 4 102.34 8.37E-02 3.13E+06 -5.04E-07 3.17E+00 8 4 2Po 3 2Po 5 4 4 102.50 8.44E-02 3.13E+06 -6.07E-07 3.80E+00 8 6 2Po 5 2Po 5 2 4 225896.81 -4.21E+00 3.01E-09 -1.33E+00 7.80E-04 9 1 2Se 1 2De 6 2 6 16.00 5.88E-04 1.57E+08 0.00E+00 0.00E+00 9 3 2Se 2 2De 6 2 6 102.33 -5.38E-01 1.34E+07 0.00E+00 0.00E+00 9 7 2De 6 2De 6 4 6 676607.81 -8.85E-01 1.75E-12 -2.40E+00 3.48E-05 10 2 2Po 3 2Po 8 2 2 75.85 0.00E+00 0.00E+00 -1.32E-08 4.09E-01 10 4 2Po 3 2Po 8 4 2 75.93 -7.96E-03 2.65E+06 -2.93E-07 9.03E+00 10 6 2Po 5 2Po 8 2 2 292.60 0.00E+00 0.00E+00 -1.27E-08 6.85E-03 10 8 2Po 5 2Po 8 4 2 292.98 -1.71E+00 6.67E+05 -1.11E-06 5.95E-01 11 1 2Se 1 2Se 7 2 2 15.17 0.00E+00 0.00E+00 -1.67E-07 6.45E+02 11 3 2Se 2 2Se 7 2 2 75.85 0.00E+00 0.00E+00 -5.70E-08 1.76E+00 11 5 2Se 4 2Se 7 2 2 292.60 0.00E+00 0.00E+00 -4.05E-08 2.18E-02 11 7 2De 6 2Se 7 4 2 292.98 -2.76E-01 1.07E+05 -4.73E-12 2.54E-06 11 9 2De 6 2Se 7 6 2 293.10 -4.16E-01 1.62E+05 0.00E+00 0.00E+00 12 1 2Se 1 2De 9 2 4 15.17 -1.77E-04 9.22E+07 6.26E-09 1.21E+01 12 3 2Se 2 2De 9 2 4 75.84 7.92E-03 1.33E+06 -9.21E-09 1.42E-01 12 5 2Se 4 2De 9 2 4 292.44 5.03E+00 9.87E+05 -3.43E-09 9.24E-04 12 7 2De 6 2De 9 4 4 292.82 1.12E+00 2.18E+05 -7.29E-08 1.96E-02 12 9 2De 6 2De 9 6 4 292.94 -4.80E-01 9.35E+04 -2.38E-07 6.38E-02 13 2 2Po 3 2Po 8 2 4 75.84 7.71E-03 1.29E+06 -9.96E-08 1.54E+00 13 4 2Po 3 2Po 8 4 4 75.92 7.98E-03 1.33E+06 -1.94E-07 2.99E+00 13 6 2Po 5 2Po 8 2 4 292.44 1.70E+00 3.33E+05 -7.27E-07 1.96E-01 13 8 2Po 5 2Po 8 4 4 292.82 1.71E+00 3.34E+05 -1.84E-07 4.95E-02 13 10 2Po 8 2Po 8 2 4 537193.06 -4.69E+01 4.40E-10 -1.33E+00 5.80E-05 14 2 2Po 3 2Fo10 2 6 75.83 1.13E-01 1.26E+07 0.00E+00 0.00E+00 14 4 2Po 3 2Fo10 4 6 75.92 -3.25E-02 3.60E+06 9.58E-09 9.84E-02 14 6 2Po 5 2Fo10 2 6 292.39 -9.05E+00 1.18E+06 0.00E+00 0.00E+00 14 8 2Po 5 2Fo10 4 6 292.77 2.59E+00 3.37E+05 -1.44E-08 2.58E-03 15 1 2Se 1 2De 9 2 6 15.17 2.65E-04 9.23E+07 0.00E+00 0.00E+00 15 3 2Se 2 2De 9 2 6 75.83 -1.19E-02 1.33E+06 0.00E+00 0.00E+00 15 5 2Se 4 2De 9 2 6 292.39 -7.54E+00 9.88E+05 0.00E+00 0.00E+00 15 7 2De 6 2De 9 4 6 292.76 4.79E-01 6.23E+04 -7.38E-08 1.32E-02 15 9 2De 6 2De 9 6 6 292.89 1.92E+00 2.49E+05 -3.64E-07 6.51E-02 16 4 2Po 3 2Fo10 4 8 75.92 1.95E-01 1.62E+07 0.00E+00 0.00E+00 16 8 2Po 5 2Fo10 4 8 292.74 -1.56E+01 1.52E+06 0.00E+00 0.00E+00 Number of E2,M1 transitions = 44 Total number of transitions (including non-spectroscopic) = 49 NT= total number of forbidden (E2,M1,E3,M2) transitions = 44 + 11 = 55 Net allowed (E1) and forbidden (E2,M1,E3,M2) transitions = = 39 + 55 = 94