C************************** 786 ******************************************c Ref. "Photoionization and Electron-Ion Recombination of He I", Sultana N. Nahar, New Astronomy (in press, 2009) C************************************************************************c He II : Energies, Oscillator strengths and decay rates for allowed (E1) and forbidden (E2,E3,M1,m2) transitions (1s to 4f) Process: He II + h\nu <-> He II* 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 = 2, 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) ---------------------------------------------- LS energies: i SLP E(Rel,Ry) cfg# 1 2Se 0.000000 1 2 2Po 3.000000 3 3 2Se 3.000002 2 4 2De 3.555556 6 5 2Po 3.555556 5 6 2Se 3.555556 4 7 2Fo 3.750000 10 8 2De 3.750000 9 9 2Po 3.750000 8 10 2Se 3.750000 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 3.0000 1.003E+10 4.16E-01 4.16E-01 0.0E+00 1 2Se: 1 5 2Po: 5 0.0000 3.5556 2.677E+09 7.91E-02 7.91E-02 0.0E+00 1 2Se: 1 9 2Po: 8 0.0000 3.7500 1.092E+09 2.90E-02 2.90E-02 1.7E-02 2 2Po: 3 4 2De: 6 3.0000 3.5556 1.035E+09 6.96E-01 6.96E-01 2.4E-04 2 2Po: 3 6 2Se: 4 3.0000 3.5556 1.011E+08 1.36E-02 1.36E-02 2.5E-02 2 2Po: 3 8 2De: 9 3.0000 3.7500 3.302E+08 1.22E-01 1.22E-01 1.0E-06 2 2Po: 3 10 2Se: 7 3.0000 3.7500 4.127E+07 3.04E-03 3.05E-03 1.6E-01 3 2Se: 2 5 2Po: 5 3.0000 3.5556 3.593E+08 4.35E-01 4.35E-01 1.1E-03 3 2Se: 2 9 2Po: 8 3.0000 3.7500 1.548E+08 1.03E-01 1.03E-01 4.9E-03 4 2De: 6 7 2Fo:10 3.5556 3.7500 2.207E+08 1.02E+00 1.02E+00 4.7E-06 4 2De: 6 9 2Po: 8 3.5556 3.7500 5.563E+06 1.10E-02 1.10E-02 2.5E-06 5 2Po: 5 8 2De: 9 3.5556 3.7500 1.127E+08 6.18E-01 6.18E-01 2.7E-04 5 2Po: 5 10 2Se: 7 3.5556 3.7500 2.938E+07 3.22E-02 3.22E-02 1.9E-06 6 2Se: 4 9 2Po: 8 3.5556 3.7500 4.907E+07 4.85E-01 4.85E-01 1.0E-03 LS transitions: Number of oscillator strengths = 14 ----------------------------------------------------------------------------- iv) Fine Structure energies: relativistic(BP): ----------------------------------------------- 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 329228.0 3.00015E+00 3 2Se( 2) 2 329228.0 3.00015E+00 4 2Po( 3) 4 329234.0 3.00020E+00 5 2Po( 5) 2 390198.0 3.55575E+00 6 2Se( 4) 2 390198.0 3.55575E+00 7 2De( 6) 4 390200.0 3.55576E+00 8 2Po( 5) 4 390200.0 3.55576E+00 9 2De( 6) 6 390200.0 3.55577E+00 10 2Po( 8) 2 411537.0 3.75020E+00 11 2Se( 7) 2 411537.0 3.75020E+00 12 2De( 9) 4 411538.0 3.75021E+00 13 2Po( 8) 4 411538.0 3.75021E+00 14 2Fo(10) 6 411538.0 3.75021E+00 15 2De( 9) 6 411538.0 3.75021E+00 16 2Fo(10) 8 411538.0 3.75021E+00 ------------------------------------------------------------------------ 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 2 303.74 3.00 0.00 1.39E-01 2.774E-01 1.00E+10 4 1 2Po 3 2Se 1 4 2 303.74 3.00 0.00 2.77E-01 -5.548E-01 1.00E+10 5 1 2Po 5 2Se 1 2 2 256.28 3.56 0.00 2.64E-02 4.447E-02 2.68E+09 5 3 2Po 5 2Se 2 2 2 1640.16 3.56 3.00 1.45E-01 1.565E+00 3.59E+08 6 2 2Se 4 2Po 3 2 2 1640.15 3.56 3.00 1.36E-02 1.467E-01 3.37E+07 6 4 2Se 4 2Po 3 2 4 1640.31 3.56 3.00 1.36E-02 2.937E-01 6.74E+07 7 2 2De 6 2Po 3 4 2 1640.11 3.56 3.00 6.96E-01 -7.513E+00 8.62E+08 7 4 2De 6 2Po 3 4 4 1640.26 3.56 3.00 6.96E-02 1.503E+00 1.72E+08 8 1 2Po 5 2Se 1 4 2 256.28 3.56 0.00 5.27E-02 -8.895E-02 2.68E+09 8 3 2Po 5 2Se 2 4 2 1640.11 3.56 3.00 2.90E-01 -3.130E+00 3.59E+08 9 4 2De 6 2Po 3 6 4 1640.25 3.56 3.00 6.26E-01 -1.353E+01 1.04E+09 10 1 2Po 8 2Se 1 2 2 242.99 3.75 0.00 9.65E-03 1.544E-02 1.09E+09 10 3 2Po 8 2Se 2 2 2 1214.94 3.75 3.00 3.42E-02 2.738E-01 1.55E+08 10 6 2Po 8 2Se 4 2 2 4686.21 3.75 3.56 1.62E-01 4.984E+00 4.91E+07 10 7 2Po 8 2De 6 2 4 4686.59 3.75 3.56 9.16E-03 5.654E-01 5.56E+06 11 2 2Se 7 2Po 3 2 2 1214.93 3.75 3.00 3.04E-03 2.429E-02 1.37E+07 11 4 2Se 7 2Po 3 2 4 1215.02 3.75 3.00 3.04E-03 4.870E-02 2.75E+07 11 5 2Se 7 2Po 5 2 2 4686.21 3.75 3.56 3.22E-02 9.943E-01 9.79E+06 11 8 2Se 7 2Po 5 2 4 4686.59 3.75 3.56 3.22E-02 1.991E+00 1.96E+07 12 2 2De 9 2Po 3 4 2 1214.92 3.75 3.00 1.22E-01 -9.740E-01 2.75E+08 12 4 2De 9 2Po 3 4 4 1215.01 3.75 3.00 1.22E-02 1.948E-01 5.50E+07 12 5 2De 9 2Po 5 4 2 4686.05 3.75 3.56 6.18E-01 -1.907E+01 9.39E+07 12 8 2De 9 2Po 5 4 4 4686.43 3.75 3.56 6.18E-02 3.815E+00 1.88E+07 13 1 2Po 8 2Se 1 4 2 242.99 3.75 0.00 1.93E-02 -3.089E-02 1.09E+09 13 3 2Po 8 2Se 2 4 2 1214.92 3.75 3.00 6.84E-02 -5.477E-01 1.55E+08 13 6 2Po 8 2Se 4 4 2 4686.05 3.75 3.56 3.23E-01 -9.965E+00 4.90E+07 13 7 2Po 8 2De 6 4 4 4686.43 3.75 3.56 1.83E-03 1.130E-01 5.56E+05 13 9 2Po 8 2De 6 4 6 4686.55 3.75 3.56 1.10E-02 1.018E+00 5.01E+06 14 7 2Fo10 2De 6 6 4 4686.37 3.75 3.56 1.02E+00 -6.279E+01 2.06E+08 14 9 2Fo10 2De 6 6 6 4686.50 3.75 3.56 4.84E-02 4.485E+00 1.47E+07 15 4 2De 9 2Po 3 6 4 1215.00 3.75 3.00 1.10E-01 -1.754E+00 3.30E+08 15 8 2De 9 2Po 5 6 4 4686.37 3.75 3.56 5.57E-01 -3.434E+01 1.13E+08 16 9 2Fo10 2De 6 8 6 4686.47 3.75 3.56 9.69E-01 -8.970E+01 2.21E+08 No of non-zero E1 transitions = 33 (I1 = 33) No of E1 transitions including (SD=0)= 33 No of lines in the table = 51 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 1640.09 -3.05E+03 5.01E-03 1.92E+02 4.03E-02 10 9 2Po 8 2De 6 2 6 4686.71 -5.91E+04 1.87E-04 1.45E+01 4.77E-05 14 1 2Fo10 2Se 1 6 2 242.99 7.27E-02 7.62E-02 0.00E+00 0.00E+00 14 3 2Fo10 2Se 2 6 2 1214.92 -2.34E+03 3.14E-02 0.00E+00 0.00E+00 14 6 2Fo10 2Se 4 6 2 4686.00 2.71E+05 2.86E-04 0.00E+00 0.00E+00 15 2 2De 9 2Po 3 6 2 1214.92 1.23E-03 1.65E-08 2.49E+01 2.34E-02 15 5 2De 9 2Po 5 6 2 4685.99 -2.63E+05 2.78E-04 4.88E+02 5.37E-04 16 1 2Fo10 2Se 1 8 2 242.99 -9.69E-02 7.62E-02 0.00E+00 0.00E+00 16 3 2Fo10 2Se 2 8 2 1214.92 3.12E+03 3.14E-02 0.00E+00 0.00E+00 16 6 2Fo10 2Se 4 8 2 4685.97 -3.62E+05 2.86E-04 0.00E+00 0.00E+00 16 7 2Fo10 2De 6 8 4 4686.35 -9.80E+04 7.76E-05 0.00E+00 1.26E-03 No of non-zero M2/E3 transitions = 11 Total number of M2/E3 transitions = 11 ---------------------------------------------------------------------------- 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 2 303.74 0.00E+00 0.00E+00 -5.31E-09 2.56E-03 5 2 2Po 3 2Po 5 2 2 1640.15 0.00E+00 0.00E+00 -1.64E-10 5.02E-07 5 4 2Po 3 2Po 5 4 2 1640.31 -2.16E+01 1.53E+03 -4.74E-09 1.45E-05 6 1 2Se 1 2Se 4 2 2 256.28 0.00E+00 0.00E+00 -1.42E-09 1.14E-03 6 3 2Se 2 2Se 4 2 2 1640.16 0.00E+00 0.00E+00 -6.29E-10 1.92E-06 7 1 2Se 1 2De 6 2 4 256.28 -1.00E-01 3.80E+04 4.92E-11 1.97E-05 7 3 2Se 2 2De 6 2 4 1640.11 9.23E+01 3.27E+03 -1.36E-10 2.07E-07 8 2 2Po 3 2Po 5 2 4 1640.11 2.16E+01 7.65E+02 -1.97E-09 3.02E-06 8 4 2Po 3 2Po 5 4 4 1640.26 2.16E+01 7.65E+02 -2.37E-09 3.62E-06 9 1 2Se 1 2De 6 2 6 256.28 1.50E-01 3.80E+04 0.00E+00 0.00E+00 9 3 2Se 2 2De 6 2 6 1640.10 -1.38E+02 3.27E+03 0.00E+00 0.00E+00 10 2 2Po 3 2Po 8 2 2 1214.93 0.00E+00 0.00E+00 -5.24E-11 3.94E-07 10 4 2Po 3 2Po 8 4 2 1215.02 -2.08E+00 6.58E+02 -1.15E-09 8.65E-06 10 5 2Po 5 2Po 8 2 2 4686.21 0.00E+00 0.00E+00 -5.01E-11 6.56E-09 10 8 2Po 5 2Po 8 4 2 4686.59 -4.39E+02 1.63E+02 -4.36E-09 5.71E-07 11 1 2Se 1 2Se 7 2 2 242.99 0.00E+00 0.00E+00 -5.83E-10 5.48E-04 11 3 2Se 2 2Se 7 2 2 1214.94 0.00E+00 0.00E+00 -2.20E-10 1.66E-06 11 6 2Se 4 2Se 7 2 2 4686.21 0.00E+00 0.00E+00 -1.60E-10 2.10E-08 11 7 2De 6 2Se 7 4 2 4686.59 -7.09E+01 2.63E+01 -1.76E-14 2.31E-12 11 9 2De 6 2Se 7 6 2 4686.71 -1.06E+02 3.95E+01 0.00E+00 0.00E+00 12 1 2Se 1 2De 9 2 4 242.99 -4.24E-02 2.10E+04 2.67E-11 1.25E-05 12 3 2Se 2 2De 9 2 4 1214.92 2.08E+00 3.29E+02 -3.57E-11 1.34E-07 12 6 2Se 4 2De 9 2 4 4686.05 1.30E+03 2.41E+02 -1.34E-11 8.80E-10 12 7 2De 6 2De 9 4 4 4686.43 2.87E+02 5.33E+01 -2.85E-10 1.87E-08 12 9 2De 6 2De 9 6 4 4686.55 -1.23E+02 2.29E+01 -9.30E-10 6.09E-08 13 2 2Po 3 2Po 8 2 4 1214.92 2.07E+00 3.29E+02 -3.94E-10 1.48E-06 13 4 2Po 3 2Po 8 4 4 1215.01 2.08E+00 3.29E+02 -7.55E-10 2.84E-06 13 5 2Po 5 2Po 8 2 4 4686.05 4.39E+02 8.16E+01 -2.86E-09 1.88E-07 13 8 2Po 5 2Po 8 4 4 4686.43 4.39E+02 8.16E+01 -7.21E-10 4.73E-08 14 2 2Po 3 2Fo10 2 6 1214.92 2.91E+01 3.08E+03 0.00E+00 0.00E+00 14 4 2Po 3 2Fo10 4 6 1215.00 -8.31E+00 8.79E+02 3.75E-11 9.39E-08 14 5 2Po 5 2Fo10 2 6 4685.99 -2.32E+03 2.88E+02 0.00E+00 0.00E+00 14 8 2Po 5 2Fo10 4 6 4686.38 6.64E+02 8.23E+01 -5.63E-11 2.46E-09 15 1 2Se 1 2De 9 2 6 242.99 6.36E-02 2.10E+04 0.00E+00 0.00E+00 15 3 2Se 2 2De 9 2 6 1214.92 -3.11E+00 3.29E+02 0.00E+00 0.00E+00 15 6 2Se 4 2De 9 2 6 4686.00 -1.94E+03 2.41E+02 0.00E+00 0.00E+00 15 7 2De 6 2De 9 4 6 4686.37 1.23E+02 1.52E+01 -2.89E-10 1.26E-08 15 9 2De 6 2De 9 6 6 4686.50 4.92E+02 6.09E+01 -1.42E-09 6.21E-08 16 4 2Po 3 2Fo10 4 8 1215.00 4.99E+01 3.96E+03 0.00E+00 0.00E+00 16 8 2Po 5 2Fo10 4 8 4686.35 -3.99E+03 3.70E+02 0.00E+00 0.00E+00 Number of E2,M1 transitions = 40 Total number of transitions (including non-spectroscopic) = 40 NT= total number of forbidden (E2,M1,E3,M2) transitions = 40 + 11 = 51 Net allowed (E1) and forbidden (E2,M1,E3,M2) transitions = = 33 + 51 = 84