c ******************* 786 **************************** c Ref: "Electron-Ion Recombination Rate Coefficients and Photoionization Cross Sections for Astrophysically Abundant Elements IV. Relativistic calculations for C~IV and C~V for UV and X-ray modeling", Sultana N. Nahar, Anil K. Pradhan, and Honglin Zhang, Astrophys. J. Suppl. 131, 375 (2000) c **************************************************** c C VI : Energies, Oscillator strengths and decay rates for allowed (E1) and forbidden (E2,E3,M1,m2) transitions (1s to 4f) Process: C VI + h\nu <-> C VI* 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 = 6, 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 27.000006 3 3 2Se 27.000015 2 4 2De 32.000004 6 5 2Po 32.000004 5 6 2Se 32.000008 4 7 2Fo 33.750004 10 8 2De 33.750004 9 9 2Po 33.750008 8 10 2Se 33.750008 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 27.0000 8.123E+11 4.16E-01 4.16E-01 0.0E+00 1 2Se: 1 5 2Po: 5 0.0000 32.0000 2.169E+11 7.91E-02 7.91E-02 0.0E+00 1 2Se: 1 9 2Po: 8 0.0000 33.7500 8.841E+10 2.90E-02 2.90E-02 1.7E-02 2 2Po: 3 4 2De: 6 27.0000 32.0000 8.383E+10 6.96E-01 6.96E-01 2.4E-04 2 2Po: 3 6 2Se: 4 27.0000 32.0000 8.187E+09 1.36E-02 1.36E-02 2.5E-02 2 2Po: 3 8 2De: 9 27.0000 33.7500 2.674E+10 1.22E-01 1.22E-01 1.0E-06 2 2Po: 3 10 2Se: 7 27.0000 33.7500 3.343E+09 3.04E-03 3.05E-03 1.6E-01 3 2Se: 2 5 2Po: 5 27.0000 32.0000 2.911E+10 4.35E-01 4.35E-01 1.1E-03 3 2Se: 2 9 2Po: 8 27.0000 33.7500 1.254E+10 1.03E-01 1.03E-01 4.9E-03 4 2De: 6 7 2Fo:10 32.0000 33.7500 1.788E+10 1.02E+00 1.02E+00 4.7E-06 4 2De: 6 9 2Po: 8 32.0000 33.7500 4.506E+08 1.10E-02 1.10E-02 2.5E-06 5 2Po: 5 8 2De: 9 32.0000 33.7500 9.125E+09 6.18E-01 6.18E-01 5.4E-04 5 2Po: 5 10 2Se: 7 32.0000 33.7500 2.380E+09 3.22E-02 3.22E-02 1.9E-06 6 2Se: 4 9 2Po: 8 32.0000 33.7500 3.974E+09 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 2964210.0 2.70119E+01 3 2Se( 2) 2 2964211.0 2.70119E+01 4 2Po( 3) 4 2964683.0 2.70162E+01 5 2Po( 5) 2 3513278.0 3.20153E+01 6 2Se( 4) 2 3513278.0 3.20154E+01 7 2De( 6) 4 3513418.0 3.20166E+01 8 2Po( 5) 4 3513418.0 3.20166E+01 9 2De( 6) 6 3513465.0 3.20171E+01 10 2Po( 8) 2 3705433.0 3.37664E+01 11 2Se( 7) 2 3705433.0 3.37664E+01 12 2De( 9) 4 3705492.0 3.37669E+01 13 2Po( 8) 4 3705492.0 3.37669E+01 14 2Fo(10) 6 3705511.0 3.37671E+01 15 2De( 9) 6 3705511.0 3.37671E+01 16 2Fo(10) 8 3705521.0 3.37672E+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 33.74 27.01 0.00 1.39E-01 3.077E-02 8.12E+11 4 1 2Po 3 2Se 1 4 2 33.73 27.02 0.00 2.77E-01 -6.151E-02 8.12E+11 4 3 2Po 3 2Se 2 4 2 211847.73 27.02 27.01 7.16E-04 9.997E-01 5.33E+01 5 1 2Po 5 2Se 1 2 2 28.46 32.02 0.00 2.62E-02 4.916E-03 2.16E+11 5 3 2Po 5 2Se 2 2 2 182.13 32.02 27.01 1.45E-01 1.736E-01 2.91E+10 6 2 2Se 4 2Po 3 2 2 182.13 32.02 27.01 1.35E-02 1.621E-02 2.72E+09 6 4 2Se 4 2Po 3 2 4 182.28 32.02 27.02 1.36E-02 3.273E-02 5.47E+09 7 2 2De 6 2Po 3 4 2 182.08 32.02 27.01 6.95E-01 -8.331E-01 6.99E+10 7 4 2De 6 2Po 3 4 4 182.24 32.02 27.02 6.96E-02 1.669E-01 1.40E+10 7 5 2De 6 2Po 5 4 2 713926.00 32.02 32.02 7.98E-04 3.750E+00 5.22E+00 8 1 2Po 5 2Se 1 4 2 28.46 32.02 0.00 5.25E-02 -9.848E-03 2.16E+11 8 3 2Po 5 2Se 2 4 2 182.08 32.02 27.01 2.89E-01 -3.465E-01 2.91E+10 8 6 2Po 5 2Se 4 4 2 714463.06 32.02 32.02 1.28E-03 5.999E+00 8.33E+00 9 4 2De 6 2Po 3 6 4 182.22 32.02 27.02 6.26E-01 -1.502E+00 8.38E+10 10 1 2Po 8 2Se 1 2 2 26.99 33.77 0.00 9.55E-03 1.696E-03 8.74E+10 10 3 2Po 8 2Se 2 2 2 134.91 33.77 27.01 3.40E-02 3.023E-02 1.25E+10 10 6 2Po 8 2Se 4 2 2 520.41 33.77 32.02 1.61E-01 5.521E-01 3.97E+09 10 7 2Po 8 2De 6 2 4 520.79 33.77 32.02 9.17E-03 6.290E-02 4.51E+08 11 2 2Se 7 2Po 3 2 2 134.91 33.77 27.01 2.97E-03 2.642E-03 1.09E+09 11 4 2Se 7 2Po 3 2 4 135.00 33.77 27.02 3.03E-03 5.390E-03 2.22E+09 11 5 2Se 7 2Po 5 2 2 520.41 33.77 32.02 3.20E-02 1.098E-01 7.89E+08 11 8 2Se 7 2Po 5 2 4 520.79 33.77 32.02 3.23E-02 2.215E-01 1.59E+09 12 2 2De 9 2Po 3 4 2 134.90 33.77 27.01 1.22E-01 -1.079E-01 2.23E+10 12 4 2De 9 2Po 3 4 4 134.99 33.77 27.02 1.22E-02 2.161E-02 4.45E+09 12 5 2De 9 2Po 5 4 2 520.25 33.77 32.02 6.17E-01 -2.112E+00 7.60E+09 12 8 2De 9 2Po 5 4 4 520.63 33.77 32.02 6.18E-02 4.236E-01 1.52E+09 13 1 2Po 8 2Se 1 4 2 26.99 33.77 0.00 1.92E-02 -3.404E-03 8.77E+10 13 3 2Po 8 2Se 2 4 2 134.90 33.77 27.01 6.81E-02 -6.049E-02 1.25E+10 13 6 2Po 8 2Se 4 4 2 520.25 33.77 32.02 3.22E-01 -1.102E+00 3.96E+09 13 7 2Po 8 2De 6 4 4 520.63 33.77 32.02 1.82E-03 1.251E-02 4.49E+07 13 9 2Po 8 2De 6 4 6 520.76 33.77 32.02 1.10E-02 1.131E-01 4.06E+08 14 7 2Fo10 2De 6 6 4 520.58 33.77 32.02 1.02E+00 -6.972E+00 1.67E+10 14 9 2Fo10 2De 6 6 6 520.71 33.77 32.02 4.84E-02 4.982E-01 1.19E+09 15 4 2De 9 2Po 3 6 4 134.98 33.77 27.02 1.09E-01 -1.946E-01 2.67E+10 15 8 2De 9 2Po 5 6 4 520.58 33.77 32.02 5.56E-01 -3.811E+00 9.12E+09 16 9 2Fo10 2De 6 8 6 520.68 33.77 32.02 9.69E-01 -9.964E+00 1.79E+10 No of non-zero E1 transitions = 36 (I1 = 36) No of E1 transitions including (SD=0)= 36 No of lines in the table = 55 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 2 182.06 -4.17E+00 3.30E+01 2.13E+01 2.65E+02 10 9 2Po 8 2De 6 2 6 520.92 -8.10E+01 1.22E+00 1.62E+00 3.14E-01 14 1 2Fo10 2Se 1 6 2 26.99 6.70E-05 3.37E+02 0.00E+00 0.00E+00 14 3 2Fo10 2Se 2 6 2 134.90 -3.21E+00 2.07E+02 0.00E+00 0.00E+00 14 6 2Fo10 2Se 4 6 2 520.20 3.71E+02 1.89E+00 0.00E+00 0.00E+00 15 2 2De 9 2Po 3 6 2 134.90 1.36E-04 8.78E-03 2.76E+00 1.54E+02 15 5 2De 9 2Po 5 6 2 520.20 -3.60E+02 1.83E+00 5.41E+01 3.53E+00 16 1 2Fo10 2Se 1 8 2 26.99 -8.94E-05 3.37E+02 0.00E+00 0.00E+00 16 3 2Fo10 2Se 2 8 2 134.90 4.28E+00 2.07E+02 0.00E+00 0.00E+00 16 6 2Fo10 2Se 4 8 2 520.18 -4.95E+02 1.89E+00 0.00E+00 0.00E+00 16 7 2Fo10 2De 6 8 4 520.55 -1.34E+02 5.10E-01 1.70E+02 8.29E+00 No of non-zero M2/E3 transitions = 11 Total number of M2/E3 transitions = 12 ---------------------------------------------------------------------------- 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 33.74 0.00E+00 0.00E+00 -4.31E-07 1.51E+02 4 2 2Po 3 2Po 3 2 4 211163.52 -3.70E-01 3.70E-10 -1.33E+00 9.54E-04 5 2 2Po 3 2Po 5 2 2 182.13 0.00E+00 0.00E+00 -1.33E-08 2.97E-02 5 4 2Po 3 2Po 5 4 2 182.28 -2.67E-01 1.12E+06 -3.84E-07 8.55E-01 6 1 2Se 1 2Se 4 2 2 28.46 0.00E+00 0.00E+00 -1.16E-07 6.77E+01 6 3 2Se 2 2Se 4 2 2 182.13 0.00E+00 0.00E+00 -5.09E-08 1.13E-01 7 1 2Se 1 2De 6 2 4 28.46 -1.24E-03 2.78E+07 3.96E-09 1.16E+00 7 3 2Se 2 2De 6 2 4 182.08 1.14E+00 2.38E+06 -1.10E-08 1.23E-02 8 2 2Po 3 2Po 5 2 4 182.08 2.66E-01 5.58E+05 -1.60E-07 1.78E-01 8 4 2Po 3 2Po 5 4 4 182.24 2.67E-01 5.58E+05 -1.92E-07 2.14E-01 8 5 2Po 5 2Po 5 2 4 713568.00 -1.33E+01 3.02E-11 -1.33E+00 2.47E-05 9 1 2Se 1 2De 6 2 6 28.46 1.86E-03 2.78E+07 0.00E+00 0.00E+00 9 3 2Se 2 2De 6 2 6 182.07 -1.71E+00 2.39E+06 0.00E+00 0.00E+00 10 2 2Po 3 2Po 8 2 2 134.91 0.00E+00 0.00E+00 -4.21E-09 2.31E-02 10 4 2Po 3 2Po 8 4 2 135.00 -2.54E-02 4.76E+05 -9.30E-08 5.10E-01 10 5 2Po 5 2Po 8 2 2 520.41 0.00E+00 0.00E+00 -4.04E-09 3.87E-04 10 8 2Po 5 2Po 8 4 2 520.79 -5.42E+00 1.19E+05 -3.52E-07 3.36E-02 11 1 2Se 1 2Se 7 2 2 26.99 0.00E+00 0.00E+00 -5.02E-08 3.44E+01 11 3 2Se 2 2Se 7 2 2 134.91 0.00E+00 0.00E+00 -1.80E-08 9.86E-02 11 6 2Se 4 2Se 7 2 2 520.41 0.00E+00 0.00E+00 -1.29E-08 1.23E-03 11 7 2De 6 2Se 7 4 2 520.79 -8.73E-01 1.92E+04 -1.46E-12 1.40E-07 11 9 2De 6 2Se 7 6 2 520.92 -1.31E+00 2.88E+04 0.00E+00 0.00E+00 12 1 2Se 1 2De 9 2 4 26.99 -5.42E-04 1.59E+07 2.06E-09 7.08E-01 12 3 2Se 2 2De 9 2 4 134.90 2.53E-02 2.38E+05 -2.90E-09 7.97E-03 12 6 2Se 4 2De 9 2 4 520.26 1.59E+01 1.76E+05 -1.09E-09 5.20E-05 12 7 2De 6 2De 9 4 4 520.63 3.54E+00 3.88E+04 -2.31E-08 1.10E-03 12 9 2De 6 2De 9 6 4 520.76 -1.52E+00 1.66E+04 -7.53E-08 3.59E-03 13 2 2Po 3 2Po 8 2 4 134.90 2.49E-02 2.34E+05 -3.17E-08 8.70E-02 13 4 2Po 3 2Po 8 4 4 134.99 2.54E-02 2.38E+05 -6.13E-08 1.68E-01 13 5 2Po 5 2Po 8 2 4 520.25 5.39E+00 5.94E+04 -2.31E-07 1.11E-02 13 8 2Po 5 2Po 8 4 4 520.63 5.41E+00 5.94E+04 -5.84E-08 2.79E-03 14 2 2Po 3 2Fo10 2 6 134.90 3.59E-01 2.25E+06 0.00E+00 0.00E+00 14 4 2Po 3 2Fo10 4 6 134.98 -1.03E-01 6.41E+05 3.03E-09 5.54E-03 14 5 2Po 5 2Fo10 2 6 520.20 -2.86E+01 2.11E+05 0.00E+00 0.00E+00 14 8 2Po 5 2Fo10 4 6 520.58 8.20E+00 6.00E+04 -4.56E-09 1.45E-04 15 1 2Se 1 2De 9 2 6 26.99 8.13E-04 1.59E+07 0.00E+00 0.00E+00 15 3 2Se 2 2De 9 2 6 134.90 -3.80E-02 2.38E+05 0.00E+00 0.00E+00 15 6 2Se 4 2De 9 2 6 520.20 -2.39E+01 1.76E+05 0.00E+00 0.00E+00 15 7 2De 6 2De 9 4 6 520.58 1.51E+00 1.11E+04 -2.34E-08 7.45E-04 15 9 2De 6 2De 9 6 6 520.71 6.07E+00 4.44E+04 -1.15E-07 3.67E-03 16 4 2Po 3 2Fo10 4 8 134.98 6.16E-01 2.88E+06 0.00E+00 0.00E+00 16 8 2Po 5 2Fo10 4 8 520.55 -4.92E+01 2.70E+05 0.00E+00 0.00E+00 Number of E2,M1 transitions = 42 Total number of transitions (including non-spectroscopic) = 44 NT= total number of forbidden (E2,M1,E3,M2) transitions = 42 + 11 = 53 Net allowed (E1) and forbidden (E2,M1,E3,M2) transitions = = 36 + 53 = 89