c ******************* 786 **************************** c Ref: "Electron-Ion Recombination Rate Coefficients and Photoionization Cross Sections for Al~XI, Al~XII, Si~XII, Si~XIV for UV and X-ray modeling", Sultana N. Nahar, New Astronomy 13, 619-638 (2008) c **************************************************** c Al XIII : Energies, Oscillator strengths and decay rates for allowed (E1) and forbidden (E2,E3,M1,m2) transitions (1s to 4f) Process: Al XIII + h\nu <-> Al XIII* 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 = 13, 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 126.750076 3 3 2Se 126.750099 2 4 2De 150.222305 6 5 2Se 150.222305 4 6 2Po 150.222443 5 7 2Fo 158.437576 10 8 2De 158.437576 9 9 2Po 158.437576 8 10 2Se 158.437576 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 126.7501 1.790E+13 4.16E-01 4.16E-01 0.0E+00 1 2Se: 1 6 2Po: 5 0.0000 150.2224 4.780E+12 7.91E-02 7.91E-02 6.3E-03 1 2Se: 1 9 2Po: 8 0.0000 158.4376 1.948E+12 2.90E-02 2.90E-02 1.7E-02 2 2Po: 3 4 2De: 6 126.7501 150.2223 1.847E+12 6.96E-01 6.96E-01 4.8E-04 2 2Po: 3 5 2Se: 4 126.7501 150.2223 1.804E+11 1.36E-02 1.36E-02 2.5E-02 2 2Po: 3 8 2De: 9 126.7501 158.4376 5.894E+11 1.22E-01 1.22E-01 1.0E-06 2 2Po: 3 10 2Se: 7 126.7501 158.4376 7.367E+10 3.04E-03 3.05E-03 1.6E-01 3 2Se: 2 6 2Po: 5 126.7501 150.2224 6.415E+11 4.35E-01 4.35E-01 1.1E-03 3 2Se: 2 9 2Po: 8 126.7501 158.4376 2.762E+11 1.03E-01 1.03E-01 0.0E+00 4 2De: 6 7 2Fo:10 150.2223 158.4376 3.940E+11 1.02E+00 1.02E+00 4.7E-06 4 2De: 6 9 2Po: 8 150.2223 158.4376 9.934E+09 1.10E-02 1.10E-02 4.5E-02 5 2Se: 4 9 2Po: 8 150.2223 158.4376 8.760E+10 4.85E-01 4.85E-01 6.2E-03 6 2Po: 5 8 2De: 9 150.2224 158.4376 2.011E+11 6.18E-01 6.18E-01 1.0E-02 6 2Po: 5 10 2Se: 7 150.2224 158.4376 5.241E+10 3.22E-02 3.22E-02 3.1E-02 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 13937928.0 1.27012E+02 3 2Se( 2) 2 13937970.0 1.27012E+02 4 2Po( 3) 4 13948385.0 1.27107E+02 5 2Se( 4) 2 16522162.0 1.50561E+02 6 2Po( 5) 2 16522163.0 1.50561E+02 7 2De( 6) 4 16525227.0 1.50589E+02 8 2Po( 5) 4 16525243.0 1.50589E+02 9 2De( 6) 6 16526258.0 1.50598E+02 10 2Po( 8) 2 17426194.0 1.58799E+02 11 2Se( 7) 2 17426200.0 1.58799E+02 12 2De( 9) 4 17427482.0 1.58811E+02 13 2Po( 8) 4 17427484.0 1.58811E+02 14 2Fo(10) 6 17427916.0 1.58815E+02 15 2De( 9) 6 17427916.0 1.58815E+02 16 2Fo(10) 8 17428132.0 1.58817E+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 7.17 127.01 0.00 1.38E-01 6.505E-03 1.78E+13 4 1 2Po 3 2Se 1 4 2 7.17 127.11 0.00 2.75E-01 -1.298E-02 1.78E+13 4 3 2Po 3 2Se 2 4 2 9601.29 127.11 127.01 3.36E-03 2.127E-01 1.22E+05 5 2 2Se 4 2Po 3 2 2 38.70 150.56 127.01 1.32E-02 3.376E-03 5.90E+10 5 4 2Se 4 2Po 3 2 4 38.85 150.56 127.11 1.38E-02 7.062E-03 1.22E+11 6 1 2Po 5 2Se 1 2 2 6.05 150.56 0.00 2.57E-02 1.025E-03 4.68E+12 6 3 2Po 5 2Se 2 2 2 38.70 150.56 127.01 1.44E-01 3.667E-02 6.41E+11 7 2 2De 6 2Po 3 4 2 38.65 150.59 127.01 6.92E-01 -1.760E-01 1.54E+12 7 4 2De 6 2Po 3 4 4 38.81 150.59 127.11 6.94E-02 3.549E-02 3.08E+11 7 6 2De 6 2Po 5 4 2 32640.64 150.59 150.56 3.72E-03 7.989E-01 1.16E+04 8 1 2Po 5 2Se 1 4 2 6.05 150.59 0.00 5.18E-02 -2.067E-03 4.72E+12 8 3 2Po 5 2Se 2 4 2 38.65 150.59 127.01 2.86E-01 -7.269E-02 6.38E+11 8 5 2Po 5 2Se 4 4 2 32454.12 150.59 150.56 5.98E-03 1.277E+00 1.89E+04 9 4 2De 6 2Po 3 6 4 38.79 150.60 127.11 6.25E-01 -3.192E-01 1.85E+12 9 8 2De 6 2Po 5 6 4 98568.75 150.60 150.59 1.11E-03 1.437E+00 5.07E+02 10 1 2Po 8 2Se 1 2 2 5.74 158.80 0.00 9.12E-03 3.440E-04 1.85E+12 10 3 2Po 8 2Se 2 2 2 28.67 158.80 127.01 3.32E-02 6.271E-03 2.70E+11 10 5 2Po 8 2Se 4 2 2 110.62 158.80 150.56 1.60E-01 1.162E-01 8.70E+10 10 7 2Po 8 2De 6 2 4 110.99 158.80 150.59 9.22E-03 1.347E-02 9.98E+09 11 2 2Se 7 2Po 3 2 2 28.67 158.80 127.01 2.72E-03 5.130E-04 2.21E+10 11 4 2Se 7 2Po 3 2 4 28.75 158.80 127.11 2.98E-03 1.130E-03 4.81E+10 11 6 2Se 7 2Po 5 2 2 110.61 158.80 150.56 3.12E-02 2.275E-02 1.70E+10 11 8 2Se 7 2Po 5 2 4 110.99 158.80 150.59 3.25E-02 4.746E-02 3.52E+10 12 2 2De 9 2Po 3 4 2 28.66 158.81 127.01 1.20E-01 -2.272E-02 4.89E+11 12 4 2De 9 2Po 3 4 4 28.74 158.81 127.11 1.21E-02 4.570E-03 9.75E+10 12 6 2De 9 2Po 5 4 2 110.46 158.81 150.56 6.10E-01 -4.439E-01 1.67E+11 12 8 2De 9 2Po 5 4 4 110.84 158.81 150.59 6.16E-02 8.992E-02 3.35E+10 12 10 2De 9 2Po 8 4 2 77662.10 158.81 158.80 6.68E-03 3.418E+00 3.70E+03 13 1 2Po 8 2Se 1 4 2 5.74 158.81 0.00 1.85E-02 -7.000E-04 1.88E+12 13 3 2Po 8 2Se 2 4 2 28.66 158.81 127.01 6.67E-02 -1.257E-02 2.71E+11 13 5 2Po 8 2Se 4 4 2 110.46 158.81 150.56 3.17E-01 -2.302E-01 8.65E+10 13 7 2Po 8 2De 6 4 4 110.83 158.81 150.59 1.80E-03 2.623E-03 9.76E+08 13 9 2Po 8 2De 6 4 6 110.96 158.81 150.60 1.10E-02 2.410E-02 8.94E+09 13 11 2Po 8 2Se 7 4 2 77957.77 158.81 158.80 8.31E-03 4.269E+00 4.56E+03 14 7 2Fo10 2De 6 6 4 110.78 158.81 150.59 1.02E+00 -1.481E+00 3.68E+11 14 9 2Fo10 2De 6 6 6 110.91 158.81 150.60 4.84E-02 1.060E-01 2.62E+10 14 12 2Fo10 2De 9 6 4 230739.34 158.81 158.81 1.18E-03 3.584E+00 9.85E+01 15 4 2De 9 2Po 3 6 4 28.74 158.81 127.11 1.09E-01 -4.128E-02 5.87E+11 15 8 2De 9 2Po 5 6 4 110.78 158.81 150.59 5.54E-01 -8.079E-01 2.01E+11 15 13 2De 9 2Po 8 6 4 231077.61 158.81 158.81 2.02E-03 6.141E+00 1.68E+02 16 9 2Fo10 2De 6 8 6 110.88 158.82 150.60 9.68E-01 -2.120E+00 3.94E+11 16 15 2Fo10 2De 9 8 6 460782.72 158.82 158.81 5.62E-04 5.116E+00 1.32E+01 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 38.63 -3.97E-02 1.62E+04 4.50E+00 1.30E+05 10 9 2Po 8 2De 6 2 6 111.12 -7.83E-01 5.88E+02 3.52E-01 1.55E+02 14 1 2Fo10 2Se 1 6 2 5.74 4.99E-09 1.28E+03 0.00E+00 0.00E+00 14 3 2Fo10 2Se 2 6 2 28.65 -3.12E-02 1.03E+05 0.00E+00 0.00E+00 14 5 2Fo10 2Se 4 6 2 110.41 3.55E+00 9.29E+02 0.00E+00 0.00E+00 15 2 2De 9 2Po 3 6 2 28.65 2.90E-05 9.59E+01 5.84E-01 7.51E+04 15 6 2De 9 2Po 5 6 2 110.41 -3.40E+00 8.91E+02 1.13E+01 1.72E+03 16 1 2Fo10 2Se 1 8 2 5.74 -6.66E-09 1.28E+03 0.00E+00 0.00E+00 16 3 2Fo10 2Se 2 8 2 28.65 4.16E-02 1.03E+05 0.00E+00 0.00E+00 16 5 2Fo10 2Se 4 8 2 110.38 -4.73E+00 9.31E+02 0.00E+00 0.00E+00 16 7 2Fo10 2De 6 8 4 110.75 -1.29E+00 2.48E+02 3.61E+01 4.04E+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 7.17 0.00E+00 0.00E+00 -9.56E-06 3.49E+05 4 2 2Po 3 2Po 3 2 4 9563.32 -1.67E-02 8.76E-05 -1.33E+00 1.03E+01 5 1 2Se 1 2Se 4 2 2 6.05 0.00E+00 0.00E+00 -2.63E-06 1.60E+05 5 3 2Se 2 2Se 4 2 2 38.70 0.00E+00 0.00E+00 -1.11E-06 2.59E+02 6 2 2Po 3 2Po 5 2 2 38.70 0.00E+00 0.00E+00 -2.91E-07 6.78E+01 6 4 2Po 3 2Po 5 4 2 38.85 -1.21E-02 1.15E+08 -8.44E-06 1.94E+03 7 1 2Se 1 2De 6 2 4 6.05 -5.65E-05 2.93E+09 8.56E-08 2.60E+03 7 3 2Se 2 2De 6 2 4 38.65 5.10E-02 2.49E+08 -2.42E-07 2.83E+01 8 2 2Po 3 2Po 5 2 4 38.65 1.18E-02 5.76E+07 -3.49E-06 4.08E+02 8 4 2Po 3 2Po 5 4 4 38.81 1.21E-02 5.76E+07 -4.23E-06 4.88E+02 8 6 2Po 5 2Po 5 2 4 32464.39 -6.02E-01 7.01E-06 -1.33E+00 2.63E-01 9 1 2Se 1 2De 6 2 6 6.05 8.47E-05 2.92E+09 0.00E+00 0.00E+00 9 3 2Se 2 2De 6 2 6 38.64 -7.66E-02 2.49E+08 0.00E+00 0.00E+00 9 5 2Se 4 2De 6 2 6 24415.30 5.66E-01 1.83E-05 0.00E+00 0.00E+00 9 7 2De 6 2De 6 4 6 96978.84 -1.27E-01 4.14E-09 -2.40E+00 1.18E-02 10 2 2Po 3 2Po 8 2 2 28.67 0.00E+00 0.00E+00 -9.00E-08 5.15E+01 10 4 2Po 3 2Po 8 4 2 28.75 -1.11E-03 4.73E+07 -2.03E-06 1.15E+03 10 6 2Po 5 2Po 8 2 2 110.62 0.00E+00 0.00E+00 -8.77E-08 8.73E-01 10 8 2Po 5 2Po 8 4 2 110.99 -2.45E-01 1.22E+07 -7.65E-06 7.54E+01 11 1 2Se 1 2Se 7 2 2 5.74 0.00E+00 0.00E+00 -1.41E-06 1.00E+05 11 3 2Se 2 2Se 7 2 2 28.67 0.00E+00 0.00E+00 -4.04E-07 2.31E+02 11 5 2Se 4 2Se 7 2 2 110.61 0.00E+00 0.00E+00 -2.78E-07 2.77E+00 11 7 2De 6 2Se 7 4 2 110.99 -3.94E-02 1.96E+06 -3.57E-11 3.52E-04 11 9 2De 6 2Se 7 6 2 111.12 -6.00E-02 2.97E+06 0.00E+00 0.00E+00 12 1 2Se 1 2De 9 2 4 5.74 -2.82E-05 1.91E+09 3.70E-08 1.32E+03 12 3 2Se 2 2De 9 2 4 28.66 1.09E-03 2.37E+07 -6.50E-08 1.86E+01 12 5 2Se 4 2De 9 2 4 110.46 7.14E-01 1.82E+07 -2.38E-08 1.19E-01 12 7 2De 6 2De 9 4 4 110.83 1.59E-01 4.00E+06 -5.08E-07 2.51E+00 12 9 2De 6 2De 9 6 4 110.96 -6.88E-02 1.72E+06 -1.66E-06 8.17E+00 13 2 2Po 3 2Po 8 2 4 28.66 1.02E-03 2.20E+07 -6.81E-07 1.95E+02 13 4 2Po 3 2Po 8 4 4 28.74 1.11E-03 2.38E+07 -1.36E-06 3.87E+02 13 6 2Po 5 2Po 8 2 4 110.46 2.38E-01 6.08E+06 -5.00E-06 2.50E+01 13 8 2Po 5 2Po 8 4 4 110.84 2.44E-01 6.12E+06 -1.28E-06 6.35E+00 13 10 2Po 8 2Po 8 2 4 77606.51 -6.74E+00 1.00E-06 -1.33E+00 1.92E-02 14 2 2Po 3 2Fo10 2 6 28.65 1.62E-02 2.34E+08 0.00E+00 0.00E+00 14 4 2Po 3 2Fo10 4 6 28.74 -4.65E-03 6.64E+07 6.67E-08 1.26E+01 14 6 2Po 5 2Fo10 2 6 110.41 -1.29E+00 2.20E+07 0.00E+00 0.00E+00 14 8 2Po 5 2Fo10 4 6 110.78 3.71E-01 6.22E+06 -1.01E-07 3.33E-01 15 1 2Se 1 2De 9 2 6 5.74 4.24E-05 1.91E+09 0.00E+00 0.00E+00 15 3 2Se 2 2De 9 2 6 28.65 -1.65E-03 2.39E+07 0.00E+00 0.00E+00 15 5 2Se 4 2De 9 2 6 110.41 -1.07E+00 1.82E+07 0.00E+00 0.00E+00 15 7 2De 6 2De 9 4 6 110.78 6.82E-02 1.14E+06 -5.13E-07 1.70E+00 15 9 2De 6 2De 9 6 6 110.91 2.75E-01 4.58E+06 -2.54E-06 8.37E+00 15 12 2De 9 2De 9 4 6 230586.19 -2.03E+00 8.74E-10 -2.40E+00 8.80E-04 16 4 2Po 3 2Fo10 4 8 28.74 2.79E-02 2.99E+08 0.00E+00 0.00E+00 16 8 2Po 5 2Fo10 4 8 110.76 -2.22E+00 2.80E+07 0.00E+00 0.00E+00 16 14 2Fo10 2Fo10 6 8 460172.34 -6.92E-01 7.04E-12 -3.43E+00 1.19E-04 Number of E2,M1 transitions = 47 Total number of transitions (including non-spectroscopic) = 53 NT= total number of forbidden (E2,M1,E3,M2) transitions = 47 + 11 = 58 Net allowed (E1) and forbidden (E2,M1,E3,M2) transitions = = 42 + 58 = 100